tour Zams

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DERS NOTLARI
(Çeviri)
Orijinal Kitap
STRUCTURE AND EVOLUTION OF SINGLE AND BINARY STARS
Ed: C.W.H. de Loore and C. Doom
Kluwer, 1992
Çeviren
3URI'UgPHU/WIL'H÷LUPHQFL
2005
1
dLIW<ÕOGÕ]ODUÕQ(YULPL
BÖLÜM 15
dø)7<,/',=/$5,1(95ø0ø
*(1(/%$.,ù
*LULú
<ÕOGÕ] HYULPLQL EHOLUOH\HQ SDUDPHWUHOHU RODQ NWOH YH NLP\DVDO ELOHúLP GÕúÕQGD \DNÕQ oLIWOHULQ HYULPLQL
EHOLUOH\HQoSDUDPHWUHGDKDYDUGÕUVLVWHPLQWRSODPNWOHVLM (=M1+M2NWOHRUDQÕq (=M2 /M1 ) ve yörünge
dönemi P<DNÕQoLIWOHULoLQHYULPKHVDSODPDODUÕ=$06¶GDNLLNLELOHúHQOHEDúODWÕODELOLUEXGXUXPGDVLVWHP
EX o SDUDPHWUH LOH WDQÕPODQÕU .WOH YH DoÕVDO PRPHQWXP DNWDUÕPÕQÕQ ROGX÷X VLVWHPOHULQ ELOHúHQOHUL
DUDVÕQGDNL HWNLOHúLPOHULQ VRQXFXQGD EX o SDUDPHWUH HYULP VÕUDVÕQGD VUHNOL GH÷LúLU (YULPOHúPHPLú
VLVWHPOHUELOHúHQOHUDUDVÕQGDNLRODVÕHWNLOHúLPGHQ|QFH
ile HYULPOHúPLúVLVWHPOHUDUDVÕQGDD\UÕP\DSDELOLUL]
nmak istHQGL÷LQGH RQODUÕQ
kütlelerinin (M), NWOH RUDQODUÕQÕQ q) ve dönemlerinin (P GD÷ÕOÕPÕ KDNNÕQGD ILNLU VDKLEL ROPDN JHUHNLU
(WNLOHúHQ oLIWOHULQ ELOLQHQ VÕQÕIODUÕ HYULPVHO WDULKoHOHUL DoÕVÕQGDQ \RUXPOD
%LOPHPL]JHUHNHQúH\EDúODQJÕoGD÷ÕOÕPIRQNVL\RQX
F ( M , q, P) d (ln M ) d (ln q ) d (ln P)
dir.
%X SDUDPHWUH X]D\Õ M-q-P X]D\Õ \DNÕQ oLIW \ÕOGÕ]ODUÕ ED]Õ GR÷DO NDWHJRULOHUH D\ÕUÕU NoN YH RUWD NWOHOL
oLIWOHUNWOHOL VLVWHPOHUKÕ]OÕ HYULP J|VWHUHQ \D GDJ|VWHUPH\HQVLVWHPOHU LOHDQDNROHWNLOHúLPOHUL \D GDLOHUL
HYUHOHUGHNL HWNLOHúLPOHUL J|VWHUHQ VLVWHPOHU (WNLOHúPH\HQ YH HWNLOHúHQ VLVWHPOHU
in gözlemleri, parametre
X]D\ÕQÕQGH÷LúLNNÕVÕPODUÕQDD]\DGDoRNHWNLHGHU
iyle F’nin belirlenmesi zordur. Bununla
onunun,
%HOOL WUGHQ oLIWOHULQ EHOLUOHQPHVLQL ]RUODúWÕUDQ VHoLP HWNLOHUL QHGHQ
ELUOLNWH|EHN,WUoLIWOHUHLOLúNLQLQFHOHPHOHUGD÷ÕOÕPIRQNVL\
F ( M , q, P) d (ln M ) d (ln q ) d (ln P) = F ( M )d (ln M ).V (q )d (ln q).W ( P)d (ln P)
úHNOLQGH
M-, q- ve P-GD÷ÕOÕP IRQNVL\RQODUÕQÕQoDUSÕPÕRODUDN \D]ÕODELOHFH÷LQL RUWD\D NR\PXúWXU EXUDGD M,
E\NNWOHOLELOHúHQLQNWOHVLGLU
%Dú \ÕOGÕ]ODUÕQ NWOHOHULQH LOLúNLQ GD÷ÕOÕP WHN \ÕOGÕ]ODUÕQNLQH EHQ]HPHNWHGL
RODQODULoLQEXGD÷ÕOÕP6DOSHWHUIRQNVL\RQX
r ve 0.9 M’den büyük kütleli
F ( M )d (ln M ) = M −2.35 d (ln M )
ile temsil edilebilir, burada ME\NNWOHOLELOHúHQLQNWOHVLGLU
.WOHRUDQÕGD÷ÕOÕPÕ
V(q), q
FLYDUÕQGDPDNVLPXPDVDKLSWLU
V(q)’nun, küçük q (=M2/M1) GH÷HUOHULQHGR÷UX
KÕ]OD D]DOGÕ÷Õ \|QQGHNL WDKPLQOHU IDUNOÕGÕU *HQHO RODUDN NDEXO HGLOHQ NWOH RUDQÕ GD÷ÕOÕPÕQÕQ VHoLP
HWNLOHULQGHQHWNLOHQPLúROPDVÕYHGD÷ÕOÕPÕQoRNGDKDG]ROPDVÕRODVÕGÕU
'|QHPGD÷ÕOÕPՁ]HULQH\DSÕODQGH÷LúLNoDOÕúPDODUORJDULWPLNG|QHPDUDOÕ÷ÕEDúÕQDoLIWOHULQVD\ÕVÕQÕQKHPHQ
KHPHQ VDELW ROGX÷X NRQXVXQGD X\XúPD KDOLQGHGLUOHU ùHNLO ¶GD NWOHQLQ ELU IRQNVL\RQX RODUDN X\JXQ
minimuma NDUúÕOÕNJHOHQG|QHPOHULoLQNDEXOHGLOHELOLUELUGD÷ÕOÕP
W ( P )d (ln P ) = 0.006d (ln P )
úHNOLQGHDOÕQDELOLU
ùHNLOHYULPOHúPHPLúVLVWHPOHULoLQ9DQ6LQDYH'H*UHYHWDUDIÕQGDQHOGHHGLOGL÷L]HUHVLVWHP
EDúÕQD WRSODP NWOHQLQ J|]OHQHQ GD÷ÕOÕPÕQÕ J|VWHUPHNWHGLU ¶GDQ 0
¶H
NDGDU RODQ DUDOÕNWD
J|]OHQPHOHUL]RUROGX÷XQGDQGúNÕúÕWPDJHULWD\IWU\DOQÕ]FDELUNDoVLVWHPJ|UOPHNWHGLU
- 4 M
DUDOÕ÷ÕQGDELUPDNVLPXPYDUGÕU'DKDE\NNWOHOHULoLQKHUELUDUDOÕNEDúÕQDORJDULWPLNRODUDNELULP
2
dLIW<ÕOGÕ]ODUÕQ(YULPL
RODQ VLVWHPOHULQ VD\ÕVÕ DUDOÕN EDúÕQD oDUSDQÕ NDGDU D]DOPDNWDGÕU %X
diyagramdan, beklenen Salpeter
GD÷ÕOÕPÕQDVDSPDQÕQQHGHQLVHoLPHWNLOHULGLU
(YULPOHúPHPLú \ÕOGÕ]ODUÕQ ¶ÕQGDQ ID]ODVÕ ¶GHQ GDKD E\N NWOH RUDQODUÕQD VDKLSWLU VLVWHPOHULQ
\DNODúÕN¶LLVHELUoLYDUÕQGDELUNWOHRUDQÕQDVDKLSWLUg]HOOLNOH¶GHQNoNNWOHRUDQOÕKLoELUVLVWHP
EXOXQDPDPÕúWÕU(YULPOHúPHPLúVLVWHPOHULQNWOHRUDQODUÕQÕQGD÷ÕOÕPÕùHNLO¶GHJ|VWHULOPLúWLU
Abt ve Levy (1976), F3 – G2V ve B2 – % WD\I DUDOÕ÷ÕQGDNLWD\IVDOoLIWOHUHLOLúNLQ ELU LQFHOHPHOHULQGHQELU
G|QHP GD÷ÕOÕPÕ HOGH HWPLúOHUGLU ùHNLO +LVWRJUDP DGHW ELOLQHQ \D GD WDKPLQ HGLOHQ G|QHP LOH
ROXúWXUXOPXúWXU
ùHNLO(YULPOHúPHPLú\DNÕQoLIWVLVWHPOHULQWRSODPNWOHOHULQLQGD÷ÕOÕPÕ9DQ6LQDYH'H*UHYH
ùHNLO (YULPOHúPHPLú oLIW VLVWHPOHULQ NWOH RUDQODUÕQÕQ GD÷ÕOÕPÕ 3RSRY KLVWRJUDP
–
DUDOÕNODUÕQGDNLGD÷ÕOÕPÕQÕJ|VWHUPHNWHGLU DUDVÕQGDGDKDLQFHELUGD÷ÕOÕPGDYHULOPLúWLU
.
q’nun 0.2 birim
3
dLIW<ÕOGÕ]ODUÕQ(YULPL
ùHNLO dLIWOHULQ \|UQJH G|QHPOHULQLQ IUHNDQVÕ $oÕN JUL U
enkli bölge, bilinen görsel yörünge
|÷HOL
sistemleri
J|VWHUPHNWH YH G] oL]JLOHU LOH EHOLUOHQPLú RODQ WD\IVDO oLIWOHU E|OJHVL 6% LOH J|VWHULOHQ LOH oDNÕúPDNWDGÕU 7DUDOÕ
bölgedeki (CPM ile gösterilen) çiftlerin, ortak öz hareketlerinden belirlenen dönemleri oldukça belirsizdir.
'D÷ÕOÕPJ|UHOLRODUDN G]GU YHWHN PDNVLPXPOXGXU'D÷ÕOÕP \ÕOFLYDUÕQGDELUPHG\DQDVKLSWLUYH¶GHQ
106JQHNDGDURODQDUDOÕNWDGDKDKRPRMHQGLU$EWYH/HY\¶\HJ|UHWD\IVDOoLIWOHULOHJ|UVHOoLIWOHUDUDVÕQGDNL
oDNÕúPD, i NL PRGOX ELU GD÷ÕOÕPÕQ ROXúPDmasÕ DoÕVÕQGDQ yeterlidir. (÷HU E|\OH ROVD\GÕ G|QPH\OH JHQLúOHPLú
oL]JLOHULQ X]XQ G|QHPOL ELU oRN WD\IVDO oLIWLQ EHOLUOHQPHVLQL HQJHOOHGL÷L YH \ÕOGÕ]ODUÕQ oR÷X LoLQ E\N
ek gerekir
ve bu dXUXPGD LNL PRGOX ELU GD÷ÕOÕP EHNOHQLUGL '|QHPGHNL DUDOÕN 8 oDUSDQÕ NDGDUGÕU YH EX GD oLIW
ROXúXPXQGDQWHN ELU ROXúXPVUHFLQLQ VRUXPOX ROGX÷XQXLQDQÕOPD] \DSPDNWDGÕU+XDQJEN]$EWYH /HY y,
1976).
X]DNOÕNODUÕQNÕVD G|QHPOL ELU oRN J|UVHOoLIWLQ EHOLUOHQPHVLQH HQJHO ROGX÷X|Q WU oLIWOHUL LQFHOHP
,
olan çiftlerdir *HQHO RODUDN JQHú FLYDUÕQGD J|]OHQHQ
$QDNRO \ÕOGÕ]ODUÕQÕQ \DNODúÕN ¶X oLIWWLU |Q WU \ÕOGÕ]ODUÕQ \DNODúÕN ¶Õ NWOH RUDQODUÕ \DQL \ROGDúÕQ
NWOHVLQLQ EDú \ÕOGÕ]ÕQNLQH RUDQÕ ¶GHQ E\N
\ÕOGÕ]ODUÕQ \DNODúÕN ¶VLQLQ oLIW \D GD oRNOX VLVWHP ROGX÷X V|\OHQHELOLU dR÷X GXUXPGD LNL ELOHúHQ
\HWHULQFH D\UÕNWÕU YH ELOHúHQOHU ELU ELUOHULQGHQ HWNLOHQPHGHQ HYULPOHúLUOHU )DNDW GL÷HU GXUXPODUGD
sistemin
EDúODQJÕo SDUDPHWUHOHULQH ED÷OÕ RODUDN ELU ELOHúHQLQ \DNÕQOÕ÷Õ ELU \ÕOGÕ]ÕQ E\\HELOHFH÷L JHOLúHELOHFH÷L
PHVDIH\L VÕQÕUOD\DELOLU YH HYULP VÕUDVÕQGD \ÕOGÕ]ODU DUDVÕQGD HWNLOHúLP RODELOLU dLIW HYULPL LoLQ HQ |QHPOL
GXUXPODUNWOHDNWDUÕPHYUHOHULLOHVLVWHPGHNLELOHúHQOHUGHQELULQLQVSHUQRYDRODUDNSDWODPDVÕQÕQ\DODoWÕ÷Õ
eWNLOHUGLU%X GXUXPGDVLVWHP \D GD÷ÕOÕU \DGDELU ELOHúHQHVDKLS RODQoLIWOHUGHELOHúHQOHUGHQ ELULQLQNWOHVL
NWOHDNWDUDQ\ROGDúÕQGDQ\Õ÷ÕúDQNWOH\OHE\\HELOLUE|\OHFHELOHúHQLQHYULPLGH÷LúLU+LGURMHQLQLoHGR÷UX
DNÕúÕ GDKD VRQUDNL HYUHOHUGH KHO\XPXQ NDUERQ RNVLMHQLQ YG QHGHQL\OH \ÕOGÕ] JHQoOHúLU YH HYULPL E\N
RUDQGDGH÷LúLU\DúDPVUHVLGH÷LúLUHYULPVUHFLGH÷LúHELOLUYHHYULPLQLQVRQVDIKDVÕEDúODQJÕoNWOHVLQGHQ
EHNOHQHQGHQWDPDPHQIDUNOÕRODELOLU
<ÕOGÕ]ODUDLOLúNLQHQ|QHPOL IL]LNVHOSDUDPHWUHRODQ NWOH\DOQÕ]FD ELU oLIWVLVWHPLQELOHúHQOHULLoLQ GR÷UXELU
úHNLOGH EHOLUOHQHELOHFH÷LQGHQ oLIW VLVWHPOHU oRN |QHPOLGLU %HOLUOL NRúXOODUGD |UWHQ oLIWOHU ELOHúHQOHULQ
JHRPHWULN D\UÕQWÕODUÕQÕQ EHOLUOHQHELOPHVLQH RODQDN YHULUOHU øNLQFL ELU \ÕOGÕ]ÕQ YDUOÕ÷Õ oRN JoO ELU HWNL\H
VDKLSWLU ELOHúHQ Lo \DSÕVÕQD ED÷OÕ RODUDN ELU GHIRUPDV\RQD X÷UD\DELOLU gUWHQ oLIWOHU GH ELOH EX WU ELU
ER]XOPD\ÕJ|]OHPHNNROD\GH÷LOGLU%XQXQODELUOLNWHEXROD\ÕQ\DQ
etkileri gözlemlenebilir: bozulma, çekim
LYPHVLQL YH \|UQJH\L GH÷LúWLUHELOLU <ÕOGÕ] \DSÕVÕQÕQ ER]XOPDVÕQD LOLúNLQ ELU oRN EHOLUWL YH ELU ELOHúHQLQ
YDUOÕ÷ÕQÕQ \ÕOGÕ]DWPRVIHULQH HWNLOHULKHPHQKHPHQELU \]\ÕOGDQEHULELOLQPHNWHGLU%XWUEHOLUWLOHUH|UQHN
RODUDNHNVHQG|QPHVL\DQVÕPDHWNLOHULYHoLIWVLVWHPOHUGHNLJD]DNÕPODUÕQÕQYDUOÕ÷ÕJ|VWHULOHELOLU%XROJXODU
\ÕOGÕ]PRGHOOHULQLQ\DSÕVÕQÕQWHVWHGLOPHVLQHRODQDNVD÷ODUODU
<DNÕQ ELU ELOHúHQLQ ELU \ÕOGÕ]ÕQ HYULP VUHFLQL WHPHOOL RODUDN GH÷LúWLUHELOHFH÷L JHUoH÷L \ÕOÕQGD 2WWR
SWUXYH WDUDIÕQGDQ β /\UDH¶QLQ WXWXOPDODU VÕUDVÕQGDNL NDUDNWHULVWLN WD\IVDO GDYUDQÕúODUÕQÕQ ELU DoÕNODPDVÕ
RODUDNELOHúHQOHUDUDVÕQGDNLJD]DNÕúÕQÕ|QHUPHVLYHEHQ]HUROD\ODUÕQGL÷HU|UWHQoLIWOHUGHJ|]OHQPHVL\OHDoÕN
ELUúHNLOGHDQODúÕODELOPLúWLU
Tek izROH ELU \ÕOGÕ]ÕQ EDúWDQ VRQD kadar olan
HYULPL JHUoHNWH o|NHQ ELU EXOXWWDQ VRQ DúDPD\D
yani
o|NPú
,
ELU FLVLP Q|WURQ \ÕOGÕ]Õ EH\D] FFH \D GD ELU NDUDGHOLN HYUHVLQH NDGDU VUHNOL ELU E]OPHGLU <ÕOGÕ] KHU
ELULQGHVÕUDVÕ\ODKLGURMHQKHO\XPYHNDUERQXQWNHWLOGL÷LDUGÕúÕNQNOHHU\DQPDHYUHOHULQLGHYUH\HVRNDUDN
4
dLIW<ÕOGÕ]ODUÕQ(YULPL
bu yok edici sonGDQ NDoÕQPD\D \D GD HQ D]ÕQGDQ ELU VUH HUWHOHPH\H oDOÕúÕU +LGURMHQ \DQPDVÕQGDQ HOGH
HGLOHQ UHDNVL\RQ UQOHUL VRQUDNL \DQPD HYUHOHULQGH \DNÕW RODUDN NXOODQÕOÕU EX \DNÕWODU nükleer
UHDNVL\RQODUÕQ PH\GDQD JHOPHVL LoLQ VÕFDNOÕN YH \R÷XQOX÷XQ \HWHULQFH \NVHN ROGX÷X \ÕOGÕ] PHUNH]LQGH \D
GD PHUNH]H \DNÕQ \HUOHUGH \DNÕOÕU WNHWLOLU <ÕOGÕ]ÕQ PHUNH]L NÕVPÕQGD DUG DUGÕQD \DNÕWODU WNHWLOGLNoH
oHNLUGH÷L EHVOH\HQ QNOHHU UHDNVL\R
suretiyle
nlar,
\ÕOGÕ]ÕQ GÕú NÕVÕPODUÕQGDQ RODQ HQHUML ND\ÕSODUÕQÕ NDUúÕODPDN
\RN ROXU %X GXUXPGD oHNLUGHN RQX oHYUHOH\HQ NDWPDQODUÕQ D÷ÕUOÕ÷Õ\OD VÕNÕúÕU YH E|\OHFH
\R÷XQOX÷X DUWDU 1NOHHU \DQPD \HUL oHNLUGHN HWUDIÕQGDNL ELU NDEX÷D ND\DU $\UÕFD
, çekirdekteki madde
VÕNÕúPÕúWÕU UHWLOHQ HQHUML ÕúÕQÕP PHNDQL]PDODUÕ\OD \ÕOGÕ]ÕQ ]DUIÕQD WDúÕQÕU dHNLUGH÷LQ |] HQWURSLVL GúHU
dHNLUGH÷LQVÕFDNOÕ÷Õ P
addenin durumuna yani elektron
\R]ODúPDVÕQD QHNDGDU \DNÕQROGX÷XQDED÷OÕRODUDN
GúHELOLU\DGDDUWDELOLU(÷HUoHNLUGH÷LQVÕFDNOÕ÷ÕYH\R÷XQOX÷X\HWHULQFH\NVHNELUGXUXPDJHOLUVHVRQUDNL
QNOHHU \DNÕW \DQPD\D EDúODU YHE|\OHFH \HQLELU QNOHHUUHDNVL\RQoHYULPLEDúODPÕúROXU<ÕOGÕ]ÕQEX \HQL
GXUXPDX\XPXVDNLQÕOÕPOÕELUúHNLOGHROXUJHoLúKHPHQKHPHQGHQJHKDOLQGHROXúXU(÷HUE|\OH ROPD]VD
oHNLUGH÷LQ |] HQWURSLVL HOHNWURQXQ \R]ODúPDVÕQÕ VD÷OD\DFDN NDGDU NoN ROXU %X GD \R]ODúPÕú oHNLUGH÷LQ
derece güçlü bir nükleer yanmaya neden olur. Artan bu enerji üretimine tepki
olarak da GÕú NÕVÕPODU JHQLúOHU ÕúÕQÕPOD HQHUML DNWDUÕPÕQÕQ Jc EX NDGDU ID]OD HQHUML\L GÕú NÕVÕPODUD
HWUDIÕQGDNL ELU NDEXNWD VRQ
WDúÕPD\D \HWPH] YH LoHUL\H GR÷UX GÕú QNOHHU \DQPD NDEX÷XQD NDGDU XODúDELOHQ GHULQ ELU \]H\ NRQYHNWLI
katmanÕROXúXU%XJHQLúOHPH\ÕOGÕ]ÕHR diyagraPÕQGDNÕUPÕ]ÕGHYOHUE|OJHVLQHGR÷UXJ|WUU
ø]ROH \ÕOGÕ]ODUOD LOJLOHQGL÷LPL] VUHFH \ÕOGÕ]ÕQ JHQLúOHPHVL G]HQOLGLU )DNDW oLIW \ÕOGÕ]ODU GXUXPXQGD EDú
 kütleli, HYULPOHúPekte olan bir \ÕOGÕ]ÕQ
; anakoldDNLoHNLUGHNWHKLGURMHQLQWNHQGL÷LDQGDNLYHKHO\XPYH
\ÕOGÕ]ÕQ JHOLúPHVL \ROGDúÕQ YDUOÕ÷ÕQGDQ GROD\Õ HQJHOOHQLU 0
\DUÕoDSÕùHNLO¶WHJ|VWHULOPLúWLUùHNLO
NDUERQ\DQPDHYUHOHULQGHNL\DUÕoDSODUÕJ|VWHUPHNWHGLU
Hidrojen yanma evresinin sonunda, 40 M¶GHQ NoN RODQ \ÕOGÕ]ODUÕQ \DUÕoDSODUÕ RQODUÕQ =$06
\DUÕçDSODUÕQÕQ – NDWÕ NDGDUGÕU EX \]GHQ E|\OHVL \ÕOGÕ]ODUGD EDúODQJÕo NWOH RUDQÕ YH GRODQPD
G|QHPOHULQH ED÷OÕ RODUDN NWOH DNWDUÕPÕ RODELOLU %X HWNL NDEXNWD KLGURMHQ \DQPD HYUHVLQLQ VRQXQGD YH
yum yakma evresinde çok daha belirgindir. Daha büyük kütleli
konvektif
IÕUODWPDQÕQ overshoot LQJ E\NO÷QH ED÷OÕGÕU dRN E\N NWOHOL \ÕOGÕ]ODUÕQ JoO konvektif IÕUODWPD LOH
hesaplanan modellerinde, konvektif çekirdek o derece büyüktür ki, hidrojen yakma evresinin sona
\DUÕoDSÕQ NDWÕQD NDGDU oÕNWÕ÷Õ KHO
\ÕOGÕ]ODUGD LVH EX KHU ]DPDQ UDVWODQDQ ELU GXUXP GH÷LOGLU YH HWNL E\N |OoGH PHUNH]GHQ
HUPHVLQGHQ GDKD |QFH YH \ÕOGÕ] U]JDUODUÕQÕQ HWNLVL\OH EDúODQJÕo NRQYHNWLI oHNLUGH÷LQ GÕú NDWPDQODUÕ
\]H\GHJ|UQUOHU\DUÕoDSNoOUYHHYULP\ROXVRODGR÷UX\|QHOLU
NWOHOLELU\ÕOGÕ]ÕQ\DUÕoDSÕQÕQ, zaPDQÕQIRQNVL\RQXRODUDNGH÷LúLPL
ùHNLO0
5
dLIW<ÕOGÕ]ODUÕQ(YULPL
.ODVLN 6FKZDU]VFKLOG NULWHUOHUL \D GD ]D\ÕI
konvektif
li modeller, HR
IÕUODWPD LOH KHVDSODQDQ E\N NWOH
GL\DJUDPÕQÕQ NÕUPÕ]Õ E|OJHVLQH GR÷UX X]DQÕUODU PXKWHPHOHQ +5 GL\DJUDPÕQGD ,úÕQÕPOÕ 0DYL 'HYOHULQ
/%9¶V EXOXQGX÷X E|OJH\H JLUGLNOHULQGH oLIW VLVWHPOHULQ E\N NWOHOL ELOHúHQOHUL WÕSNÕ NWOHOL WHN
\ÕOGÕ]ODUGDROGX÷XJLELJoOYHG|QHPOLNWOHND\ÕSODUÕJ|VWHULUOHUDWPRVIHUKHO\XPEDNÕPÕQGDQ]HQJLQOHúLU
YH \ÕOGÕ] VROD GR÷UX KDUHNHW HGHU %X DúDPDGD \ÕOGÕ] E]O\RU RODFD÷ÕQGDQ PXKWHPHOHQ NWOH DNWDUÕPÕ
olmayacak ve model konvektif IÕUODWPDGXUXPXQGDNLLOHD\QÕVRQXFXYHUHFHNWLU
<ÕOGÕ] HYULPL RUWDN |]HOOLNOHUH VDKLS \ÕOGÕ] JUXSODUÕQÕQ J|]OHQHQ |]HOOLNOHULQL DoÕNODPDN \D GD WHN WHN
VLVWHPOHUL PRGHOOHPHN LoLQ NODVLN ELU DUDoWÕU %X GXUXP KHP WHN \ÕOGÕ]ODU KHP GH oLIW VLVWHPOHU LoLQ
JHoHUOLGLU $PDo J|]OHQHQ |]HOOLNOHUL DoÕNODPDN ROGX÷XQGDQ oLIWLQ HYULP GXUXPXQXQ VHoLPL J|]OHPOHUO
e
EHOLUOHQLU%X\]GHQ\DNÕQoLIWVLVWHPOHULoLQPHYFXWHYULPKHVDSODPDODUÕHOGHNLJ|]OHPOHUGHQ\DUDUODQÕODUDN
EHOLUOHQLU %X J|]OHPOHU J|]OHPVHO JUOWOHUGHQ VRQ GHUHFH HWNLOHQPLúWLUOHU NÕVD G|QHPOLOHUL \DNDODPDN
GL÷HUOHULQH J|UH GDKD NROD\GÕU oQN J|]OHP SURJUDP NRPLWHOHUL GDKD oRN NÕVD J|]OHP ]DPDQODUÕQD L]LQ
YHUPH\HH÷LOLPOLGLUOHUEXQHGHQOHX]XQG|QHPOLVLVWHPOHUGDKDD]J|]OHQPLúOHUYHGL÷HUOHULQHJ|UHGDKDD]
DQODúÕOPÕúODUGÕU7DULKVHORODUDNHYULPKHVDSODPDODUÕJ|]OHPVHOHWNLOHUGHQHWNLOHQPLúGLUYHD\QÕVÕQÕUODPDODU
QHGHQL\OH \RN GHQHFHN NDGDU D] VD\ÕGD HYULP GL]LVL PHYFXWWXU $\UÕFD EDúND IDNW|UOHU GH HYULP
KHVDSODPDODUÕ LoLQ
gereken
EDúODQJÕo SDUDPHWUHOHULQLQ VHoLPLQL HWNLOH
mektedir. Çift sistemlerin evrimi için
oRN GDKD JHQHO ELU \DNODúÕP DQFDN VRQ ]DPDQODUGD EDúOD\DELOPLúWLU 6RQUDNL NHVLPOHUGH EX NRQX D\UÕQWÕOÕ
RODUDNHOHDOÕQDFDNWÕU
<|UQJHDoÕVDOPRPHQWXPX
Kütleleri M1, M2 YH \DUÕoDSODUÕ R1, R2 RODQ YH VÕUDVÕ\OD r1 ve r2 \DUÕFDSOÕ oHPEHU \|UQJHOHUGH, v1 ve v2
KÕ]ODUÕ\ODGRODQDQYHDUDODUÕQGDNLX]DNOÕN A RODQùHNLOLNL\ÕOGÕ]J|] |QQHDODOÕP%DúODQJÕoWDE\N
kütleli olan ELOHúHQ EDú \ÕOGÕ] RODUDN DGODQGÕUÕODFDN YH R HYULP VÕUDVÕQGD \ROGDú \ÕOGÕ] GDKD E\N NWOHOL
olsa bile yine GH EDú \ÕOGÕ] RODUDN NDODFDNWÕU <ÕOGÕ]ODUÕQ NWOHOHULQLQ NWOH PHUNH]LQGH WRSODQGÕ÷ÕQÕ
YDUVD\DFD÷Õ] E|\OHFH KHU ELU ELOHúHQLQ oHNLP SRWDQVL\HOL \DNODúÕN RODUDN ELU QRNWD NWOHQLQNL LOH WHPVLO
HGLOPLúRODFDNWÕU
%XGXUXPGD\|UQJHDoÕVDOPRPHQWXPX
J = M 1 v1 r1 + M 2 v 2 r2
(15.1)
LOHLIDGHHGLOHELOLUYHKHULNL\ÕOGÕ]D\QÕDoÕVDOKÕ]ODUDVDKLSRODFD÷ÕQGDQ
v1 = ω r1 ; v 2 = ω r2
(15.2)
J = ( M 1 r12 + M 2 r22 )ω
(15.3)
olur. Sonuç olarak
r1 M 2
=
r2 M 1
(15.4)
dLIW<ÕOGÕ]ODUÕQ(YULPL
6
ùHNLO dLIW VLVWHPLQ |÷HOHUL ELOHúHQOHULQ oHPEHU \|UQJHOHUGH GRODQGÕNODUÕ YDUVD\ÕOPÕúWÕU øNL ELOHúHQLQ |÷HOHUL
kütleleri M1, M2PHUNH]HX]DNOÕNODUÕr1, r2ELOHúHQOHUDUDVÕX]DNOÕNAYH\|UQJHKÕ]ODUÕv1, v2’dir.
r1
M2
=
r1 + r2 M 1 + M 2
r1
M2
r
M1
; 2 =
=
A M1 + M 2
A M1 + M 2
ya da
r1 =
AM 2
AM 1
; r2 =
M1 + M 2
M1 + M 2
(15.5)
olur. Bu ifadeleri denklem 15.3¶GH\HULQH\D]GÕ÷ÕPÕ]GD


M 22
M 12
2
+
J = M 1 A2
M
A
ω
2
2
2
(M 1 + M 2 )
(M 1 + M 2 ) 

(15.6)
ya da
J = A2
M 1M 2
ω
M1 + M 2
(15.7)
elde edilir. Buradan
ω 2 A3 = G ( M 1 + M 2 ),
ω=
2π
,
P
P : dolanma dönemi
HúLWOLNOHULQLQ\DUGÕPÕ\OD
J2 =
ω 2 A 4 (M1M 2 ) 2
(M 1 + M 2 ) 2
=
GA( M 1M 2 ) 2
M1 + M 2
(15.8)
elde edilir.
15.3. Kritik Roche Hacmi
'g1(16ø67(0/(5'(327$16ø<(/
R1 ve R2, kütleleri M1 ve M2 olan ve A \DUÕoDSOÕ oHPEHU \|UQJHOHUGH GRODQDQ LNL \ÕOGÕ]
A¶QÕQ\ÕOGÕ]\DUÕoDSODUÕLOHD\QÕPHUWHEHGHQROGX÷XQXYDUVD\DFD÷Õ]$\UÕFDG|QPHQLQHú
]DPDQOÕ\DQL ω = Ω ROGX÷XQXYDUVD\DFD÷Õ]6LVWHPVDDWLQWHUVL\|QGH ω DoÕVDOKÕ]ÕLOHG|QPHNWHGLUùLPGL
\ÕOGÕ]ODUÕQ NWOHOHULQGHQ oRN GDKD NoN m NWOHOL ELU SDUoDFÕN GúQHOLP .WOH PHUNH]LQGH EXOXQDQ YH
VLVWHPOHELUOLNWHG|QHQELUJ|]OHPFL\HJ|UHEXSDUoDFÕ÷ÕQKDUHNHWLDúD÷ÕGDYHULOHQFm kuvveti ile belirlenir:
<DUÕoDSODUÕ
GúQHOLPEXUDGD
Fm = FM 1 + FM 2 + Fmerkezkaç + Fcoriolis ,
(15.9)
burada, Fmerkezkaç ve FcoriolisG|QHQELUUHIHUDQVVLVWHPLQLQVHoLOPLúROPDVÕQGDQGROD\ÕRUWD\DoÕNDn terimlerdir;
temel eylemsiz bir sistemde Fmerkezkaç = 0 ve Fcoriolis ¶GÕU3QRNWDVÕQGDNL ψ potansiyeli ùHNLO
ψ =
GM 1 GM 2 ω 2 s 2
+
+
r1
r2
2
m NWOHVLQLQ ELOHúHQOHUH RODQ
r1 ve r2LOHNWOHPHUNH]LQHX]DNOÕ÷ÕGD s LOHJ|VWHULOPLúWLU
LOH YHULOLU EXUDGD VRQ WHULP VLVWHPLQ G|QPHVL QHGHQL\OH RUWD\D oÕNPÕúWÕU
X]DNOÕNODUÕVÕUDVÕ\OD
7
dLIW<ÕOGÕ]ODUÕQ(YULPL
Dönen sistemdeki geometri.
ùHNLO
ùHNLO %LU oLIW VLVWHPLQ HúSRWDQVL\HO \]H\OHUL YH EHú /DJUDQJLDQ QRNWDVÕ <ÕOGÕ]ODU QRNWD NWOH RODUDN J|] |QQH
siyel yüzey (kritik
DOÕQPÕúWÕU (úSRWDQVL\HO \]H\OHU DLW ROGXNODUÕ SRWDQVL\HO GH÷HUOHUL LOH HWLNHWOHQPLúWLU .ULWLN HúSRWDQ
5RFKHOREXGDLúDUHWOHQPLúWLU6LVWHPLQNWOHPHUNH]LLVHLúDUHWLLOHJ|VWHULOPLúWLU
$\QÕ SRWDQVL\HOH VDKLS RODQ 3 QRNWDODUÕQÕQ NPHVL ELU HúSRWDQVL\HO \]H\L ROXúWXUXU <ÕOGÕ] PHUNH]OHULQLQ
\DNÕQÕQGDNL HúSRWDQVL\HO \]H\OHULKHPHQ KHPHQ NUHVHOGLU 'ÕúDUÕ\D GR÷UXJLGLOGLNoH NUHVHOOLNWHQJLGHUHN
D\UÕOÕUODU %X HúSRWDQVL\HO \]H\OHU DUDVÕQGDQ \DOQÕ]FD ELU WDQHVL Lo /DJUDQJH QRNWDVÕ GHQLOHQ YH LNL \ÕOGÕ]
DUDVÕQGD \HU DODQ /1 QRNWDVÕQGD NHQGLVL\OH NHVLúLU %X \]H\H Lo NULWLN 5RFKH \]H\L GHQLU øo NULWLN 5RFKH
\]H\L KHU ELUL ELOHúHQOHUGHQ ELUL HWUDIÕQGD RODQ LNL E|OJH WDQÕPODU YH EX E|OJHOHUH 5RFKH OREX GHQLU
<DOQÕ]FDELUELOHúHQLoHYUHOH\HQHúSRWDQVL\HO\]H\OHUL\ÕOGÕ]ODUÕQ5RFKHOREODUÕQÕQLoLQGHNDOÕUODU
(úSRWDQVL\HO \]H\OHU NWOHOHUL ELUOHúWLUHQ GR÷UX ]HULQGH \HU DODQ o
bunlar,
semer benzeri noktaya sahiptirler;
D\QÕ GR÷UX ]HULQGH EXOXQDQ o /DJUDQJLDQ QRNWDVÕGÕU /DJUDQJLDQ QRNWDODUÕQÕQ GL÷HU LNL WDQHVL
WDEDQODUÕ NWOH PHUNH]OHULQL ELUOHúWLUHQ GR÷UX SDUoDVÕ RODQ LNL HúNHQDU oJHQLQ WHSH QRNWDODUÕGÕU %|\OHFH
WRSODP EHú /DJUDQJLDQ QRNWDVÕ YDUGÕU ùHNLO EX EHú /DJUDQJLDQ QRNWDVÕQÕ KHU LNL \ÕOGÕ] HWUDIÕQGDNL
HúSRWDQVL\HO\]H\OHULYH\ÕOGÕ]ODUÕQ5RFKHOREODUÕQÕJ|VWHUPHNWHGLU
1%ø5%2<87/8+(6$3/$0$/$5 DURUMUNDA ROCHE YARIÇAPI
<ÕOGÕ]
PHUNH]OHULQLQ
FLYDUÕQGD
HúSRWDQVL\HO
\]H\OHU
\DNODúÕN
RODUDN
X]DNODúWÕNoD NUHVHO úHNLOGHQ VDSPDODU GD JLGHUHN GDKD E\N ROXU
NUHVHOGLU EX
PHUNH]OHUGHQ
ψ potansiyelinin belOL ELU GH÷HUL LoLQ
HúSRWDQVL\HO\]H\OHU\ÕOGÕ]PHUNH]OHULDUDVÕQGDRUWDNELUQRNWD\DVDKLSROXUODU
8
dLIW<ÕOGÕ]ODUÕQ(YULPL
5RFKHOREODUÕWDPRODUDNNUHVHOROPDVDODUGD
“
”
, bir küreden çok da IDUNOÕGH÷LOOHUGLU5RFKHOREXQXQKDFPLQH
RR ile gösterilir. Buna göre
HúLWELUNUHQLQ\DUÕoDSÕ 5RFKH\DUÕoDSÕ RODUDNDGODQGÕUÕOÕUYH
4
π R R3 = Roche lobunun hacmi .
3
5RFKH\DUÕoDSÕ
(15.11)
M1, M2NWOHOHULLOHDUDODUÕQGDNLAX]DNOÕ÷ÕQDED÷OÕGÕU3DF]\QVNL5RFKH\DUÕoDSÕLoLQ
DúD÷ÕGDNL\DNODúÕNLIDGH\LYHUPLúWLU
RR
M
= 0.38 + 0.2 log q, q = 1 , 0.3 < q < 20 için
A
M2
(15.12)
1/ 3
 1 
RR

= 0.46224
A
 1 + 1/ q 
, q ≤ 0.8 için .
(15.13)
'DKDGR÷UXLIDGHOHULVHú|\OHGLU
RR
= 0.37771 + 0.20247 log q + 0.01838(log q )2 + 0.02275(log q )3 , q > 0.1
A
LoLQ
RR
= 0.37710 + 0.21310 log q − 0.00800(log q )2 + 0.00660(log q )3 , q < 0.1
A
LoLQ
(15.14)
qRUDQÕ\HULQHqDOÕQDUDNGD\ROGDúELOHúHQLQRR5RFKH\DUÕoDSÕHOGHHGLOLU
.WOHDNWDUÕPÕYH\|UQJHQLQHYULPL
BiU \ÕOGÕ] gel-git \D GD 5RFKH OREXQX GROGXUGX÷XQGD \DSÕVÕQD LOLúNLQ VÕQÕUODPDODU GH÷LúLU <ÕOGÕ] VDELW
NWOHVL LOH GDKD ID]OD HYULPOHúHPH] YH 5RFKH OREXQXQ LoLQGHNL KDFPLQL NRUXPD\D oDOÕúDFD÷ÕQGDQ NWOH
ND\EHWPHN]RUXQGDNDOÕU%|\OHFH\ÕOGÕ]
, hacmini Roche lobuna uydurarak evrimini sürdürür.
dHPEHU \|UQJHOL ELU oLIW VLVWHPLQ \|UQJH DoÕVDO PRPHQWXPX GHQNOHPL LOH YHULOLU
Ω DOÕQDUDN
J yör =
M 1M 2
ΩA 2
M1 + M 2
yazabiliriz. AktDUÕODQ
ω yerine
(15.15)
PDGGHQLQ ELU PLNWDUÕQÕQ VLVWHPL WHUN HWWL÷LQL YDUVD\DOÕP EX GXUXPGD \|UQJH
D\UÕNOÕ÷ÕQÕQGH÷LúLPL

J yör
A
M 1  M 1   M 1
= −2 1 − (1 − α ) 1 − α 
+
2

A
M 2 2  M 1 + M 2   M 1
J yör

(15.16)
úHNOLQGH\D]ÕODELOLU.RUXQXPOXHYULP\DQLVLVWHPGHQNWOHND\EÕROPDGÕ÷ÕGXUXPGD

M  M
A
= −21 − 1  1
A
 M 2  M1
elde ederiz.
ise daha basit olarak
(15.17)
9
dLIW<ÕOGÕ]ODUÕQ(YULPL
.WOH DNWDUÕPÕ
M 1 < 0 , M 1 M 2 < 1 GXUXPXQGD JHQLúOH\HQ ELU \|UQJH\H YH M 1 M 2 > 1 durumunda da
NoOHQ ELU \|UQJH\H \RO DoDU (÷HU \ÕOGÕ] U]JDUODUÕ\OD VLVWHPGHQ NWOH ND\EÕ ROPDVÕ GXUXPXQGD ROGX÷X
(
gibi, α > 0 LVH\|UQJHQLQHYULPLDWÕODQPDGGHQLQ|]DoÕVDOPRPHQWXPXRODQ α −1 J yör / M
)
LIDGHVLQHVÕNÕ
VÕNÕ\D ED÷OÕ ROXU %X DoÕVDO PRPHQWXP KDNNÕQGD oRN D] ELOJL VDKLEL ROGX÷XPX]GDQ \ÕOGÕ] U]JDUODUÕ\OD
PDGGHND\EÕQÕQELUoLIWVLVWHPLQHYULPLQHRODQHWNLVLVRQGHUHFHEHOLUVL]GLU
α = 0 ROVD ELOH oLIWLQ HYULPL NRUXQXPVX] RODELOLU gUQH÷LQ E|\OHVL ELU GXUXP \|UQJH DoÕVDO PRPHQWXPXnun, gel-git HWNLOHúimleri VRQXFXQGD G|QPH DoÕVDO PRPHQWXPXQD G|QúWUOPHVL VÕUDVÕQGD RUWD\D oÕNDELOLU
*HQHORODUDNEXGXUXP\|UQJHHYULPLLoLQoRN|QHPOLGH÷LOGLUoQNoRN\DNÕQELOHúHQOLVLVWHPOHUGÕúÕQGD
\|UQJH DoÕVDO PRPHQWXPX
J yör G|QPH DoÕVDO PRPHQWXPXQGDQ oRN E\NWU dRN NÕVD G|QHPOL
VLVWHPOHUGHGRODQPDRNDGDUKÕ]OÕGÕUNLDoÕVDOPRPHQWXPX
J yör
J yör
=−
32 G 3
M 1 M 2 (M 1 + M 2 )A − 4 s −1
5 c5
(15.18)
nin evrimini
önemOL |OoGH HWNLOHU 6LVWHP \HWHULQFH \DNÕQVD LOH YHULOHQ DoÕVDO PRPHQWXP LIDGHVLQGHNL
EDVNÕQ WHULP ROXU YH EX GXUXPGD E\N NWOHOL ELOHúHQH NWOH DNWDUÕPÕ ROVD ELOH A / A ifadesi negatif olur.
RUDQÕ\OD DNWDUDQ oHNLPVHO GDOJDODU VDOÕQÕU EN] /DQGDX DQG /LIVFKLW] YH EX GD \|UQJH
%|\OHVL\DNÕQVLVWHPOHUGHNoNNWOHOLELOHúHQVSLUDOOHUoL]HUYHVLVWHPJLGHUHNGDKDGD\DNÕQODúÕU
.WOHND\EHGHQ\ÕOGÕ]GDQELOHúHQLQHNWOHDNWDUPDKÕ]Õ\DNODúÕNRODUDN
M =
ψs
∫
ψc
ρ cs
dA
dψ
dψ
(15.19)
ρ (ψ ) ve cs (ψ ) , L1FLYDUÕQGDNL\R÷XQOXNYHVHVKÕ]ÕGÕU ψ s
ve ψ c LVH VÕUDVÕ\OD 5RFKH OREX YH \ÕOGÕ] \]H\LQGHNL PHUNH]NDo NXYYHWL LoLQG]HOWLOPLú SRWDQVL\HOOHULGLU
A, L1FLYDUÕQGDNLDNÕPWSQQNHVLWDODQÕGÕUoHNLPSRWDQVL\HOL/DJUDQJLDQQRNWDVÕFLYDUÕQGDVHUL\HDoÕODUDN
ED÷ÕQWÕVÕLOHYHULOHELOLU-HGU]HMHFEXUDGD
NHVLWDODQÕ
dA
= −2π (1 − φ )−1 / 2 φ Ω − 2
dψ
(15.20)
hesaplanabilir (Savonije, 1979). Burada φ NWOH RUDQÕ q’nun boyutsuz bir fonksiyonu, Ω ise
\|UQJHDoÕVDOKÕ]ÕGÕU. ∆ (ψ − ψ ) IDUNÕ
s
c
ED÷ÕQWÕVÕ\OD
 GM 1 
∆R
∆ψ = −
 RRc 
ED÷ÕQWÕVÕ\OD\DUÕoDSODUDUDVÕQGDNL
(15.21)
∆R = (R − Rc ) IDUNÕQDG|QúWUOHELOLU
<DUÕoDSÕQ NWOH ND\EÕQD WHSNLVL YH NWOH ND\EÕ QHGHQL\OH 5RFKH \DUÕoDSÕQGD RUWD\D oÕNDQ GH÷LúLP ED÷ÕQWÕVÕQGDYHULOGL÷L]HUHNWOHND\EÕKÕ]ÕQÕQRUDQÕQÕEHOLUOHUOHU
.WOHDNWDUÕPLúOHPL
.WOH DNWDUÕPÕ KDNNÕQGD ILNLU VDKLEL ROPDN LoLQ \ÕOGÕ]ÕQ NWOHVL D]DOGÕNoD \ÕOGÕ] YH 5RFKH \DUÕoDSODUÕQÕQ
GH÷LúLPLQL ùHNLO GLNNDWH DOPDPÕ] JHUHNLU ø]ROH ELU \ÕOGÕ]ÕQ \DUÕoDSÕQÕQ HYULPL VDELW NWOH LOH GúH\
′
GR÷UXOWXGDNL $% oL]JLVL\OH J|VWHULOPLúWLU <DNÕQ oLIW VLVWHPOHUGH \DUÕoDS NWOH DNWDUÕPÕQÕQ EDúODGÕ÷Õ %
QRNWDVÕQGDNL 5RFKH \DUÕoDSÕ RODQ
r1GH÷HULQH XODúÕOÕQFD\D NDGDU DUWDU 0DGGHGH÷LúLPLQLQEDúODQJÕo HYUHOHUL
VUHVLQFH \ÕOGÕ] \DUÕoDSÕ KHPHQ KHPHQ VDELW NDOÕU %& IDNDW GDKD VRQUD NWOH ND\EÕ GHYDP HWWLNoH \DUÕoDS
r1 D]DOÕU <|UQJH NoOU M1¶LQ D]DOÕ\RU ELU
fonksiyonu olarak r1¶LQGH÷LúLPL%¶GHQ(¶\HNDGDURODQr1H÷ULVL\OHJ|VWHULOPLúWLU
D]DOÕU &'1 .WOH ND\EÕ EDúODGÕ÷ÕQGD 5RFKH \DUÕoDSÕ
10
dLIW<ÕOGÕ]ODUÕQ(YULPL
%DúYH\ROGDúELOHúHQLQM1 ve M2 NWOHOHULHúLWROGX÷XQGDr1 ¶GH(QRNWDVÕQGDNLPLQLPXPGH÷HULQHXODúÕUM1
< M2 ROGX÷XQGD r1 \HQLGHQ DUWDU (' \DQL \|UQJH \HQLGHQ JHQLúOHU % LOH & DUDVÕQGD R > r1 ROGX÷XQGDQ
EDú \ÕOGÕ]ÕQ NWOHVLQLQ D]DOPDVÕ LoLQ NWOH ND\EÕ JHUHNOLGLU ,úÕQÕPOÕ ]DUIODU LoLQ EX GXUXP ÕVÕVDO ]DPDQ
|OoH÷LQGH PH\GDQD JHOLU
R1 H÷ULVL GÕú NDWPDQODUÕQÕ DWDUDN NWOHVLQL D]DOWDQ ÕVÕVDO GHQJHGHNL ELU \ÕOGÕ]ÕQ
\DUÕoDSÕQÕQQDVÕOGH÷LúWL÷LQLJ|VWHUPHNWHGLU&QRNWDVÕQÕQ|WHVLQGHEDú\ÕOGÕ]ÕQ\DUÕoDSÕ5RFKH\DUÕoDSÕQGDQ
küçüktür.
ùHNLO .WOH GH÷LúLPLQLQ ROGX÷X ELU oLIW VLVWHP
deki
EDú \ÕOGÕ]ÕQ \DUÕoDSÕ LOH 5RFKH \DUÕoDSÕQÕQ GDYUDQÕúÕ %&'1
,
D]DODQNWOHOLGHQJHPRGHOLQLQ\DUÕoDSÕQÕJ|VWHUPHNWHGLU
øNLRODVÕOÕNGLNNDWHDOÕQPDOÕGÕU
1.
2.
R1 < r1oLIWD\UÕNGXUXPDJHOLU
(÷HU \HQL ELU QNOHHU \DQPD HYUHVL EDúODUVD \ÕOGÕ] 5RFKH OR
bunu doldurur ve yeniden kütle
ND\EÕPH\GDQDJHOLUIDNDWEXVHIHU]DPDQ|OoH÷LQNOHHU]DPDQ|OoH÷LGLU&'
%|\OHFHLNLNWOHGH÷LúLPHYUHVLoLIWVLVWHPOHULQHYULPLLOHLOLúNLOHQGLULOHELOLU
1.
(q=M1/M2).
2.
+Õ]OÕ ELU NWOH GH÷LúLP HYUHVL EX HYUHGH VLVWHPLQ NWOH RUDQÕ
q > 1’den q < 1’e ters döner
M2¶QLQ\DYDúoDDUWWÕ÷ÕELUHYUHJHOLU
%XKÕ]OÕHYUHGHQVRQUD\ROGDúÕQNWOHVL
4
– 105 \ÕO PHUWHEHVLQGH ROGXNoD NÕVD RODELOLU %|\OHFH NWOH DNWDUÕPÕ VÕUDVÕQGDNL
VÕUDGDROXUENzùHNLO15.8):
1. A –%ELULQFL\ÕOGÕ]QNOHHU]DPDQ|OoH÷LQGHJHQLúOHU.
2. B –&ÕVÕVDO]DPDQ|OoH÷LQGHKÕ]OÕELUNWOHDNWDUÕPÕPH\GDQDJHOLU
+Õ]OÕ HYUH ROD\ODU úX
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gel-git \D GD 5RFKH OREXQX GROGXUGX÷XQGD \DSÕVÕQD LOLúNLQ VÕQÕUODPDODU GH÷LúLU <ÕOGÕ] VDELW
NWOHVL LOH GDKD ID]OD HYULPOHúHPH] YH 5RFKH OREXQXQ LoLQGHNL KDFPLQL NRUXPD\D oDOÕúDFD÷ÕQGDQ NWOH
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suretiyle, hacmini Roche lobuna uydurarak evrimini sürdürür.
11
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<ÕOGÕ] PDGGHVL GDKD ]L\DGH PHUNH]L NÕVÕPODUGD \R÷XQODúWÕ÷ÕQGDQ \ÕOGÕ]ODU Lo \DSÕODUÕQÕ NWOH ND\EÕQD J|UH
n gel-git
ve \ÕOGÕ]ÕQ KLGURVWDWLN GHQJHVL ER]XOPD\DFDN úHNLOGH DWÕODELOLUOHU )DNDW ÕVÕVDO GHQJH zaman
|OoH÷L \DQL QNOHHU HQHUML UHWLPL LOH DWPRVIHULN HQHUML ND\EÕ DUDVÕQGDNL GHQJHQLQ ]DPDQ |OoH÷L, dinamik
D\DUODPD \HWHQH÷LQH VDKLSWLUOHU 'Õú NÕVÕPODU R NDGDU LQFHGLU NL \ROGDúÕQ HWNLVL\OH RUWD\D oÕND
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GH÷LúPHGHQNDODELOLU\DGDGL÷HUELUGH÷LúOHLoNÕVÕPODUÕQWHSNLVLDG\DEDWLNRO
abilir.
'ø1$0ø.=$0$1g/d(öø1'(.h7/(.$<%,
5RFKH OREXQX GROGXUDQ \ÕOGÕ] VRQ GHUHFH \NVHN RUDQGDNWOHND\EHWVHELOH 5RFKHOREXQXQLoLQGHNDODPD]
.WOH ND\EHGHQ \ÕOGÕ]ÕQ NWOH ND\EHWPH KÕ]Õ \DOQÕ]FD /1 QRNWDVÕQGDQ JHoHQ ]DUIÕQ VHV KÕ]ÕQGDNL
geQLúOHPHVL\OH belirlenmektedir. ,VÕ GHQJHVLQGHNL ÕúÕQÕPOÕ ]DUID VDKLS \ÕOGÕ]ODU GLQDPLN NWOH DNWDUÕPODUÕQD
NDUúÕ NDUDUOÕGÕUODU %XQXQOD ELUOLNWH, GHULQ \]H\ NRQYHNWLI NXúDNOÕ \ÕOGÕ]ODU LOH \R]ODúPÕú \ÕOGÕ]ODU GLQDPLN
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GD \DNÕQÕQGD YH\D DOW DQDNROGD EXOXQX\RUVD \D GD H÷HU \ÕOGÕ] \R]ODúPÕú LVH GLQDPLN NDUDUVÕ]OÕN NRúXOODUÕQÕ
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r. Kütle
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,6,6$/=$0$1g/d(öø1'(.h7/(.$<%,
koruyabilseydi\DUÕoDSÕ
ve bu da daha büyük bir
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5RFKH \DUÕoDSÕQGDQ E\N ROXUGX YH oRN GDKD E\N NWOH ND\EÕ RUWD\D oÕNDUGÕ
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, devler kolunun solundaki
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da,
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NWOHOL ELOHúHQ 5RFKH OREXQX GROGXUGX÷XQGD PH\GDQD JHOLU .WOH ND\EÕ \ÕOGÕ] ]DUIÕQÕQ GHQJH GXUXPXQ
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M
t KH
(15.22)
burada, tKHNWOHND\EHGHQ\ÕOGÕ]ÕQÕVÕVDO\DGD.HOYLQ-+HOPOKROW]]DPDQ|OoH÷LROXS
t KH =
E pot
L
=
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RL
M2
≈ 3 ×10
RL
7
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(15.23)
M RLJQHúELULPLQGH
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1h./((5=$0$1g/d(öø1'(.h7/($.7$5,0,
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]DPDQ |OoH÷LQGHNL NWOH DNWDUÕPÕ \ÕOGÕ]ÕQ
çekirdekte hidrojen yakma evresinde iken ROXúDQ KÕ]OÕ kütle
12
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DNWDUPD HYUHVLQGHQ VRQUD PH\GDQD JHOLU 1NOHHU ]DPDQ |OoH÷L GLQDPLN \D GD ÕVÕVDO ]DPDQ |OoHNOHULQGHQ
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Denklem 15.12 ve 15.13, M1’den M2¶\H NWOH DNWDUÕPÕ ROGX÷XQGD R R / A GH÷HULQLQ GDLPD D]DODFD÷ÕQÕ
J|VWHUPHNWHGLU .WOH DNWDUÕPÕ VÕUDVÕQGD H÷HU NWOH RUDQÕ q = M / M ELUGHQ NoN LVH 5RFKH \DUÕoDSÕQÕQ
1
2
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M2
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M1
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M2
q < 1 oluncaya kadar devam
k (bkz. kesim 15.3.3), böylece A ve RRoche’un ikisi de
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M
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Belirli miktarda
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böylece \ÕOGÕ] ÕVÕVDO GHQJHVLQL \HQLGHQ VD÷ODPD\D oDOÕúWÕ÷ÕQGD, E]OPH H÷LOLPL J|VWHUHFHNWLU 'ROD\ÕVL\OH
kütle transferi, \ÕOGÕ]ÕQDG\DEDWLN olarak JHQLúOHPHsinden sonraki bR\XWODUÕQDVÕNÕFDED÷OÕGÕU
DG\DEDWLNRODUDNJHQLúOHU
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ni engelleyen bir durum yoktur
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türü meydana gelir. %X \ROOD \ÕOGÕ] GÕú NÕVÕPODUÕQ SHú
SHúH JHOHQ KÕ]OÕ JHQLúOHPHOHUL VÕUDVÕQGD EX ROD\ KÕ]OÕ PHUNH]L VÕNÕúPD\OD ELU DUDGD ROPDNWDGÕU NULWLN
hacmini doldurur..ULWLNKDFPHXODúÕOÕUXODúÕOPD]GDNWOHDNWDUÕPÕEDúODU,úÕWPDGúHUPLQLPXPELUGH÷HUH
XODúÕUYHWHNUDUDUWDU Çok GúNNWOHOHULoLQKLGURMHQNDEX÷XQzayfla PDVÕ\ODPHUNH]GHHOHNWURQ\R]ODúPDVÕ
EDúODU %X GXUXPGD PHUNH]LQ VÕNÕúPDVÕ \DYDúODU YH EX QHGHQOH ]DUIÕQ KÕ]OÕ JHQLúOHPH HYUHVL, GROD\ÕVÕ\OD GD
KÕ]OÕNWOHDNWDUÕPHYUHVLROPD]
C türü: Bu durum, çok ileri evrelerde, KHO\XPXQ \DQPD\DEDúODPDVÕQGDQVRQUD5RFKH\DUÕoDSÕQÕQ
\ÕOGÕ]\DUÕoDSÕQÕDúWÕ÷Õ]DPDQRUWD\DoÕNDU
14
dLIW<ÕOGÕ]ODUÕQ(YULPL
da ortaya
kütle aktarmaya devam eder: AB türü: A türü NWOH DNWDUÕP
evresinden sonra B türü NWOHDNWDUÕPÕROXúXU\DGD%&türü: A türünü, C WUNWOHDNWDUÕPÕizler. %LUNÕUPÕ]Õ
GHYGH KHO\XPXQ WXWXúPDVÕ QHGHQL\OH NWOH DNWDUÕPÕQÕQ NHVLQWL\H X÷UDGÕ÷Õ GXUXP LVH JHQellikle BB türü
RODUDNDGODQGÕUÕOÕU.
%X o GXUXPXQ ROXúXPODUÕ ùHNLO ¶GD EHWLPOHQPLúWLU %XQODUÕQ \DQÕQGD PHOH] GXUXPODU
oÕNDELOLU NWOH ND\EHGHQ \ÕOGÕ] LNL GXUXPGD
ùHNLO 'H÷LúLN HYULP DúDPDODUÕ
–ZAMS, merkezi H-WNHQPHVL NÕUPÕ]Õ QRNWD +H-WXWXúPDVÕ– LoLQ \ÕOGÕ] NWOHVLQLQ
IRQNVL\RQX RODUDN \ÕOGÕ] \DUÕoDSODUÕQÕQ GH÷LúLPL <ÕOGÕ]ÕQ ELU oLIW VLVWHPLQ EDú ELOHúHQL RODUDN J|] |QQH DOÕQPDVÕ
halinde, NWOH DNWDUÕPÕQÕQ $ % YH & türleri J|VWHULOPLúWLU $\UÕFD G|QHPOHUL – JQ DUDVÕQGD RODQ oLIW
sistemlerdeki EDú ELOHúHQOHULQ 5RFKH \DUÕoDSODUÕ GD J|VWHULOPLúWLU ùHNLOGH NWOH RUDQÕ ELU RODUDN NXOODQÕOPÕú ROPDVÕQD
NDUúÕQNWOHRUDQÕQÕQGL÷HUGH÷HUOHULNXOODQÕOGÕ÷ÕQGDGDúHNLOoRNID]ODGH÷LúPHPHNWHGLU
.RUXQXPOXNWOHDNWDUÕPÕ
<ÕOGÕ] 5RFKH OREX LoLQH JHUL JHOGL÷LQGH NWOH DNWDUÕPÕ VRQD HUHU %LU \ÕOGÕ]ÕQ HYULPVHO JHQLúOHPHVL HVDV
RODUDN \ÕOGÕ]ÕQ Lo NÕVÕPODUÕQGDNL oHNLUGHNOHULQ ELUOHúHUHN GDKD D÷ÕU oHNLUGHNOHU ROXúWXUPDODUÕQÕ VD÷OD\DQ
QNOHHU ELUOHúPHOHULQ QHGHQ ROGX÷X NLP\DVDO GH÷LúLPOHU LOH \DNÕWÕQÕ WNHWPHNWH RODQ \R]ODúPÕú oHNLUGH÷LQ
J|UQP YH JHOLúLPLQH ED÷OÕGÕU
çevrimi
Böylece, ya
\ÕOGÕ]ÕQ \R]ODúPÕú oHNLUGH÷LQGH \HQL ELU QNOHHU ELUOHúPH
,
+ YH\D +H \DQPDVÕ EDúODGÕ÷ÕQGD oHNLUGH÷LQ VÕQÕUÕQGD \DQPDNWD RODQ NDEXNODUÕQ
D]DODFD÷ÕQGDQ GROD\Õ \D GD \ÕOGÕ]ÕQ HQHUML ND\QDNODUÕQÕ
besleyen
n
]DUIÕ
etkisi
WNHQPHVL\OH EX JHQLúOHPHQLQ
. Gerçekte, atmosferdeki hidrojen EROOX÷XQXQ D]DOPDVÕ \ÕOGÕ]ÕQ \DUÕoDSÕQÕQ NoOPHVLQH
neden olur. $÷ÕUOÕNRODUDN QRUPDOGHFLYDUÕQGDRODQDWPRVIHULNKLGURMHQEROOX÷X GH÷HULQHGúW÷QGH
GXUDFD÷Õ DoÕNWÕU
RSDNOÕNE\NRUDQGDGH÷LúLUYHDWPRVIHUo|NHU
.WOH DNWDUÕP HYUHVLQLQ EDúODQJÕFÕ YH VRQX ùHNLO ¶GD J|VWHULOPLúWLU %X úHNLOGH \ÕOGÕ] NWOHVLQLQ ELU
IRQNVL\RQXRODUDN\ÕOGÕ]\DUÕoDSÕQÕWHPVLOHGHQH÷ULOHULOJLOLHYULPDúDPDODUÕ6ÕIÕU\DúDQNRO
-=$06NÕUQÕ]Õ
QRNWD \DQL PHUNH]L KLGURMHQ \DQPDVÕ VUHVLQFH HYULP oL]JLVLQLQ XODúWÕ÷Õ HQ VD÷ QRNWDPHUNH]GH KLGURMHQLQ
15
dLIW<ÕOGÕ]ODUÕQ(YULPL
WNHWLOPHVL KHO\XPWXWXúPDVÕNDUERQ WXWXúPDVÕLoLQ J|VWHULOPLúOHUGLU (÷HU EX \DUÕoDSODUÕ \DNÕQoLIWLQEDú
,
e
na
Bununla
\ÕOGÕ]ÕQÕQ 5RFKH \DUÕoDSÕ LOH WDQÕPODUVDN GL\DJUDP EL]H NWOH DNWDUÕPÕQÕQ QHU GH EDúOD\ÕS QHUHGH VR
HUHFH÷LQL \DQL EDúND GH÷LúOH $ % YH & WU NWOH DNWDUÕPODUÕQD NDUúÕOÕN JHOHQ NÕVÕPODUÕ J|VWHULU
ELUOLNWHHWNLOHúHQELUoLIWLQVRQDúDPDVÕQÕEHOLUOHPHNLoLQ\|UQJHHYULPLQLQGHGLNNDWHDOÕQPDVÕJHUHNOLGLU
Korununmlu evrim durumunda, iki biOHúHQLQ GH÷LúHQ X]DNOÕNODUÕ YH \|UQJH G|QHPLQLQ GH÷LúLPL (15.8)
denklemi ile verilen
J2 =
GA( M 1M 2 ) 2
M1 + M 2
ED÷ÕQWÕVÕQGDQNROD\FDDQODúÕOÕU
A=
C
( M 1M 2 ) 2
veya
Hem J hem de M1 + M2VDELWNDOGÕNODUÕQGDQ
A  M 1o M 2o 

=
A o  M 1M 2 
2
(15.24)
yazabiliriz, buUDGD R LQGLVL EDúODQJÕo GXUXPXQX YH YH LQGLVOHUL GH, VÕUDVÕ\OD EDú YH \ROGDú ELOHúHQOHUL
göstermektedir. CELUVDELWROXSEDúODQJÕoNRúXOODUÕQÕQ\DUGÕPÕ\OD
C = A o ( M 1o M 2o ) 2
ED÷ÕQWÕVÕ
(15.25)
ile verilir. µ = M 2 / M1 WDQÕPODPDVÕ\OD)ED÷ÕQWÕVÕQÕ
A (1 + µ ) 2 µ o
=
Ao (1 + µ o ) 2 µ
(15.26)
biçiminde yazabiliriz. Dönem ise,
M M
P = Po  1o 2o
 M 1M 2



3
(15.27)
ED÷ÕQWÕVÕ\ODYHULOLU
%Dú YH \ROGDúÕQ
M1, M2 kütleleri ve yörüngH \DUÕ E\N HNVHQL A¶QÕQ YHULOPHVL\OH .HSOHULQ \DVDVÕ
NXOODQÕODUDN\|UQJHG|QHPL
log P = 1.5 log A − 0.5 log( M 1 + M 2 ) − 0.936
(15.28)
ED÷ÕQWÕVÕQGDQKHVDSODQDELOLUEXUDGD\DUÕE\NHNVHQX]XQOX÷XAJQHú\DUÕoDSÕ biriminde, yörünge dönemi
P gün biriminGHYHELOHúHQOHULQM1, M2NWOHOHULGHJQHúNWOHVLELULPLQGHGLU
5RFKH OREX LOH D\QÕ KDFLPOL ELU NUHQLQ \DUÕoDSÕ \DQL 5RFKH \DUÕoDSÕ ED÷ÕQWÕVÕ\OD YHULOLU
Kütle
DNWDUÕPÕVUGNoHEDú YH \ROGDúELOHúHQLQNWOHOHULYHEXQXQVRQXFXQGDGD5RFKH\DUÕoDSODUÕGH÷LúLU%LULP
NWOHRUDQÕLoLQELOHúHQOHUDUDVÕQGDNLX]DNOÕ÷ÕQIRQNVL\RQXRODUDN5RFKH\DUÕoDSÕ
RR
= 0.38 veya log A = log RR + 0.42
A
(15.29)
ED÷ÕQWÕVÕ\ODYH\|UQJHG|QHPLGH
log P = 1.5 log RR − 0.5 log M1 − 0.456
ED÷ÕQWÕVÕ\OD
(15.30)
verilir. BuED÷ÕQWÕ\DUGÕPÕ\ODùHNLONWOHRUDQÕRODQoLIWlerin dönemlerini, kütlelerinin bir
IRQNVL\RQXRODUDNJ|VWHUHQùHNLO¶DG|QúWUOHELOLU
dLIW<ÕOGÕ]ODUÕQ(YULPL
16
Toplam kütle M1 + M2 LOH WRSODP \|UQJH DoÕVDO PRPHQWXPX J¶QLQ NRUXQGX÷X YH Hú]DPDQOÕ dönmenin
YDUVD\ÕOGÕ÷Õ GXUXPGD NWOH DNWDUÕPÕQÕQ GHYDP HWWL÷L ELU oLIW sistemin dolanma dönemi, ùHNLO 1’de
J|VWHULOGL÷LJLELGH÷LúHFHNWLU
KWOH DNWDUÕP HYUHVL VUHVLQFH, sistemden kütlH YH DoÕVDO PRPHQWXP ND\EÕ ROGX÷XQGDQ GROD\Õ JHUoHNWH
durum çok dDKDNDUPDúÕNWÕU
ùHNLO ZAMS’tan, C-WXWXúPDVÕQD NDGDU RODQ HYULPOHUL VUHVLQFH HúLW NWOHOL YH LOJLOL 5RFKH \DUÕoDSODUÕ \ÕOGÕ]
dönemleri. ZAMS, merkezi H-WNHQPHVL NÕUPÕ]Õ QRNWD +H-WXWXúPDVÕ JLEL
\DUÕoDSODUÕQD HúLW RODQ \DNÕQ oLIW VLVWHPOHULQ
fDUNOÕH÷ULOHUùHNLO¶GDJ|VWHULOHQ\DUÕoDSODUDNDUúÕJHOPHNWHGLU
 + 1 MoLIWVLVWHPLQLQNRUXQXPOXNWOHDNWDUÕPÕYDUVD\ÕPÕ
M1 kütlesinin fonksiyonu olarak dönem GH÷LúLPL
ùHNLO%DúODQJÕoGRODQPDG|QHPLJQRODQELU0
DOWÕQGDEDúELOHúHQLQLQ
.258180/8(95ø0
øOHUOHPHQLQ HQ EDVLW \ROX \ROGDú \HULQH EDú \ÕOGÕ]ÕQ D\UÕQWÕOÕ \DSÕVÕQÕ KHVDSODPDN YH \ROGDúÕQ NWOHVLQGHNL
GH÷LúLPL \DOQÕ]FD \DUÕ E\N HNVHQ X]XQOX÷X LOH G|QHPGHNL GH÷LúLPOHUL KHVDSODPDN DPDFÕ\OD GLNNDWH
17
dLIW<ÕOGÕ]ODUÕQ(YULPL
DOPDNWÕU.WOHDNWDUÕPHYUHVLVUHVLQFHNWOHEDú\ÕOGÕ]GDQND\EHGLOLUYHYHULOHQELU]DPDQDUDOÕ÷ÕLoHULVLQGH
EDú \ÕOGÕ]ÕQ Lo \DSÕVÕEX GXUXPD X\JXQ RODUDN \HQLGHQ D\DUODQÕU .WOHOHUH YHELOHúHQOHUDUDVÕQGDNLX]DNOÕ÷D
ED÷OÕ RODQ \|UQJH SDUDPHWUHOHUL KHVDSODQDELOLU <ROGDúÕQ Lo \DSÕVÕ KHVDSODQPD] YH EDVLWoH EDú \ÕOGÕ]GDQ
DWÕODQ PDGGHQLQ \ROGDúÕQ NWOHVLQH HNOHQGL÷L YDUVD\ÕOÕU 6RQUD GD GH÷LúLN NWOH YH GH÷LúLN G|QHPOL oLIWOHULQ
evrimleri, gözlenen sistemleri ve Algoller, Wolf-Rayet çiftleri ve X-ÕúÕQoLIWOHULJLELGH÷LúLN \ÕOGÕ]JUXSODUÕQÕ
DoÕNODPDGDNXOODQÕOÕU
.WOH DNWDUÕP HYUHVL úX úHNLOGH HOH DOÕQÕU \ÕOGÕ]ÕQ \DUÕoDSÕ 5RFKH \DUÕoDSÕ
RR¶GHQ NoN NDOGÕ÷Õ VUHFH EDú
\ÕOGÕ]ÕQHYULPLEDú \ÕOGÕ]VDQNLELUWHN\ÕOGÕ]PÕúJLELGLNNDWHDOÕQDUDNKHVDSODQÕU<DUÕoDS5RFKH\DUÕoDSÕQD
HúLW ROGX÷XQGD \ÕOGÕ]ÕQ KDFPLQL NoOWPHN YH \DUÕoDSÕ 5RFKH \DUÕoDSÕQD HúLW RODUDN WXWDELOPHN DPDFÕ\OD
R = RR úHNOLQGH ELU VÕQÕU GH÷HU NRúXOX NXOODQÕODUDN \DSÕODELOLU Alternatif
olarak, verilen bir sÕQÕULoHULVLQGH R’nin RR’den küçük NDOPDVÕ VD÷ODQDELOLUhoQFELU \RORODUDN GD DWÕODQ
PDGGHPLNWDUÕ∆MLOH\ÕOGÕ]YH5RFKH\DUÕoDSODUÕDUDVÕQGDNL∆rIDUNÕDUDVÕQGDELUED÷ODQWÕNXUXODELOLU
\HWHUOL RUDQGD NWOH DWÕOÕU %X Lú
Bunun \DOQÕ]FD ELU LON \DNODúÕP RODFD÷Õ DoÕNWÕU Çok daha ayrÕQWÕOÕ \|QWHPOHU D\QÕ HYULP NRGX LoHULVLQGH
ELOHúHQOHULQKHULNLVLQLQGHLo\DSÕKHVDSODPDODUÕQÕLoHUmelidir.
.25818068=(95ø0
.RUXQXPOX
HYULP
VHQHU\RVX
KHU
]DPDQ
JHoHUOL
GH÷LOGLU
YH
J|]OHQHQ
VLVWHPOHULQ
SDUDPHWUHOHULQL
DoÕNOD\DELOPHN LoLQ NWOH YH DoÕVDO PRPHQWXP ND\ÕSODUÕ GD GLNNDWH DOÕQPDOÕGÕU %XQXQ \DQÕQGD oLIW
VLVWHPOHULQ D\UÕN HYUHOHUL VÕUDVÕQGD
,
\ÕOGÕ] U]JDUODUÕQÕQ QHGHQ ROGX÷X NWOH ND\ÕSODUÕ GD J|] |QQH
DOÕQPDOÕGÕU
.RUXQXP YDUVD\ÕPÕQÕQ JHoHUOL ROPDGÕ÷Õ GXUXPODUGD NWOH DNWDUÕPÕQÕQ
ilk
DúDPDVÕQÕQ VUHVL LQDQÕOPD]
RUDQGDX]D\DELOLUYHNWOHGH÷LúLPLQGHQVRQUDRUWD\DoÕNDQVLVWHPNRUXQXPOXGXUXPGDNLQGHQIDUNOÕRODELOLU
6LVWHPLWHUNHGHQNWOHLVWHU\ÕOGÕ]U]JDUODUÕYDVÕWDVÕ\ODROVXQLVWHUNWOHDNWDUÕPÕVÕUDVÕQGDROVXQVLVWHPGHQ
DoÕVDO PRPHQWXP ND\EÕQD QHGHQ ROXU %LOHúHQOHU DUDVÕQGDNL YH FLYDUODUÕQGDNL JD] DNÕPODUÕQÕQ GDYUDQÕúÕQD
LOLúNLQ ELOJLOHULPL] HNVLN YH DQFDN QLWHO \DSÕGD ROGX÷XQGDQ VLVWHPGHQ NWOH YH DoÕVDO PRPHQWXP ND\EÕQÕQ
etkilerini ancak bir çok serbest parametre yarGÕPÕ\ODEHOLUOH\HELOLUL]
.WOHND\EÕLOHNWOH\Õ÷ÕúPDK]ÕELUELUOHULQHDúD÷ÕGDNLúHNLOGHED÷ODQDELOLU
dM r
dM d
,
= −β
dt
dt
(15.31)
burada Mr ve Md VÕUDVÕ\OD DOÕFÕ LOH vericinin kütleleridir. %X ED÷ÕQWÕGD NDoÕQÕOPD] RODQ \ÕOGÕ] U]JDUODUÕ\OD
NWOH ND\EÕ KHVDED NDWÕOPDPÕúWÕU β parametresi keyfi olarak seçilebilir (β RODFD÷Õ DoÕNWÕU β = 1,
korunuPOXGXUXPDNDUúÕOÕNJHOLU- βVLVWHPLWHUNHWWL÷LGúQOHQPDGGHQLQNHVULGLU
%D]Õ GXUXPODUGD NWOH ND\EÕ LOH RUWD\D oÕNDQ
açÕVDO PRPHQWXP ND\EÕ
ROGXNoD L\L ELU úHNLOGH WDKPLQ
edilebilir.
1.
<ÕOGÕ] U]JDUODUÕ\OD NWOH ND\EÕ \ÕOGÕ] U]JDUODUÕ\OD NWOH ND\EÕQÕQ -HDQV PRGXQD +XDQJ J|UH
ROXúWX÷X
yDQLQRNWDVDONWOH RODUDNJ|]|QQHDOÕQDQ \ÕOGÕ]GDQNUHVHOVLPHWULde YH \ÕOGÕ]GDQ EHOLUOLRUDQGD
ki yükseNKÕ]ODUODROGX÷XNDEXOHGLOLU%XGXUXPGDG|QHPYH
DoÕVDOPRPHQWXPWDúÕQÕPÕQD\RODoDFDNúHNLOGH
D\UÕNOÕ÷ÕQGH÷LúLPL
P
M + M 2i 2
)
= ( 1i
Pi
M1 + M 2
(15.32)
A M 1i + M 2i
=
Ai
M1 + M 2
A, M ve P VÕUDVÕ\OD ELOHúHQOHU DUDVÕQGDNL D\UÕNOÕ÷Õ WRSODP NWOH\L YH VLVWHPLQ
dolanma dönemini göstermektedir.
ED÷ÕQWÕODUÕ\OD YHULOLU EXUDGD
18
dLIW<ÕOGÕ]ODUÕQ(YULPL
2) L2¶GHQ NWOH ND\EÕ %LOHúHQOHUGHQ ELULQL WHUN HGHQ GúN KÕ]ODUD Vahip JD]ÕQ DoÕVDO PRPHQWXPX sistemi
terk etmesinden önce, gel-git etkileri nedeniyle daha da artar.$oÕVDOPRPHQWXPND\EÕ 1.65ω A2 ED÷ÕQWÕVÕ\OD
ω A2 GH÷HULQGHQ NoN ROGX÷X -HDQV
modundan tahmin edilenden büyüktür. $VOÕQGD bu, L2 QRNWDVÕQGDQ NDoDQ PDGGHQLQ DoÕVDO momentumuyla
WDKPLQ HGLOHELOLU EX WDKPLQ |]JQ DoÕVDO PRPHQWXP ND\EÕQÕQ GDLPD
NDUúÕODúWÕUÕODELOLU GH÷HUGHGLU %XQXQOD ELUOLNWH \ÕOGÕ] U]JDUODUÕQGD KÕ]ODU \HWHULQFH E\NWU YH EX QHGHQOH
-HDQVPRGXL\LELU\DNODúÕPGÕU
L2¶GHQJHoHQHúSRWDQVL\HO\]H\Lni dolGXUGX÷XQGD
meydana gelir. %X GXUXPGD |]JQ DoÕVDO PRPHQWXP ND\EÕ \DNODúÕN RODUDN 1.75ω A2 ROXS NWOH RUDQÕQGDQ
%XGXUXPGH÷HQELUoLIWVLVWHPLQGÕúNULWLN\]H\LQL\DQL
ED÷ÕPVÕ] YH VLVWHPLQ NHQGLVLQLQ DoÕVDO PRPHQWXPXQGDQ oRN GDKD E\NWU VLVWHPLQ NHQGLVL LoLQ DoÕVDO
momentum q( 1 − q)ω A2 ¶GLU(Q\NVHNGH÷HULQHq ¶WHXODúÕUEXGXUXPGDDoÕVDOPRPHQWXP 0.25ω A2
olur. %|\OHFH DoÕVDOPRPHQWXP VLVWHPLQ NHQGLVLQLQ |]JQ DoÕVDOPRPHQWXPXQun \DNODúÕN RODUDN NDWÕGÕU.
%XWUNWOHND\EÕ\|UQJHG|QHPLYHELOHúHQOHUDUDVÕQGDNLD\UÕNOÕ÷ÕQE\NRUDQGDNoOPHVLQHQHGHQROXU
'L÷HU WP GXUXPODUGD NWOH YH DoÕVDO PRPHQWXP ND\ÕSODUÕQÕ WDKPLQ HGHELOPHN RODQDNVÕ]GÕU LVWLVQDL WHN
\RO DoÕVDO PRPHQWXP ND\EÕQÕ EHOLUWHQ ELU VHUEHVW SDUDPHWUH NXOODQPDNWÕU .WOH DNWDUÕP VÕUDVÕQG
a, yörünge
DoÕVDOPRPHQWXPXQXQWRSODPNWOH\H
J = Mα
(15.33)
úHNOLQGH\DGDHúGH÷HURODUDN
∆J
∆M α
)
= 1 − (1 −
J
M
(15.34)
, burada α
tirilmeyecek bir sabittir. YÕOGÕ]ODUÕQ NWOHOHUL LOH
yörünge dönemi ile sistemin
D\UÕNOÕ÷Õ da hesaplanabilir. 5RFKH OREX WDúPDVÕ ROD\Õ RULMLQDO RODUDN -HGU]HMHF EN] 3DF]\Q]ki ve
Sienkiewicz, 1972) WDUDIÕQGDQ JHOLúWLULOHQ WUGHQ EDVLWOHúWLULOPLú bir KLGURGLQDPLN \DNODúÕPOD WDQÕPODQDELOLU
úHNOLQGH ED÷OÕ ROGX÷X NDEXO HGLOHELOLU
GH÷Lú
\|UQJH DoÕVDO PRPHQWXPXQGDQ \DUDUODQÕODUDN NULWLN \DUÕoDSODU \DQÕQGD
%DVLWPRGHOHJ|UHDNDQPDGGH\Õ÷ÕúPD\ÕOGÕ]ÕQÕQ \]H\NDWPDQODUÕQDEXNDWPDQODUÕQVDKLSROGX÷XHQWURSL
LOH\XPXúDNELUúHNLOGHGúHU %XYDUVD\ÕPKDNOÕJ|UQPHNWHGLUoQN\ÕOGÕ]\]H\LQLQDQFDNoRNNoNELU
kesri, çarpan maddeden, bir leke ya da ekvatoryal
ELU NXúDN YDVÕWDVÕ\OD HWNLOHQLU GúHQ PDGGHQLQ GLQDPLN
EDVÕQFÕ LKPDO HGLOHELOLU <Õ÷ÕúDQ PDGGHQLQ QHGHQ ROGX÷X NLQHWLN HQHUML ID]ODOÕ÷Õ GD÷ÕODFDN úRN E|OJHVLQLQ
yüksek VÕFDNOÕ÷Õ QHGHQL\OH EX HQHUML PRU|WH YH ;-ÕúÕQODUÕ úHNOLQGH \D\ÕPODQDFDNWÕU (÷HU, kütle kazanan
\ÕOGÕ] \D GD RODVÕ ELU \Õ÷ÕúPD GLVNL úLGGHWOL ELU úHNLOGH JHQLúOHPH]VH, senkronizasyon devam edebilir ve
yörünge çember olarak kalabilir. Korunumlu kütle aktDUÕPÕQÕ GHVWHNOH\HQ dinamik nedenler olabilir. Küçük
0DFK VD\ÕVÕQD VDKLS DNDQ JD], L1 FLYDUÕQGDNL NoN ELU Eölgede ses KÕ]ÕQGD ELU JHoLú \DSDELOLU NWOH
ND]DQDQÕQ 5RFKH OREXQD JLUHU YH EX \]H\ LoHULVLQGH WX]DNODQÕU (÷HU DNÕQWÕ NHQGLVLQe ya da kütle alan
\ÕOGÕ]ÕQ \]H\LQH oDUSDUVD yörünge enerjisi GD÷ÕOÕU YH PDGGH NWOH ND]DQDQ \ÕOGÕ]ÕQ SRWDQVLyeli içerisinde
GHULQOHUHGúHUYHVLVWHPGHQNWOHND\EÕROPD]
.WOH\Õ÷ÕúPDVÕ
-Helmholtz zaPDQ |OoH÷LQGH -bu süre genel
arak
.WOH ND]DQDQ \ÕOGÕ] PDGGH\L NWOH ND\EHGHQ \ÕOGÕ]ÕQ .HOYLQ
-
RODUDN NWOH ND]DQDQ \ÕOGÕ]ÕQNLQGHQ IDUNOÕGÕU \Õ÷ÕúWÕUÕU %X GXUXPGD NWOH ND]DQDQ \ÕOGÕ] ER\XW RO
úLGGHWOL ELU úHNLOGH E\U5RFKHOREXQX GROGXUXU YH ELUGH÷HQVLVWHP ROXúXU6RQUDNLHYULPDúDPDVÕ |QFHNL
durumlardan farkOÕROXU
'H÷PHHYUHVLVUHVLQFHNWOHDNWDUÕPKÕ]ÕKHULNL\ÕOGÕ]ÕQGDD\QÕHúSRWDQVL\HO\]H\LGROGXUPDODUÕJHUHNWL÷L
NRúXOX LOH EHOLUOHQLU %X YDUVD\ÕP \HWHULQFH GR÷UXGXU RUWDN ]DUIÕQ OREODUÕ DUDVÕQGDNL EDVÕQo IDUNOÕOÕNODUÕ
QHGHQL\OHHúSRWDQVL\HONRúXOXQGDQVDSPDLKPDOHGLOHELOLU
Kütle aktarÕP
HYUHVL VUHVLQFH NWOH ND\EHGHQ \ÕOGÕ] JLGHUHN GÕú NDWPDQODUÕQÕ ND\EHGHU YH oHNLUGHN
kar; böylece, NWOH ND]DQDQ \ÕOGÕ] WDUDIÕQGDQ \Õ÷ÕúWÕUÕODQ PDGGH
BX úHNLOGH \Õ÷ÕúDQ PDGGH ]DUI
WHSNLPHOHULQLQ ROGX÷X NDWPDQODU RUWD\D oÕ
KHO\XP EDNÕPÕQG
an,
NHQGL NDWPDQODUÕQD J|UH oRN GDKD ]HQJLQ ROXU
NDWPDQODUÕQGDQ GDKD E\N ELU PROHNOHU D÷ÕUOÕ÷D VDKLS ROXU YH NWOH ND]DQDQ \ÕOGÕ] WHUVLQH G|QPú
PROHNOHUJUDGL\HQWOLELU]DUIJHOLúWLULU
azalmakWDGÕU
Dengesiz olan bu zarfta, molekülHUD÷ÕUOÕN\]H\GHQ,PHUNH]HGR÷UX
19
dLIW<ÕOGÕ]ODUÕQ(YULPL
Büyük µPROHNOD÷ÕUOÕNOÕ \ÕOGÕ]PDGGHVLQLQGDKDNoNµPROHNOD÷ÕUOÕNOÕNDWPDQODUÕQ]HULQHEÕUDNÕOPDVÕ
durumu, bir miktar tuzlu suyun, VR÷XN WDWOÕ VX NDWPDQÕ ]HULQH EÕUDNÕOPDVÕ durumuyla NDUúÕODúWÕUÕOabilir; bu
durumda, ara \]GH SDUPDN EHQ]HUL ELU NDUDUVÕ]OÕN JHOLúLU 6WHUQ 9HURQLV %X NDUDUVÕ]OÕ÷ÕQ
JHQHO DGÕ ³ÕVÕVDO WDúÕQÕP konveksiyonu (thermohaline convection)” dur ve ona ED]HQ ³\DODQFÕ NRQYHNVL\RQ´
da denir.
Bu ÕVÕVDOWDúÕQÕP NDUÕúÕPÕQÕ, astrofizikte E\NPROHNOHUD÷ÕUOÕNOÕPDGGHQLQGDKDNoNPROHNOHUD÷ÕUOÕNOÕ
PDGGH ]HULQGH EÕUDNÕOPDVÕ LOH RUWD\D oÕNDQ WUGHQ NRQYHNVL\RQ GXUXPX\OD NDUúÕODúWÕUDELOLUL]. Bu konudaki
JHQHO WDUWÕúPDODU LoLQ &R[ YH *LXOL 6SLHJHO =DKQ YH 3DFNHW ¶H EDNÕODELOLU Bu
ÕVÕVDOWDúÕQÕP NDUÕúÕPÕLoLQ]DPDQ|OoH÷L\Õ÷ÕúPD]DPDQ|OoH÷LQGHQoRNNÕVDGÕUYHEXQHGHQOH ona,DQOÕNELU
süreçJ|]\OHEDNÕODELOLU.
bu nedenle, çekirdek
elir. %X NDWPDQODU \ROGDúD
.WOH DNWDUÕP HYUHVL VUHVLQFH NWOH YHUHQ ELOHúHQ GÕú NDWPDQODUÕQÕ DWDU YH
WHSNLPHOHULQLQ GHYDP HWWL÷L GDKD DOW NDWPDQODU J|UQU \]H\ NDWPDQÕ KDOLQH J
DNWDUÕOGÕ÷ÕQGDE\N ELU
EÕUDNÕOPÕú ROXU
Bu
µ PROHNO D÷ÕUOÕNOÕNDWPDQODU RULMLQDONLP\DVDOELOHúLPH VDKLSNDWPDQODUÕQ]HULQH
VXUHWOH WHUV \|QO ELU PROHNOHU D÷ÕUOÕN JUDGL\HQWL RUWD\D oÕNPÕú ROXU YH EX GXUXP
NDUDUVÕ] ELU GXUXPD QHGHQ ROXU .WOH YHUHQ YH DODQÕQ GH÷LúHQ KLGURMHQ EROOXNODUÕ NDUÕúÕP ]HULQH \DSÕODQ
.
oHúLWOLYDUVD\ÕPODULoLQùHNLO ¶GHJ|VWHULOPLúWLU
Helyumca]HQJLQ]DUIOÕ\ÕOGÕ]PRGHOOHUiQRUPDOEROOXNOXPRGHOOHULQVROXQGD\HUDOÕUODUùHNLOGH÷LúLN
NWOHOHULoLQ QRUPDO NLP\DVDO NDUÕúÕPOÕX KRPRMHQ NLP\DVDONDUÕúÕP =$06 PRGHOOHUL LOHKHO\XPFD
]HQJLQ ]DUIOÕ X
\ÕOGÕ] NWOHVLQLQ ¶XQX içeren helyumca zengin zarf) modelleri göstermektedir.
=DPDQ |OoH÷L WDKPLQOHULNDUÕúÕP]DPDQ|OoH÷LQLQ NWOH DNWDUÕP ]DPDQ|OoH÷LQGHQ oRN GDKD NÕVDROGX÷XQX
göstermektedir.%XQHGHQOHÕVÕVDOWDúÕQÕPNDUÕúÕPÕDQOÕNELUROJXRODUDNJ|]|QQHDOÕQDELOLU
dLIW<ÕOGÕ]ODUÕQ(YULPL
20
ùHNLO .WOH ND\EHGHQ VWWH YH \Õ÷ÕúDQ ELU \ÕOGÕ]ÕQ DOWWD NLP\DVDO SURILOL ùHNLO G|UW RODVÕ GXUXPX
göstermektedir: A <Õ÷ÕúDQ PDGGHQLQ kimyasal ELOHúLPL DOÕFÕ \ÕOGÕ]ÕQNL\OH D\QÕ B) Helyum ID]ODOÕ÷ÕQÕQ
D]DOGÕ÷Õ NDWPDQODUGD birikim; böyleFH NoN PROHNO D÷ÕUOÕNOÕ NDWPDQODUÕQ VWQGH, E\N PROHNO D÷ÕUOÕNOÕ
katmanlarÕQROXúXmu; C<DUÕ-NDUÕúÕPG]GúH\oL]JLROPDNVÕ]ÕQÕVÕVDOWDúÕQÕPNDUÕúÕPÕD<DUÕ-NDUÕúÕPOÕ
H÷ULoL]JLÕVÕVDOWDúÕQÕPNDUÕúÕPÕ
ùHNLO Kütleleri 2 - 9 M
araVÕQGDNL QRUPDO NDUÕúÕPOÕ, X = 0.7 (noktalar), KRPRMHQ \ÕOGÕ]ODU LOH
helyumca zengin, X = 0.3, modeller LoL ERú oHPEHUOHU -burada He-zengin katmanlar, \ÕOGÕ] NWOHVLQLQ
%10’unu içermektedir- için ZAMS modellerinin Hertsprung-5XVVHOGL\DJUDPÕ
21
BÖLÜM 16
.hdh.9(257$.h7/(/ødø)76ø67(0/(5ø1(95ø0ø
16*LULú
1NOHHU \DQPD VUHVLQFH \ÕOGÕ]ÕQ \DUÕoDSÕ DUWDU (÷HU \ÕOGÕ] ELU \DNÕQ oLIW VLVWHPLQ \HVL LVH \DUÕoDSWDNL EX
DUWÕú \ROGDúÕQ YDUOÕ÷Õ QHGHQL\OH VÕQÕUOÕGÕU (÷HU \DUÕoDSÕQ ROGXNoD KDVVDV RODUDN EHOOL RODQ NULWLN GH÷HUL
, hatta VLVWHPGHQ NWOH ND\EÕ olabilir ya da bir
halka veya diskte kütle birikimi meydana gelebilir. %X NWOHDNWDUÕPÕDúDPDVÕQÕQKHVDSODPDODUÕDQFDNEHOLUOi
\DNODúÕPODUÕQ NDEXO HGLOPHVL\OH RODQDNOÕ RODELOLU Hidrodinamik ve küresel simetriden sapmalar (dönme ve
DúÕOÕUVD ELOHúHQOHUGHQ ELULQGHQ GL÷HULQH NWOH DNWDUÕPÕ EDúODU
oHNLPVHO HWNLOHU JHQHOOLNOH GLNNDWH DOÕQPD] YH \|UQJH JHQHOOLNOH oHPEHU RODUDN HOH DOÕQÕU %LOHúHQOHULQ
dönmeleri yörünge hareketi ile senkronize oOPXú
YDUVD\ÕOÕU <DNÕQ oLIW VLVWHPOHULQ HYULPL ELOHúHQOHULQ
NWOHOHULQHNWOHRUDQÕQDYH\|UQJHG|QHPLQHED÷OÕGÕU
*|] |QQH DOÕQDQ \ÕOGÕ]ÕQ NULWLN HúSRWDQVL\HO \]H\OHU
iyle
ED÷ODQWÕOÕ RODUDN oLIW VLVWHPLQ GXUXPX o
-
NDWHJRUL\HD\UÕODELOLUD\UÕN\DUÕ D\UÕNYHGH÷HQHYUHOHU
, görsel çiftler ile
i verebiliriz. <DUÕ-D\UÕN ELU VLVWHPGH ELOHúHQOHUGHQ ELUL NULWLN KDFPLQL
GROGXUPXúNHQ \ROGDúÕ GROGXUPDPÕúWÕU Bu türe örnek olarak, Algol türü çiftleri ve β /\UDH¶\Õ YHUHELOLUL]
$\UÕNHYUHVÕUDVÕQGDELOHúHQOHULQKLoELULNULWLNKDFLPOHULQLGROGXUPD]%XWUH|UQHNRODUDN
HYULPOHúPHPLú WD\IVDO oLIWOHU
'H÷HQELUVLVWHPGHLVHELOHúHQOHULQLNLVLGHNULWLNKDFLPOHULQLGROGXUPXúWXU|UQH÷LQ:80D\ÕOGÕ]ODUÕ
Doldurma faktörü genellikle f
LOH J|VWHULOLU YH LNL \ÕOGÕ] DUDVÕQGDNL GH÷PH GHUHFHVLQLQ ELU |OoVGU
L1’den geçen yüzeyin
L2 ve L1¶GHQJHoHQ\]H\OHULQHúSRWDQVL\HOOHUL
fDUNÕQDRUDQÕRODUDNWDQÕPODQÕU <DUÕ-D\UÕNVLVWHPOHULoLQf = 0; L2’den geçen ortak bir yüzeye sahip GH÷HQELU
sistem için de f = 1’dir.
'ROGXUPD IDNW|U \ÕOGÕ] \]H\LQLQ HúSRWDQVL\HOL LOH Lo /DJUDQJLDQ QRNWDVÕ
HúSRWDQVL\HOLDUDVÕQGDNLIDUNÕQGÕúYHLo/DJUDQJLDQQRNWDODUÕ
$\UÕN VLVWHPOHUGHKHULNL ELOHúHQ GH oR÷XQOXNOD QRUPDO DQD NRO \ÕOGÕ]ÕGÕU (YULP KHVDSODPDODUÕ =$06¶WDQ
BüyüN NWOHOL \ÕOGÕ] EDú \ÕOGÕ] RODUDN LVLPOHQGLULOLU YH NWOHVL M1 ile gösterilir; onun küçük kütleli
M2 LOH J|VWHULOLU %Dú YH \ROGDúÕQ EX úHNLOGHNL WDQÕPODPDVÕ
EDúODQJÕoWDE\NNWOHOLRODQELOHúHQHYULP süresince meydana gelen NWOHDNWDUÕPODUÕQÕQELUVRQXFXRODUDN
sistemin küçük kütleli ELOHúHQL KDOLQH JHOVH ELOH GH÷LúWLULOPH] 'L÷HU WP \ÕOGÕ] SDUDPHWUHOHUL LoLQ GH DOW
EDúODU
ELOHúHQL LVH \ROGDú RODUDN DGODQGÕUÕOÕU YH NWOHVL
LQGLVLEDú\ÕOGÕ]YHDOWLQGLVLGH\ROGDú\ÕOGÕ]LoLQNXOODQÕOÕUYHKHUKDQJLELUNDUÕúÕNOÕ÷DQHGHQROPDPDNLoLQ
NWOH ND\EHGHQ \ÕOGÕ] ³ND\EHGHQ´ \D GD ³YHULFL´ RODUDN YH NWOH ND]DQDQ \ÕOGÕ] GD ³ND]DQDQ´ \D GD ³DOÕFÕ´
olarak belirtilir. Bu durumda alt indis olarak l (kaybeden), d (verici), g (gazanan) ve r DOÕFÕ harfleri
NXOODQÕODFDNWÕU%DúODQJÕoGXUXPXi (initial) ve son durum da f (final) alt indisleri ile gösterilecektir.
Küçük ve orta kütleli çiftlere örnekler Çizelge 16.1 – $¶GD YHULOPLúWLU %LOLQHQ WP \DUÕ-D\UÕN VLVWHPOHUGH
5RFKH OREXQX GROGXUPD\DQ \ÕOGÕ] ELU DQD NRO \ÕOGÕ]ÕGÕU YH RQXQ \ROGDúÕ bir alt devdir. %X \ROGDúÕQ NWOHVL
GDLPD
DQD
NRO
\ÕOGÕ]Õ
RODQ
EDú
\ÕOGÕ]ÕQNLQGHQ
J|]NPHNWHGLUOHU QRUPDO \ÕOGÕ]ODU GXUXPXQGD
NoNWU
%X
VLVWHPOHU
JDULS
GDYUDQÕúOÕ
RODUDN
L ≈ M 3.5 ED÷ÕQWÕVÕ JHoHUOL YH \DúDP VUHVL t ≈ ML−1 ya da
t ≈ M −2.5 dur.'DKDE\NNWOHOL\ÕOGÕ]GDKDLOHULHYULPDúDPDVÕQGDROPDOÕGÕUIDNDWJ|]OHPOHUEXQXQE|\OH
ROPDGÕ÷ÕQÕ J|VWHUPHNWHGLU Bu durum, Algollerin listesinden (Çizelge 16.1 – B) J|UOHELOLU HYULPOHúPLú
ELOHúHQler -JHULWUWD\IOÕRODQELOHúHQler – daha küçük kütlelere sahiptir.
%X SDUDGRNVXQ ELU DoÕNODPDVÕ &UDZIRUG WDUDIÕQGDQ EXOXQPXúWXU GDKD LOHUL HYULP EDVDPD÷ÕQGD RODQ
-
ELOHúHQ RULMLQDO RODUDN GDKD E\N NWOHOL RODQGÕU IDNDW \DUÕ D\UÕN ELU HYUH VUHVLQFH ELOHúHQLQH NWOH
DNWDUPDVÕQHGHQL\OHúLPGLNLGDKDNoNNWOHOLELOHúHQKDOLQHJHOPLúWLU
-
6LVWHPOHUD\UÕNGDQ \DUÕ D\UÕN YH PXKWHPHOHQ GH÷HQHYUH\H HYULPOHúHELOLUOHU dHNLP DODQÕQÕQGDYUDQÕúÕLoLQ
\ÕOGÕ]ODUQRNWDNWOHRODUDNHOHDOÕQÕUODUEXGXUXPGDHúSRWDQVL\HO\]H\OHULQJHRPHWULVL5RFKHPRGHOLEN]
.HVLPLOHEHOLUOHQLUYH\DOQÕ]FDELOHúHQOHULQ
q (= M 2 / M 2 ) NWOHRUDQÕQDED÷OÕGÕU
22
Çizelge 16.1 – A
ø\LELOLQHQNoNNWOHOLoLIWOHU3RSSHU
6R÷XND\UÕNVL
stemler
Çizelge 16.1 – B
Algol sistemler (Popper, 1980)
+HU ELU ELOHúHQ LoLQ NULWLN \DUÕoDS \DQL ELULQFL /DJUDQJLDQ QRNWDVÕ
L1¶GHQ JHoHQ HúSRWDQVL\HO \]H\LQ
oHYUHOHGL÷L KDFPH 5RFKH KDFPL HúLW KDFLPOL ELU NUHQLQ \DUÕoDSÕ EHOLUOHQHELOLU +HU LNL ELOHúHQ GH 5RFKH
KDFLPOHULQLDúWÕNODUÕQGDGH÷HQELUVLVWHPHVDKLSROPXúROXUX]%XGXUXPGD\ÕOGÕ]ODU
L1FLYDUÕQGDNLELUER÷D]
YDVÕWDVÕ\ODELUELUOHULQHIL]LNVHORODUDNED÷OÕGÕUODUYHRUWDNELUHúSRWDQVL\HO\]H\LGROGXUXUODU
23
%LU VLVWHPGH NWOH DNWDUÕPÕ ROGX÷XQGD ELOHúHQOHU DUDVÕQGDNL X]DNOÕN YH \|UQJH GRODQPD G|QHPLQLQ
-
GH÷LúHFH÷LDoÕNWÕUEN] GHQNOHPOHUL%\NNWOHOLELOHúHQNWOHND\EHWWL÷LQGHNLEXPDGGHRQXQ
\ROGDúÕ WDUDIÕQGDQ \Õ÷ÕúÕU \|UQJH NoOU NWOH ND\EHGHQ NoN NWOHOL ROGX÷XQGD LVH \|UQJH E\U
.oN NWOHOL ELOHúHQLQ ELU DOW GHY ROGX÷X $OJRO VLVWHPOHUL GXUXPXQGD NoN NWOHOLGHQ E\N NWOHOL
,
ELOHúHQHNWOHDNWDUÕOPDNWDGÕUYHEXQHGHQOH ELOHúHQOHUDUDVÕQGDNLX]DNOÕNYHGRODQPDG|QHPLDUWPDNWDGÕU
øONRODUDNE\NNWOHOL\ÕOGÕ]\ROGDúÕQDNWOHDNWDUÕUYH\|UQJHNoOUEDú\ÕOGÕ]ÕQ5RFKHOREXGDNoOU
ve kütle
ND\EÕQÕQ KÕ]Õ DUWDU øNL \ÕOGÕ] HúLW NWOHOL ROGXNODUÕQGD DUDODUÕQGDNL X]DNOÕN
dD PLQLPXP GH÷HULQH
XODúÕU 6RQUDNL NWOH DNWDUÕPÕ \|UQJH\L JHQLúOHWLU YH VRQXQGD GD NWOH ND\EHGHQ \ÕOGÕ] DUWÕN 5RFKH OREXQX
e
GROGXUDPD\DFDNKDOHJHOLUYHE|\OHFHNWOHDNWDUÕPÕELUVRQD ULúPLúROXU
.HVLP¶GH DoÕNODQGÕ÷Õ JLELNWOH ND\EÕ DQFDN \ÕOGÕ] \DUÕoDSÕQÕQ DUWWÕ÷ÕHYUHOHUGH \DQL PHUNH]LKLGURMHQ
yanma evresinde (A evresi), kabukta hidrojen yanma evresinde (B evresi) ya da helyum yanma evresinde (C
HYUHVLEDúOD\DELOLU
=$06¶D YDUGÕNODUÕQGD ELOHúHQOHULQ KLo ELULQLQ 5RFKH OREODUÕQÕ DúPDGÕNODUÕ \DQL VLVWHPLQ D\UÕN ROGX÷X
YDUVD\ÕPÕ\ODLúHEDúODUÕ]7DNLSHGHQHYULPVÕUDVÕQGDKHULNLELOHúHQLQ
de
\DUÕoDSÕ
büyür. Daha büyük kütleli
RODQ GDKD KÕ]OÕ HYULPOHúHFH÷LQGHQ JHUHNOL NRúXOODUÕQ VD÷ODQPDVÕ\OD EX \ÕOGÕ] VRQXQGD 5RFKH OREXQX
Temsili olarak, Algol sistemlerin orijini dikkate DOÕQDELOLU
Algoller, ya merkezi hidrojen yanma evresi (A evresi)VÕUDVÕQGDNL\DGDVRQUDNLHYUHOHU%HYUHVLVÕUDVÕQGDNL
NWOHDNWDUÕP\ROX\OD,LNLúHNLOGHROXúDELOLUOHU%LULQFLGXUXPGDEDú \ÕOGÕ]NWOHVLQLQ\DNODúÕNRODUDN \DUÕVÕQÕ
GROGXUXU YH E|\OHFH NWOH GH÷LúLPL EDúODU
5105 \ÕOGDQ GDKD NÕVD ELU VUHGH DNWDUÕU YH EX VXUHWOH \ROGDú ELOHúHQ VLVWHPLQ E\N NWOHOL ELOHúHQL KDOLQH
gelir. %X HYUHGHQ VRQUD NWOH ND\EHGHQ ELU DOW GHYGLU PHUNH]LQGH KDOD KLGURMHQ \DQPDNWDGÕU IDNDW GÕú
NÕVÕPODUÕQGD QRUPDO ana kol \ÕOGÕ]ODUÕQD nazDUDQ GDKD D] NWOH YDUGÕU %|\OHVL ELU \ÕOGÕ]ÕQ PHUNH]L YH
ÕúÕWPDVÕ D\QÕ NWOHOL QRUPDO ELU \ÕOGÕ]GDQ EHNOHQHQGHQ GDKD E\NWU Hesaplamalar, \ÕOGÕ]ÕQ evrimi
VÕUDVÕQGDki JHQLúOHPHVLQL PLO\RQODUFD \ÕO GHYDP HWWLUPHVLQH UD÷PHQ NWOH DNWDUÕPÕQÕQ DQFDN oRN GúN ELU
KÕ]ODGHYDPHGHFH÷LQLJ|VWHUPHNWHGLU
,
, hidroMHQ\DQPDNDEX÷X\ODoHYULOL\R]ODúPÕúELUKHO\XP
2.4 M¶GHQ NoN ROGX÷X GXUXPODUGD PH\GDQD JHOLU Böylesi
øNLQFLROXúXPWULVHDQFDN EDú\ÕOGÕ]ÕQNWOHVLQLQ
oHNLUGH÷LQLQ ROXúDELOPHVLQLQ VW OLPLWL RODQ
\ÕOGÕ]ODU 5RFKH OREODUÕQÕ GROGXUGXNODUÕQGD oRN \NVHN KÕ]ODUOD NWOH DNWDUÕUODU 6RQXQGD JHUL\H \R]ODúPÕú
KHO\XP oHNLUGH÷L LOH VÕ÷ ELU KLGURMHQ ]DUID VDKLS RODQ NDEXNWD KLGURMHQ \DNDQ YH KDOD 5RFKH OREXQX
GROGXUX\RU RODQ YH EX QHGHQOH GH \ROGDúÕQD GúN KÕ]ODUOD GD ROVD PLO\RQODUFD \ÕO
kütle aktarmaya devam
HGHFHNRODQELUDOWGHYNDOÕU
% HYUHVL NWOH DNWDUÕPÕ\OD ROXúDQ $OJROOHU $ WU LOH ROXúDQODUGDQ WDPDPHQ IDUNOÕ Lo \DSÕODUD VDKLS
basitELUúHNLOGHbu sonuca varmak LPNDQVÕ]GÕU Ancak, bazen, kütle belirlemesi yoluyla, A
ve B duUXPODUÕQÕ D\ÕUPDN RODQDNOÕ ROXU WRSODP NWOHOHUL 0’in DOWÕQGD olan sistemlerin, B türü kütle
DNWDUÕPÕ\OD ROXúWXNODUÕQÕ KHPHQ KHPHQ NHVLQ RODUDN V|\OH\HELOLUL] |UQH÷LQ $OJRO λ Tau). Küçük kütleli
ROPDODUÕQDNDUúÕQ
\ÕOGÕ]ODULoLQLVHNHVLQELUúH\V|\OHQHPH]
16.2. Evrim türleri
.oN NWOHOL oLIWOHULQ VÕQÕIODPDVÕ\OD HYULPOHULQLQ VRQ DúDPDVÕQGD JHUL\H NDODQ NWOHOHUL &KDQGUDVHNKDU
OLPLWLQL DúPD\DQ EDú ELOHúHQOL VLVWHPOHUL DQOD\DELOLUL] dHúLWOL KHVDSODPD VHULOHULQH J|UH EDú \ÕOGÕ]ÕQ NWOHVL
12 M - 14 MGH÷HULQLDúDPD]gQFHNLE|OPGHDoÕNODQGÕ÷Ձ]HUHNWOHDNWDUÕPÕQÕQELUoRNoHúLWLQLGLNNDWH
alabiliriz.
$(95(6ø0(5.(=ø+ø'52-(1<$10$
SI SIRASINDA.ø.h7/('(öøùø0ø
%Dú \ÕOGÕ] 5RFKH OREXQX GROGXUPD\D EDúODGÕ÷ÕQGD KÕ]OÕ ELU NWOH DNWDUÕP HYUHVL EDúODPÕú ROXU %Dú \ÕOGÕ]ÕQ
NWOHVLQLQE\NELUNÕVPÕ\ROGDúDDNWDUÕOÕU%DúODQJÕoWDE\NNWOHOLRODQ\ÕOGÕ]EDú\ÕOGÕ]VLVWHPLQNoN
.
kritik hacminiGROGXUPD\DGHYDPHWWL÷L\DYDúELUNWOHDNWDUÕP evresi gelir.%XúHNLOGHELU\DUÕ-D\UÕN
VLVWHP ROXúPXú ROXU =$06¶WD EDúODQJÕo NLP\DVDO ELOHúLPL X = 0.602, Z = 0.044’tür. %LOHúHQOHU =AMS
ELOHúHQOHUL DUDVÕQGDNL X]DNOÕN, EDú \ÕOGÕ]ÕQ 5RFKH OREXQX KLGURMHQ \DQPD HYUHVL VÕUDVÕQGD GROGXUDFD÷Õ
úHNLOGHGLU%XGXUXPGDEDú\ÕOGÕ]ÕQX\JXQ\DUÕoDSÕRR = 11.60 R
olur.$\QÕNWOHOLELUWHN\ÕOGÕ]ÕQ\DUÕoDSÕ
ise, hidrojen yanma evresinin sonunda 11.7 RGH÷HULQHXODúÕU
NWOHOLELOHúHQLKDOLQHJHOLU\DQLVLVWHPLQNWOHRUDQÕWHUVLQHG|QHU %XKÕ]OÕNWOHDNWDUÕPHYUHVLQLWDNLEHQEDú
\ÕOGÕ]ÕQ
24
ùHNLO $ WU LoLQ NWOHOL ELU \DNÕQ oLIW VLVWHPLQ HYULPL =DPDQ PLO\RQ \ÕO FLQVLQGHQ \|UQJH G|QHPL LVH JQ
ELULPLQGH YHULOPLúWLU %Dú \ÕOGÕ] PHUNH]L KLGURMHQ \DQPD HYUHVL VÕUDVÕQGD 5RFKH OREXQX GROGXUXU YH \ROGDúÕQ
DNWDUPD\D EDúODU ùHNLOGH NWOH DNWDUÕPÕQÕQ LNL HYUHVL J|VWHULOPLúWLU +Õ]OÕ HYUHGH 0
a kütle
’den biraz fazla bir kütle
\DOQÕ]FD\ÕOLoHULVLQGHDNWDUÕOÕUNHQEXHYUH\L\DYDúELUNWOHDNWDUÕPHYUHVLL]OHU6L\DKGDLUHOHUKLGURMHQ
-zengin, gri
çemberler ise helyum-zengin bölgeleri göstermektedir (Kippenhahn ve Weigert, 1967).
su, karakteristik nicelikleriyle birlikte
daùHNLO¶GHJ|VWHULOPLúWLU
øOJLOL ED]Õ HYUHOHU LoLQ HYULP VHQHU\R
\ROODUÕ
DKÕ]OÕNWOHDNWDUÕPÕ0
ùHNLO ¶GH YH VLVWHP
in evrim
’den 3.73 M’e)
7
%Dú \ÕOGÕ] NULWLN \DUÕoDSÕQD \ÕO VRQXQGD XODúÕU +LGURMHQ EROOX÷X ¶GHQ GH÷HULQH GúHU
Hidrostatik dengeyi yeniden kurabilmek için, alt
katmanlar JHQLúOHPHN ]RUXQGD NDOÕUODU %X JHQLúOHPH LoLQ JHUHNOL RODQ HQHUML ÕúÕWPDGDQ KDUFDQÕU YH E|\OHFH
.WOHDNWDUÕPHYUHVLVUHVLQFHNWOHGÕúNDWPDQODUGDQDWÕOÕU
\ÕOGÕ]ÕQÕúÕWPDVÕGúHUùHNLO+Õ]OÕNWOHDNWDUÕPHYUHVLQLQVRQXQGDÕúÕWPD\HQLGHQDUWDU
ùHNLO %LU 0
+ 5 M VLVWHPLQLQ HYULPL %Dú \ÕOGÕ]ÕQÕQ HYULPL NDOÕQ oL]JL LOH J|VWHULOPLúWLU .WOH DNWDUÕPÕQÕQ
EDúODQJÕFÕD LOH YH KÕ]OÕNWOHDNWDUÕP HYUHVLQLQ VRQX ELOHJ|VWHULOPLúWLUEGHQF \H NDGDU \DYDúHYUHGLU$\UÕFD
MNWOHOLWHNELU\ÕOGÕ]ÕQHYULP\ROXGDJ|VWHULOPLúWLU
25
b) yaYDúNWOHDNWDUÕPÕ
Konvektif merkezde
sürmektedir<ÕOGÕ]\DNODúÕN PLO\RQ \ÕO VUHVLQFH5RFKH \]H\LQGHQPDGGHDNWDUPD\D
-8
YHGROD\ÕVL\OHNWOHND ybetmeye (10
M\ÕO-1 mertebesinde) deam eder. <ROGDú ELUNDoPLO\RQ \ÕOER\XQFD
$UWÕNEDú\ÕOGÕ]ÕQNLP\DVDOHYULPLNWOHND\EHWPH\HQELU\ÕOGÕ]ÕQNL\OHD\QÕúHNLOGHROXU
KLGURMHQ \DQPDVÕ
=$06 \DNÕQÕQGDNDOÕU%XHYUHGHVLVWHP $OJROOHULQ NDUDNWHULVWLN|]HOOLNOHULQLJ|VWHULU3HN HYULPOHúPHPLú
RODQ E\N NWOHOL ELOHúHQ =$06 \DNÕQÕQGD LNHQ =$06¶WDQ D\UÕOPÕú RODQ NoN NWOHOL ELOHúHQ 5RFKH
OREXQX GROGXUPXúWXU %Dú \ÕOGÕ]ÕQ NWOHVL 0
PHUNH]LKLGURMHQEROOX÷X
X = 0.002’dir.
GH÷HULQH JHOGL÷LQGH NWOH DNWDUÕPÕ GXUXU EX GXUXPGD
Çizelge 16.2
Bir 9 M + 5 M sisteminin evrimi
M1 ve M2 EDú YH \ROGDú \ÕOGÕ]ODUÕQ NWOHOHUL AELOHúHQOHU DUDVÕQGDNL X]DNOÕN R1 \ÕOGÕ]ÕQ RR LVH 5RFKH OREXQXQ JQHú
ELULPLQGH\DUÕoDSÕGÕUXoHNLUGHNWHNLKLGURMHQEROOX÷XDEYHFLVH+5GL\DJUDPÕQGDNLNRQXPODUÕJ|VWHUPHNWHGLU
Çizelge 16.3
Bir 2 M + 1 M sisteminin evrimi (Kippenhahn, Kohl, Weigert, 1967)
Çizelgede \Dú, EDú YH \ROGDú ELOHúHQLQ M1 ve M2 kütleleri, gün biriminde P dolanma dönemi, durum –D\UÕN G \DUÕD\UÕN VG; ÕúÕWPD L HWNLQ VÕFDNOÕN Teff YH EDú \ÕOGÕ]ÕQ DWPRVIHULN KLGURMHQ EROOX÷X Xat parameWUHOHUL YHULOPLúWLU Orijinal
NDUÕúÕPX = 0.602, Y = 0.354, Z ¶WU6RQNRORQGDNLKDUIOHULVHùHNLO¶HJ|nGHUPH\DSPDNWDGÕU
26
+ 1 M sisteminin B evresi evrimi. Evrim süresi t PLO\RQ \ÕO GRODQPD G|QHPL JQ ELULPLQdedir.
Siyah daireler hidrojen-zengin, gri çemberler ise helyum-zengin bölgeleri göstermektedir.
ùHNLO %LU 0
.hdh..h7/(%(95(6ø
(1 M < M1 < 2.8 M)
o
ve bu nedenle ]DUIÕQKÕ]OÕJHQLúOHGL÷LELUHYUHJ|UOPH] HidrojeniQL\DNPÕúRODQoHNLUGH÷LQNWOHVL,
M < 2.8 M için 0.35 M¶GHQNoNWUVÕFDNOÕNDUWÕúÕ+H-\DQPDVÕQDL]LQYHUHFHNG]H\GHGH÷LOGLU Hidrojen
NDEX÷XQ \RNROPDVÕ\ODNWOHDNWDUÕPÕVRQDHUHU<ÕOGÕ]ELUEH\D]FFHROXU0
+ 1 MNWOHOL \DNÕQoLIW
VLVWHPLQ%WUHYULPLùHNLO¶WH, +5GL\DJUDPÕQGDNLHYULP\ROODUÕLVHùHNLO¶WHJ|VWHULOPLúWLU
+LGURMHQ NDEX÷X ]D\ÕIODGÕ÷ÕQGD PHUNH]GH HOHNWU Q \R]ODúPDVÕ PH\GDQD JHOLU 0HUNH]L VÕNÕúPD \DYDú
KÕ]GDGÕU
27
+ 1 M\DNÕQoLIWVLVWHPLQLQEDú\ÕOGÕ]ÕQDLOLúNLQHYULP\ROODUÕ
ùHNLOdL]HOJH¶WHYHULOHQúHPD\DJ|UHELU0
1RUPDO KLGURMHQ EROOX÷X
X = 0.7 (ZAMS) ile X
KHO\XP VÕIÕU \Dú DQD NROX +H =$06 LoLQ VÕIÕU \Dú DQD NROODUÕ GD
J|VWHULOPLúWLU(YULP\ROODUՁ]HULQGHNLKDUIOHUdL]HOJH¶HJ|QGHUPH\DSPDNWDGÕU
16.2.3. ORT$.h7/(%(95(6ø0 < M1 < 14 M)
Çekirdek kütlesi, hidrojenini WNHWPLú bir oHNLUGH÷LQ ÕVÕVDO NDUDUOÕOÕ÷Õ LoLQ JHUHNOL RODQ &KDQGUDVHNKDU kütlesinden daha
büyüktür. 0HUNH]L VÕNÕúPD oRN KÕ]OÕ ROXU YH oO DOID LúOHPL EDúODU %X KÕ]OÕ JHQLúOHPH KÕ]OÕ ELU NWOH DNWDUÕP HYUHVLQH
neden olur. %DúODQJÕo G|QHPL JQ RODQ ELU 0 + 8 M sisteminin evrimi (De Greve ve de Loore,
1976) ùHNLOúX úHNLOGHROXU hLGURMHQ \DQPD HYUHVLQLQ |PU \DNODúÕN PLO\RQ \ÕOPHUWHEHVLQGH iken
-5
NWOH GH÷LúLPLQLQ VUHVL \DNODúÕN RODUDN \ÕOGÕU KWOH ND\EÕQÕQ RUWDODPD GH÷HUL 5.2 10
M\ÕO-1 ve
-4
-1
PDNVLPXP GH÷HUL GH M\ÕO ’dir. +HO\XP \DQPDVÕ PLO\RQ \ÕO VUHU VRQUD \R]ODúPÕú KHPHQ
KHPHQHúVÕFDNOÕNOÕELUoHNLUGHNJHOLúLU<ÕOGÕ]+5GL\DJUDPÕQGDVD÷DGR÷UXLOHUOHU.WOHDNWDUÕPÕQÕQLNLQFL
0.94 M NWOHOL ELU &2 oHNLUGH÷LQH YH 0 kütleli bir helyum atmosferine sahip
kütleli, çok ince, aktif bir helyum kabuk
kD\QD÷Õ YDUGÕU 2 10-5 M\ÕO-1 mertebesindeki \DYDú ELU NWOH DNWDUÕP HYUHVL \ÕO VUHU sonra helyum
NDEXN ND\QD÷Õ WNHWLOLU NDOÕQWÕQÕQ NWOHVL M ’dir. .WOH GH÷LúLPLQLQ VRQXQGD EDú \ÕOGÕ] KLGURMHQFH
]HQJLQ ]DUIÕQÕQ QHUHGH\VH WDPDPÕQÕ ND\EHGHU sonuç kütle 0.264 M ’dir. Bu son kütle o kadar küçüktür ki,
HYUHVL EDúODU <ÕOGÕ]
ROXUEXQODUÕQ DUDVÕQGDWRSODP HQHUMLQLQ ¶Q UHWHQ0
+H DVOD WXWXúDPD] YH \ÕOGÕ] VR÷XPD\D EDúODU <ÕOGÕ] KHO\XP VÕIÕU \Dú DQD NROXQD +H=$06 GR÷UX
HYULPOHúHPH] YH EH\D] FFHOHULQ EXOXQGX÷X E|OJH\H GR÷UX LOHUOHU +HVDSODPDODUÕQ VRQXQGD \ÕOGÕ]ÕQ
yDUÕoDSÕD\QÕNWOHOLLGHDOELUEH\D]FFHQLQ&KDQGUDVHNKDUOLPLWLQLQ\DNODúÕNRODUDNLNLNDWÕGÕU<ÕOGÕ]KDOHQ
toplam kütlesinin %0.9’una sahip olan, hidrojence zengin bir zarfa sahiptir, böylece o, ölmekte olan hidrojen
\DQPD]DUIOÕKRPRMHQROPD\DQELU beyaz cücedir.
-
0HUNH]GHNLQ|WULQRODUÕQNDWNÕVÕDUWDUPHUNH]LVÕFDNOÕND]DOÕUIDNDW\DUÕ \R]ODúPÕúE|OJHOHUGHEXE|OJHOHUGHNL
E]OPHQHGHQL\OHVÕFDNOÕNDUWPD\DGHYDPHGHU.DEXNHQHUMLND\QD÷Õ\RNWXUEXQHGHQOHGHELUEWQRODUDN
E]OPH J|]OHQLU +Õ]OÕ E]OPH \DNODúÕN \ÕO Q|WULQR ND\ÕSODUÕQÕ NDUúÕOD\DPD] YH ÕúÕWPD GúHU
Buradan itibaren (log Teff = 5.2) beyaz cüce HYUHVLQHGR÷UX HYULPEDúODU.WOHOHUL0¶GHQE\N \ÕOGÕ]ODU
LoLQ \DSÕODQ KHVDSODPDODUDWPRVIHUik KLGURMHQ EROOX÷XQXQ \DNODúÕk olarak ROGX÷XQGD,NWOH ND\ÕSODUÕQÕQ
VRQDHUGL÷LQLJ|VWHUPLúWLU
28
ùHNLO%DúODQJÕoG|QHPLJQRODQELU0
Loore, 1976).
+ 8 MVLVWHPLQLQEDú\ÕOGÕ]ÕQDLOLúNLQHYULP\ROX'H*UHYHYHGH
(YULPKHVDSODPDODUÕ
16.3.1. KORUNUMLU9(.25818068=(95ø0
(YULP\ROODUÕQÕQKHVDSODPDODUÕQGDúXRODVÕOÕNODUÕGLNNDWHDODELOLUL]
Korunumlu evrim için, WRSODPNWOHYHDoÕVDOPRPHQWXPVDELWRODUDNHOHDOÕQÕU.WOHDNWDUÕPÕEDúODGÕ÷ÕQGD
NWOH DWÕOÕU YH DWÕODQ EX NWOH \ROGDúÕQ NWOHVLQH HNOHQLU %X LNL ELOHúHQLQ NWOHOHULQGHNL GH÷LúLPGHQ KDUHNHW
HGHUHNGHVLVWHPLQGRODQPDG|QHPLQGHNLGH÷LúLPLOHELOHúHQOHULQ5RFKH\DUÕoDSODUÕQÕQGH÷LúLPLKHVDSODQÕU
Korunumsuz evrim içinNWOHYHDoÕVDOPRPHQWXPGDNLGH÷LúLPOHUKHVDEDNDWÕOÕU Böylesi bir dDYUDQÕúGH÷HQ
sistemlerinGLNNDWHDOÕQPDVÕQDL]LQYHULU%XGXUXPGD \ROGDúWDUDIÕQGDQ \Õ÷ÕúWÕUÕOPD\DUDNVLVWHPLWHUNHGHQ
ELU GLVNWH \D GD RUWDN ELU ]DUI LoHULVLQGH ELULNWLULOHQ NWOH NHVUL LoLQ ELU WDQÕPODPD JHUHNLU D\QÕ úH\ DoÕVDO
momentum için de yaSÕOPDOÕGÕU
'DKD |QFH %|OP ¶WH EHOLUWLOGL÷L ]HUH KHVDSODPDODUÕ EDú \ÕOGÕ]ÕQ HYULPLQH VÕQÕUOD\DUDN YH \ROGDúÕQ
NWOHVLQGHNLGH÷LúLPL\DOQÕ]FDVLVWHPLQGRODQPDG|QHPLQGHNLGH÷LúLPLEHOLUOHPHGHNXOODQPDN \DGDKHULNL
ELOHúHQLQHYULPLQLHú]DPDQOÕRO
arak hesaplamak \ROODUÕQÕQLNLVLGHRODVÕGÕU
Korunumsuz durumu için NWOH YH DoÕVDO PRPHQWXP ND\ÕSODUÕ PXWODND GLNNDWH DOÕQPDOÕGÕU .WOH DNWDUÕP
∆MNWOHPLNWDUÕ\ÕOGÕ]5RFKHOREXQXQLoLQGHNDODFDNúHNLOGHEHOLUOHQir;
HYUHVLVUHVLQFHEDú\ÕOGÕ]GDQDWÕODQ
NWOH ND\EÕ ]DPDQ |OoH÷L LOH \Õ÷ÕúPD ]DPDQ |OoH÷LQLQ GR÷DO RODUDN EHQ]HU ROPDPDODUÕ QHGHQL\OH DWÕODQ
β kesrinin yani β ∆MPLNWDUÕQÕQ\ROGDúWDUDIÕQGDQ\Õ÷ÕúWÕUÕOGÕ÷ÕYDUVD\ÕODELOLU
NWOHQLQ\DOQÕ]FD
$oÕVDOPRPHQWXPND\EÕLoLQGH EHQ]HU ELULúOHP \DSÕODELOLUH÷HUG|QPHDoÕVDOPRPHQWXPX LKPDO HGLOLUYH
ELU \D GD KHU LNL ELOHúHQGHQ DWÕODQ PDGGHQLQ VLVWHPL WHUN HWWL÷L YDUVD\ÕOÕUVD DWÕODQ EX NWOH LOH WDúÕQDQ
ND\EHGLOHQDoÕVDOPRPHQWXPKHVDSODQDELOLU
29
.HVLUVHONWOHND\EÕ
c
c = ∆M /( M 1i + M 2i )
(16.1)
ED÷ÕQWÕVÕ LOH LIDGH HGLOHELOLU 6LVWHPL WHUN HGHQ PDGGH LOH WDúÕQDQ DoÕVDO PRPHQWXP LVH -HDQV \DNODúÕPÕ
NXOODQÕODUDN
∆J = cJ
(16.2)
úHNOLQGH GH÷HUOHQGLULOHELOLU
6RQXo RODUDN .HSOHU¶LQ oQF \DVDVÕQD J|UH ELOHúHQOHU DUDVÕ X]DNOÕN YH
GRODQPDG|QHPLQLQGH÷LúLPOHULLoLQ
A (1 − c) 2 ( M 1i M 2i ) 2 ( M 1 + M 2 )
=
Ai
( M 1M 2 ) 2 ( M 1i + M 2i )
(16.3)
P (1 − c) 3 ( M 1i M 2i ) 3 ( M 1 + M 2 )
=
Pi
( M 1 M 2 ) 3 ( M 1i + M 2i )
(16.4)
in fonksiyonu
LIDGHOHULQL \D]DELOLUL] (÷HU NHVLUVHO DoÕVDO PRPHQWXP ND\EÕQÕ VLVWHPGHQ DWÕODQ J|UHOL NWOHQ
olarak ifade edersek, c için çok daha genel bir ifade elde edebiliriz
c = c(∆M /( M1 + M 2 )) .
(÷HU
∆MNWOHVLQLQDWÕOPDVÕQGDQVRQUDVLVWHPGHNDODQDoÕVDOPRPHQWXPXd = 1 – c ile temsil edersek
d(O) = 1,
d(1) = 0
0 ”d ”
(16.5)
elde ederiz.(÷HU
∑ ∆M k = ∆M
(16.6)
k
ise, bu durumda
d(
∆M
∆M k
)=
d(
)
M 1i + M 2i
M 1k −1 + M 2k −1
k
∏
(16.7)
olur. Bir d IRQNVL\RQXQXQ EXOXQPXú ROGX÷XQX YDUVD\GÕ÷ÕPÕ]GD YH ED÷ÕQWÕODUÕQÕ VD÷OD\DQ
fonksiyon ailesi bir bütün olarak belirlenebilir.
d(
∆M
∆M
) =1−
M 1i + M 2i
M 1i + M 2i
(16.8)
IRQNVL\RQXYHED÷ÕQWÕODUÕQÕVD÷ODGÕ÷ÕQGDQ
∆M
∆M
) = (1 −
)α α ≥ 0
M1i + M 2i
M1i + M 2i
DLOHVLGHVD÷ODU%XGXUXPGDc’yi
dα (
cα (
∆M
∆M
) = 1 − (1 −
)α α ≥ 0
M1i + M 2i
M1i + M 2i
úHNOLQGH\HQLGHQ\D]DELOLUL]
(16.9)
30
%HOOL ELU HYULP HYUHVL VUHVLQFH ELOHúHQOHUGHQ ELUL WDUDIÕQGDQ ND\EHGLOHQ PDGGH \ROGDúÕ WDUDIÕQGDQ
β, bu kütle kesrini göstersin, yani
β = ( M 2 − M1 ) / ∆M .
\Õ÷ÕúWÕUÕODELOLU
(16.10)
%XGXUXPGDELOHúHQOHUDUDVÕQGDNLX]DNOÕNLOHG|QHPGHNLGH÷LúLPOHUL
A
M + M 2 2α +1 M 1i M 2i 2
=( 1
)
(
)
Ao
M 1i + M 2i
M 1M 2
(16.11)
P
M + M 2 3α +1 M 1i M 2i 3
=( 1
)
(
)
Po
M 1i + M 2i
M 1M 2
biçiminde yazabiliriz, burada M2, (16.10) ile verilir.
ø.ø%ø/(ù(1ø1(95ø0ø
(ú]DPDQOÕHYULPLoLQELUNRGNXOODQÕODUDNKHULNLELOHúHQLQ\DSÕVÕDQODúÕODELOLU
Bu durumdaKHULNLELOHúHQLQ
,
\DUÕoDSODUÕ YH RQODUÕQ 5RFKH \DUÕoDSODUÕ KHVDSODQÕU YH EX GD \ÕOGÕ] \DUÕoDSODUÕ LOH 5RFKH \DUÕoDSODUÕ
DUDVÕQGDNDUúÕODúWÕUPD\DSPD\DRODQDNVD÷ODU
Bu suretle, VRQUDNLGH÷PHHYUHOHULJ|]GHQNDoÕUÕOPDPÕúYHRQD
J|UH GDYUDQÕOPÕú ROXU <Õ÷ÕúPD \ÕOGÕ]ÕQÕQ GDYUDQÕúÕ úX úHNLOGH DQODúÕODELOLU EX \ÕOGÕ] NWOH \Õ÷ÕúPDVÕ
QHGHQL\OH JHQoOHúLU YH |PU |QHPOL |OoGH DUWD
bilir.
*HQoOHúHQ EX \ROGDú \ÕOGÕ] 5RFKH OREXQX GD
GROGXUDELOLUYHE|\OHFHWHUVLQHG|QPúELUNWOHDNWDUÕPHYUHVLRUWD\DoÕNDELOLU
(YULP KHVDSODPDODUÕQGDNL VÕQÕUODPDODU úXQODUGÕU VLVWHP GÕú NULWLN \]H\LQL L2
QRNWDVÕQGDQ JHoHQ Hú
SRWDQVL\HO \]H\DúPDGÕ÷ÕVUHFHKHVDSODPDODUNRUXQXPOXGXUXPDJ|UH\DSÕOÕUGÕúNULWLN \]H\DúÕOGÕ÷ÕQGD
ise sistemden olaVÕ NWOH ND\ÕSODUÕ GD GLNNDWH DOÕQÕU .WOHQLQ VLVWHPGHQ NDoDELOPHVL LoLQ HQ D]ÕQGDQ L2
QRNWDVÕ LOH 5RFKH OREXQXQ SRWDQVL\HO HQHUMLOHUL DUDVÕQGDNL IDUNÕ VD÷ODPD\D \HWHFHN E\NONWH ID]ODGDQ ELU
.
, bu enerjiQLQ E\NO÷ q = 1 için, 0.27 GM/A ile
hesaplanabilir..WOHRUDQÕQÕQJHQLúELUDUDOÕ÷ÕQGDEXGH÷HUROGXNoDWLSLNWLU%D÷ÕQWÕ\DJ|UHJHQLúVLVWHPOHUGH
kütlenin sistemden kaçabilmesi, \DNÕQ VLVWHPOHUH J|UH GDKD NROD\GÕU NWOH RUDQÕQÕQ Xo GH÷HUOHULQGH 27
oDUSDQÕ\HULQLoRNGDKDNoNELUoDUSDQDEÕUDNÕUYHEu nedenle de, büyük kütleli sistemlerde kütlenin sistemi
terk etmesi çok daha kolay olur.
HQHUML\H JHUHNVLQLPL YDUGÕU %LULP NWOH EDúÕQD
M + 1 M
sistemiQLQ KHU LNL ELOHúHQLQLQ GH /RRUH YH 'H *UHYH WDUDIÕQGDQ KHVDSODQDQ HYULP \ROODUÕQÕ D\QÕ EDúODQJÕo
(ú ]DPDQOÕ HYULP GH÷HULQLQ NRQWURO HGLOPHVL DPDFÕ\OD EDúODQJÕo G|QHPL JQ RODQ ELU G|QHPLQHVDKLSD\QÕELU VLVWHPLQEDú\ÕOGÕ]ÕQÕQ.LSSHQKDKQ.RKOYH:HLJHUWWDUDIÕQGDQKHVDSODQDQ
HYULP \ROX\OD NDUúÕODúWÕUPDVÕQÕ ùHNLO ¶GD YHUL
yoruz.
*|UOHFH÷L JLEL KHU LNL EDú \ÕOGÕ]ÕQ HYULP \ROODUÕ
ROGXNoDX\XúPDNWDGÕU+HULNLGXUXPGDGDGH÷PHHYUHVLROXúPDPDNWDGÕUELOHúHQOHULQHYULP\ROODUÕD\UÕD\UÕ
KHVDSODQDELOLU \DQL LON RODUDN EDú \ÕOGÕ]ÕQ HYULPL KHU DGÕPGD VLVWHPGHQ NWOH ND\EÕQÕGD LoHUHFHN úHNLOGH
KHVDSODQGÕNWDQ VRQUD PDGGHQLQ \Õ÷ÕúWÕ÷Õ \ROGDúÕQ HYULPL GH KHVDSODQDELOLU .LSSHQKDKQ YH DUN 7DUDIÕQGDQ
EDú\ÕOGÕ]LoLQKHVDSODQDQHYULP\ROXGDKD|QFHùHNLO¶WHJ|VWHULOPLúWL
.WOHRUDQÕYHG|QHPLQVLVWHPLQGDYUDQÕúՁ]HULQGHNLHWNLOHULQLLQFHOHPHNDPDFÕ\OD
MNWOHOLEDú\ÕOGÕ]D
VDKLS RODQ ELU VLVWHPLQ Hú ]DPDQOÕ HYULPL L]OHQHELOLU 'H÷PH HYUHVLQLQ ROXS ROPD\DFD÷Õ EDúODQJÕo NWOH
M+ 8.1 M sistemi,
M\ÕO¶OÕN PDNVLPXP
GH÷HULQHXODúÕUYHDWPRVIHULNKLGURMHQEROOX÷XNWOHRODUDNYHULFL\ÕOGÕ]GD¶GHQ¶HYHDOÕFÕ\ÕOGÕ]da da
RUDQÕQD YH EDúODQJÕo G|QHPLQH ED÷OÕGÕU %DúODQJÕo G|QHPL JQ RODQ ELU koUXQXPOX HYULPLQ NODVLN \ROXQX WDNLS HGHU ùHNLO .WOH ND\ÕS KÕ]Õ -4
¶GHQ¶\HGúHU9HULFL\ÕOGÕ]GDQJHUL\HNDODQKHO\XP\DQPDHYUHVLER\XQFDHYULPOHúLUVRQUD\HQLGHQ
M
ile 10 M DUDVÕQGDRODQEDú\ÕOGÕ]ODULoLQPH\GDQDJHOLUYH helyum kabuk kayQD÷ÕQGDQHQHUMLoÕNÕúÕQÕQQHGHQ
JHQLúOHUYHEXVXUHWOHNWOHDNWDUÕPÕQÕQLNLQFLHYUHVLEDúODU.WOHDNWDUÕPÕQÕQEXLNLQFLHYUHVLNWOHOHUL
ROGX÷X KHO\XP ]DUI JHQLúOHPHVLQLQ ELU VRQXFX RODUDN DWPRVIHULN KLGURMHQ EROOX÷X NWOH RODUDN YHULFL
\ÕOGÕ]GD¶GHQ¶HYHDOÕFÕ\ÕOGÕ]GDGD¶GHQ¶\HGúHU
Bir 10 M+ 8 MVLVWHPLLoLQ\DSÕODQNRUXQXPOXKHVDSODPDODUEN].HVLPLOHNDUúÕODúWÕUPDGH÷PH
HYUHVLQLQ J|UOPHGL÷L EX GXUXPGD Hú ]DPDQOÕ HYULP VRQXoODUÕQÕQ NRUXQXPOX HYULP LOHHOGH HGLOHQOHUOH oRN
L\LX\XúWX÷XQXJ|VWHUPHNWHGLU
%DúODQJÕo G|QHPL JQ RODQ ELU 0
+ 5.4 M sistemi için, kütle DNWDUÕPÕQÕQ EDúODPDVÕQGDQ \DNODúÕN
¶OLNELUNWOHDNWDUÕOGÕ÷ÕQGD,ELUGH÷PHHYUHVLPH\GDQDJHOLU. Bu
RODUDN\ÕOVRQUD\DNODúÕNRODUDN0
31
GH÷PHHYUHVLNWOH RUDQÕ WHUVG|QQFH\H NDGDU \DNODúÕN RODUDN \ÕOGHYDPHGHU %Dú \ÕOGÕ]ÕQ NWOHVL
M¶HGúW÷QGHGH÷PHHYUHVLVRQDHUHU6RQUDNLHYULPVUHFL|QFHNLGXUXPGDNLJLELROXU
ùHNLO%DúODQJÕoG|QHPLJQRODQELU0
+ 1 MVLVWHPLQLQGH/RRUHYH'H*UHYHWDUDIÕQGDQELUHú]DPDQOÕ
HYULP NRGX LOH KHVDSODQDQ HYULP \ROODUÕQÕQ .LSSHQKDKQ YH :HLJHUW WDUDIÕQGDQ GDKD |QFH KHVDSODQDQ HYULP
\ROODUÕ LOH NDUúÕODúWÕUPDVÕ (ú ]DPDQOÕ KHVDSODPDODUÕQ EDú \ÕOGÕ]Õ NDOÕQ oL]JL LOH \Õ÷ÕúDQ \ROGDú \ÕOGÕ]ÕQ HYULP \ROX LVH
]HULQGH LoL ERú oHPEHUOHULQ EXOXQGX÷X LQFH oL]JL LOH J|VWHULOPLúWLU .LSSHQKDKQ YH :HLJHUW¶ÕQ HYULP \ROX LVH ]HULQGH
QRNWDODUEXOXQDQoL]JLLOHJ|VWHULOPLúWLU
32
ùHNLO%DúODQJÕoG|QHPLJQRODQELU0
]DPDQOÕKHVDSODQDQHYULP\ROODUÕ
+ 8.1 MVLVWHPLQLQNWOHDNWDUÕPÕQÕQHUNHQ%HYUHVLQHJ|WUHQHú
+ 2.7 MVLVWHPLQLQEDúYH
Xc1 ve Xc2 LOH NWOH RUDQÕQÕQ HYULPL 0HUNH]L KLGURMHQLQ GH÷LúLP KÕ]Õ\OD
ùHNLO%DúODQJÕoG|QHPLJQRODQYH$HYUHVLQHGR÷UXHYULPOHúPHNWHRODQELU0
\ROGDú \ÕOGÕ]ODUÕQÕQ PHUNH]L KLGURMHQ EROOXNODUÕ
ED÷ODQWÕOÕRODUDNNWOHRUDQÕLNLNH]WHUVLQHG|QHU
.h7/(25$1,1,17(56ø1('g10(6ø
(ú ]DPDQOÕ HYULP KHVD÷ODPDODUÕ oLIW VLVWHPOHULQ HYULPOHUL VÕUDVÕQGD ED]Õ GXUXPODUGD NWOH RUDQÕQÕQ WHUVLQH
G|QPHVL GXUXPXQXQ \DúDQGÕ÷ÕQÕ RUWD\D NR\PDNWDGÕU gUQHN RODUDN EDúODQJÕo G|QHPL JQ RODQ ELU M+ 2.7 M VLVWHPLQLQ $ WU HYULPL 3DFNHW HOH DOÕQDELOLU +Õ]OÕ ELU NWOH DNWDUÕP HYUHVL VÕUDVÕQGD
NWOH RUDQÕ WHUVLQH G|QHU .WOH ND]DQDQ \ROGDúÕQ PHUNH]L KLGUÕMHQ \DQPDVÕ KÕ]ODQÕU E|\OHFH \ROGDúÕQ
PHUNH]LQGHNLKLGURMHQEROOX÷X
Xc2EDú\ÕOGÕ]ÕQPHUNH]L NÕVPÕQDQD]DUDQGDKDKÕ]OÕRODUDND]DOÕU Xc2 ≈ 0.4
ROGX÷XQGD \ROGDúÕQ JHQLúOHPHVL VRQXFXQGD 5RFKH OREX WDúPDVÕQÕQ PH\GDQD JHOPHVL QHGHQL\OH NWOH RUDQÕ
WHUVLQH G|QHU .WOH RUDQÕ ELU NH] GDKD PH\GDQD JHOLU YH WD]H KLGURMHQLQ EDú \ÕOGÕ]ÕQ PHUNH]L NÕVPÕQGD
NDUÕúPDVÕQHGHQL\OH
Xc1DUWDU6LVWHPDUWÕNELU\DUÕ-D\UÕNWÕUùLPGLNLGXUXPGDVLVWHPLQE\NNWOHOLRODQEDú
L2’den geçen kritik yüzeye
ELOHúHQLGDKDKÕ]OÕ HYULPOHúLUYH ELUPGGHWVRQUD \HQLGHQ5RFKHWDúPDVÕ ROXúXU
daha çabuk uODúÕOÕU E\N |OoHNOHUGH NWOH YH DoÕVDO PRPHQWXP ND\ÕSODUÕ ROXúXU VRQXoWD LNL \ÕOGÕ]ÕQ
ELUOHúPHVLQH QHGHQ RODQ LoH GR÷UX ELU VSLUDO KDUHNHWL RUWD\D oÕNDU .WOH RUDQÕ YH EROOX÷XQ HYULP ùHNLO
¶GHJ|VWHULOPLúWLU
, kütOH RUDQÕQÕQLNL NH] WHUVLQH G|QG÷ EX DUGÕúÕN NWOH DNWDUÕP HYUHOHUL LOH
ortaya koyar. Örnek olarak, bDúODQJÕoG|QHPL 2.27 gün olan
bir 9 M+ 5.4 M sisteminin3DFNHWWDUDIÕQGDQKHVDSODQDQHYULPJ|]GHn geçirilebilir.
(ú ]DPDQOÕ HYULP KHVDSODPDODUÕ
ELUD]GDKDNDUPDúÕN GXUXPODUÕQROXúDELOHFH÷LQL
16.4. KonvektifIÕUODWPDOÕHú]DPDQOÕHYULP
GeniúOHPLú NDUÕúÕP GLNNDWH DOÕQGÕ÷ÕQGD \ÕOGÕ]ÕQ HYULPL \DOQÕ]FD PHUNH]L KLGURMHQ \DQPD HYUHVL VUHVLQLQ
DUWPDVÕ GROD\ÕVÕ\OD GD \ÕOGÕ]ÕQ DQD NRO |PUQQ X]DPDVÕ EDNÕPÕQGDQ GH÷LO D\QÕ ]DPDQGD, \ÕOGÕ]ÕQ Lo
NÕVPÕQGD KLGURMHQ SURILOLQGHNL JUDGL\HQWLQ NRQYHNWLI PHUNH]L NÕVPÕQ o|NPHVLQLQ ELU VRQXFX RODUDN \]H\H
GDKD\DNÕQROPDVÕEDNÕPÕQGDQGDGH÷LúLU
Konvektif
ktadaki
konvektif IÕUODWPDOÕ PRGHOOHU GXUXPXQGD oRN
IÕUODWPDQÕQ GLNNDWH DOÕQGÕ÷Õ YH DOÕQPDGÕ÷Õ KHVDSODPDODUÕQ NDUúÕODúWÕUPDVÕ NÕUPÕ]Õ QR
\DUÕoDSÕQ \DQL DQDNRO VÕUDVÕQGD XODúÕODQ PDNVLPXP \DUÕoDSÕQ
33
GDKD E\N ROGX÷XQX J|VWHUPHNWHGLU %XQXQ ELU VRQXFX RODUDN \DNÕQ oLIW VLVWHPOHUGH % YH $ HYULP
GXUXPODUÕQÕQJ|UHOLROXúXPODUÕ
konvektif IÕUOatmadan önemli ölçüde etkilenecektir.
konvektif IÕUODWPD GLNNDWH DOÕQGÕ÷ÕQGD NWOH DNWDUÕPÕQÕQ A, B ve C
konvektif IÕUODWPDQÕQGLNNDWHDOÕQPDGÕ÷Õ%GXUXPXLoLQDOWOLPLW
de÷HUOHULQL J|VWHUPHNWHGLU ùHNLO NWOH RUDQÕ 9 RODQ \DNÕQ oLIWler için VRQXoODUÕ J|VWHUPHNWHGLU IDUNOÕ
ùHNLO \DNÕQ oLIW G|QHPOHULQLQ
GXUXPODUÕQDRODQDNVD÷OD\DQDOWOLPLWOHULLOH
HYULPOHúPH GXUXPODUÕQÕQ RUWD\D oÕNPDVÕ NWOH RUDQÕQD DQFDN ]D\ÕIoD ED÷OÕGÕU .WOH RUDQÕQÕQ DOÕQPDVÕ
durumunda, ùHNLO¶GD%GXUXPXQDDLWRODQH÷UL,\DOQÕ]FDELUNDoPLOLPHWUH\XNDUÕ\DGR÷UXND\PDNWDGÕU
k
bir 10 M+ 8 M çift sisteminin, Roxburgh kriterine uygun, konvektif
$GXUXPXNWOHDNWDUÕPÕQÕQNDUDNWHULVWLN|]HOOLNOHULQLRUWD\DNR\PD DPDFÕ\ODEDúODQJÕoG|QHPLJQRODQ
IÕUODWPDOÕ HYULPL EDúODQJÕo G|QHPL
JQ RODQ YH D\QÕ NWOHOL ELU VLVWHPLQ 6FKZDU]VFKLOG NULWHUL\OH KHVDSODQDQ HYULPL
yle
NDUúÕODúWÕUÕODELOLU
Konvektif IÕUODWPDVRQXoODUÕùHNLO¶GDYHULOPLúWLU
Konvektif
M \ROGDúD DNWDUÕOÕU %X
MDNWDUÕOÕU.WOHDNWDUÕPÕQÕQEDúODPDVÕQGDQ
IÕUODWPD GXUXPXQGD KÕ]OÕ NWOH DNWDUÕP HYUHVL VUHVLQFH \DNODúÕN HYUH\L\DYDúELUNWOHDNWDUÕPHYUHVLL]OHUYHEXHYUHGHGH
6
\DNODúÕN \ÕO VRQUDNL EHOLUOL ELU DQGD RULMLQDO RODUDN \ROGDú ELOHúHQ RODQ \ÕOGÕ] RULMLQDO RODUDN EDú
ELOHúHQ RODQ \ÕOGÕ]Õ JHoHUHN VLVWHPLQ GDKD HYULPOHúPLú ELOHúHQL KDOLQH JHOLU 5RFKH OREXQX GROGXUXU
NHQGLVLQLQ $ GXUXPX NWOH DNWDUÕPÕQÕ EDúODWÕU YH E|\OHFH ELU GH÷HQ VLVWHP RUWD\D oÕNDU 7HUVLQH NWOH
DNWDUÕPÕEDúODGÕ÷ÕQGDRULMLQDOEDú \ÕOGÕ]ÕQÕúÕWPDVÕQRUPDONWOHND\EHGHQELU \ÕOGÕ]LoLQRODQODD\QÕúHNLOGH
6
GúHU 'H÷PH HYUHVL \DNODúÕN RODUDN \ÕO VUHU 6LVWHP \DNODúÕN RODUDN M ND\EHGHU <ROGDúÕQ
da sistem,
PHUNH]L KLGURMHQ \DQPDVÕQÕQ VRQXQGD GH÷PH ER]XOXU YH % GXUXPX NWOH DNWDUÕPÕ EDúODU 6RQXQ
PHUNH]LKLGURMHQPLNWDUÕ M
olan, 6.37 MNWOHOLELUDQDNRO\ÕOGÕ]ÕLOHKHO\XP\DNPD\DEDúODPÕúRODQ
MNWOHOLELU\ÕOGÕ]DVDKLSROXU
34
ùHNLO <DNÕQ oLIW VLVWHPOHULQ $ % YH & GXUXPODUÕQD LOLúNLQ DOW OLPLW G|QHPOHUL JQ ELULPL
ND\EÕ YH RUWDúLGGHWWHNL
nde). Düz çizgiler, kütle
konvektif IÕUODWPDLOH\DSÕODQ KHVDSODPDODUÕQ'RRP VRQXFXQX J|VWHUPHNWHLNHQ NHVLNOL
çizgi, B durumu, Schwarzschild merkezi için (Vanbeveren, 1980) limit dönemleri göstermektedir.
+ 8 M oLIW VLVWHPLQLQ EDú YH \ROGDú ELOHúHQLQLQ HYULP \ROODUÕ
(Sybesma, 1987). .HVLNVL] oL]JLOHU D\UÕN HYUHOHUL NHVLNOL oL]JLOHU LVH EDú \ÕOGÕ]GDQ \ROGDúD NWOH DNWDUÕP HYUHOHULQL
göstermektedir; kareler tersine kütlHDNWDUÕPGXUXPXQX\DQL\ROGDúÕQNWOHND\EHGHQELOHúHQROGX÷XGXUXPXYHoJHQOHU
ùHNLO %DúODQJÕo G|QHPL JQ RODQ ELU 0
GHGH÷PHHYUHOHULQLJ|VWHUPHNWHGLU
2UWDYHGúNNWOHOLoLIWVLVWHPWUOHUL
$/*2/6ø67(0/(5ø
Algol-VLVWHPOHUL\DUÕD\UÕNVGVLVWHPOHUROXS5RFKHOREXQXGROGXUPXúRODQNoNNWOHOLELOHúHQ\ROGDúÕQD
NWOHDNWDUPDNWDGÕU.oNELOHúHQEDúODQJÕoWDGDKDE\NNWOHOLROXSGDKDKÕ]OÕHYULPOHúPLúRODQGÕU Kütle
RUDQÕq = Ml / Mg ¶QLQGD÷ÕOÕPÕWHNPDNVLPXPOXROXSPDNVLPXP–FLYDUÕQGDGÕU Kütle oranÕGD÷ÕOÕPÕ
ùHNLO¶GHYHULOPLúWLU.
'DKDE\NNWOHOLELOHúHQOHULQNWOHOHUL
– 4 MFLYDUÕQGDELU]LUYH\HVDKLSROXS\Õ÷ÕOPDNoNNWOHOHUH
mleri
GR÷UX GDKD ID]ODGÕU NWOH DNWDUDQ VLVWHPOHUGHNL E\N NWOHOL ELOHúHQOHULQ NWOHOHUL D\UÕN DQDNRO VLVWH
için olandan daha küçüktür.
M DOÕFÕQÕQ
ise 5.60 M¶GLU 2UWDODPD G|QHP JQ YH RUWDODPD NWOH RUDQÕ YHULFLDOÕFÕ ¶GLU .WOH RUDQODUÕQÕQ
bir IRQNVL\RQX RODUDN WRSODP NWOH YH DoÕVDO PRPHQWXP ]HULQH \DSÕODQ ELU LQFHOHPH D\UÕN VLVWHPOHU LoLQ
NWOHOHULOHDoÕVDOPRPHQWXPODUÕQNWOHRUDQÕQGDQED÷ÕPVÕ]ROGX÷XQXRUWD\DNR\PXúWXU+DOEXNL\DUÕ-D\UÕN
0XKWHPHOHQ NWOH RUDQÕ LOH G|QHP LOLúNLOL GH÷LOGLU $OJRO YHULFLQLQ RUWDODPD NWOHVL \DNODúÕN VLVWHPOHU GXUXPXQGD EX SDUDPHWUHOHU DUDVÕQGD NWOH DNWDUÕP HYUHVL VUHVLQFH WRSODP NWOHQLQ D]DOGÕ÷ÕQD
-
LúDUHW HGHQ ELU LOLúNL YDUGÕU .oN NWOH RUDQOÕ \DUÕ D\UÕN VLVWHPOHULQGDKD LOHUL HYULP DúDPDVÕQGD ROGXNODUÕ
-
r. Son kütle (Mf),
NDEXO HGLOHELOLU <DUÕ D\UÕN VLVWHPOHU KDOHQ NWOH DNWDUÕP DúDPDVÕQGD RODQ VLVWHPOHUGL
EDúODQJÕoNWOHVL
MiNXOODQÕODUDNDúD÷ÕGDNLúHNLOGHEXOXQDELOLU'H*UHYH
M f = M i /(9.645 − 0.342M i ),
M f = 0.04M i
1.62
2 M< M < 11 M için
(3.11)
11 M< M < 30 M için.
(3.12)
%X NXUDPVDO LOLúNLOHU LOH J|]OHPOHULQ NDUúÕODúWÕUPDVÕ J|]OHQHQ \ÕOGÕ]ODUÕQ NWOHOHULQLQ GDKD \DUÕVÕQÕ
DNWDUPDODUÕJHUHNWL÷LQLRUWD\D NR\PDNWDGÕU%XQHGHQOH$OJROOHUNWOHDNWDUÕPHYUHVLQLQVRQXQGDGH÷LOOHUGLU
35
Konvektif
IÕUODWPD YHULOHQ ELU
M için, son kütlenin daha büyük olmDVÕ YH NWOH GH÷LúLP HYUHVLQGH YHULFLQLQ
ÕúÕWPDVÕQÕQ6FKZDU]VFKLOGGXUXPXLoLQEHNOHQHQGHQGDKDE\NROPDVÕúHNOLQGHELUHWNL\HVDKLSWLU0HUNH]L
IÕUODWPHoHNLUGHNOHUL6FKZDU]VFKLOGoHNLUGHNOHULQGHQE\NWUYHEXQHGHQOHYHULOHQELU
MfGH÷HULLoLQGDKa
küçük bir MiGH÷HULYHGDKDE\NELUEDúODQJÕoNWOHRUDQÕGH÷HULJHUHNLU
q = Ml / Mg¶QLQ $OJRO VLVWHPLQH LOLúNLQ GD÷ÕOÕPÕ 1RNWDODU q¶QXQ DUDOÕNODUÕ\OD
. φ (q) fonksiyonu, belli bir q GH÷HULQLQ ± 0 DUDOÕ÷Õ LoHULVLQGHNL RUWDODPD NWOH RUDQÕQD VDKLS RODQ
sistemlerin kesrini göstermektedir (Giuricin ve Mordirossian, 1981).
ùHNLO .WOH RUDQÕ
LúDUHWOHQPLúWLU
q = 0.5 ve P = 2 gün için, konvektif
1987):
IÕUODWPD GXUXPXQGD VRQ NWOHOHU úX úHNLOGH LIDGH HGLOHELOLU 6\EHVPD
M f = M i1.41 − 6.16
$GXUXPXNDOÕQWÕODUÕLoLQ
M f = M i1.72 − 21.92
%GXUXPXNDOÕQWÕODUYH
(16.13)
Mi > 6 M için.
(16.14)
%LULODJQDUDVÕQGDNLG|QHPOHULQoR÷XVHoLPHWNLVLQGHQGROD\ÕKDWDOÕGÕU']HOWPHVRQUDVÕQGDG|QHPOHULQ
D\UÕNVLVWHPOHUHQD]DUDQGDKDNoN ROGX÷XEXOXQPXúWXU%XLVHNWOHGH÷LúLPLVÕUDVÕQGDDoÕVDOPRPHQWXP
ND\EÕ ROGX÷XQD LúDUHW HGHU
GeUoHNWHQ GH GHQNOHPLQH J|UH D LoLQ E\N ELU GH÷HU NXOODQÕOPDGÕNoD
G|QHPLQDUWPDVÕJHUHNLU
n olan bir 5 M + 4 M VLVWHPLQGHQEDúOD\DUDNNWOHQLQVRQNWOHQLQ
β DoÕVDO
PRPHQWXPXQNRUXQGX÷XYHNRUXQPDGÕ÷Õα
GXUXPODUDLOLúNLQVRQdönemi hHVDSOD\ÕQÕ]
3UREOHP%DúODQJÕoG|QHPLJ
¶Õ ROGX÷X ELU HYUH LoLQ NRUXQXPOX NWOH DNWDUÕP NRUXQXPVX] NWOH DNWDUÕP 13 –JQDUDVÕQGDNLX]XQG|QHPOL $OJROVLVWHPOHU GHNHúIHGLOPLúWLURQODU:6HUSHQWLV \ÕOGÕ]ODUÕRODUDN
VÕQÕIODQGÕUÕOÕUODU%WQ:6HUSHQWLV\ÕOGÕ]ODUÕRSWLNWD\IODUÕQGDVDOPDoL]JLOHULROXúWXUDPD\DFDNNDGDUVR÷XN
RODQ ELU \ÕOGÕ]ÕQ RSWLN VUHNOLOL÷L LOH X\XPOX RODQ YH EX QHGHQOH GH VÕFDN ELU ND\QDN ROGX÷XQD LúDUHW HGHQ
salma çizgileri (Balmer çizgileri) gösterirler. ³6HUSHQWLGH´ WD\IODUÕ
RUWDN NDUDNWHULVWLN RODUDN 89¶GH
gösterirler. 2SWLN ELOHúHQler
ve NWOH ND]DQDQ ELU \Õ÷ÕúPD GLVNLQH VDKLS VÕFDN ELOHúHQLQLQ
Böylesi sistemlere örnek olarak Beta Lyrae, SX Cas, W Ser
\DNODúÕN .¶OÕN VÕFDN ELU VUHNOLOLN ]HULQH ELQPLú JoO VDOPD oL]JLOHUL
GDKD VR÷XNWXU %X VLVWHPOHU ELU VR÷XN \ÕOGÕ]
ROXúWXUGXNODUÕ ELU PRGHO LOH DoÕNODQÕUODU
verilebilir.
SalPDoL]JLOHULPXKWHPHOHQPDGGHDNÕPÕYH\Õ÷ÕúPDVÕLOHLOLúNLOLGLUiyonizasyon da,HQSODVÕRODUDN,VÕFDNELU
OHNH\DGDGLVNLQLoNÕVPÕQGDNLVÕFDN ELUE|OJHLOHLOLúNLOLGLU 6ÕFDNELOHúHQL oHYUHOH\HQPDGGH \ÕOGÕ]NHQGLVL
\ROGDúÕQ DUNDVÕQGD J|UOPH] ROGX÷XQGD ELOH WDPDPHQ |UWOPH] YH NDEXN oL]JLOHULQLQ EHOLUOL ELOHúHQOHUL
VUHNOL KLGURMHQ ÕúÕQÕPÕQÕQ JHUL ]HPLQLQGH J|UOU RODUDN NDOÕUODU 'DKD VRQUDODUÕ NÕVD G|QHPOL $OJRO
36
VLVWHPOHULQ GH EHQ]HU WD\IVDO |]HOOLNOHU J|VWHUGL÷L EXOXQGX YH EX QHGHQOH JoO DNWL
vite, muhtemelen tüm
Algol sistemlerde mevcuttur.
257$.<$ù$0/,<,/',=/$5
2UWDN \DúDPOÕ \ÕOGÕ]ODU WD\IODUÕQGD JoO NÕUPÕ]Õ VUHNOLOLN LOH ]D\ÕI PDYL VUHNOLOL÷H VDKLS NDUDNWHULVWLN
, uzun dönHPOL \ÕOGÕ]ODUGÕU 2UWDN \DúDPOÕ \ÕOGÕ]ODU
dönemli olarak patlamalar gösterirler. ,úÕQÕP WD\IÕ ROGXNoD JDULSWLU YH X]XQ VUH DQODúÕODPDPÕúWÕU )RWR÷UDI
VR÷XUPD |]HOOLNOHUL YH SDUODN VDOPD oL]JLOHUL EXOXQDQ
SODNODUÕQGDNoNVÕFDNELUELOHúHQLQYDUOÕ÷ÕPRU|WHGHNHQGLQLHOHYHUPLúWLU
Örnek sistemler: 964 gün dönemli HBV 475, 760 gün dönemli Z And, V1016 CYG, RR Tel, RX Pup, CI
Cyg’dir. <DNODúÕN RODUDN FLYDUÕQGD RUWDN \DúDPOÕ \ÕOGÕ] ELOLQPHNWe ve bunlar \DúOÕ GLVN |EH÷LQH DLW
gözükmektedirler. Gözlenen M-WU |]HOOLNOHU JHUL WU ELU \ÕOGÕ] GHY LOH LOLúNLOHQGLULOHELOLUNHQ PDYL
süreklilik ile salma çizgileri ancak VÕFDNELU\ROGDúWDQND\QDNODQÕ\RUROPDOÕGÕU
'L÷HU WDUDIWDQ NWOH YH NLQHWLN PRPHQWXP ND\EÕQÕQ RUDQÕ KDNNÕQGD KLo ELU ELOJL\H VDKLS ROPDGÕ÷ÕPÕ]GDQ
GROD\Õ J|]OHQHQ |]HOOLNOHU LOH EDúODQJÕoWDNL JD] EXOXWODUÕQÕQ EDúODQJÕo NRúÕXOODUÕQÕ LOLúNLOHQGLULUNHQ oRN
GLNNDWOL ROXQPDOÕGÕU 'DKDVÕ PDQ\HWLN DODQODUÕQ \ÕOGÕ] G|QPHVL YH VLVWHPLQ HYULPL ]HULQH RODQ HWNLVL JLEL
GL÷HUIDNW|UOHUGXUXPXGDKDGDNDUPDúÕNODúWÕUPDNWDGÕU
16.5.3. .$7$./ø60ø.'(öøù(NLER
Kataklismik GH÷LúHQOHULQ genel özellikleri
, genellikle, GHMHQHUH ELU \ÕOGÕ] \DQL ELU EH\D] FFH LOH kimi zaman ELU NÕUPÕ]Õ GHY
bazen bir cüce ve bazen de ELU GHMHQHUH \ÕOGÕ]GDQ ROXúPXú çift sistemOHU ROGXNODUÕ NDEXO HGLOLU Kataklismik
.DWDNOLVPLN GH÷LúHQOHULQ
GH÷LúHQOHULQVWDQGDUWPRGHOLQGH\ROGDúELUDQDNRO\ÕOGÕ]Õ\DQLKLGURMHQ\DNDQELU\ÕOGÕ]GÕU
<DNODúÕN VLVWHPLQ \|UQJH G|QHPL ELOLQPHNWHGLU G|QHPOHU LOH VDDW DUDVÕQGD GH÷LúPHNWHGLU
<ROGDúÕQWD\IÕQÕQELOLQGL÷LVLVWHPOHUGHEX*.\D
da M türündendir.<ROGDúÕQELUFFHROGX÷XGXUXPODUGD o,
KLGURMHQ\DNDQELUDQDNRO\ÕOGÕ]ÕGÕU'L÷HUGXUXPODUGD|]HOOLNOHVDDWLQDOWÕQGDNLG|QHPOHUHVDKLSRODQODUGD
\ROGDú GR÷UXGDQ J|]OHQHPH] YH RQODUÕQ DQDNRO \ÕOGÕ]Õ ROGX÷XQGDQ HPLQ ROXQDPD] <ROGDú
, Roche lobunu
,
GROGXUPXúWXU YHEXQHGHQOH GHEH\D]FFH\H GR÷UX PDGGH DNÕúÕ YDUGÕU0DQ\HWLN DODQÕQ\RNOX÷XQGD GúHQ
PDGGH EDú \ÕOGÕ]ÕQ HWUDIÕQGD ELU \Õ÷ÕúPD GLVNL ROXúWXUXU 0DGGH DNÕPÕQÕQ \Õ÷ÕúPD GLVNLQH oDUSWÕ÷Õ \HU
“parlak leke” dir. (÷HU JoO ELU PDnyetik alan mevcutsa, alan çizgileri, GúHQ PDGGH\L ELOHúHQLQ PDQ\HWLN
XoODNODUÕQD GR÷UX \|QOHQGLULU 'LNLQH KÕ] |OoPOHUL PHYFXW RODQODU DUDVÕQGD ELU LVWLVQD RODUDN (0 &\J
,
GÕúÕQGDNLVLVWHPOHULQKHSVLQGH EH\D]FFHEDú\ÕOGÕ]ÕVLVWHPLQE\NNWOHOLELOHú
enidir.
.DWDNOLVPLNGH÷LúHQOHULQ ELUoRNWUYDUGÕU
Novalar: ELU oLIW VLVWHPLQ GHMHQHUH EDú \ÕOGÕ]ÕQÕQ VÕFDN ]DUIÕQGD hidrojenin ani
RODUDN ELUOHúPHVL +Õ]OÕ
\NVHOPHYH\DYDúGúPHOLoRNE\NELUSDWODPDROXU
Tekrarlayan novalar: novalardakini andÕUDQ ROJXODUGÕU IDNDW JHQOLNOHU GDKD GúNWU $UGÕúÕN SDWODPDODU
DUDVÕQGDNLVUH–\ÕOGÕU
Cüce novalar:
<Õ÷ÕúDQ PDGGH PLNWDUÕQÕQ DQLGHQ \NVHOPHVLQH ED÷OÕ RODUDN \Õ÷ÕúPD GLVNLQLQ SDUODNOÕ÷ÕQÕQ
DQLGHQ\NVHOPHVL&FHQRYDODUVÕNYHNoNSDWODPDO
ar gösterirler.
1RYD EHQ]HUOHUL SDWODPD VÕUDVÕQGD FFH QRYDODUD \D GD SDWODPD |QFHVL YH\H VRQUDVÕQGD QRYDODUD EHQ]HUOHU
8;8UVDH0DMDULV\ÕOGÕ]ODUÕ
0DQ\HWLN \Õ÷ÕúDQ \ÕOGÕ]ODU ÕúÕNODUÕ GDLUHVHO XoODúPÕúWÕU 'H÷LúHUHN D\ODU YH\D \ÕOODU VUHQ \NVHN Y
e alçak
düzeyler gösterirler.
.DWDNOLVPLNGH÷LúHQOHULQ
yörünge dönemleri
<DNODúÕN VLVWHPLQ G|QHPL ELOLQPHNWHGLU G|QHPOHU GDNLND := 6JH LOH VDDW GDNLND DUDVÕQGD
n bir tekrarlayan nova ve GK
Per, 1.99 gün dönemli bir nova. '|QHP ERúOX÷X \DQL YH VDDW DUDOÕ÷ÕQGD KLo ELU G|QHPLQ J|]OHQHPHPLú
GH÷LúLUøNL LVWLVQD ELOLQL\RU 7&RURQDH %RUHDOLV \|UQJHG|QHPL JQ ROD
37
ROPDVÕ YH G|QHP GD÷ÕOÕP H÷ULVLQLQ GDNLNDQÕQ DOWÕQGD NHVNLQ ELU úHNLOGH VRQD HUPHVL ùHNLO GúQGUFGU
ùHNLO.DWDNOLVPLNGH÷LúQOHULQ\|UQJHG|QHPOHULQLQKLVWRJUDPÕ5LWWHU
+HPG|QHPNHVLQWLVLOLPLWLQLQKHPGHG|QHPERúOX÷XQXQELUJHFHOLNJ|]OHPoHYULPLQLDúPDPDVÕQHGHQL\OH
bX|]HOOLNOHU\|UQJHVHOG|QHPOLOL÷LQEHOLUOHQHELOLUOL÷Lterminolojisiyle DoÕNODQDPD]
'|QHP GD÷ÕOÕPÕQÕQ NDUDNWHULVWLNOHULQL DoÕNOD\DELOPHN LoLQ J|]OHQHQ DUDOÕNODUGD GH÷HQ VLVWHP KDOLQH JHOHQ
bir kaç çiftin ROXúWX÷XQXYHHWNLOHúHQVLVWHPOHULQ\DEXG|QHPDUDOÕNODUÕQDhiç HYULPOHúHPHGLNOHULQL
ZAMS kütlelerinin alt limitinin (0.085 M)
birazDOWÕQGD bir kütleye sahip, hidrojence-]HQJLQGHMHQHUHELU \ROGDúDNDUúÕOÕN JHOHQG|QHP GDNLNDGÕU 30
GDNLND FLYDUÕQGDNLE|\OHVLQHNoN G|QHPOHULQEXOXQPDPÕúROPDVÕ JHUoH÷L oLIWOHULQ HYULPLnin (kataklismik
GH÷LúHQOHU olmadan önce), KLGURMHQ \DQPDVÕ LoLQ JHUHNOL RODQ PLQLPXP NWOHden daha büyük bir kütleye
\DOQÕ]FD
\D GD oRN KÕ]OÕ HYULPOHúWLNOHULQL NDEXO HWPHN JHUHNPHNWHGLU
VDKLS\ROGDú\ÕOGÕ]ÕQJHUHNWL÷LDQODPÕQDJHOLU
.WOHDNWDUÕPÕ
KDWDNOLVPLN
GH÷LúHQOHUGHNL \ROGDú ELOHúHQO
er kütle kaybedenlerdir. YÕ÷ÕúPD
GLVNLQLQ VÕFDN OHNHQLQ YH
WLWUHPHOHULQYDUOÕ÷ÕNWOHND\EÕQÕQGR÷UXGDQNDQÕWODUÕGÕU$\UÕFDFFHQRYDYHQRYDSDWODPDODUÕQÕQJHQHOOLNOH
NWOHDNWDUÕPÕQÕQEHOLUWLVLROGX÷XGúQOU*HUoHNWHQGHELUFFHQRYDSDWODPDVÕQÕQPXKWHPHOHQ\ROGDúÕQ
NWOH DNWDUPDVÕQGDNL NDUDUVÕ]OÕNODUÕQ \D GD \Õ÷ÕúPD GLVNLQLQ NHQGL OLPLW oHYULP NDUDUVÕ]OÕNODUÕQÕQ ELU VRQXFX
RODUDN \Õ÷ÕúPD GLVNLQLQ SDUODPDVÕQÕQ ELU VRQXFX RODUDN RUWD\D oÕNWÕ÷Õ NRQXVXQGDNL NDQÕWODU ROGXNoD
JHOLúPLúWLU $NWDUÕODQ
.WOHDNWDUÕPKÕ]Õ
madde, yROGDúÕQ NDEXO HGLOHQ HYULP durumuyla uyumlu olarak, hidrojence zengindir.
ile 10-8.5 M\ÕO-1 DUDVÕQGDGÕU
-10.5
.WOH DNWDUÕPÕQÕ NRQWURO HGHQ PHNDQL]PD oHNLPVHO ÕúÕQÕP \D GD PDQ\HWLN IUHQOHPHGLU EN] .HVLP Çekimsel ÕúÕQÕP NDWDNOLVPLN GH÷LúHQOHU LoLQ EDVNÕQ ELU HYULPVHO PHNDQL]PD haline gelebilir. Gözlemler,
JUDYLWDV\RQHO ÕúÕQÕPÕQ WHN EDúÕQD NWOH DNWDUÕPÕQÕ NRQWURO HWPH\H her zaman \HWHUOL RODPD\DFD÷ÕQÕ
göstermektedir. 2ODVÕ GL÷HU ELU PHNDQL]PD ise \ROGDúWDQ JHOHQ PDQ\HWLN RODUDN oLIWOHúPLú ELU \ÕOGÕ]
U]JDUÕQÕQ QHGHQ RODFD÷Õ PDQ\HWLN frenlemedir (bkz. Kesim 18.5.2). ³(QJHOHQPLú PDQ\HWLN IUHQOHPH´
modeli, G|QHPERúOX÷XQXQ]HULQGHELUNDo-9 M\ÕO-1GH÷HULQGHki\NVHNNWOHND\ÕSKÕ]ODUÕQÕve dönem
-10
ERúOX÷XQun aOWÕQGDise 10
M\ÕO-1GH÷HULQGHkiGúNNWOHND\ÕSKÕ]ODUÕQÕWDKPLQHWPHNWHGLU
1 – 2 MNWOHOLo|NPúELUELOHúHQLOHMFLYDUÕQGDNLGúNNWOHOLELUELOHúHQGHQROXúQXúG|QHPOHUL
VDDW \D GDGDKDNoN RODQ \DNÕQ oLIWVLVWHPOHULQHYULPLoHNLPVHOÕúÕQÕPÕQ VHEHEROGX÷X yörüngeGDUDOPDVÕ
38
VRQXFXQGDRUWD\DoÕNDQNWOHDNWDUÕPÕLOHEHOLUOHQLU.WOHND\ÕSKÕ]ÕNDWDNOLVPLNGH÷LúHQOHUOHX\XPOXRODUDN
\DNODúÕN -10
M \ÕO-1 mertebesindedir. dRN NÕVD \|UQJH G|QHPOHULQGH .HOYLQ-Helmholtz zaman öloH÷L
oHNLPVHO ÕúÕQÕP ]DPDQ |OoH÷LQL DúWÕ÷Õ LoLQ \ROGDú ÕVÕVDO GHQJHGH GH÷LOGLU %X DúDPDGD \ROGDú GHMHQHUH
oldukça 60 – 75 GDNLNDOÕN PLQLPXP ELU yörünge dönemine eULúLOLU %X PLQLPXP G|QHP NDWDNOLVPLN
GH÷LúHQOHULoLQ\|UQJHG|QHPLGD÷ÕOÕPH÷ULVLQGHNLNÕVDG|QHPDQLNHVLQWLVLLOHHúWXWXODELOLU
:80D6ø67(0/(5
'H÷HQoLIWOHU KHULNLVLGH5RFKHOREXQXWDúPÕú YH VÕ÷ELURUWDN]DUIJHOLúWLUPLúRODQELUELULQHoRN \DNÕQ LNL
\ÕOGÕ]GDQROXúXUODU%XNXUDPVDOWDQÕPODPDGDQKDUHNHWOHJ|]OHPVHOVRQXoODUDXODúÕODELOLU
-
GDPEÕOEHQ]HULúHNLOOHULRQODUÕQoR÷XQXQ|UWHQRODFD÷ÕQDLúDUHWHGHU
JHUHN L]GúPVHO DODQÕQ GH÷LúLPLQLQ JHUHNVH \]H\ SDUODNOÕN GH÷LúLPLQLQ NHQDU NDUDUPDVÕ oHNLP
Bunlar, ön tür
özellikleridir. :80D \ÕOGÕ]ODUÕ oRN \D\JÕQ olup,
NDUDUPDVÕ VUHNOL ROPDVÕ QHGHQL\OH WXWXOPDODU DUDVÕQGDNL ÕúÕN GH÷LúLPOHUL VUHNOL ROPDOÕGÕU
GH÷HQ oLIWOHU LOH :8 0DMRULV \ÕOGÕ]ODUÕQÕQ NDUDNWHULVWLN
JQHúNRPúXOX÷XQGDNLWP|UWHQoLIWOHULQ¶LQL\DGDEWQ)YH*WU\ÕOGÕ]ODUÕQ\DNODúÕNRODUDN¶LQL
WHúNL
l ederler.
WUMa sistemleri için, gözlemsel özelliklerin WPQ VD÷OD\DQ ELU GH÷HQ modeli yapmak oldukça zordur.
%D]Õ :80D VLVWHPOHUL QNOHHU ]DPDQ |OoH÷LQGHQ GDKD KÕ]OÕ ELU ]DPDQ |OoH÷LQGH HYULPOHúLUOHU YH ÕVÕVDO
WUMa sistHPOHULQLQ\DúODUÕROGXNoDEHOLUVL]ROXSWDKPLQOHU5 107 - 5 109
mektedir. 'H÷HQ VLVWHPOHULQ RULMLQL DQDNRO |QFHVL ELUOHúPH RODUDN veya DoÕVDO PRPHQWXP
GHQJHGHQD\UÕOPDPH\GDQDJHOLU
\ÕO DUDVÕQGD GH÷Lú
ND\EÕ \D
da ELOHúHQOHUGHQ ELULQLQ JHQLúOHPHVL QHGHQL\OH GH÷HQ VLVWHPOHU GXUXPXQD HYULPOHúPH
RODUDN
DoÕNODQDELOLU
'H÷HQ VLVWHPOHULQ VRQX ELOHúHQOHULQ PXKWHPHOHQ RUWDN ELU ]DUI LoHULVLQGH oRN KÕ]OÕ G|QHQ WHN ELU \ÕOGÕ]
ROXúWXUDFDNúHNLOGHELUOHúPHOHULRODELOLU
Son,ELUD\UÕN\DGD\DUÕ-D\UÕNGXUXPGDRODELOLU
Dönemler 0.22 ile 0.62 gQDUDVÕQGDGH÷LúLUWD\IWUOHULLVH)¶GDQ.¶DNDGDUGÕU2UWDODPDNWOHRUDQÕ
olup alt limiti 0.07 ve üst limiti 0.87’dir. Toplam kütle 1- 2 M (0.9 M ile 2.3 M DUDVÕQGD FLYDUÕQGDGÕU
,úÕN H÷ULOHUL HúLW GHULQOLNWH PLQLPXPODUD VDKLSWLU ,úÕN H÷ULlerinin analizlerinden, WUMa sistemlerinin
ELOHúHQlerLQLQ \DNÕQ VÕFDNOÕNODUD VDKLS ROGXNODUÕ DQODúÕOÕU %XQXQOD ELUOLNWH ELOHúHQOHUGHQ ELULQGH OHNH \D GD
OHNHOHULQROXSROPDPDVÕQDED÷OÕRODUDNELOHúHQOHUDUDVÕQGDSDUODNOÕN YH VÕFDNOÕNIDUNOÕOÕNODUÕRUWD\DoÕNDELOLU
.XUDPFÕODU DoÕVÕQGDQ HQ |QHPOL |]HOOLN :80D VLVWHPOHULQLQ ROGXNoD GúN NWOHOL ROPDODUÕ YH KLo ELULQGH
ELOHúHQOHULQ
NWOHOHULQLQ
HúLW
ROPDPDVÕGÕU
Kütle –
ÕúÕWPD
ED÷ÕQWÕVÕ
DOÕúÕOPDGÕNWÕU
%D]Õ
VLVWHPOHU
HYULPOHúPHPLúJ|]NPHNWHGLUOHU
Kuramsal yorumlama
6ÕFDNOÕNODUÕQKHPHQKHPHQHúLWROPDVÕQHGHQL\OH
L1  R1 

=
L2  R2 
2
(16.15)
yazabiliriz, burada L1 ve L2 ELOHúHQOHULQ J|]OHQHQ \]H\ ÕúÕWPDODUÕ YH R1 ve R2 LVH RQODUÕQ HúSRWDQVL\HO
\]H\OHULQLQ \DUÕoDSODUÕGÕU 6LVWHP GH÷HQ ROGX÷XQGDQ KHU LNL ELOHúHQ HúLW SRWDQVL\HOH VDKLSWLU EX DúD÷ÕGDNL
gibi bir kütle –\DUÕoDSED÷ÕQWÕVÕ\ODLIDGHHGLOHELOLU
R1  M 1
=
R2  M 2
β

 .

(16.16)
Kopal (1978), io5RFKHOREODUÕQGDβ
2
M 
L1  R1 
 =  1 
=
L2  R2 
 M2 
–
2β
≈
ROGX÷XQXEXOPXúWXU
Bu da, 2β ≈1 olmDVÕQHGHQL\OH
M1
M2
(16.17)
–
úHNOLQGHELUNWOH ÕúÕWPDED÷ÕQWÕVÕYHULU +DOEXNLJQHúJLELELUDQDNRO\ÕOGÕ]ÕLoLQNWOH ÕúÕWPDED÷ÕQWÕVÕ
39
L1  M 1 

=
L2  M 2 
4
(16.18)
úHNOLQGHGLU
enlerin merNH]L NRúXOODUÕ, RQODUÕQ GH÷HQ ROPDODUÕ JHUoH÷LQGHQ KDUHNHW HGHUHN normal kütle – ÕúÕWPD
Lnuc için daha fazla JHoHUOL RODPD\DFD÷ÕQÕ NDEXO HGHUHN GH÷LúWLULOHPH] Yüzey
VÕQÕU NRúXOODUÕQGDNL GH÷LúLNOLNOHU PHUNH]L EDVÕQo YH VÕFDNOÕN ]HULQGH oRN NoN ELU HWNL GR÷XUXU Bu
QHGHQOH KHU LNL \ÕOGÕ]ÕQ ÕúÕWPDODUÕQÕ SD\ODúWÕNODUÕ VRQXFXQD YDUÕUÕ] EDú \ÕOGÕ] ∆L RUDQÕQGD ELU HQHUML\L
%LOHú
ED÷ÕQWÕVÕQÕQ QNOHHU ÕúÕWPD
\ROGDúÕQDDNWDUÕUYHE|\OHOLNOH
L1nuc − ∆L1 L2 nuc − ∆L2
=
M1
M2
(16.19)
úHNOLQGHELUGHQJHGXUXPXNXUXOPXúROXU
Muhtemelen bu enerji,RUWDN]DUIÕQLo5RFKHOREXQXQ]HULQGH\ÕOGÕ]ODUDUDVÕQGDL\LELUGH÷PHQLQROGX÷XELU
yerde üretilmektedir. Ortak zarf muhtemelen tamamen konvektiftir.
üzerine keyfi bir ∆L HQHUMLVL HNOHQLUNHQ EDú \ÕOGÕ]ÕQ
r. ∆L enerjisi, sistem dengede olacak YH GH÷HQ kalacak úHNLOGH VHoLOLU Bu
GúQFHOHUOH PRGHOOHU \DSÕODELOLU IDNDW =$06 modelleri için yöntem geçersizdir. Gerçekte, WUMA
sistemleri için kütle – ÕúÕWPD ED÷ÕQWÕVÕ β ≈1 üssünü gerektirirken, ZAMS modelleri için, 2β = 4 üssü
gereklidir. Bu ise ancak M1 = M1NRúXOX\ODVD÷ODQÕUDQFDNEXGXUXPJ|]OHPOHULOHoHOLúLU.XLSHUSDUDGRNVX
'H÷HQ oLIWOHULQ oR÷X VD\ÕVDO PRGHOL ROJXVDOGÕU \ROGDú
ÕúÕWPDVÕ D\QÕ RUDQGD D]DOWÕOÕ
sistemlerin, ELU ÕVÕVDO ]DPDQ |OoH÷LQGH HYULPOHúPLú ROGXNODUÕ ve dengede
olmaGÕNODUÕ LOHUL VUOPúWU %LU ÕVÕVDO ]DPDQ |OoH÷LQGHki HYULPOHúPHnin GH÷PHQLQ RUWDGDQ NDONPDVÕQD
neden olaca÷Õ DQODúÕOPDNWDGÕU %X JHUoH÷L DoÕNODPDN LoLQ oHYULPVHO GDYUDQÕúODU |QHUHQ PRGHOOHU “ÕVÕVDl
durulma” PRGHOOHUL RODUDN DGODQGÕUÕOÕUODU 2OD\ODU ]LQFLUL ùHNLO YH ùHNLO ¶WH J|VWHULOPLúWLU
%LU oRN WDUWÕúPDGD GH÷HQ
6HQHU\RúXúHNLOGHGLU
ùHNLO ¶GHNL NHVLNOL NDOÕQ oL]JL GH÷PH NRúXOXQX J|VWHUPHNWHGLU 'LQDPLN GHQJH GXUXPXQGD KHU LNL
\ÕOGÕ] GD EX oL]JL ]HULQGH EXOXQPDOÕGÕU .HVLNOL LQFH oL]JL WHN \ÕOGÕ]ODU LoLQ =$06 NRúXOXQX
göstermektedir. 3QRNWDVÕQGDNL EDú \ÕOGÕ]ÕQ, ÕVÕVDOYHGLQDPLNGHQJHGH ROGX÷XQXYDUVD\DOÕP GLQDPLNGHQJH
\ROGDúÕ6′¶GHROPD\D]RUODU2ÕVÕVDOGHQJHGHROPDGÕ÷ÕQGDQ6¶GHNLGHQJH\HGR÷UXJHQLúOHPH\HoDOÕúÕU
ùHNLO ,VÕVDO GXUXOPD PRGHOL .DOÕQ NHVLNOL oL]JL GH÷PH NRúXOXQX WHPVLO HWPHNWHGLU øQFH NHVLNOL oL]JL WHN \ÕOGÕ]ODU
LoLQ =$06 NRúXOXQXJ|VWHUPHNWHGLU%Dú \ÕOGÕ] ÕVÕVDOYH 3FLQVLQGHQ GLQDPLN GHQJHGH EDúOÕ\RU GLQDPLNGHQJH \ROGDúÕ
S′¶GHROPD\D]RUODU2ÕVÕVDOGHQJHGHROPDGÕ÷ÕQGDQÕVÕVDOGHQJH\HXODúPDNLoLQ6¶\HGR÷UXJHQLúOHU2UWD\DoÕNDQKDILI
JHQLúOHPHEDú\ÕOGÕ]DGR÷UXPDGGHDNWDUÕPÕQDQHGHQROXU%LOHúHQOHUDUDVÕQGDNLX]DNOÕNDUWDUYHGH÷PHVRQDHUHU.WOH
vH HQHUML DNWDUÕPÕ GXUXU <ROGDú E]OU EDú \ÕOGÕ] JHQLúOHU YH EDú \ÕOGÕ]Õ =$06 NRQXPXQD XODúPDVÕQGDQ |QFH 5/2)
EDúODU 'HYDPHGHPNWOH DNWDUÕPÕ E\NNWOHOL EDú\ÕOGÕ]GDQNoNNWOHOL \ROGDúDELOHúHQOHUDUDVÕQPGDNL X]DNOÕ÷ÕQ
D]DOPDVÕQDYHGH÷PHHYUHVLQLQ \HQLGHQROXúPDVÕQDQHGHQROXU'H÷PH \HQLGHQROXúXQFD\ROGDúÕVÕVDOGHQJH \DUÕoDSÕQD
XODúÕQFD\DNDGDUJHQLúOHUNWOHDNWDUÕPÕWHUVLQHG|QHUYHoHYULP\HQLGHQEDúODPÕúROXU
40
ùHNLO:80D\ÕOGÕ]ODUÕLoLQÕVÕVDOGXUXOPDPRGHOLDoÕNODPDPHWLQGHYHULOPLúWLU
+DILIoHJHQLúOHPHQHGHQL\OH EDú \ÕOGÕ]DGR÷UXNWOHDNWDUÕPÕEDúODU .RUXQXPOX NWOHDNWDUÕPÕ
durumunda,
NWOHDNWDUÕPÕ NoN NWOHOLGHQE\N NWOHOL\H ROGX÷XQGDQ ELOHúHQOHU DUDVÕQGDNLX]DNOÕN E\U YH GH÷PH
sona erer. Kütle ve eneUML DNWDUÕPÕ GXUXU <ROGDú E]OU YH \DUÕoDSÕ =$06 GH÷HULQH \DNODúÕU EDú \ÕOGÕ]
E\U YH =$06 NRQXPXQD \HUOHúPHGHQ |QFH 5/2) \HQLGHQ EDúODU 'HYDP HGHQ NWOH DNWDUÕPÕ EDú
\ÕOGÕ]ÕGDQ \ROGDúD \DQL E\N NWOHOLGHQ NoN NWOHOL\H ELOHúHQOHU DUDVÕQGDNL
yeni bir
GH÷PH GXUXPX ROXúPDVÕQD
yol açar.
a\UÕNOÕ÷ÕQ NoOPHVLQH YH
durumunda, kütle
.RQYHNWLI ]DUIOÕ NoN NWOHOL ELU \ROGDú
\Õ÷ÕúPDVÕ \DUÕoDSÕ D]DOWÕFÕ ELU HWNL\H VDKLS RODFDN YH
yeni bir GH÷PH GXUXPXQXQ ROXúPDVÕ GÕú NÕVÕPODUÕ
mELUúHNLOGHRODFDNWÕU'H÷PH\HQLGHQNXUXOXQFD
ÕúÕQÕPVDORODQELU\ROGDúGXUXPXQGDNLQHJ|UHGDKD\DYDú
\ROGDú ÕVÕVDO GHQJH \DUÕoDSÕQD XODúÕQFD\D NDGDU JHQLúOHU NWOH DNWDUÕPÕ WHUVLQH G|QHU YH ROJXODU oHYULPL
en, çevrimin D\UÕN HYUH \D GD ]D\ÕI
süresi, gözlemlerin aksine çok uzundur. .WOH DNWDUÕPÕ PXKWHPHOHQ NRUXQXPOX GH÷LOGLU YH DoÕVDO
PRPHQWXPND\ÕSODUÕLoLQbelirtiler YDUGÕU .WOHND\EÕELOHúHQOHUDUDVÕQGDGDKDNoND\UÕNOÕ÷DQHGHQROXUYH
böyleFH GDKD JoO YH GDKD X]XQ VUHOL GH÷PH HYUHVL NXUXODELOLU ADoÕVDO PRPHQWXP ND\EÕ LoLQ HQ RODVÕ
mekanizma manyetik frenlemedir.
\HQLGHQ EDúODU %XQXQ L\L oDOÕúDQ ELU PRGHO RODUDN J|UQPHVLQH UD÷P
GH÷PH
Manyetik
frenlemenin bir sonucX RODUDN WHN \ÕOGÕ]ODU GDKD \DYDú G|QHUOHU Halbu ki, çekimsel sürtünmenin, rüzgar
WDUDIÕQGDQ WDúÕQDQ DoÕVDO PRPHQWXPX \|UQJH DoÕVDO PRPHQWXPXQGDQ DOPDVÕQÕ VD÷ODPDVÕ nedeniyle, çift
VLVWHPOHUGDKDKÕ]OÕG|QHUOHU%XVUHFLQ]DPDQ|OoH÷LELOLQPHPHNWHGLU Bir çift sistemELUWHN\ÕOGÕ]ÕQNLQGen
GDKD E\N ELU WRSODP DoÕVDO PRPHQWXPa sahiptir ve bunun sonucu olarak da bir çift sistemin dönme
5]JDUOD NWOH ND\EÕ YH PDQ\HWLN DODQÕQ ELUOHúLPL PDQ\HWLN IUHQOHPH\H \RO DoDU +XDQJ KÕ]ODQPDVÕWHN\ÕOGÕ]ÕQG|QPH\DYDúODPDVÕQGDQGDKD\DYDúROPDOÕGÕU'L÷HUWDUDIWDQGDKDE\NG|QPHKÕ]Õ
nedeniyle manyetik aktivite de daha büyüktür. *QHúLQ GDYUDQÕúÕQGDQ HNVWUDSRODV\RQ \DSDUVDN JQQ
DOWÕQGDNLG|QHPOHUHVDKLSoLIWOHULQG|QPHKÕ]ODQPDVUHVL
10
\ÕOGDQNÕVDROPDOÕGÕU
-
øOHULHYULPDúDPDVÕQGDNLoLIWOHUGúNNWOHOL; ÕúÕQoLIWOHULSDWOD\ÕFÕODUJDODNWLNúLúLPND\QDNODUÕYHNUHVHO
NPHND\QDNODUÕ\DNÕQoLIWOHULQILQDODúDPDODUՁ]HULQHRODQ%|OP¶GHLQFHOHQHFHNWLU
41
BÖLÜM 17
%h<h..h7/(/ø<$.,1dø)7/(5ø1(95ø0ø
*LULú
%\N NWOHOL oLIWOHU LOH EDú \ÕOGÕ]ÕQÕQ EDúODQJÕo =$06 NWOHVL 0
¶GHQ E\N RODQ oLIWOHUL \DQL \ÕOGÕ]
Bu etki nedeniyle baúODQJÕoWDNL NRQYHNWLI
oHNLUGH÷LQ NDWPDQODUÕ \]H\GH J|UQUOHU YH EX QHGHQOH GH DWPRVIHULN KLGURMHQ EROOX÷X GúHU Büyük
U]JDUODUÕ\OD NWOH ND\EHGHQ E\N NWOHOL \ÕOGÕ]ODUÕ DQOÕ\RUX]
NWOHOLOHU JLEL NoN NWOHOL \ÕOGÕ]ODU LoLQ GH NWOH DNWDUÕPÕ PHUNH]L KLGURMHQ \DQPDVÕ LOH KHO\XP \DQPDVÕ
VÕUDVÕQGD PH\GDQD JHOLU Bü\N NWOHOL \ÕOGÕ]ODU LoLQ U]JDUOD NWOH ND\EÕ \|UQJH |÷HOHULQLQ GH÷LúPHVLQH
neden olur (bkz. denklem 15.34).
.RQYHNWLI E|OJHQLQ VÕQÕUÕQÕ EHOLUOHPHN DPDFÕ\OD 6FKZDU]VFKLOG NULWHULQL X\JXODGÕ÷ÕPÕ]GD
G|QHP GD÷ÕOÕPÕQÕQ GLNNDWH DOÕQPDVÕ GXUXPXQ
da,
homojen bir
% YH & HYUHOHULQLQ JHQLú ELU \|UQJH G|QHPL DUDOÕ÷ÕQÕ
NDSVDGÕNODUÕ YH RQODUÕQ HYULPLQ HQ \D\JÕQ WUOHUL ROG÷X RUWD\D oÕNDU $ WUQH J|UH HYULPOHúHQ VLVWHPOHULQ
kesri küçüktür; 10 M’den NoN EDú \ÕOGÕ] NWOHOHUL LoLQ RUDQ ¶GDQ GúNWU Büyük kütleler için bu
oran daha büyüktür; O-WU \ÕOGÕ]ODU LoLQ RUDQ ¶GHQ E\NWU $QFDN H÷HU PHUNH]GHQ IÕUODWPD GLNNDWH
DOÕQÕUVD EX GXUXPGD |]HOOLNOH GH E\N NWOHOL \ÕOGÕ]ODU LoLQ $ GXUXPX GDKD |QHPOL KDOH JHOLU. Büyük
NWOHOHU LoLQ \DOQÕ]FD $ GXUXPX X\JXQdur ve en büyük kütleler için Roche loEX WDúPDVÕ ELOH PH\GDQD
JHOPH]EXVRQGXUXPGD\DQLHQE\NNWOHOL\ÕOGÕ]ODUGXUXPXQGD\ÕOGÕ]GDKD|QFHGHQ\ÕOGÕ]U]JDUODUÕ\OD
,
RODQ\NVHNGHUHFHGHQNWOHND\EÕQHGHQL\OH KLGURMHQ\DQPDVÕQÕQHUNHQHYUHOHULQGHVRODGR÷UXKDUHNHWHWPLú
olur.
% YH & GXUXPODUÕQGD EDú \ÕOGÕ]ÕQ HYULPL NWOH DNWDUÕPÕQÕQ NRUXQXPOX ROXS ROPDPDVÕQGDQ oRN ID]OD
etkilenmez. dR÷X GXUXPGD EDú \ÕOGÕ] 5RFK OREXQGDQ WDúPD\D EDúODU EDúODPD] JHULGH NDODQ KLGURMHQFH
]HQJLQ]DUIÕQoR÷X\ÕOGÕ]ÕQEDúODQJÕoWRSODPNWOHVLQLQ¶LQHXODúÕUdenklem (15.23) ile verilen dinamik
(Kelvin – HelmholW]]DPDQ|OoH÷LQGHND\EHGLOLU
t KH = 3 10 7
M2
RL
(17.1)
\ÕO
, pratik olarak, JHUL\H \DOQÕ]FD EDú
EXUDGD WP QLFHOLNOHU JQHú ELULPOHULQGHGLU .WOH DNWDUÕPÕQGDQ VRQUD
\ÕOGÕ]ÕQ oHNLUGH÷L NDOÕU %X NDOÕQWÕ HVDV RODUDN KHO\XP YH ELU PLNWDU GD D÷ÕU HOHPHQWOHUGHQ LEDUHWWLU
, evrimLQ VRQUDNL DúDPDODUÕ KHO\XP oHNLUGH÷LQ HYULPL LOH
+HO\XPXQ EX úHNLOGH EDVNÕQ ROPDVÕ QHGHQL\OH
belirlenebilir.
%\NNWOHOL\DNÕQoLIWOHULQWUOHUL
17.2.1. O-TÜRÜ YILDIZLAR, KÜTLELER VE YARIÇAPLAR
1. Kütleler
<ÕOGÕ]ODUÕQNWOHOHUL\DOQÕ]FDoGXUXPGDGR÷UXGDQEHOLUOHQHELOLU
-
<|UQJHOHULELOLQHQYHWULJRQRPHWULNÕUDNVÕPODUÕPHYFXWRODQJ|UVHOoLIWOHUGXUXUP
u,
*|UVHO ELU \|UQJH WDKPLQL \DSÕODELOHQ YH KHU LNL ELOHúHQLQ GLNLQH KÕ]ODUÕQÕQ ELOLQGL÷L J|UVHO oLIWOHU
durumu,
-
dLIWoL]JLOL|UWHQoLIWOHUGHÕúÕNYHGLNLQHKÕ]H÷ULOHULQLQDQDOL]L
O-WU \ÕOGÕ]ODU LoLQ X]DNOÕNODUÕ oRN E\N ROGX÷XQGDQ J|UVHO \|UQJH belirlenemez. Kütleleri GR÷UXGDQ
EXODELOHFH÷LPL] WHN \|QWHP oLIW oL]JLOL WD\IVDO |UWHQ oLIWOHU GXUXPXGXU Örten olmayan çiftler durumunda
\DOQÕ]FD PLQLPXP NWOH GH÷HUOHUL
( M sin 3 i) ve
D\UÕFD H÷HU \ROGDúÕQ WD\IÕ J|UQP\RUVD EX GXUXPGD GD
yaOQÕ]FDNWOHIRQNVL\RQX
f ( M ) = ( M 2 sin i ) 3 /( M 1 + M 2 ) 2
elde edilebilir.
(17.2)
42
<DUÕoDSODU
<DUÕoDSODUÕ EHOLUOHPHQLQ WHPHO \ROX ELU |UWHQ oLIWLQ KHU LNL ELOHúHQLQLQ
R1/a ve R2/a ile verilen kesirsel
\DUÕoDSODUÕQÕNXOODQPDNWÕU2QODUÕúÕNH÷ULOHULQLQDQDOL]LQGHQEXOXQDELOLUOHU(÷HULNLWD\IGDJ|UOHELOL\RUYH
ölçülebiliyorsa, aGH÷HULYHEXQGDQGDGR÷UXVDOoDSODUGR÷UXGDQKHVDSODQDELOLU
Garmany ve ark. (1980), bilinen tüm O-WU\ÕOGÕ]ODUÕQELUOLVWHVLQLYHUPLúOHUGLU2-WU\ÕOGÕ]ODULoin, kütleler
LOH \DUÕoDSODUÕQ GR÷UXGDQ KHVDSODQDELOGL÷L GXUXPODUÕQ VD\ÕVÕ oRN GúNWU g]HWOH 2-WU \ÕOGÕ]ODUÕQ
kütlelerinin 20 M’den büyük ve üst limitinin 60 – 100 MROGX÷XV|\OHQHELOLU(QE\NNWOHOHL2-türü çift
+' VLVWHPL 3ODVNHWW \ÕOGÕ]Õ ROXS NWOH IRQNVL\RQX f(M) = 12.40 M ¶GLU %XQXQOD ELUOLNWH \ROGDúÕQ
WD\IÕQÕQ PXKWHPHOHQ HWUDIÕQGDNL JD] DNÕPÕQGDQ HWNLOHQPLú ROPDVÕ QHGHQL\OH NWOH IRQNVL\RQXQXQ EX
GH÷HULQLQ\RUXPODQPDVÕVRQGHUHFH]RUGXU'H÷LúLNoDOÕúPDODUGDQEDú\ÕOGÕ]LoLQ
de 60 – 90 MDUDVÕQGDNLNWOHWDKPLQOHULHOGHHGLOPLúWLU
– 100 MYH\ROGDúLoLQ
Çizelge 17.1. O-WUWD\IVDOoLIWOHULQ\|UQJHHOHPDQODUÕ\ODNWOHYH\DUÕoDSGH÷HUOHUL
HD veya BD
1337
Tayf
Türü
O9.5
P
(gün)
3.5
12323
19820
25638/9
35921
36486
37041
37043
47129
48099
57060
O9
O9
O9.5
O9.5
O9.5
O9.0
O8.5
O7.5
O6.5
O8.5
3.1
3.4
2.7
4.0
5.7
21.0
29.1
14.4
3.1
4.4
57061
75759
93205
93206
QZ Car
93403
100213
135240
149404
150136
151564
E326331
152218
152219
152248
155775
159176
165052
166734
167771
175514
191201
193611
E228766
E228854
+40°4220
198846
199579
206267
209481
215835
O9.0
O9
O3
O9
O9
O6
O7-8
O9
O9
O5
O9.5
O8
O9
O9.5
O7
O9.5
O7
O7
O7
O8
O8.0
B0.3
B0V
O7
O6.5
O7
O9.8V
O6.5
O6
O8.5
O5.5
154.9
33.3
6.1
20.7
6.0
15.1
1.39
3.9
9.8
2.7
4.6
5.6
5.4
4.2
6.0
7.0
3.4
6.1
34.5
4.0
1.6
8.33
2.88
10.7
1.9
6.6
3.00
48.6
3.7
3.1
2.1
QXPDUDVÕ
M1sin3i
M2sin3i
10.1
12.9
18.9
9.2
21.6
8.1
f (M)
M1
M2
R1
R2
Ref.
19
18.3
23
22.5
13.9
11.5
8.9
9.5
1
2
21.7
8.4
13.0
10.0
3
40.5
58*
23.9
64*
19.1
9.0
8
4
19
23
23
30
18.6
12.3
14.8
5
6
63.3
24.5
10.1
6.4
8
52.5
23.8
31.0
15.8
17.1
7.3
11.6
6.2
8
3
34.3
36.8
12.5
13.7
8
40.2
39.6
18.0
19.7
8
28
19.1
22.1
46.4
26.9
10.7
17.5
22.5
18.6
19.0
9.6
11.4
11.0
16.2
9.2
3.5
9.8
11.3
7
8
7.5
8
3
21.8
23.0
10.7
11.6
8
0.004
0.382
0.605
1.530
15.9
9.4
12.400
0.63
20
0.38
24
17.8
39
14.3
15
1.690
0.200
10.500
5.2
23.5
3.4
15.8
1.6
14.8
2.7
8.2
1.590
0.102
0.412
13.4
10.7
24.4
22.5
10.8
2.5
28
2.7
11.4
2.2
28
2.3
13.9
14.2
34
37.3
31
16.2
13.0
14.4
23
32.7
9
16.9
0.689
0.556
43.9
0.374
18.3
6.2
23.4
6.4
2.9
19.1
Referanslar: 1.Wood (1963); 2. Hutchings and Hill (1987); 3. Popper (1980); 4. Hutchings and Cowley
(1976); 5. Sahade (1959); 6. Hutchings (1977); 7. Vitrichenko (1971); 8. Doom and de Loore (1984).
*
100 M ve 90 M’lik kütle GH÷HUOHUiGHUHI¶GHQDOÕQPÕúWÕU
43
Çizelge 17.2. Conti (1975)’e göre, O-WU\ÕOGÕ]ODUÕQNWOHYH\DUÕoDSODUÕ
Tayf Türü
03
04
05
05.5
06
06.5
M/ M
ZAMS
120
90
60
45
37
30
R/ R
V
14.5
13.5
11.8
11.0
10.2
9.6
R/ R
If
19.1
20.0
20.9
20.9
21.9
21.9
M/ M
ZAMS
28
25
23
21
19
18
Tayf Türü
07
07.5
08
08.5
09
09.5
R/ R
V
8.7
8.3
8.3
7.9
7.8
7.8
R/ R
If
22.9
22.9
23.4
24.6
24.6
24.0
O-WU \ÕOGÕ]ODU LoLQ DoÕVDO oDSODU 8QGHUKLOO YH DUN 8QGHUKLOO YH +DQEXU\ %URZQ YH DUN
WDUDIÕQGDQ HOGH HGLOPLúWLU <|UQJH HOHPDQODUÕ ELOLQHQ 2-WU WD\IVDO oLIWOHU LoLQ NWOH YH \DUÕoDS
GH÷HUOHUL dL]HOJH ¶GH YHULOPLúWLU <DUÕoDSODUÕQ GR÷UXGDQ |OoPOHUL RUWDODPDVÕ 5
olan ve 5 – 20 R
DUDVÕQGD GH÷LúHQ \DUÕoDS GH÷HUOHUL YHUPHNWHGLU 'H÷LúLN WD\I WU YH ÕúÕWPD VÕQÕIÕQGDQ 2-WU \ÕOGÕ]ODU LoLQ
&RQWL¶GHQDOÕQDQNWOHYH \DUÕoDSGH÷HUOHULdL]HOJH¶GHYHULOPLúWLU dHúLWOLÕúÕWPDVÕQÕIODUÕQGDQ2WU\ÕOGÕ]ODUÕQ\DUÕoDSODUÕdL]HOJH¶WHYHULOPLúWLU
Çizelge 17.3. O-WU\ÕOGÕ]ODULoLQ8QGHUKLOOYHDUNYH8QGHUKLOOWDUDIÕQGDQ\DSÕODQ55 tahminleri
Tayf Türü
O9.5
O9
O8.5
O8
O6.5
O6
O5
O4
O3
V
7.4
8.6
III
II
10.1
9.2
23.8
30.2
15.9
16.5
16.2
17.0
If
18.3
19.8
Ia
36.9
9.5
12.5
11.9
11.7
20.3
19.8
3. O-WU\ÕOGÕ]ODUGDoLIWOHULQVÕNOÕ÷Õ
O-WU \ÕOGÕ]ODUÕQ \DNODúÕN ¶Õ ± 7) oLIW VLVWHPGLU YH NWOH RUDQODUÕ oR÷XQOXNOD ¶WHQ E\NWU Bu
bulgu, \NVHN D\ÕUPDOÕ WD\IODUÕQÕQ DOÕQPDVÕQD RODQDN VD÷OD\DFDN RUDQGD SDUODN RODQ 67 O-türü yÕOGÕ]ÕQ oLIW
ROPD VÕNOÕ÷ÕQÕ LQFHOH\HQ *DUPDQ\ YH DUN WDUDIÕQGDQ EXOXQPXúWXU Muhtemelen, örnek içerisinde
EHOLUOHQHPHPLú RODUDN NDOan çiftler ancak bir kaç tanedir. Wolf – 5D\HW \ÕOGÕ]ODUÕQÕQ oLIW ROPD VÕNOÕ÷Õ GD 2türü sistemlerinkine benzer olup FLYDUÕQGDGÕU
olan çift sistem yoktur. dR÷X VLVWHP \DNODúÕN RODUDN LOH
güQ DUDVÕQGDNL G|QHPOHUH VDKLSWLU oRN D] VD\ÕGD VLVWHP – 100 gün DUDVÕQGD G|QHPOHUH VDKLSWLU Kütle
oranlarÕ ELU FLYDUÕQGD maksimuma sahiptir ve bu durum muhtemelen ROXúXP PHNDQL]PDVÕ\OD DoÕNODQDELOLU
%LOHúHQOHUL ROGXNoD IDUNOÕ NWOHOHUH VDKLS
3DUoDODQDUDN
ROXúDQ
gözükmektedir.
VLVWHPOHUGH
VLVWHPOHUGH
ELOHúHQOHULQ
NDEDFD
HúLW
NWOHOL
ROPDVÕQÕ
EHNOHPHN
0XKWHPHOHQ HúLW ROPD\DQ NWOHOHUH VDKLS ELOHúHQOHUH J|WUHQ PHNDQ
oDOÕúPDPDNWDGÕU
J|VWHUPHNWHGLU|UQHNGD÷ÕOÕPÕ
ùHNLO
PHYFXW
|UQHNOHU
LoLQ
NWOH
RUDQÕ
DNOD
\DWNÕQ
izmalar, büyük kütleli
YH
G|QHP
GD÷ÕOÕPÕQÕ
PJQHNVLNROGX÷XQGDQWDPDPODQPD\ÕEHNOHPHNWHGLU
q = 0.8 – FLYDUÕQGD PDNVLPXP \DSQ ELU q
q-GD÷ÕOÕPÕQÕQ PDNVLPXP
Abt ve Levy (1978)’e göre, tüm dönemler dikkate
.ÕVD G|QHPOL GL÷HU WD\I WUQGHQ oLIWOHU GH \DNODúÕN RODUDN
GD÷ÕOÕPÕQD VDKLSOHUGLU ùHNLOGHQ J|UOHFH÷L ]HUH GDKD X]XQ G|QHPOL VLVWHPOHUGH
yerinin küçük q GH÷HUOHULQH GR÷UX ND\PD H÷LOLPL YDUGÕU
-0.25
DOÕQGÕ÷ÕQGDWD\IVDOoLIWOHUq
EHQ]HULELUIUHNDQVGD÷ÕOÕPÕQDVDKLSWLUEN]ùHNLO
+LGURMHQ \DQPDVÕ VUHVLQFH NWOHOL oLIWOHULQ KHU LNL ELOHúHQL GH U]JDUODU QHGHQL\OH NWOH ND\EHGHUOHU NWOH
ND\EÕ ÕúÕWPD YH GROD\ÕVÕ\OH NWOH LOH LOLúNLOL ROGX÷XQGDQ HQ E\N NWOH ND\EÕ EDúODQJÕoWD HQ E\N NWOHOL
RODQELOHúHQGHROXU6RQXoRODUDND\UÕNHYUHVUHVLQFHNWOHRUDQÕELUGH÷HULQHGR÷UXGH÷LúLU2
-türü çiftler
44
ùHNLO (YULPOHúPHPLú NWOHOL \DNÕQ oLIWOHULQ NWOH RUDQÕ GD÷ÕOÕPÕ NÕVD G|QHPOL VLVWHPOHU *DUPDQ\ &RQWL YH
0DVVH\¶GHQDOÕQPD.ÕVDYHX]XQG|QHPOLOHULQWRSOXFDGD÷ÕOÕPÕ$EWYH/HY\¶WDUDIÕQGDQYHULOPLúWLU
HYULPOHULQHELUFLYDUÕQGDNLNWOHRUDQODUÕ\ODEDúODGÕNODUÕQGDQ
–GDKD|QFHGHEHOLUWWL÷LPL]LJLELEXRUDQ\ÕOGÕ]
-
U]JDUODUÕ\OD GDKD GD JoOHQHQ ELU NDUDNWHULVWLNWLU KHU LNL \ÕOGÕ] GD \DNODúÕN RODUDN D\QÕ WDULKoH\H VDKLSWLU
-
\DQLELOHúHQOHUDQDNROGDQQHUHGH\VHSHú SHúHHYULPOHúLUOHU%XLVH; ÕúÕQoLIWOHULQLQHYULPL LoLQVRQGHUHFH
önemli sonuçlara sahiptir.
.WOHOL \ÕOGÕ]ODU KLGURMHQL &12 oO oHYULPL LOH KHO\XPD G|QúWUUOHU hoO &12 oHYULPL GHQJH\H
larda meydana gelirler.
H÷LOLPOLGLU \DQL oHYULPGHNL WP UHDNVL\RQODU D\QÕ KÕ]
.WOHOL \ÕOGÕ]ÕQ LoLQGH EX
GHQJH\H ELU NDo RQELQ \ÕOGD \DQL QNOHHU ]DPDQ |OoHNOHULQLQ oRN NoN ELU NHVULQGH XODúÕOÕU 'HQJH
NXUXOGX÷XQGD oR÷X &12 HOHPHQWOHUL
14
1¶\H G|QúWUOU ú|\OH NL Lo QNOHHU \DQPD E|OJHOHULQGHNL 1
EROOX÷XNR]PLNEROOX÷XQ\DNODúÕNNDWÕLNHQ&LVHNDWFLYDUÕQGDELUEROOXNHNVLNOL÷LJ|VWHULU
8
helyum
12
Üçlü
α LúOHPOHUL o +H oHNLUGH÷LQL, bir & SDUoDFÕ÷ÕQD YH LNLQFLO α−\DNDODPD LúOHPOHUL GH
\DQPDVÕ EDúODU
C’u, O’e ve O’niQ ELU NÕVPÕQÕ GD Ne ve Mg’D G|QúWUU dHNLUGHNWH KLGURMHQ \DQPDVÕ VRQXQGD \ÕOGÕ] ELU
Wolf -5D\HW \ÕOGÕ]ÕQÕQ, |QFHELU:1 \ÕOGÕ]ÕQÕQ VRQUDGDELU:& \ÕOGÕ]ÕQÕQ kimyasal kompozisyonuna sahip
olur.
dHNLUGHNWHKLGURMHQ \DQPDVÕ VRQXQGD PHUNH]L VÕFDNOÕN .¶QLQ]HULQH oÕNDUYH PHUNH]LNÕVÕPGD
17.2.2. WOLF – RAYET YILDIZLARI
Wolf – 5D\HW \ÕOGÕ]ODUÕQÕQ \DNODúÕN \DUÕVÕ \DNÕQ çift sistemlere aittir ve bunODUÕQGD KHPHQ KHPHQ ¶X ELU
O-WU \ÕOGÕ] LoHULU O-WU ELOHúHQOL :ROI – 5D\HW \ÕOGÕ]ODUÕQÕQ E\N NÕVPÕ oLIW oL]JLOL oLIWOHUGLU (SB2)
böylece her ikL ELOHúHQLQ de GLNLQH KÕ] GH÷LúLPOHUL |OoOHELOPHNWHGLU Bununla birlikte, :5 ELOHúHQLQGHNL
VDOPD oL]JLOHULQLQ JHQLúOHPHVL YH EXQXQ GD \|UQJH o|]POHPHOHULQGH -30’a varan belirsizliklere yol
DoPDVÕ QHGHQL\OH oR÷X GXUXPGD WD\IVDO \|UQJHQLQ EHOLUOHQPHVL RODQDNVÕ]GÕU dLIW oL]JLOL :5 \ÕOGÕ]ODUÕQÕQ
ölçülen parametreleri ÇizelgH¶WHYHULOPLúWLU
Dönemler, O-WUoLIWOHUGHROGX÷XJLELoR÷XQOXNODJQOHUPHUWHEHVLQGHGLUMsin3iGH÷HUL:5NWOHOHULQLQ10
– 20 MFLYDUÕQGDROGX÷XQDLúDUHWHGHU <|UQJHLQLNOL÷L:5oLIWOHULQLQVDGHFHVÕQÕUOÕELUNÕVPÕLoLQ \DÕúÕN
H÷ULVLQGHQ \D GD SRODULPHWULGHQ HOGH HGLOHELOPLú YH ELOHúHQOHULQ NWOHOHUL EHOLUOHQHELOPLúWLU Elde edilen
NWOHOHU dL]HOJH ¶WH YHULOPLúWLU :5 \ÕOGÕ]ODUÕQÕQ NWOHOHUL - 5 M ’den, 40 - 50 M ¶H \D\ÕOÕUNHQ
RUWDODPD NWOH:1 \ÕOGÕ]ODUÕLoLQ M , WC türleri için de 13.5 M ’dir. 2UWDODPD NWOHRUDQÕ :52%
:1YH:&WUOHULLoLQVÕUDVÕ\ODYH¶GLU
Tek çizgili ve oldukca küçük kütle fonksiyonlu
f ( M ) = ( M 2 sin i ) 3 /( M 1 + M 2 ) 2 < 0.3
(17.3)
45
bir oRN :5 \ÕOGÕ]Õ EHOLUOHQPLúWLU YH EX GXUXP RQODUÕQ, GúN NWOHOL ELOHúHQOHUH VDKLS ROGX÷XQD LúDUHW HGHr.
Çizelge 17.5’de, bu tür sistemlerin dönem, kütle ve gökada düzlemine olan z X]DNOÕNODUÕQD LOLúNLQ YHULOHU
o
OLVWHOHQPLúWLU YöUQJH LQLNOL÷Lnin bilinmHGL÷L GXUXPODUGD 7 ’lik bir RUWDODPD GH÷HU ve görünmeyen ikinci
ELOHúHQLoLQGHM ¶OLNELUNWOHNDEXOHGLOPLúWLU
Çizelge 17.4. 2%ELOHúHQOL:ROI-5D\HW\ÕOGÕ]ODUÕQÕQNWOHOHUL
+'øVLP
Tayf Türü
Dönem
E320102
HD90657
HD94546
HD190918
CX Cep
HD193576(a)
HD193077
HD193928
HD211853
(GP Cep)
E311884
HD92740
HD186943
HD197406
HD214419(b)
CD-45°
AS422 22
HD62910
HD63099
HD94305
HD113904(c)
HD97152
HD193793
HD152270
HD68273
HD137603
HD168206(d)
WN3+O5-7
WN4+04-6
WN4+O7
WN4.5+O9.5Ia
WN5+O8V
WN5+O6
WN6+c?(ya da B ?)
WN6
WN6+O
(O+O)(ecl)
WN6+O5
WN7+abs.
WN4+O9.5V
WN7
WN7+O
WN7
WNC
WN6+WC??
WC5+O7
WC+O6-8
WC6+O9.5/B0I
WC7+O9.5-BOI
WC7+O4.5
WC7+O5-8
WC8+O9I(9HO
WC5+BOIa
WC8+O8-9III-V
8.83?
8.255
4.831
112.8
2.1269
4.2124
2.324
21.64
6.688
6.34
80.35
9.55
4.317
1.641
23.9
22?
85.37
14.7
18.82
18.431
7.886
7.9y
8.893
78.50
26.9
29.712
'Õú
(÷LP
MWR
MOB
>8
61±5(ecl)
46
15
>50
78±1
----78±1
>5.5
12±2
(7)
(15)
5-12
10
>20-80
(q=0.55)
(14)
97
24±4
(17)
(35)
12-2
26
>10-60
0
0.64
67-90
76.9
0.1
0
0
----0
67±4
65±1
------(55)
----43±3
>9
35±8
80±7
<20.
76±4
43±6
>48
16
(60)
31±1
------(10)
>15
--11±3
>17
7(+12,-3)
19(+7,-2)
(>5)
(12±1)
51±15
(q=2?)
(35)
(12.4)
2
------(35)
>32
--18±5
140
18(+34,-7)
35(+13,-3)
(>27)
24±1
merkezlik
0
0.04
0.
0.43
0
0
0
--0
DoÕVÕ
0
0
0.7
0
0.4
0
0
(26)
WR
21
31
133
151
139
138
141
153
47
22
127
148
155
145
8
9
30
48
42
79
11
70
113
Referanslar: Smith and Maeder, 1989; Schulte-Ladbeck, 1989; Van der Hucht et. al. 1988.
(a): V44&\JE&4&HSF0XVG&%6HU
Çizelge 17.5. Küçük kütle fonksiyonlu tek çizgili Wolf-5D\HW\ÕOGÕ]ODUÕ
WR kütleleri, 57o¶ONELU\|UQJHH÷LNOL÷LYH0¶OLNELU\ROGDúNWOHVLNDEXOHGLOHUHNKHVDSODQPÕúWÕU
+'øVLP
HD187282
HD50896
HD97950
HD143414
HD191765
HD192163
HD193077
HD197406
HD86161
HD96548
HD177320
HD209BAC
HD164270
*
Tayf Türü
WN4
WN5
WN6
WN6
XN6
WN6
WN6
WN7
WN8
WN8
WN8
WN8
WC9
Dönem
3.85
3.763
3.772
7.690
7.44
4.50
2.3238
4.3173
10.73
4.762
1.7616
2.3583
1.7556
f (M)
0.003
0.015
0.154
0.007
0.0055
0.00024
0.0009
0.28
0.00024
0.0005
0.0019
0.0005
0.00146
MWR
14
5.7
1.1
8.6
10
53
27
0.6*
53
36
18
36
21
.DUD'HOLN%LOHúHQOL%\N.WOHOL%LU:5<ÕOGÕ]Õ2OPD2ODVÕOÕ÷Õ
z (pc)
-324
-160
-63
-973
+55
+67
+37
+735
-110
-209
-502
+192
-242
46
Xat ¶OL ELU \ROGDúÕQÕQ
– 5D\HW \ÕOGÕ]ÕQÕQ NLP\DVDO NDrakteristiklerine
%WQ NWOHOL \DNÕQ oLIWOHU ELU 2% \ÕOGÕ]Õ LOH oHNLUGH÷LQGH KHO\XP \DNDQ
ROXúWXUGX÷X ELU GXUXPGDQ JHoHFHNWLU %X \ROGDú ELU :ROI
sahip olacak fakat bir Wolf – 5D\HW \ÕOGÕ]Õ JLEL J|UQPH\HELOHFHNWLU $QFDN \DOQÕ]FD HQ E\N NWOHOL
RODQODUGD \ÕOGÕ] U]JDUODUÕ ELU :ROI – 5D\HW WD\IÕ UHWPH\H \HWHFHN NDGDU JoO RODFDNWÕU Roche lobu
WDúPDVÕ VRQUDVÕQGDNL GúN NWOH NDOÕQWÕODUÕ KÕ]OD E]OHUHN .¶OLN HWNLQ VÕFDNOÕNODUD XODúDFDNODUGÕU
(÷HUEX \ÕOGÕ]:ROI
– 5D\HW \ÕOGÕ]ODUÕQÕQVDOPD |]HOOLNOHULQLUHWPH]LVH oHNLUGH÷LQGH KHO\XP \DNDQ \ÕOGÕ]
J|UQPH]RODUDNNDODFDNWÕU
2%1dø)7/(5ø
2% \ÕOGÕ]ODUÕ JoO D]RW YH ]D\ÕI NDUERQ oL]JLOHUL J|VWHULUOHU 2QODU JHQHOOLNOH \]H\OHULQGH KLGURMHQ
\DQPDVÕQÕQ &12 UQOHULQL J|VWHUHQ 2% \ÕOGÕ]ODUÕ RODUDN \RUXPODQÕUODU
Onlar, H-5 GL\DJUDPÕQGD =$06
Onlar,
\DNÕQÕQGD 9 ÕúÕWPD VÕQÕIÕ ROGX÷X NDGDU =$06¶ÕQ oRN X]DNODUÕQGD , ÕúÕWPD VÕQÕIÕ GD EXOXQXUODU
:DOERUQ
YH
%LVLDFFKL
/RSH]
YH
)LUPDQL
WDUDIÕQGDQ
D\UÕQWÕOÕ
RODUDN
LQFHOHQPLúOHUGLU 2%1 \ÕOGÕ]ODUÕ DUDVÕQGD oLIW ROPD VÕNOÕ÷Õ HQ D] ¶GLU %ROWRQ YH 5RJHUV EHONLGH
%100’dür.
2%1 \ÕOGÕ]ODUÕQD |UQHNOHU dL]HOJH ¶GD YHULOPLúWLU dLIW ROGX÷X GR÷UXODQDQODU LoLQ G|QHP YH
HD 163181 için
kütleler M1 = 13 M, M2 = 22 M’ dir (Hutchings, 1975); BN bLOHúHQL\ROGDúÕQGDQmGDKDSDUODNWÕUYHEX
nedenle sistemin,JHoPLúWH5RFKHOREXWDúPDVÕJHoLUGL÷LGúQOHELOLU
NWOHIRQNVL\RQODUÕYHULOPLúWLU*HQHOOLNOH 2%1 \ÕOGÕ]Õ GDKD E\N ÕúÕWPDOÕ RODQ ELOHúHQGLU
Çizelge 17.6. 2%1<ÕOGÕ]ODUÕ– OBN Çiftleri
.LPOL÷L
HD12323
HD72754
HD163181
HD193516
HD201345
E235679
HD48279
HD218195
Tayf Türü
ON9V
BN2pe
BN0.5Iae
BN0.7IV
ON9V
BN2.5Ib
f (M)
0.0033
18.8
0.043
Tayfsal çift
5.9
Dönem (gün)
3.07
33.07
12
4.01
225.2
1DUWPÕú&QRUPDO
1DUWPÕú&QRUPDO
Referans
BR
T
H
BR
BR
BR
W
W
BR: Bolton and Rogers, 1978; T: Thackery,1971; H: Hutchings, 1975; W: Walborn, 1976
17.2.4. OB KAÇAKLARI
Blaauw (1961), Vitrichenko, Gershberg ve Metik (1965), Bekenstein ve Bowers (1974), Cruz-Gonzales ve
DUN 6WRQH YH &DUUDVFR YH DUN WDUDIÕQGDQ \DSÕODQ NLQHPDWLN oDOÕúPDODUGDQ
– 40 km s-1) sahiplerdir.%XQODU³NDoDN\ÕOGÕ]ODU´
olarak isimlendirilir. O-WUNDoDNODUÕQNHVUL (Conti, Leep ve Lore, 1977) ile %49 (Stone, 1979) DUDVÕQGD
tahmin edilmektedir. %ODDXZ NDoDN \ÕOGÕ]ODUÕQ E\N NWOHOL \DNÕQ oLIW VLVWHPOHULQ RULMLQDO EDú
EXOXQGX÷X]HUHED]Õ2% \ÕOGÕ]ODUÕoRN\NVHNKÕ]ODUD
\ÕOGÕ]ÕQÕQVSHUQRYDSDWODPDVÕQGDQVRQUDNLELUHYULPDúDPDVÕROGX÷XQXLOHULVUPHNWHGLU(÷HUEXJHUoHNLVH
NDoDNODUÕQ E\N ELU NÕVPÕQÕQ VÕNÕúÕN ELU ELOHúHQ LoHUPHVL JHUHNLU %XQXQOD ELUOLNWH oLIW NDoDNODUÕQ DQFDN
küçük bir kesrinin, standart kütleli X-ÕúÕQoLIWOHULQLQG|QHPOHULRODQ–JQDUDOÕ÷ÕQGDNLG|QHPOHUHVDKLS
ROPDODUÕ QHGHQL\OH EXQODUGDNL RODVÕ VÕNÕúÕN FLVLPOHULQ EHOLUOHQHELOPH RODVÕOÕ÷Õ oRN NoNWU .DoDNODUÕQ
WD\IODUÕ QRUPDOGLU YH NLP\DVDO ELOHúLPOHULQGH ELU DQRUPDOOLN J|UOPH]
OB kaoDNODUÕQÕQ NXUDPVDO olarak
EHNOHQHQNHVUL5RFKHOREXWDúPDVÕVÕUDVÕQGDNLNWOHDNWDUÕPÕLoLQ\DSÕODQNDEXOOHUHVÕNÕFDED÷OÕGÕU(÷HUEDú
\ÕOGÕ] WDUDIÕQGDQ ND\EHGLOHQ NWOHQLQ \DOQÕ]FD ¶VL \ROGDú WDUDIÕQGDQ \Õ÷ÕúWÕUÕOPÕúVD NL EX \D\JÕQ RODUDN
kabul edLOHQGH÷HUGLUEXGXUXPGD2-WU\ÕOGÕ]ODUÕQ\DNODúÕNRODUDN¶LVÕNÕúÕNELUELOHúHQHVDKLSROPDOÕGÕU
(Meurs ve van den Heuvel, 1989)..RUXQXPOXGXUXPGDEXNHVULQGH÷HULROXU
%\NNWOHOL\DNÕQoLIWOHULQHYULPL
'DKD|QFHEHOLUWLOGL÷L]HUH%|OPNWOHDNWDUÕPÕEDú\ÕOGÕ]ÕQPHUNH]LKLGURMHQ \DQPDHYUHVLVÕUDVÕQGD
$YH\DNDEXN\DQPDVÕVÕUDVÕQGD%\DGDKHO\XPXQWNHWLOPHVLQGHQVRQUD&EDúOD\DELOLU
A durumu, son
GHUHFH NÕVD G|QHPOL VLVWHPOHU LOH VÕQÕUOÕGÕU oQN EX GXUXP 5RFK OREODUÕQÕQ NoN ROPDVÕ DQODPÕQD JHOLU
(÷HU VLVWHP ELU NDo KDIWDOÕN ELU G|QHPH VDKLS LVH EX GXUXPGD NWOH DNWDUÕPÕ DQFDN EDú \ÕOGÕ]ÕQ NÕUPÕ]Õ GHY
47
HYUHVLQH HYULPOHúPHVLQGHQ VRQUD EDúOD\DFDNWÕU <DOQÕ]FD VRQ GHUHFH E\N G|QHPOL VLVWHPOHULQ EDú
\ÕOGÕ]ODUÕ \ROGDúODUÕQD NWOH DNWDUPDGDQ NÕUPÕ]Õ GHY HYUHVLQGHQ JHoHUHN HYULPOHúHELOLUOHU
Böylece büyük
NWOHOL \DNÕQ oLIWOHULQ E\N ELU NÕVPÕ % GXUXPX NWOH DNWDUÕPÕQGDQ JHoHUHN HYULPOHúLUOHU %X QHGHQOH
, B durumu kütle
Bir örnek olarakEDúODQJÕoG|QHPLJQRODQ M+22.5 M sisteminin, 0.5
E\N NWOHOL \DNÕQ oLIWOHUGHNL NWOH DNWDUÕPÕQD LOLúNLQ HYULP KHVDSODPDODUÕQÕQ oR÷X
DNWDUÕPÕQÕGLNNDWHDOÕUODU
\Õ÷ÕúPD oDUSDQOÕ E|\OHFH EDú \ÕOGÕ]GDQ ND\ERODQ PDGGHQLQ ¶VL \ROGDú WDUDIÕQGDQ \Õ÷ÕúWÕUÕOPDNWDGÕU
Hú]DPDQOÕHYULPLùHNLO¶GHJ|VWHULOPLúWLU (YULPLQHQ|QHPOLDGÕPODUÕLVHdL]HOJH¶GHYHULOPLúWLU
:5 oLIWOHUL \D GÕú NDWPDQODUÕQ \ÕOGÕ] U]JDUODUÕ\OD DWÕOPDVÕ \ROX\OD \D GD EDú \ÕOGÕ]GDQ \ROGDúD NWOH
DNWDUÕPÕ LúOHPL\OH ROXúXUODU
Merkezi hidrojen yanPDVÕ VÕUDVÕQGD \ÕOGÕ] U]JDUODUÕ QHGHQL\OH NWOH D]DOÕU
q (=M2/M1 NWOH RUDQÕ YH G|QHP DUWDU
'DKD E\N NWOHOL \ÕOGÕ]ODUGD EX HWNL GDKD JoO ROGX÷XQGDQ
(denklem 15.34).
ùHNLO%DúODQJÕoG|QHPLJQRODQ0
+22.5 M sisteminin evrimi (de Loore ve De Greve, 1992).
dL]HOJH%DúODQJÕoG|QHPLJQRODQ0
Zaman
\ÕO
%Dú%LOHúHQLQ(YULP%DVDPD÷Õ
0
8181000
8339000
Anakol
8365000
.WOHDNWDUÕPÕQÕQLON
8367670
8371020
8376770
9136970
%Dú\ÕOGÕ]ÕQNÕUPÕ]ÕQRNWDVÕ
XC1=0
EDVDPD÷ÕQÕQEDúODQJÕFÕ
0LQLPXPÕúÕQÕPJF
+HOLXPWXWXúPDVÕ
øONNWOHND\ÕSEDVDPD÷ÕQÕQ
sonu
.DUERQWXWXúPDVÕ
+22.5 M sisteminin evrimi
Dönem
(gün)
8.94
10.11
10.17
Kütle
Nokta
25
23.26
23.18
A
B
C
Anakol
10.18
23.16
D
øONWRSODQPDQÕQ
10.32
10.96
16.30
15.18
E
F
9.69
17.85
G
øNLQFL%LOHúHQLQ
(YULP%DVDPD÷Õ
EDúODPDVÕ
øONWRSODQPD
EDVDPD÷ÕQÕQ
Kütle
Nokta
22.50
21.41
21.36
21.35
basa
mak
24.78
27.44
I
J
K
27.99
L
M
N
O
sonu
4.91
24.07
H
27.63
P
Böylece, WR çiftleri, EDú \ÕOGÕ]ÕQ KLGURMHQFH ]HQJLQ GÕú NDWPDQODUÕQÕ \D \ÕOGÕ] U]JDUODUÕ YDVÕWDVÕ\OD WÕSNÕ
kaybetmesi yoluyla ya da bu
NDWPDQODUÕ \ROGDúÕQD DNWDUPDVÕ VXUHWL\OH ROXúXUODU Büyük kütleli ZAMS sistemleriQLQ EDú \ÕOGÕzODUÕQÕQ
WHN \ÕOGÕ]ODUGD ROGX÷X JLEL \DQL \ROGDú LOH KHU KDQJL ELU HWNLOHúLP ROPDNVÕ]ÕQ
HYULPL\D6FKZDU]VFKLOGNULWHUOHULQLGLNNDWHDODQNODVLNHYULPNRGXLOH\DGDPHUNH]LIÕUODWPD\ÕLoHUHQHYULP
kodu ile hesaplanabilir.
48
q (=M2/M1 YH JHUoHN G|QHPLQEDúODQJÕo G|QHPLQH RUDQÕ P/Pi parametrelerinin, hidrojen
yanmasÕNWOHDNWDUÕPÕYH:ROI–5D\HWHYUHOHULVÕUDVÕQGDNLHYULPOHULúXúHNLOGHGLU
.WOHNWOHRUDQÕ
-
<ÕOGÕ]U]JDUODUÕHYUHVLVÕUDVÕQGDKHPEDúKHPGH\ROGDú \ÕOGÕ]ÕQNWOHOHULD]DOÕU%Dú\ÕOGÕ]ÕQ \DQLGDKD
E\NNWOHOLELOHúHQLQNWOHND\EÕQÕQGDKDE\NROPDVÕQHGHQL\OHNWOHRUDQÕ
-
büyür.
büyür, dönem
küçülür.
Wolf –5D\HWHYUHVLVÕUDVÕQGDKHO\XP\ÕOGÕ]ÕQÕQNWOHVL– 5 10-5 M\ÕO-1RUDQÕQGDD]DOÕUE|\OHFHNWOH
.WOH DNWDUÕPÕ VÕUDVÕQGD NRUXQXPOX NWOH DNWDUÕPÕ GLNNDWH DOÕQGÕ÷ÕQGD NWOH RUDQÕ
RUDQÕYHG|QHPE\U
BuQODU
JHUHN 6FKZDU]VFKLOG NULWHUOHULQLQ X\JXODQPDVÕ JHUHNVH PHUNH]L IÕUODWPDQÕQ GLNNDWH DOÕQPDVÕ
GXUXPXODUÕQGD RUWD\D oÕNDQ JHQHO H÷LOLPOHUGLU %\N NWOHOL \DNÕQ oLIWOHU
NWOH DNWDUÕPODUÕ LoLQ
Schwarzschild kriterlerinin dikkate alan
ve korunumlu ve korunumsuz
HYULP KHVDSODPDODUÕ 9DQEHYHUHQ YH DUN
WDUDIÕQGDQ YH PHUNH]L IÕUODWPDOÕ HYULP KHVDSODPDODUÕ GD 'RRP 6\EHVPD YH GH
/RRUH YH 'H *UHYH WDUDIÕQGDQ \DSÕOPÕúWÕU .ODVLN \|QWHP YH PHUNH]L IÕUODWPD LOH HOGH HGLOHQ VLVWHP
SDUDPHWUHOHUL DUDVÕQGDNL IDUNODU 'H *UHYH YH GH /RRUH ¶Q \XNDUÕGDEHOLUWLOHQKHVDSODPD VRQXoODUÕQD
.
qEDú\ÕOGÕ]ÕQ
gerçek kütlesi ve P/Pi parametrelerinLQ GH÷LúLPLQL J|VWHUPHNWHGLU .WOH DNWDUÕPÕ VÕUDVÕQGD YH NRUXQXPOX
NWOHDNWDUÕPÕGLNNDWHDOÕQGÕ÷ÕQGD VLVWHPLQ RODQ EDúODQJÕoNWOH RUDQÕ M ¶OLNELUEDú \ÕOGÕ]LoLQ
GH÷HULQH YH M ¶OLN ELU EDú \ÕOGÕ] LoLQ GH GH÷HULQH oÕNDU (÷HU WP PDGGHQLQ VLVWHPL WHUN HWWL÷L
GD\DQDUDNROXúWXUXODQùHNLO¶GHDoÕNRODUDNRUWD\DNRQPXúWXU ùHNLOVÕUDVÕ\ODNWOHRUDQÕ
YDUVD\ÕOÕUVDNWOHRUDQÕGDKDD]DUWDUYHDoÕVDOPRPHQWXPND\EÕQHGHQL\OHG|QHPNoOU
ùHNLO %\N NWOHOL \DNÕQ oLIWOHULQ NWOH RUDQÕQÕQ \ÕNDUÕGD EDú \ÕOGÕ]ÕQ NWOHVLQLQ RUWDGD YH JHUoHN G|QHPLQ
EDúODQJÕo G|QHPLQH RUDQÕQÕQ DOWWD KLGURMHQ \DQPD HYUHVLQGH % GXUXPX NWOH DNWDUÕP HYUHVLQGH YH :5 HYUHVL
VÕUDVÕQGDNLHYULPL6RO6FKZDU]VFKLOGoHNLUGHNOHULVD÷PHUNH]LIÕUODWPD
49
$WPRVIHUGHNL KLGURMHQ EROOX÷X \DNODúÕN RODUDN ¶Q DOWÕQD GúW÷QGH NWOH DNWDUÕPÕ VRQD HUHU
IÕUODWPD
KLGURMHQFH
]HQJLQ
]DUIÕQ
NWOHVLQL
D]DOWWÕ÷ÕQGDQ
¶ON
EX
HúLN
GH÷HUH
Merkezi
6FKZDU]VFKLOG
GXUXPXQGDNLQHQD]DUDQGDKD|QFHXODúÕOÕUYHE|\OHFH\ROGDúDGDKDD]NWOHDNWDUÕOPÕúROXU
35 – 40 M¶L DúDQ EDú \ÕOGÕODU LoLQ YH 3 – 5 gQ DúDQ G|QHPOHU LoLQ % GXUXPX NWOH DNWDUÕPÕ PH\GDQD
gelmez. %X \ÕOGÕ]ODU oHNLUGHNWH KLGURMHQ \DQPDVÕ VRQUDVÕQGD derhal +5 GL\DJUDPÕQÕQ PDYL NÕVPÕQD GR÷UX
\RO DOÕUODU YH NÕUPÕ]Õ GHYOHU E|OJHVLQH HYULPOHúPH]OHU øNL ELOHúHQ DVOD HWNLOHúPH] YH WHN \ÕOGÕ] gibi
HYULPOHúLUOHU 35 – 40 M ¶OLN EXHúLN GH÷HU FLYDUÕQGDNWOH DNWDUÕPÕQGDQ \ÕOGÕ] U]JDUODUÕ\ODNWOH ND\EÕQD
GR÷UX \DYDú ELU JHoLú YDUGÕU \ÕOGÕ] QH NDGDU E\N NWOHOL LVH ]DUIÕQÕQ, \ÕOGÕ] U]JDUODUÕ\OD sürüklenerek
sistemi terk eden NÕVPÕRNDGDUbüyükYH\ROGDúDDNWDUÕODQNÕVPÕGDRNDGDUNoNROXU
:5HYUHVLQLQEDúODQJÕFÕQGDNLNDOÕQWÕQÕQEDú \ÕOGÕ]ÕQ EDúODQJÕoNWOHVLQLQELUIRQNVL\RQXRODUDNLIDGHHGLOHQ
NWOHVL dL]HOJH ¶GH YHULOPLúWLU :5 \ÕOGÕ]ODUÕQÕQ PRGHOOHQPHVLQGH PHUNH]L IÕUODWPDQÕQ
dahil edilmesi,
D\QÕEDúODQJÕoNWOHVLLoLQNODVLN\|QWHPHQD]DUDQGDKDE\NELU:5\ÕOGÕ]ÕYHULU
Çizelge 17.8
α'H÷HUL
Parametrelendirme
0
Mf = 0.590 Mi – 4.40
0.25
Mf = 0.550 Mi – 3.00
1.5
Mf = 0.816 Mi – 5.237
Problem 17.1: 20, 40, 60, 80 ve 100 MNWOHOLEDú\ÕOGÕ]NDOÕQWÕODUÕQÕQNWOHDNWDUÕPÕVRQXQGDNLNWOHOHULQL
NODVLN HYULP GXUXPX YH PHUNH]GHQ IÕUODWPD GXUXPX LoLQ NDUúÕODúWÕUÕQÕ] GH÷HULQGHNLELU NWOH RUDQÕQGDQ
YH JQON ELU G|QHP GH÷HULQGHQ EDúOD\DUDN G|QHP VRQXQGDNL NWOH RUDQÕ YH G|QHP GH÷HUOHULQL
KHVDSOD\ÕQÕ]
:5 oLIWOHULQLQ NRUXQXPOX HYULP LOH HOGH HGLOHQ NWOH RUDQODUÕ J|]OHQHQ GH÷HUOHU LOH X\XPOX GH÷LOGLU
20 – 30 M
kütOHOL :5 \ÕOGÕ]ODUÕQÕ DoÕNOD\DELOPHN DPDFÕ\OD EWQ VLVWHPOHU LoLQ EDúODQJÕo NWOH RUDQODUÕQÕn 0.5’ten
NoNROGX÷Xnu kabul etmek gerekir ki bu da,DoÕNoDJ|]OHPOHULOHoHOLúHQELUGXUXPGXU(÷HUWHUVLQHRODUDN
NRUXQXPOXYDUVD\ÕPÕ\ODWDKPLQHGLOHQNWOHRUDQODUÕEWQ:5\ÕOGÕ]ODUÕLoLQROGXNoDE\NWU
EDú \ÕOGÕ]ÕQ ND\EHWWL÷L NWOHQLQ ELU NÕVPÕQÕQ VLVWHPL WHUN HWWL÷L YDUVD\ÕOÕUVD NWOH DNWDUÕPÕ VÕUDVÕQGD \ROGDú
GDKD D] NWOH \Õ÷ÕúWÕUPÕú YH E|\OHFH GH GDKD NoN ELU NWOH GH÷HULQH XODúPÕú ROXU NL EX GD :5 \ÕOGÕ]ODUÕ
LoLQJ|]OHPOHUOHGDKDL\LX\XúDQELUGXUXPGXU
:5 \ÕOGÕ]ODUÕQÕQ J|]OHQHQ G|QHPOHULQLQDoÕNODPDVÕELU SUREOHP WHúNLOHWPH]
– JQ EDúODQJÕoG|QHPOL
oLIWOHU % GXUXPX NWOH DNWDUÕP HYUHVLQH HYULPOHúHELOLUOHU VLVWHPL WHUN HGHQ PDGGH D\QÕ ]DPDQGD DoÕVDO
momentum da götürür. .XUDPVDO HYULP \ROODUÕQÕQ J|]OHPOHU LOH NDUúÕODúWÕUPDVÕQGDQ EDú \ÕOGÕ]ÕQ ND\EHWWL÷L
α = 1.5) modeller
GXUXPXQGD\DNODúÕNRUWDGHUHFHGHQPHUNH]LIÕUODWPDOÕ α PRGHOOHULoLQ\DNODúÕN
PDGGHQLQ |QHPOL ELU NÕVPÕQÕQ VLVWHPL WHUN HWWL÷L DQODúÕOÕU E\N PHUNH]L IÕUODWPDOÕ %\NNWOHOL \DNÕQoLIWOHULQHYULPLQGHPHUNH]GHQIÕUODWPDQÕQGDKLO HGLOPHVLQLQ RUWD\DNR\GX÷X|QHPOL ELU
VRQXo oHNLUGHNWH KLGURMHQ \DQPDVÕ VÕUDVÕQGD XODúÕODQ \DUÕoDSÕQ NODVLN 6FKZDU]VFKLOG GXUXPXQGD HOGH
HGLOHQGHQ GDKD E\N ROPDVÕ E|\OHFH GH $ GXUXPX LoLQ HOGH HGLOHQ PDNVLPXP
dönemin daha büyük
ROPDVÕGÕU %X LVH J|]OHQHQ :5 oLIWOHULQLQ |QHPOL ELU NÕVPÕQÕQ $ \D GD $% GXUXPODUÕQGDQ ELUL \ROX\OD
ROXúWXNODUÕDQODPÕQDJHOLU
– 5D\HW \ÕOGÕ]ÕQGDQ
böylesi bir gariplik ancak, kütle
RUDQÕQÕQ \DNODúÕN RODUDN FLYDUÕQGD ROPDVÕ GXUXPXQGD PH\GDQD JHOHELOLU çünkü bu durumda, her iki WR
evresi, yani EDú YH \ROGDúÕQ :5 HYUHOHUL, bir biUOHULQL oRN \DNÕQGDQ WDNLS HGHU. Ancak \Õ÷ÕúPD \ÕOGÕ]ÕQÕQ
'H÷LúLN HYULP DúDPDODUÕ ]LQFLUL EDúODQJÕo NWOH RUDQÕQD VÕNÕ VÕNÕ\D ED÷OÕGÕU øNL :ROI
ROXúDQ oLIW VLVWHPOHU JLEL JDULS \DSÕODUÕQ ROXúXPX ROGXNoD VÕUDGÕúÕGÕU
JHQoOHúPHVL YH |PUQQ X]DPDVÕ ELU oRN GXUXPGD EDú \ÕOGÕ]ÕQ :5 HYUHVLQLQ \ROGDúÕQ :5 HYUHVLQLQ
EDúODPDVÕQGDQGDKD|QFHVRQDH
rmesine neden olur.
50
*|]OHPOHULOHNDUúÕODúWÕUPD
%Dú \ÕOGÕ]Õ M NWOHVLQH VDKLS NWOH RUDQÕ YH EDúODQJÕo G|QHPL JQ RODQ E\N NWOHOL ELU \DNÕQ
oLIWVLVWHPLQ HYULPL=$06¶WDQ EDú \ÕOGÕ]ÕQ EH\D] FFHHYUHVLQH \RODOÕU +HULNL ELOHúHQGHKLGURMHQ \DQPD
HYUHVL VLUDVÕQGD \ÕOGÕ] U]JDUODUÕ\OD NWOH ND\EHGHU 0HUNH]L KLGURMHQLQ WNHQPHVLQGHQ NÕVD ELU VUH VRQUD
NWOHDNWDUÕPÕEDúODU.WOH DNWDUÕPÕ NRUXQXPOX RODUDNPH\GDQD JHOLU +HULNLELOHúHQLQ +5GL\DJUDPÕQGDNL
L – Log Teff YH ùHNLO ¶GHNL Mvis – Log Teff GL\DJUDPODUÕQGD J|VWHULOPLúWLU
Log L’den Mvis¶H G|QúP &RQWL ¶nin WPÕúÕQÕP G]HOWPHOHUL NXOODQÕODUDN \DSÕOPÕúWÕU Çizelge 17.9
ise sistem parametrelerinin evrimini göstermektedir.
HYULPL ùHNLO ¶GHNL /RJ
4. Bir 26 + 23.4 M VLVWHPLQLQ EDú NDOÕQ oL]JL YH \ROGDú LQFH oL]JL ELOHúHQLQLQ +5 GL\DJUDPÕQGDNL HYULP
ùHNLO \ROODUÕ+DUIOHUPHWLQLoLQGHDoÕNODQPÕúWÕU<DWD\HNVHQLQVWNÕVPÕQGDWD\IWUOHULGHEHOLUWLOPLúWLU
ùHNLO%LU0
sisteminin Mvis – Log TeffGL\DJUDPÕQGDNLHYULPL
51
Çizelge 17%DúODQJÕoG|QHPLJQRODQELU26 + 23.4 M sisteminin evrimi
HRD
106\ÕOOÕN
1RNWDODUÕ
\DúODU
A
0
B
7.97
C
8.27
D
8.28
E
8.281
F
8.282
G
8.282
H
8.282
I
8.283
J
8.283
K
8.286
L
8.291
Kütle 1
Kütle 2
26
23.4
23.92
22.86
13.70
22.84
23.69
22.84
19.17
27.35
17.22
29.30
15.66
30.95
14.69
31.83
13.79
32.72
12.89
33.62
11.62
34.88
11.42
35.31
log Teff 1
log Teff 2
4.57
4.56
4.36
4.55
4.42
4.55
4.21
4.54
4.12
4.28
4.10
4.10
4.12
4.22
4.13
4.30
4.13
4.40
4.14
4.51
4.15
4.60
4.18
4.60
log L 1
log L 2
4.89
4.78
5.25
4.82
5.29
4.85
5.28
4.87
5.06
5.77
5.12
5.12
5.16
5.78
5.22
5.77
5.27
5.73
5.33
5.65
5.42
5.40
5.46
5.29
-Mbol 1
-Mbol 2
7.53
7.24
8.44
7.36
8.54
7.44
8.51
7.49
7.96
9.74
8.11
8.11
8.21
9.76
8.36
9.74
8.49
9.64
8.64
9.44
8.86
8.81
8.96
8.64
-Mvis 1
-Mvis 2
3.9
3.95
6.10
4.32
6.00
4.33
7.5
4.40
7.50
7.80
7.60
8.40
7.20
8.34
7.40
6.40
7.79
4.50
7.94
6.19
8.16
5.56
7.76
5.39
5.21
4.60
5.13
4.59
5.05
4.59
5.03
4.58
5.00
4.59
4.57
4.53
4.46
4.50
5.22
5.30
4.86
5.31
4.65
5.32
4.56
5.32
4.46
5.35
5.36
5.40
5.44
5.48
8.36
8.56
7.46
8.59
6.94
8.61
6.71
8.64
6.46
8.68
8.71
8.81
8.91
9.01
3.90
5.06
3.86
5.06
2.96
5.11
2.46
5.14
2.21
5.16
5.06
5.06
5.31
5.06
Wolf-5D\HW(YUHVLQLQ%DúODJÕFÕ
M
8.330
N
8.454
P
8.654
11.32
35.18
7.69
35.10
5.28
Q
8.779
4.70
R
8.880
4.27
S
T
U
V
10.000
11.000
12.000
12.540
34.66
34.03
32.92
32.39
ùHNLO J|UVHO E|OJHGH EDú YH \ROGDúÕQ DUDVÕQGDNL J|UQU SDUODNOÕN IDUNODUÕQÕ J|VWHUPHNWHGLU 3DUODNOÕN
IDUNÕQÕQ m
¶GHQ D] ROGX÷X GXUXPGD KHU LNL ELOHúHQLQ GH \DOQÕ]FD J|UVHO E|OJHGH J|UQG÷ YDUVD\ÕPÕ\OD
,
KDQJL ELOHúHQLQ EDú \ROGDú \D GD KHU LNLVL GH J|UVHO E|OJHGH J|UOHELOHFH÷LQL EHOLUOH\HELOLUL] ùHNLO
DQDNROGD D\UÕN HYUH VUHVLQFH KHU LNL ELOHúHQLQ GH J|UQU ROGX÷XQX RUWD\D NR\PDNWDGÕU %Dú \ÕOGÕ]ÕQ
E]OPH HYUHVL ER\XQFD SDUODNOÕN IDUNÕ
1m’in üstündedir, E|\OHFH \DOQÕ]FD EDú \ÕOGÕ] J|UOHELOLU Kütle
Kütle
DNWDUÕPÕQÕQ EDúODPDVÕQGDQ KHPHQ VRQUD \ROGDúÕQ ÕúÕWPDVÕ DUWDU YH E|\OHFH KHU LNL ELOHúHQ GH J|UOU
DNWDUÕPÕQGDQ VRQUD KHO\XP \DNDQ \ÕOGÕ]ÕQ ÕúÕWPDVÕ DUWÕN J|UVHO E|OJHGH J|UOU RODQ \ROGDúÕQÕQNLQGHQ oRN
–
GDKDGúNWU$UWÕNVLVWHPJ|UOPH\HQELU:ROI 5D\HWELOHúHQOLELU2
-türü\ÕOGÕ]GÕU
52
ùHNLO %LU 0
çiftinin, NWOH DNWDUÕPÕQGDQ KHPHQ |QFH DNWDUÕP VÕUDVÕQGD YH VRQUDVÕQGD EDú YH \ROGDú
ELOHúHQOHULQLQ J|UVHO SDUODNOÕNODUÕ DUDVÕQGDNL IDUN $QDNROGD D\UÕN HYUH VÕUDVÕQGD KHU LNL ELOHúHQ GH J|UQUGU .ÕUPÕ]Õ
UHG SRLQW LOH PDYL QRNWD %3 EOXH SRLQW DUDVÕQGD ∆0 IDUNÕ P¶GHQ ID]ODGÕU YH E|\OHFH \DOQÕ]FD EDú \ÕOGÕ]
görülür..WOHDNWDUÕPÕQGDQKHPHQVRQUD\ROGDúÕQÕúÕWPDVÕDUWDUYHE|\OHFHKHULNLELOHúHQGHJ|UOU.WOHDNWDUÕPÕQGDQ
QRNWD 53
VRQUD KHO\XP \DNDQ \ÕOGÕ]ÕQ ÕúÕWPDVÕ DUWÕN J|UVHO E|OJHGH J|UOU GXUXPGD RODQ \ROGDúÕQ ÕúÕWPDVÕQGDQ oRN GDKD
örülmeyen bir Wolf –5D\HWELOHúHQOLELU2-WU\ÕOGÕ]GÕU
GúNWU$UWÕNVLVWHPJ
53
BÖLÜM 18
<$.,1dø)7(95ø0ø1ø1621$ù$0$/$5,
18*LULú
<DNÕQ oLIWOHULQ NDUDUOÕ QNOHHU \DQPD VUHoOHULQLQ VRQXQGDNL NDGHUOHUL EDú \ÕOGÕ]ÕQ NWOHVLQH ED÷OÕGÕU (÷HU
NDOÕQWÕ&KDQGUDVHNKDUOLPLWLQLQDOWÕQGDNDOÕ\RUVDRELUEH\D]FFHGLU(÷HU \ROGDúWDQ5RFKHOREXQXGROGXUPDVÕ
GXUXPXQGDELUNWOHDNWDUÕPÕV|]NRQXVXLVHELUSDWODPDPH\GDQDJHOHELOLUEX
na7LS,VSHUQRYDVÕ denir. (÷HU
veya bir kara delik
NDOÕQWÕ&KDQGUDVHNKDUOLPLWLQLDúÕ\RUVD7LS,,VSHUQRYDVÕROXúXUYHNDOÕQWÕELUQ|WURQ\ÕOGÕ]Õ
RODELOLU\DGDJHUL\HKLoELUNDOÕQWÕNDOPD\DELOLU
7LS ,D VSHUQRYDODUÕ ELU EH\D] FFH ND\QDNOÕGÕUODU (÷HU R ELU oLIW VLVWHPLQ \HVL LVH QRUPDO ELU \ÕOGÕ] RODQ
,
Beyaz cücenin yüzeyi öyle güçlü bir úHNLOGH ÕVÕQÕU NL
kadar güçlü nükleer reaksiyonlar meydana gelir. Bu nedenle bu tür süpernovalar çok
\ROGDúWDQ EH\D] FFHQLQ \]H\LQH PDGGH DNWDUÕODELOLU
\ÕOGÕ]Õ IHODNHWH X÷UDWDFDN
SDUODNWÕU
7LS ,, YH PXKWHPHOHQ 7LS ,E VSHUQRYDODUÕ Lo NÕVPÕQGD EWQ PDGGHQLQ GHPLUH G|QúPú ROGX÷X E\N
NWOHOLELU\ÕOGÕ]ÕQSDWODPDVÕVRQXFXQGDROXúXUODU<ÕOGÕ]E]OUYHSDWODU1RUPDORODUDN\ÕOGÕ]SDWODGÕ÷ÕQGDELU
NÕUPÕ]Õ
süper devdir.
<ÕOGÕ] \DNODúÕN RODUDN ¶VL KLGURMHQGHQ LEDUHW RODQ VH\UHOPLú ELU GÕú NDWPDQD VDKLSWLU
a hidrojen çizgileri görülür. 7LS , YH 7LS ,, VSHUQRYDODUÕQ ÕúÕN H÷ULOHUL
4.5’teJ|VWHULOPLúWLU
%X úHNLOGH SDWOD\DQ ELU \ÕOGÕ]ÕQ WD\IÕQG
DUDVÕQGDNLIDUNOÕOÕNODUùHNLO
Tayfsal gözlemlerden elde edilen verilere göre, patlayan
104 km s-1 PHUWHEHVLQGHNL KÕ]ODUOD X]D\D DWÕOÕU $WÕODQ NDWPDQODU ELU NDo JQ LoHULVLQGH
NDOÕQWÕVLVWHPLWHUNHWPLúROXUYHDUWÕN|QHPOLELUHWNLJ|VWHUemezler.
3DWODPD PH\GDQD JHOGL÷LQGH \|UQJH |÷HOHUL GH÷LúLU
\ÕOGÕ]ÕQ GÕú NÕVÕPODUÕ
%XQXQODELUOLNWHSDWODPDNUHVHORODUDNVLPHWULNGH÷LOGLU6SHUQRYDNDOÕQWÕODUÕDVOD
tam olarak küresel simetrik
GH÷LOOHUGLU YH E\N DVLPHWULOHU J|VWHULUOHU 'RSSOHU ND\PDODUÕQGDQ HOGH HGLOHQ KÕ] |OoPOHUL JHQLúOHPHQLQ Hú
\|QOGD÷ÕOPDGÕ÷ÕQÕ RUWD\D NR\PDNWDGÕU 'DKDVÕJ|NDGDG]OHPLHWUDIÕQGDNLDWDUFDODUÕQGD÷ÕOÕPÕEX \ÕOGÕ]ODUÕQ
GR÷XPODUÕ VÕUDVÕQGD HNVWUDGDQ \DNODúÕN RODUDN NP
(Gunn ve Ostriker, 1970; Ruderman, 1972).
2ODVÕ HOHNWURPDQ\HWLN HWNLOHU YH SDWOD\DQ \ÕOGÕ]ÕQ G|QPHVL
VRQXFXQGDGÕúNDWPDQODUÕQÕQDWÕOPDVÕVÕUDVÕQGDJ|
RUWD\DoÕNDQEXHNVWUDWHNPHJ|VWHUL
s-1¶OLN ELU |] KDUHNHW ND]DQGÕNODUÕQÕ RUWD\D NR\PDNWDGÕU
zlenen asimetrilerLQQHGHQLRODUDNDWDUFDQÕQGR÷XPXVÕUDVÕQGD
lir.
3DWODPDQÕQ ELU VRQXFX RODUDN EDú \ÕOGÕ]ÕQ GÕú NÕVÕPODUÕQÕQ DWÕOPDVÕ YH DWÕODQ EX NDWPDQODUÕQ GL÷HU ELOHúHQH
oDUSPDVÕ\ODoLIWVLVWHPLQ\|UQJHVLGH÷LúL
r.
9DUVD\ÕPODU
Bir patlama öncesi sistemin, \|UQJH GH÷LúLPOHUL LOH VRQ DúDPD GDYUDQÕúODUÕQÕQ KHVDSODQPDVÕ LoLQ JHQHOOLNOH
DúD÷ÕGDNLEDVLWOHúWLULFLYDUVD\ÕPODU\DSÕOÕU
1. VSHUQRYDSDWODPDVÕoLIWLQ\|UQJHG|QHPLQHJ|UHNÕVDRODQELU]DPDQGLlimi içerisinde olur;
2. SDWODPDVÕUDVÕQGDROXúDQQ|WURQ\ÕOGÕ]Õ\DNODúÕNRODUDN– 2 MFLYDUÕQGDELUNWOH\HVDKLSWLU
3. 6SHUQRYD NDEX÷XQXQ DWÕOPDVÕQGDNL DVLPHWULOHUL KHVDED NDWPDN DPDFÕ\OD, ROXúXPX VÕUDVÕQGD nötron
-1
\ÕOGÕ]ÕQÕQNDEX÷XQRUWD\DoÕNWÕ÷ÕEDú \ÕOGÕ]ÕQPHUNH]LQHJ|UH vn = 100 km s ’lik göreli ELU|]KDUHNHWND]DQGÕ÷Õ
kabul edilir. MRPHQWXPXQ NRUXQXPXQHGHQL\OH NUHVHO VLPHWULN RODUDN DWÕODQ NDWPDQODUWHUV \|QGH vs = vn Mn/
MsLOHYHULOHQELUKÕ]HOGHHGHUOHUEXUDGDMn ve MsVÕUDVÕ\ODQ|WURQ\ÕOGÕ]ÕQÕQYHNDEX÷XQNWOHVLGLU
)ÕUODWÕODQ Hú PHUNH]OL GÕú NÕVÕPODUÕQ KÕ] YH \R÷XQOXNODUÕQÕQ Hú \|QO RODUDN GD÷ÕOGÕ÷Õ YDUVD\ÕOÕU 'DKDVÕ EX
katmanlar, NDOÕQWÕ oLIW VLVWHPL WHUN HGLQFH÷H YH GROD\ÕVÕ\OH KHU KDQJL ELU |QHPOL HWNLOHUL NDOPD\ÕQFD\D Nadar bu
GXUXPXQGH÷LúPHGHQNRUXQGX÷Xkabul edilir.
%X LVH IÕUODWÕODQ NDWPDQODUÕQ NUHVHO VLPHWULVL GLNNDWH DOÕQGÕ÷ÕQGD \ROGDúÕQ \|UQJHVLQLQ Lo NÕVPÕQGDNL
JHQLúOH\HQ NDWPDQODUÕQ QRNWD NWOH RODUDN
dikkate
DOÕQDELOHFH÷L DQODPÕQD JHOLU \ROGDúÕQ \|UQJHVLQLQ GÕú
NÕVPÕQGDNLNDWPDQODUÕQVLVWHP]HULQHKHUKDQJLELUHWNLVL\RNWXU
54
+HO\XP\ÕOGÕ]ODUÕQÕQVRQDúDPDVÕ
(YULPKHVDSODPDODUÕ0
¶LQ DOWÕQGD NWOH\H VDKLS RODQKHO\XP \ÕOGÕ]ODUÕQÕQKHO\XP NDEXN \DQPDVÕ VÕUDVÕQGD
JHQLúOH\HUHN DOW GHY \D GD VSHUGHYOHUH HYULPOHúHELOHFHNOHULQL J|VWHUPHNWHGLU E|\OHFH 5RFKH OREODUÕQGDQ ELU
NHUH GDKD WDú
arak
]DUIODUÕQÕ NÕVPHQ \D GD EHONL
de tamamen kaybederler. dLIW VLVWHPOHUGH E|\OHVL HYULPOHúPH
|UQHNOHUL.HVLP¶GHYHULOPLúWLU
,
sistematik olarak inceleyelim (bkz. Nomoto, 1981; Habets, 1983).
ùLPGL KHO\XP \ÕOGÕ]ODUÕQÕQ LOHUL HYULPOHULQL KHP WHN \ÕOGÕ]ODU KHP GH ELU oLIW VLVWHPLQ ELOHúHQOHUL GXUXPX LoLQ
18.3.1. MHe < 2 M DURUMU
a)
7HN\ÕOGÕ]ODU
KabukdaKLGURMHQ\DQPDVÕVÕUDVÕQGD&2-oHNLUGH÷L\R]ODúÕUYHGÕúNDWPDQODUNÕVDELU]DPDQ|OoH÷LQGHJHQLúOHU C
\DQPDVÕ EDúODU EDúODPD] WP oHNLUGHN \DQDU NDUERQ DQL \DQPDVÕ YH VRQXQGD GD ELU VSHUQRYD PXKWHPHOHQ
7LS,VSHUQRYDVÕRODUDNSDWODU$UQHWWYHJHUL\HKLoELUNDOÕQWÕNDOPD]
b) Çift sistemler
ÇiIWVLVWHPGXUXPXQGDGHYELOHúHQLQ]DUIÕQÕQ\ROGDúÕQDDNWDUÕOPDVÕQHGHQL\OHDQL\DQPDROXúPD] vH\DOQÕ]FDELU
CO beyaz cücesi meydana gelir.
18.3.2. 2 M < MHe < 2.3 M DURUMU
çok JoOELUúHNLOGH\R]ODúPDPÕúWÕU ve kaUERQGDKDVDNLQELUúHNLOGH\DQDUDN
geride 1.2 – 1.4 MNWOHDUDOÕ÷ÕQGDNLGHMHQHUHELU2- Ne -0JoHNLUGH÷LEÕUDNÕU +HO\XPoHNLUGH÷LQGÕúÕQGDNL
NÕVÕPODUGD \DNÕOÕUoHNLUGH÷LQ NWOHVL DUWDU YH ]DUI JHQLúOHU.DOÕQWÕ – 1.4 M
kütleli bir O - Ne - Mg beyaz
cücesidir.
%XGXUXPGD&2oHNLUGHNNDOÕQWÕVÕ
a)
7HN\ÕOGÕ]ODU
- Ne - 0J oHNLUGH÷LQLQ
,
Elektron yakaODPDVSHUQRYDVÕVRQXQGDELUQ|WURQ\ÕOGÕ]ÕROXúWXUXU
.DEXNWD KHO\XP \DQPDVÕ QHGHQL\OH 2
Chandrasekhar limitine
yüksek olur ve zarf çöker.
NWOHVL DUWDU
XODúÕOGÕ÷ÕQGD PHUNH]L\H÷LQOLN0J]HULQGHHOHNWURQ\DNDODQPDVÕQD\RODoDFDNGHQOL
b) Çift sistemler
5RFKHOREXWDúPDVÕPH\GDQDJHOLUYH]DUIDWÕOÕU
18.3.3. MHe > 2.3 M DURUMU
- Ne - 0J oHNLUGH÷L, &KDQGUDVHNKDU OLPLWLQL DúDU YH EWQ oHNLrdek
Sonunda, çekirdeNOHULQ SDUoDODQPDVÕ (photodisintegration) nedeniyle
.DUERQ \DQPDVÕQGDQ VRQUD JHUL\H NDODQ 2
\DQPDVÕ HYUHOHULQGHQ JHoHUHN HYULPOHúLU
çöken ELU)HoHNLUGH÷LROXúXUYHELUQ|WURQ\ÕOGÕ]Õ\DGDELUNDUDGHOLNPH\GDQDJHOLU
a)
7HN\ÕOGÕ]ODU
Kütleleri 2.8 M¶GHQE\NRODQ\ÕOGÕzlar,ELUoHNLUGHNSDUoDODQPDVÕVSHUQRYDVÕGXUXPXQDHYULPOHúLUOHU
b) Çift sistemler
55
<DNODúÕN 0
¶GHQ E\N NWOHOL JHQLú oLIWOHU – JQ G|QHPOL oHNLUGHN SDUoDODQPDVÕ VSHUQRYDVÕ
GXUXPXQD HYULPOHúLUOHU =DUIÕQ 5RFKH OREX WDúPDVÕ\OD DWÕOPDVÕQGDQ |QFH NDEXNWD KHO\XP \DQPDVÕ \ROX\OD
E\PHVLLoLQoHNLUGHNGDKDD]]DPDQDVDKLSROGX÷XQGDQNÕVDG|QHPOLoLIWOHU
Özetle,
deEXVÕQÕU0’dir.
4 M < M1 < 8 M DUDOÕ÷ÕQGD, \DNÕQ oLIW VLVWHPOHULQ EDú \ÕOGÕ]ODUÕ WHN \ÕOGÕ]ODUGD
< M1 < 10-14 M
DUDOÕ÷ÕQGD LVH \DNÕQ oLIWOHULQ EDú \ÕOGÕ]ODUÕ ELU 2-Ne-0J EH\D] FFHVL ROXúWXUXUODUNHQ, WHN \ÕOGÕ]ODU HOHNWURQ
EDúODQJÕo NWOHVLQLQ
ROGX÷XJLELDQLNDUERQWXWXúPDVÕQDHYULPOHúPHN\HULQHELU&2EH\D]FFHVLROXúWXUXODU0
\DNDODPDo|NPHVLQHHYULPOHúLUOHUYHVRQXQGDGDQ|WURQ\ÕOGÕ]ÕROXUODU
.DUERQ \DQPDVÕQGDQ VRQUDNL 2
-Ne-0J NDOÕQWÕVÕ &KDQGUDVHNKDU OLPLWLQL DúDU YH VRQXo RODUDN GD WP oHNLUGHN
\DQPDDúDPDODUÕQGDQJHoHU(QVRQRODUDNIRWRQODoHNLUGHNSDUoDODQPDVÕ\ROX\ODo|NHQELU)HoHNLUGH÷LROXúXU
ve bir nötron\ÕOGÕ]Õ\DGDELUNDUDGHOLNPH\GDQDJHOLU
%LU oLIW VLVWHP GXUXPXQGD ]DUIÕQ ELU NÕVPÕ \D GD WDPDPÕ ND\EHGLOLU oHNLUGHN WÕSNÕ ELU WHN \ÕOGÕ]GDNL JLEL
GDYUDQÕU YHVRQXQGDELUQ|WURQ\ÕOGÕ]ÕROXúXU
Son derece büyük çekirdek kütleleri (M > 60 M, yaklaúÕN 0¶OLN ELU WRSODP NWOH\H NDUúÕOÕN JHOLU
GXUXPXQGDoHNLUGHNoLIWROXúXPo|NPHVLQHHYULPOHúLUYHPXKWHPHOHQne tek,QHGHoLIW\ÕOGÕ]GXUXPXnda geride
ELUNDOÕQWÕEÕUDNPD]
18.4. Tip II –'úNNWOHOL;-ÕúÕQoLIWOHUL/0;5%
/0;5%¶/(5ø1g=(//ø./(5ø
DúN NWOHOL ND\QDNODU JHQHOOLNOH ]RQNODPD]ODU YH oR÷XQOXNOD J|NDGD PHUNH]L \DNÕQODUÕQGD \D GD NUHVHO
NPHOHUGHEXOXQXUODU2QODUÕQELUoR÷XSDWOD\ÕFÕGÕU\DQL;-ÕúÕQ\H÷LQOL÷LELUVDQL\HLoHULVLQGHELUNDoNDGLUNDGDU
artar ve bunu onlarca saniye süren azalma evresi izler. DúN NWOHOL VLVWHPOHUGHNL EDVNÕQ ÕúÕN ND\QD÷Õ
PXKWHPHOHQ \ROGDúÕQ DWWÕ÷Õ PDGGH LOH EHVOHQHQ ELU \Õ÷ÕúPD GLVNLGLU G|NDGD úLúLPindeki kaynaklar ile küresel
NPHOHUGHNL ND\QDNODUÕQ EHQ]HUOL÷L, RQODUÕQ WHN ELU VÕQÕI ROXúWXUGXNODUÕQÕ RUWD\D NR\PDNWDGÕU 'DKDVÕ SDWOD\ÕFÕ
kaynaklarÕQ optik tayflarÕ, bir X-ÕúÕQoLIWLRODQ YH Balmer salma çizgili bir mavi süreklilik ile He II (4686 Å), N
III ve C III (4640 Å) salma çizgileri gösteren Sco X-1’i QWD\IÕQDEHQ]HPHNWHGLU
Bu tayf, NDWDNOLVPLN GH÷LúHQOHUGHNL \Õ÷ÕúPD GLVNi tayflarÕQD da benzemektedir. <ROGDúÕQ GúN ÕúÕWPDVÕ YH 6FR
X-¶LQ NÕVD G|QHPL JQ VÕNÕúÕN ROPD\DQ \ÕOGÕ]ÕQ SDWOD\ÕFÕ \ÕOGÕ]ODUÕQ J|UQPH\HQ ELOHúHQOHULne benzer
olarak ELUNÕUPÕ]ÕFFHROGX÷XQXDNODJHWLUmektedir.
18.4.2. KÜRESEL KÜME KAYNAKLARI
Küresel kümelerde X-ÕúÕQND\QDNODUÕQÕQROXúXPRUDQÕ\NVHNWLUNPHGHND\QDNJ|]OHQPLúROXSEXRUDQ,
37
J|NDGD RUWDODPDVÕQGDQ oRN GDKD \NVHNWLU Tüm gökadada, ÕúÕWPDODUÕ 10
erg s-1 GH÷HULQL DúDQ ÕúÕWPDQÕQ EX
-8
-1
GH÷HUL ×10
M \ÕO GH÷HULQGH ELU NWOH ND\EÕ RUDQÕQD NDUúÕOÕN JHOLU 100 FLYDUÕQGD X-ÕúÕQ ND\QD÷Õ
bilinmektedir.
105 – 106 \ÕOGÕ]SF3JLEL \NVHN \R÷XQOXNODUGD \DNÕQoDUSÕúPDODU YH \DNDODPDODU \ROX\ODoLIW VLVWHP ROXúXPX
J|NDGDQÕQGL÷HU \HUOerine göre GDKD \NVHNELURODVÕOÕ÷D VDKLSWLU <ÕOGÕ]ODUÕQ J|UHOL KÕ]ODUÕNoNWU YHE|\OHFH
\ÕOGÕ] \DNDODPD VÕUDVÕQGD gerekli olan az miktardaki enerji ]DWHQ LON oDUSÕúPD VÕUDVÕQGD \HWHULQFH ND]DQÕOPÕú
ROPDNWDGÕU
.UHVHO
NPH
ND\QDNODUÕ
PXKWHPHOHQ
QRUPDO
ELU
\ÕOGÕ]ÕQ
ELU
Q|WURQ
\ÕOGÕ]Õ
WDUDIÕQGDQ
yDNDODQPDVÕ\OH ROXúPXúODUGÕU 4 – 5 M DUDOÕ÷ÕQGDNL WHN \ÕOGÕ]ODU HQLQGH VRQXQGD oDUSÕúDFDNODUÕQGDQ NUHVHO
8
NPHOHUGH ROXúXPODUÕQÕQ LON \ÕOÕ LoHULVLQGH ELQOHUFH Q|WURQ \ÕOGÕ]ÕQÕQ ROXúPDVÕ EHNOHQLU Bu nötron
\ÕOGÕ]ODUÕQÕQEHOOLELUNHVULNPH\LWHUNHWPLúROVDGDNoNELURUDQKDOHQPHYFXWWXU Onlar, kümedeki ortalama
\ÕOGÕ] NWOHVLQL DúDQ NWOHOHUH VDKLSWLUOHU YH EX QHGHQOH GH NPHQLQ PHUNH]LQdH \Õ÷ÕOPÕúODUGÕU <ÕOGÕ]
\R÷XQOX÷XQXQYHoDUSÕúPDRODVÕOÕ÷ÕQÕQ\NVHNROGX÷X\HUOHUGH\ÕOGÕ]\DNDODPDVUHoOHULPH\GDQDJHOHELOLU
%LU NUHVHO NPHGHQ NDoPD KÕ]Õ \DNODúÕN RODUDN NP
s-1’dir.
5DG\R DWDUFDODUÕ GR÷XPODUÕ VÕUDVÕQGD HNVWUD ELU
LWPH ND]DQGÕNODUÕQGDQ J|UHFHOL RODUDN GDKD \NVHN KÕ]ODUD VDKLSWLUOHU
YalnÕ]FD KÕ]ODUÕ NDoPD KÕ]ÕQGDQ daha
,
NoNRODQHQ \DYDúQ|WURQ \ÕOGÕ]ODUÕNPHGHNDOÕUODUdR÷XQ|WURQ \ÕOGÕ]ÕQÕQ E\NNDoDNKÕ]ODUÕPXKWHPHOHQ
56
oLIW VLVWHPOHULQHYULPOHúPLú ELOHúHQOHULQLQ SDWODPDVÕYH VLVWHPLQGD÷ÕOPDVÕQÕQ ELU VRQXFXGXUGúN KÕ]OÕQ|WURQ
\ÕOGÕ]ODUÕLVHWHN\ÕOGÕ]ODUÕQ
evrimlerinin son evreleridir.
(YULPOHULQH oLIW VLVWHPOHUGH EDúOD\DQ NUHVHO NPHOHUGHNL Q|WURQ \ÕOGÕ]ODUÕ VLVWHPLQ GD÷ÕOPDVÕ\OD WHN \ÕOGÕ]
haline gelebilir ve kümeyi terk edebilirler.7HN \ÕOGÕ]ODUÕQNPHGHNDODQQ|WURQ \ÕOGÕ]ÕNDOÕQWÕODUÕLVHGDKDVRQUD
ELUELOHúHQ\DNDOD\DELOLUYHEXVXUHWOHGúNNWOHOL;-ÕúÕQoLIWOHULQHHYULPOHúHELOLUOHU
18.4.3 *g.$'$ùøùø0.$<1$./$5,
*|NDGDúLúLPLQGHNL\ÕOGÕ]ODUNUHVHONPHOHUGHNLQGHQGDKDE\NKÕ]ODUDVDKLSWLUOHU'DKDVÕ \ÕOGÕ]\R÷XQOX÷X
,
Chandrasekhar limiti
– oksijen beyaz cücelerinin,Q|WURQ\ÕOGÕ]ODUÕGXUXPXQDo|NHELOHFHNOHULEXOXQPXúWXUYHD\QÕ
úH\LQ \DNÕQ oLIWOHUdeki O – Ne – 0J EH\D] FFHOHUL LoLQ GH JHoHUOL ROGX÷X J|UOPHNWHGLU Sistemler genellikle
ED÷OÕVÕQÕUOÕNDOÕUODU0XKWHPHOHQ, bu X-ÕúÕQND\QDNODUÕNDWDNOLVPLNGH÷LúHQOHULQHYULPVHOUQüdürler.
oRN GDKD GúNWU EX QHGHQOH \ÕOGÕ] \DNDODPDVÕ oRN ]RUGXU IDNDW J|] DUGÕ GD HGLOHPH]
\DNÕQÕQGDNLNDUERQ
X-ÕúÕQSDWOD\ÕFÕODUÕQÕQJ|]OHmsel karakteristikleri, bunlardaDQLWHUPRQNOHHUWHSNLPHOHU\DQLQ|WURQ\ÕOGÕ]ODUÕQÕQ
\]H\OHULQGH KHO\XP ELUOHúPHOHUL ROGX÷XQX J|VWHUPHNWHGLU 'úN NWOHOL VÕIÕU \Dú DQDNRO oLIWOHUL ELU NWOH
– oksijen beyaz cücesi ile ELU QRUPDO \ÕOGÕ]GDQ
bir SDUODNOÕN
DUWÕúÕ J|VWHUmeleri NÕVD ELU VUH LoHULVLQGH ÕúÕWPD PDNVLPXPXQD XODúÕp VRQUD GD oRN GDKD \DYDú ELU úHNLOGH
ROPDN NRúXOX\OD HVNL SDUODNOÕNODUÕQDG|Qmeleri nedeniyle, birerNDWDNOLVPLN GH÷LúHQGLUOHU%H\D] FFH ELOHúHQLQ
HWUDIÕQGD ELU \Õ÷ÕúPD GLVNL YDUGÕU .WOH DNWDUÕPÕ QHGHQL\OH EH\D] FFHQLQ NWOHVL DUWDU YH EX da elektron
\DNDODPDo|NPHVLQHYHELUQ|WURQ\ÕOGÕ]ÕQÕQROXúPDVÕQDQHGHQROXU%X\ROODVLVWHPELUGúNNWOHOL;-ÕúÕQoLIWL
olabilir. Bu son durum sonraki kesimde incelenecektir.
DNWDUÕP HYUHVLQGHQ JHoPHN VXUHWL\OH ELU KHO\XP \D GD NDUERQ
ROXúDQYHG|QHPOHULVDDWFLYDUÕQGDRODQVLVWHPOHUHHYULPOHúLUOHU %XDúDPDGDNLoLIWOHU\ÕOGÕ]ODUÕQ
18.5. 'úNNNWOHOL;-ÕúÕQoLIWOHULQLQRULMLQL
(95ø00$''($.7$5,0,
-
'úN NWOHOL ; ÕúÕQ oLIWOHUL YH oR÷X NDWDNOLVPLN GH÷LúHQOHU GúN NWOHOL QRUPDO \ROGDúÕQGDQ PDGGH
çöNPú ELU \ÕOGÕ] GHMHQHUH ELU FFH ELU Q|WURQ \ÕOGÕ]Õ ya da bir kara delik) içerirler. øNL
li =$06 ELOHúHQLQGHQ EDúOD\DQ ELU HYULP VHQDU\RVX ùHNLO ¶GH J|VWHULOPLúWLU %Dú \ÕOGÕ] 5RFKH
\Õ÷ÕúWÕUPDNWD RODQ
GúN NWOH
OREXQX GROGXUPXúWXU NWOH DNWDUÕPÕ ELU RUWDN ]DUIÕQ ROXúPDVÕQD \RO DoDU YH EX ]DUI GDKD VRQUDNL DúDPDODUGD
-cücesi ile bir normal
ir. %X HYUHGH VLVWHP NDWDNOLVPLN GH÷LúHQ RODUDN DGODQGÕUÕOÕU 6RQUDNL ELU DúDPDGD DUWÕN
normal olarak \ROGDú ELOHúHQRODQ úLPGLNL EDú \ÕOGÕ]ÕQ5RFKH OREXQXGROGXUDFD÷ÕQÕYH \DUÕ-D\UÕNHYUHVUHVLQFH
\ROGDúÕQD PDGGH DNWDUDFD÷ÕQÕ GúQHELOLUL] %X DúDPDGDQ Vonra sistem, bir He- ya da CO-FFHVL LOH \ÕOGÕ]
U]JDUODUÕ\ODNWOHND\EHWPHNWHRODQELUNÕUPÕ]ÕGHYELOHúHQLoHUPHNWHGLU <ROGDú5RFKHOREXQXGROGXUXUYH&2-
JHQLúOH\HUHN J|UQPH] ROXU 2UWDN ]DUIÕQ ND\EROPDVÕQGDQ VRQUD VLVWHP ELU +H \D GD &2
\ROGDú \ÕOGÕ] LoHUPHNWHG
FFHVLQHGR÷UXRODQNWOHDNWDUÕPÕRQXQNWOHVLQLQDUWPDVÕQDQHGHQROXU
<Õ÷ÕúDQ PDGGH WDUDIÕQGDQ
kenGL &KDQGUDVHNKDU OLPLWLQL DúPD\D ]RUODQDQ EH\D] FFH bir elektron yakalama
o|NPHVLQH X÷UD\DELOLU &DQDO YH 6FKDW]PDQ YH &DQDO ,VHUQ YH /DED\ WDUDIÕQGDQ \DSÕODQ
KHVDSODPDODU
&KDQGUDVHNKDU
]RUODQDELOHFH÷LQLJ|VWHUPLúWLU
OLPLWLQH
oRN
\DNÕQ
RODQ
ELU
&2
-cücesinin bu anlamda bir çöküntüye
57
-
ùHNLO'úNNWOHOL; ÕúÕQoLIWOHULLoLQRODVÕVHQDU\R
Çift sistemlerdeki 3 – 8 M
56
51
erg mertebesinde olan
DoDELOHQ \R]ODúPÕú &- \DQPDVÕ ROXU YH PDGGH
1L¶H G|QúU Üretilen ve yDNODúÕN HQHUML EH\D] FFH\L GD÷ÕWPD\D \HWHFHN E\NONWHGLU Özel NRúXOODU DOWÕQGD NDUERQ NDEXNWD \DNÕOGÕ÷ÕQGD
NoN ELU NDOÕQWÕ NDODELOLU 7DDP DE 1RPRWR Bir CO-FFHVLQLQ EX QNOHHU SDWODPDVÕ WDP \D GD
%LUEH\D]FFHQLQNWOH\Õ÷ÕúPDVÕQDNDUúÕWHSNLVLEH\D]FFHQLQNDUÕúÕPÕQDED÷OÕGÕU
DUDOÕ÷ÕQGDNL NWOHOHUH VDKLS RODQ EDú \ÕOGÕ]ODUÕQ NDOÕQWÕODUÕ RODQ &2 EH\D] FFHOHULQGH WHUPRQNOHHU NDoD÷D \RO
NÕVPHQPXKWHPHOHQELUWLS,VSHUQRYDVÕLOHELUWXWXODELOLU
– 0J EH\D] FFHOHUL LoLQ oHNLUGHN \R÷XQOX÷X HOHNWURQ \DNDODPD HúLN
Bu da elektron –\DNDODPDo|NPHVLQHYHELUQ|WURQ\ÕOGÕ]ÕQÕQROXúPDVÕQDQHGHQROXU
(Miyaji ve ark. 1980, Sugimoto ve Nomoto, 1980).
'L÷HU WDUDIWDQ PDGGH \Õ÷ÕúWÕUDQ 1H
GH÷HULQLQ|WHVLQHDUWDELOLU
Belki de en önemli etken budur.
%H\D]FFHELOHúHQLQVRQXQXEHOLUOH\HQGL÷HUELUHWNHQ\Õ÷ÕúPDQÕQRUDQÕGÕU
,
. 10-9 M\ÕO-1¶LQ DOWÕQGDNL \Õ÷ÕúPDRUDQODUÕLoLQ EXDQL SDUODPDODUR kadar güçlü olur ki,
\Õ÷ÕúDQ PDGGHQLQ oRN E\N NÕVPÕ EHONL GH WDPDPÕ IÕUODWÕOÕU, böylece beyaz cücenin kütlesi artmaz. Büyük
-9
\Õ÷ÕúPD RUDQODUÕ M\ÕO-1 - 10-8 M\ÕO-1 LoLQ DQLSDUODPDODU]D\ÕIWÕU, \Õ÷ÕúDQPDGGHQLQ oR÷X NDOÕU YH EH\D]
cücenin kütlesi artar. 4.10-8 M\ÕO-1¶GHQE\N\Õ÷ÕúPDRUDQODUÕLoLQELUNDUERQWXWXúPDVÕROXúXU
.oN \Õ÷ÕúPD RUDQODUÕ LoLQ ELULNWLULOHQ KLGURMHQ EHOLUOL ELU EDúODQJÕo NWOHVLQL DúWÕ÷ÕQGD JoO ELU QNOHHU DQL
parlama IODú ile
\DNÕOÕU
58
.h7/($.7$5,00(.$1ø=0$/$5,
üçlü LMXRB’ler için genellikle Roche lobu
cisim, VLVWHPLQ GDKD E\N NWOHOL ELOHúHQLGLU E|\OHFH NoN
NWOHOL ELOHúHQGHQRODQ NWOH DNWDUÕPÕ NDUDUOÕ RODFDNWÕU 5RFKHOREX WDúPDVÕLoLQ LNLPHNDQL]PD YDUGÕU çekimsel
'úNNWOHOL \ÕOGÕ]ODUÕQ JoO \ÕOGÕ]U]JDUODUÕRODPD\DFD÷ÕQGDQ J
WDúPDVÕ \ROX\OD NWOH DNWDUÕPÕ
gereklidir.
6ÕNÕúÕN
ÕúÕPDLOHDoÕVDOPRPHQWXPND\EÕ\DGDQNOHHUHYULP
/0;5%¶OHU LoLQ HYULP KLND\HVL úLPGLOLN WDP RODUDN DoÕN GH÷LOGLU %L] EXUDGD ED]Õ RODVÕ GXUXPODUÕ J|]GHQ
JHoLUHFH÷L]EN]ùHNLO¶GHNLHYULPVHQDU\RVX
-
$QDNROFFHVLQGHQ5RFKHOREXWDúPDVÕ
KüçükNWOHOL\R]ODúPÕú\ÕOGÕ]GDQ5RFKHOREXWDúPDVÕ
<R]ODúPDPÕúKHO\XP\ÕOGÕ]ODUÕQGDQ5RFKHOREXWDúPDVÕ
.ÕUPÕ]ÕGHYOHUGHQ5RFKHOREXWDúPDVÕ
*|]GHQJHoLULOHFHNELUoRNGXUXPLoLQ\DUÕoDSYHNWOHDUDVÕQGDELULOLúNLJHUHNOLGLUEX
amaçla
R =γ Mδ
(18.1)
úHNOLQGHELUED÷ÕQWÕNXOODQÕODFDN
ve fDUNOÕGXUXPODULoLQSDUDPHWUHOHULQIDUNOÕGH÷HUOHULDOÕQDFDNWÕU
$QDNROFFHVLQGHQ5RFKHOREXWDúPDVÕ
ani SDWODPDODUÕ J|VWHUHQ JHoLFL ND\QDNODUGÕU &HQ ;-4, Aql
X-1 gibi). Bu ani patlamalar PXKWHPHOHQ FFH QRYDODUÕQ DQL SDWODPDODUÕ\OD benzerdir (Robinson, 1976). Bu
geçici kaynaklardaki VÕNÕúÕN ROPD\DQ FLVLP 5RFKH OREX WDúPDVÕ\OD NWOH DNWDUDQ * – . WD\I WUQGHQ GúN
%LU oRN GúN NWOHOL ; ÕúÕQ oLIWL ND\QDNODUÕ ; ÕúÕQ
NWOHOLDQDNRO\ÕOGÕ]ODUÕRODUDNJ|UQUOHU
Bir K5 V
Çizelge 1.2’den elde edilebilir: kütle = 0.69 M\DUÕoDS R ELU Q|WURQ \ÕOGÕ]ÕQÕQ NWOHVL LoLQ – 1.5 M GH÷HUL DOÕQDELOLU %X GXUXPGD NWOH RUDQÕ YH 5RFKH
%L] EXUDGD ELU . FFHVL LOH ELU Q|WURQ \ÕOGÕ]ÕQGDQ ROXúDQ ELU VLVWHPLQ HYULPLQL J|]GHQ JHoLUHFH÷L]
\ÕOGÕ]ÕQÕQ\DUÕoDSYHNWOHVLLoLQWDKPLQLGH÷HUOHU
\DUÕoDSÕEN]GHQNOHP
R
= 0.38 + 0.2 log 0.5 = 0.32
A
(18.2)
olur.
<|UQJHQLQoHNLPVHOÕúÕPD
(GR)LOHGH÷LúPHVLLoLQJHUHNOLNDUDNWHULVWLN]DPDQ|OoH÷LED÷ÕQWÕVÕQGDQHOGH
edilebilir:
J yörünge
J yörünge
=−
32 G 3
M 1 M 2 (M 1 + M 2 ) A −4
5 c5
V
−
(18.3)
ve böylece
t GR = −
J yörünge
J yörünge
=
1.22 10 9 A 4
M 1M 2 (M 1 + M 2 )
\ÕO
olur, burada M1, M2 ve AJQHúELULPOHULQGHGLU
K cücesinin Roche lobunuGROGXUGX÷XQXYDUVD\DUVDN
(18.4)
59
A=
0.83
R ≅ 2.59 R
0.32 (18.5)
elde ederiz.%XQDNDUúÕOÕNJHOHQG|QHPLVHGHQNOHP¶GHQ
log P = 1.5 log A − 0.5 log( M1 + M 2 ) − 0.936 = −0.474
(18.6)
P ≅ 0.336 gün = 8.06 saat
olur.
Problem 18.1: G|] |QQH DOÕQDQ VLVWHP LoLQ oHNLPVHO ÕúÕPD ]DPDQ |OoH÷LQL KHVDSOD\ÕS, HOGH HWWL÷LQL] GH÷HUL
QNOHHU]DPDQ|OoH÷LLOHNDUúÕODúWÕUÕQÕ]
dHNLPVHO ÕúÕPD ]DPDQ |OoH÷L QNOHHU ]DPDQ |OoH÷LQLQ \DNODúÕN RODUDN
DNWDUÕPÕWDPDPHQ5RFKHOREX
üçte biri mertebesindedir böylece kütle
nun büzülmesiyle yönetilir.
Problem 18.2: Denklem 18.2’yi, 15.16’da yerine yazarak ve α
DODUDN NWOH DNWDUÕP KÕ]Õ LoLQ ELU WDKPLQ
\DSÕQÕ]
M
M
A
2
= 2( 1 − 1) 1 −
.
A
M2
M 1 t GR
(18.7)
<DUÕoDSLOHNWOHDUDVÕQGD
úHNOLQGHELUED÷ÕQWÕNDEXOHGLOLUVH
A
1 M
= (δ − ) 1
A
3 M1
HOGHHGLOLUYH ED÷ÕQWÕODUÕQÕQ NDUúÕODúWÕUÕOPDVÕQGDQ LVHNWOHDNWDUÕPKÕ]Õ
(18.8)
M 1
M1
LoLQ\DNODúÕNELULIDGH
elde edebiliriz. $QDNROFFHOHULLoLQED÷ÕQWÕVÕQGDγ = 1 ve δ =0.5DOÕQDELOLUE|\OHFH
M 1
1
1
=
M 1 tGR M 1 / M 2 − 13 / 12
(18.9)
ya da
M 1
1
1
≈
M 1 tGR M 1 / M 2 − 1
elde ederiz.
(18.10)
60
Problem 18.3: (18.3), (18.9) ve (15.13) ED÷ÕQWÕODUÕQÕ ELUOHúWLUHUHN NWOH DNWDUÕP KÕ]ÕQÕ, \ÕOGÕ] NWOHVLQLQ ELU
fonksiyonu olarak KHVDSOD\ÕQÕ] Çizelge 1.2’den yararlanarak, γ ve δ SDUDPHWUHOHUL LoLQ \XNDUÕGD |QHULOHQ
GH÷HUOHULGR÷UXOD\ÕQÕ]
%X GXUXP ELU DQDNRO FFHVL LoLQ NWOH DNWDUÕPÕQÕQ QHGHQ ROGX÷X oHNLPVHO ÕúÕPDQÕQ
M 1 ≈ 10 −10 M\ÕO-1
PHUWHEHVLQGHROGX÷XQXJ|VWHULU
X-ÕúÕQÕúÕWPDVÕ
LX =
GM X M
R
mertebeVLQGH NWOHVL \DNODúÕN 0 FLYDUÕQGDGÕU,
böylece küçük kütleli X-ÕúÕQ ND\QD÷Õ oLIWOHULQ ;-ÕúÕQ ÕúÕWPDODUÕ \DNODúÕN RODUDN 36 erg s-1 mertebesindedir. Bu
ise küçük kütleli parlak X-ÕúÕQ ND\QDNODUÕQÕ DoÕNODPD\D \HWHUOL GH÷LOGLU %LU PDQ\HWLN \ÕOGÕ] U]JDUÕQÕQ QHGHQ
-9
RODFD÷Õ G|QPH IUHQOHPHVL NWOH DNWDUÕPÕQÕ 10
M\ÕO-1 GH÷HULQLQ ELU NDo NDWÕQD NDGDU KÕ]ODQGÕUÕ\RU RODELOLU
(Verbunt ve Zwan, 1981).
ED÷ÕQWÕVÕ\OD YHULOLU %LU Q|WURQ \ÕOGÕ]ÕQÕQ \DUÕoDSÕ NP
.oNNWOHOL<R]ODúPÕú\ÕOGÕ]ODUGDQ5RFKHOREXWDúPDVÕ
9
-
%LU NÕUPÕ]Õ FFH Q|WURQ \ÕOGÕ]Õ VLVWHPLQLQ HYULPLQL \|QOHQGLUHQ oHNLPVHO ÕúÕPD \ÕOOÕN
olurken, QNOHHU ]DPDQ
10
|OoH÷LQLQ ]DPDQ |OoH÷L bir zaman öOoH÷LQGH
\ÕO PHUWHEHVLQGHGLU .WOH DNWDUÕPÕ QHGHQL\OH \ÕOGÕ]
=$06¶DSDUDOHORODUDNDúD÷Õ\DGR÷UXHYULPOHúLU
anakoluQ HQ DOWQRNWDVÕQD
, kütlesi ∼0.1 M \DUÕoDSÕ ∼0.2 R YH ÕúÕWPDVÕ GD ∼0.01 L’dir. %|\OHFH DUWÕN ÕVÕVDO ]DPDQ |OoH÷L
|QFHNLQLQ \DNODúÕN NDWÕ NDGDU YH EX QHGHQOH GH tGR LOH KHPHQ KHPHQ D\QÕ PHUWHEHGHGLU Tc NULWLN GH÷HULQ
DOWÕQD LQHFH÷LQGHQ PHUNH]L KMLGURMHQ \DQPDVÕ GXUXU &FH \ÕOGÕ] \R]ODúÕU %X GXUXPGD NWOH- \DUÕoDS LOLúNLVL,
.WOHQLQ D]DOPDVÕ\OD ÕVÕVDO ]DPDQ |OoH÷LGHGDKDKÕ]OÕ ELU úHNLOGH DUWDU &FHELOHúHQ
XODúWÕ÷ÕQGD
\DNODúÕNRODUDN
R = 0.013(1 + X ) 5 / 3 M −1 / 3 (Paczynski 1967a) ya da
R = 0.03M −1 / 3 (denklem 18.1’deki γ =0.03 ve δ =-GH÷HUOHULLoLQ
ED÷ÕQWÕODUÕ LOHU
verilir. R ≈ M −1 / 3 LOLúNLVL NWOHVL D]DOGÕ÷ÕQGD \ÕOGÕ]ÕQ JHQLúOH\HFH÷L DQODPÕQD JHOLU Bu ise
\|UQJHQLQ JHQLúOH\HFH÷LQL LPD HGHU DNVL WDNWLUGH \R]ODúPÕú GH÷HQ ELOHúHQ 5RFKH OREXQX WDúDUGÕ %|\OHFH
|QFHOHUL GDUDOÕ\RU RODQ \|UQJH \HQLGHQ JHQLúOHU EDúND ELU GH÷LúOH G|QHP ELU PLQLPXP GH÷HUH GR÷UX NÕVDOÕU
3DF]\QVNL YH 6LHQNLHZLF] YH :HEELQN YH DUN WDUDIÕQGDQ \DSÕODQ KHVDSODPDODU EX PLQLPXP
G|QHPLQ \DNODúÕN RODUDN GN ROGX÷XQX RUWD\D NR\PXúWXU <R]ODúPÕú KHO\XP \ÕOGÕ]ÕQÕQ \DUÕoDSÕ D\QÕ NWOHOL
bir H-]HQJLQ\R]ODúPÕúFFH\ÕOGÕ]ÕQ \DUÕoDSÕQGDQoRNGDKDNoNWU\DNODúÕNRODUDN \DUÕVÕNDGDU'ROD\ÕVÕ\OD
yörüngesi de daha küçük olabilir. 5RFKH OREX WDúPD HYUHVL VÕUDVÕQGD ELU +H EH\D] FFHVLQGHQ ELU Q|WURQ
-8
-1
\ÕOGÕ]ÕQDRODQNWOHDNWDUÕPKÕ]Õ M \ÕO GH÷HULQHXODúDELOLUYHEXGH÷HUSDUODNELU;-ÕúÕQND\QD÷ÕQÕQJFQ
DoÕNOD\DELOLU
<R]ODúPDPÕúELUKHO\XP\ÕOGÕ]ÕQGDQ5RFKHOREXWDúPDVÕ
-
,VÕGHQJHVLQGHNLVDIKHO\XPGDQROXúPXú\ÕOGÕ]ODUÕQ\DNODúÕNNWOH \DUÕoDSLOLúNLVL3DF]\QVNLWDUDIÕQGDQ
, (18.1) denklemindeki γ =0.2 ve δ =0.86 GH÷HUOHULQHNDUúÕOÕN JHOPHNWHGLU Bu da
(18.8) ED÷ÕQWÕVÕQÕQ\DNODúÕNRODUDN
úHNOLQGH YHULOPLúWLUEX ED÷ÕQWÕ
61
biçiminde, \D]ÕODELOHFH÷LDQODPÕQDJHOLU
Problem 18.4: Küçük kütlHOL DQDNRO GXUXPXQGDQ EDúOD\DUDN EX GXUXP LoLQ \Õ÷ÕúPD KÕ]ÕQÕ |OoHNOHQGLULQL] A
4
4
X]DNOÕ÷ÕQÕQ \Õ÷ÕúPD KÕ]ÕQD LOLúNLQ denklemlere A úHNOLQGH JLUGL÷LQL YH E|\OHFH \Õ÷ÕúPD KÕ]ÕQÕQ kat büyük
-8
-1
RODFD÷ÕQÕGROD\ÕVÕ\OHGH0 M \ÕO PHUWHEHVLQGHRODFD÷Õ gerçe ÷LQGHQ\DUDUODQÕQÕ]
'DKD JHQLú \|UQJHOL oLIWOHU EX úHNLOGH HYULPOHúPH\HELOLUOHU RQODU EXQXQ \HULQH ELU NÕUPÕ]Õ GHY ELOHúHQOL oRN
JHQLúoLIWOHUGXUXPXQDHYULPOHúHELOLUOHU.LSSHQKDKQYHDUN
Benzer sistemler,
\ÕOGÕ] \R÷XQOX÷XQXQ oRN \NVHN ROGX÷X NUHVHO NPHOHUGHNL ELU NÕUPÕ]Õ GHYLQ ELU Q|WURQ
\ÕOGÕ]ÕWDUDIÕQGDQ\DNDODQPDVÕ\ODGDROXúDELOLU
(Sutantyo, 1975; Hills ve Day, 1976).
%LUNÕUPÕ]ÕGHYGHQ5RFKHOREXWDúPDVÕ
-
in DWDVÕ ROan sistemler muhtemelen, helezonik
ge dönemi 0.5 gün
FLYDUÕQGDNLGH÷HUOHUHLQHU<DNODúÕN M NWOHOL\ÕOGÕ]ODULoLQEXGH÷HULQDOWÕQGDNLG|QHPOHUGHHYULPEDVNÕn bir
.DWDNOLVPLN GH÷LúHQOHU LOH NoN NWOHOL ; ÕúÕQ oLIW VLVWHPOHULQ
úHNLOGHGDUDODQ\|UQJHOLELURUWDN]DUIHYUHVLER\XQFDHYULPOHúLUOHU<|UQJHGDUDOÕUYH\|UQ
úHNLOGH oHNLPVHO ÕúÕPD LOH \|QOHQGLULOLU YH EX GD \|UQJHQLQ GDUDOPDVÕQD \RO DoDU 7DDP YH DUN %X
VLVWHPOHULQ ED]ÕODUÕQGD VRQUDNL HYULPOHúPH ELU DQDNRO \ÕOGÕ]Õ \D GD ELU NoN NWOHOL \R]ODúPÕú \ÕOGÕ]ÕQ 5RFKH
OREXWDúPDVÕúHNOLQGHGLU
Daha gHQLúVLVWHPOHUGHE\NNWOHOLELOHúHQNÕUPÕ]ÕGHYGXUXPXQDHYULPOHúHELOLU(÷HUEXELOHúHQLQNWOHVLoRN
E\NGH÷LOVHELU\R]ODúPÕúKHO\XPoHNLUGH÷LJHOLúHELOLU+LGURMHQ\DQPDNDEX÷XGÕúDYHLoHUL\HGR÷UXJHQLúOHU
Böylece hidrojence zengin zarf giderek KHO\XPFD ]HQJLQOHúLUNHQ KLGURMHQ \DQPDVÕQÕQ VRQXFXQGD GDKD ID]OD
KHO\XPXQ oHNLUGH÷H HNOHQPHVLQLQ ELU VRQXFX RODUDN KHO\XP oHNLUGH÷LQ NWOHVL VUHNOL RODUDN DUWDU Enerjinin
QHUHGH\VHWDPDPÕoHNLUGHNWHUHWLOLU
Çekirdek kütlesindeki M C E\PHVLLOH\ÕOGÕ]ÕQL ÕúÕWPDVÕDUDVÕQGD
M C ≈ vL
úHNOLQGHELULOLúNLYDUGÕUJUDPPDGGHGHNLKLGURMHQ\DQPDVÕ
X
LOHVDOÕQDQHQHUML
E = mc 2 = 0.7 × 0.007(3 ×1010 ) 2 = 4.41× 1018 HUJ V −
dir, böylece L = 4.41 × 1018 M C olur;
JQHú ELULPOHULQH G|QúWUG÷P]GH YH oHNLUGHN E\PHVLQL
de
\ÕO
ELULPLQGHLIDGHHWWL÷LPL]GH
M C = 1.32 × 10 −11 L
elde ederiz.*HQLúOHPH]DPDQÕ.HOYLQ-+HOPKROW]]DPDQ|OoH÷LQGHQoRNE\NROGX÷Xndan,
R
>> t KH
R
çeNLPVHO ÕúÕWPD LKPDO HGLOHELOHFHN NDGDU Nüçüktür.
dHNLUGHN NWOHVLQLQ E\PHVL \DUÕoDSÕQ E\PHVLQH YH
ÕúÕWPDQÕQDUWPDVÕQDQHGHQROXU%XLVHGHYNROXQXQoÕNÕúÕQDNDUúÕOÕNJHOLU
62
, 0.2 M’lik bir çekirdek kütlesi için,
yaNODúÕN×108\ÕOVUHQYH3×10-9 M\ÕO-1GH÷HULQGHELUNWOHDNWDUÕPKÕ]ÕEXOPXúODUGÕU
.WOHDNWDUÕPKÕ]Õ:HEELQNYHDUNWDUDIÕQGDQKHVDSODQPÕúWÕURQODU
18.6. Kütleli X-ÕúÕQoLIWOHUL
-
.h7/(/ø; ,ù,1dø)7/(5ø1ø10;5%¶V7h5/(5ø
çift X-ÕúÕQ ND\QDNODUÕQÕQ ELU Q|WURQ \ÕOGÕ]Õ \D GD ELU NDUD GHOLN
NDUPDúÕNWD\IOÕJoO;-ÕúÕQND\QDNODUÕQÕQL\LELOLQHQELUVÕQÕIÕQÕQ\HVLGLUOHU2QODUD\QÕ]DPDQGD,JHQoÕúÕQÕPOÕ
\ÕOGÕ]ODU LOHGHLOLúNLOLGLUOHU Bunlar, WU ND\QDNODURODUDNVÕQÕIODQGÕUÕOÕUODU%X JUXS IDUNOÕ |]HOOLNOHUH VDKLS LNL
*|]OHPOHU VRQXFXQGD oR÷X EHONL GH EWQ
LoHUGLNOHULQH GDLU NDQÕWODU EXOXQPXúWXU 2QODUÕQ ELU NÕVPÕ DWDUFD oLIW ; ÕúÕQ ND\QD÷Õ ELU NÕVPÕ GD ROGXNoD
DOWJUXEDD\UÕODELOLUOHU
1. Standard sistemler: StandardVLVWHPOHU NDOÕFÕND\QDNODUGÕU \DQL;-ÕúÕQODUÕ G]HQOL ELUG|QHPOLOL÷H VDKLSWLU YH
RSWLN ÕúÕN oÕNWÕODUÕ LVH VÕNÕúÕN \ÕOGÕ]ÕQ RSWLN ELOHúHQ ]HULQGH QHGHQ ROGX÷X oHNLPVHO ER]XOPDODUÕQ \RO DoWÕ÷Õ
HOLSVRLGDO GH÷LúLPOHU J|VWHULU 2SWLN ELOHúHQ 5RFKH OREXQX QHUHGH\VH GROGXUPXúWXU YH VLVWHP G]HQOL RODUDN
tutulmalar gösterebilir. Böylesi biU NDo RQ VLVWHP ELOLQPHNWHGLU YH VRQ GHUHFH JoO VDOPD oL]JLOHUL \DUGÕPÕ\OD
RQODUÕWDQÕPODPDNNROD\GÕU
-62
Bu sistemlerin atDODUÕ 2%-\ÕOGÕ]ODUÕGÕU Bu X-ÕúÕQ ND\QDNODUÕQÕQ ELU oR÷X DWDUFDGÕU Atma
dönemleri 0.75- GN DUDVÕQGD GH÷LúLU X-ÕúÕQ VDODQ ELOHúHQLQ 'RSSOHU EHOLUOHPHOHUL YH EX ND\QDNODUÕQ
ED]ÕODUÕQGDNL J|UVHO J|]OHPOHU Q|WURQ \ÕOGÕ]Õ LOH RSWLN ELOHúHQLQLQ \|UQJHOHULQin belirlenebilmesine olanak
VD÷ODU Bu yörüngelerden yararlanÕODUDN VLVWHPLQ NWOH RUDQÕ YH ELOHúHQlerin kütleleri elde edilebilir. Nötron
\ÕOGÕ]ODUÕQÕQEHOLUOHQHQNWOHOHUL M
yöresinde iken,RSWLNELOHúHQOHULQLQNWOHOHUL0’den, 40 M’e kadar
de÷HUOHUDODELOPHNWHGLU
'|QHPOHUNÕVDROXSJQLOHJQDUDVÕQGDGÕUELUD\GDQELUD]GDKDX]XQELUG|QHPHVDKLSRODQ8
VLVWHPL ELU LVWLVQDGÕU
2. Geçici Sistemler: Bu grupta opWLN ELOHúHQOHU 5RFKH OREODUÕQÕ GROGXUPDPÕú RODQ %H \ÕOGÕ]ODUÕGÕU dR÷XQOXNOD
tutulma yoktur ve düzenOL HOLSVRLGDO GH÷LúLP J|]OHQPH] Kütleleri –standard kütleli X-ÕúÕQ oLIWOHULQNLQGHQ
GúNWU- 10 M
ile 20 M DUDVÕQGD GH÷LúLU %X JUXED \H RODQ ELU oRN FLVLPGHQ DOÕQDQ ;-ÕúÕQ DNÕODUÕ VDELW
ROPD\ÕSDQLSDWODPDODUJ|VWHUPHNWHGLU
Büyük kütleli X-ÕúÕQoLIWOHULQGHQL\LELOLQHQOHULQED]Õ|]HOOLNOHULdL]HOJH¶GHYHULOPLúWLU
Çizelge 18.1. Çok iyi bilinen X-ÕúÕQoLIWOHULVWDQGDUGND\QDNODUYHJHoLFLOHUYHRQODUÕQWHPHO|]HOOLNOHUL
;,úÕQÕ.D\QD÷Õ
4U1700-37
=HD153919
4U1900-40
=VelaX-1
=HD77581 Cyg
X-1
=4U1956+35
=HDE226868
Cen X-3
=4U1119-60
4U1538-52
SMC X-1
LMC X-4
4U0352-+30 =X
Per
Tayf Türü
%Dú\ÕOGÕ]ÕQ
<ROGDú\ÕOGÕ]ÕQ
Dönem
<|UQJHDoÕNOÕ÷Õ
O6.5f
Kütlesi
30
kütlesi
2
3.41180
A (R biriminde)
20
B0.5Ib
21.7
1.5-3
8.96
51
O9.7Iab
>25
9
5.607
43
O6.5IIIc
18
1
2.087
18.3
B0.5Iab
O9.5V-III
20±8
15
20
3.73
0.9
1.3
3.893
1.4083
27.4
16.9
O9.5
≈20
>2
580
820
Referanslar
Vanbeveren (1977)
Avni (1976)
Mason ve ark.
Tananbaum ve
Tucker (1974)
Van Paradijs
Chevalier ve
Ilovaisky (1974)
De Loore ve ark.
(1979)
63
-
.h7/(/ø; ,ù,1dø)7/(5ø1ø1(95ø0ø
Standard kütleli X-ÕúÕQoLIWOHUL
-
-
.DOÕFÕVWDQGDUGNWOHOL; ÕúÕQoLIWOHULYH%H; ÕúÕQoLIWOHUL\ÕOGÕ]U]JDUODUÕ\ODNWOHND\EÕYHNWOHDNWDUÕPÕJLEL
DUGÕúÕN VUHoOHULQ VRQXFX RODUDN ELU VSHUQRYD SDWODPDVÕQÕQ ROXúPDVÕ YH
bu suretle
o|NPú FLVLPOHULQ Q|WURQ
\ÕOGÕ]ODUÕQÕQ\DGDNDUDGHOLNOHULQROXúPDVÕ\ROX\ODGR÷UXGDQGR÷UX\DNWOHOL\DNÕQoLIWVLVWHPOHUGHQROXúXUODU
%XJQ NDEXO HGLOHQ JHQHO J|Uú LNL ÕúÕWPDOÕ ELOHúHQGHQ ROXúDQ ELU NWOHOL \DNÕQ oLIW VLVWHPLQ LON RODUDN NWOH
GH÷LúLPL YH VRQXQGDNL ELU SDWOD
mayla
ve bu suretle X-ÕúÕQ ND\QD÷Õ GXUXPXQD
Kütleli X-ÕúÕQ ND\QDNODUÕQÕQ HYULPLQH LOLúNLQ LON
VÕNÕúÕN ELOHúHQLQ ROXúPDVÕ
HYULPOHúWLNOHUL úHNOLQGHGLU YDQ GHQ +HXYHO YH +HLVH D\UÕQWÕOÕ KHVDSODPDODU GH /RRUH YH 'H *UHYH WDUDIÕQGDQ \D\ÕQODQPÕúWÕU 'DKD LOHUL ELU DúDPDGD NWOHOL
\ÕOGÕ]5RFKHOREXQXGDGROGXU
arak madde kaybeder. 6LVWHPLQG|QHPLúLGGHWOLELUúHNLOGHGúHUYHQ|WURQ\ÕOGÕ]Õ
-
KHOH]RQLNRODUDNELOHúHQLQH \DNODúÕU %X \ROOD oRNNÕVD G|QHPOL ELU oLIWLQ ROXúPDVÕ\ODLNLQFLELU ; ÕúÕQDúDPDVÕ
ROXúDELOLU 6RQXQGD \ROGDú GD SDWODU YHLNL D\UÕ Q|WURQ \ÕOGÕ]ÕQGDQ ROXúDQ ELU VLVWHP RUWD\D oÕNDU øON VSHUQRYD
SDWODPDVÕQGDQVRQUDSDWOD\DQ\ÕOGÕ]ÕQVLVWHPLQGDKDNoNNWOHOLELOHúHQLROPDVÕQGDQGROD\ÕVLVWHPED÷OÕNDOÕU
%XQXQOD ELUOLNWH LNLQFL SDWODPDQÕQ VLVWHPL GD÷ÕWPD DoÕVÕQGDQ oRN GDKD \NVHN ELU RODVÕOÕ÷D VDKLS ROPDVÕQD
UD÷PHQHQGHUELUNDoGXUXPGDVLVWHPED÷OÕNDOÕUYHLNLQ|WURQ\ÕOGÕ]ÕELUoLIWDWDUFDVLVWHPLROXúWXUXUODU
Standard
X-ÕúÕQND\QDNODUÕLoLQHYULPúHPDVÕùHNL¶GHJ|VWHULOPLúWLU
- 3 MRODQ \ÕOGÕ]ODUÕ
dikkate aliyoruz. .RUXQXPOX HYULPOHúPH \D GD RUWD GHUHFHGHQ NWOH ND\EÕ GXUXPXQGD EDú \ÕOGÕ]ÕQ o|NPH
DQÕQGDNLNDOÕQWÕVÕGDKDNoNNWOHOLELOHúHQRODFDNWÕU&HPEHU\|UQJHOLELUoLIWVLVWHPLQELOHúHQOHULDUDVÕQGDNLA
%XUDGD GR÷UXGDQoHNLUGHN o|NPHVLDúDPDVÕQD HYULPOHúWLNOHULLoLQ oHNLUGHN NWOHOHUL
X]DNOÕ÷Õ
A (1 + q) 2 q 0
=
A0 (1 + q 0 ) 2 q
(18.4)
ED÷ÕQWÕVÕQDJ|UHGH÷LúLU
DDKDNoN NWOHOLELOHúHQLQ SDWODPDVÕ, simetrik olmDVÕ KDOLQGH VLVWHPLGD÷ÕWPD\DFDN YH bir asimetrik patlama
GXUXPXQGD ELOH VLVWHP GD÷ÕOPD\DELOHFHNWLU NRUXQXPOX RODUDN HYULPOHúHQ ELU VLVWHPGHNL VÕNÕúÕN \ÕOGÕ] SUDWLN
RODUDN KHU GXUXPGD VLVWHPH ED÷OÕ NDODFDNWÕU 'H &X\SHU GH /RRUH YDQ GHQ +HXYHO De Cuyper ve ark.
1977).%WU\DGDJHo$WUNWOHDNWDUÕPÕQGDQVRQUDNLNDOÕQWÕNWOHVL
log M 1 f = −1.13 + 1.42 log M 1
X =YHZ =LoLQ9DQEHYHUHQ
log M 1 f = −1 + 1.4 log M 1
X =YHZ =LoLQ7XWXNRY YH<XQJHOVRQ
(18.5)
ED÷ÕQWÕODUÕLOHWDKPLQHGLOHELOLU
hesaplamalara, NWOH RUDQÕQÕQ
q-1 úHNOLQGHNLJ|UHOLRODUDNNoNEDúODQJÕoGH÷HUOHULLOH EDúODPDNJHUHklidir. Bununla birlikte bu seneryo,
küçük q-1 GH÷HUOL VLVWHPOHULQ DúÕUÕ GH÷PH DúDPDVÕQD GR÷UX JHOLúHFHNOHUL JHUoH÷L \]QGHQ oRN GD JHUoHNoL
görünmemektedir. Bunun nedeni, \Õ÷ÕúPD ]DPDQ |OoH÷LQLQ NWOH ND\EÕ ]DPDQ |OoH÷LQGHQ GDKD E\N ROPDVÕ
E|\OHFH DOÕFÕ \ÕOGÕ]ÕQ GD 5RFKH OREXQX GROGXUPDVÕ YH EX VXUHWOH GH RUWDN ELU ]DUI LOH oHYULOL, dH÷HQ bir
NRQILJXUDV\RQXQ RUWD\D oÕNPDVÕGÕU 'L÷HU WDUDIWDQ NWOH DNWDUÕPÕ QHGHQL\OH NoN NWOH RUDQOÕ VLVWHPOHUGHNL A
X]DNOÕ÷ÕDNWDUÕPER\XQFDoRNNoOUYHNWOHOHUHúLWOHQGL÷Lnde sistem minimum D\UÕNOÕ÷DXODúÕU
.RUXQXPOX NWOH DNWDUÕPÕ\OD LNL JQON \|UQJH G|QHPOHUL HOGH HGHELOPHN LoLQ
q-1 LoLQ D\UÕNOÕN \DUÕ\DGúHU%|\OHFH NRUXQXPOXYDUVD\ÕPÕ DOWÕQGD JQGHQ GDKD NÕVDRODUDNJ|zlenen
VSHUQRYD VRQUDVÕ \|UQJHG|QHPOHULQL DoÕNODPDN LPNDQVÕ] J|UQPHNWHGLU2UWDN ELU]DUI ROXúWXUXOGX÷XQGD L2
ya da L3¶GHQ NWOH ND\EÕ EHNOHQPHOLGLU %X \ROOD PH\GDQD JHOHQ NWOH ND\EÕ ELOHúHQOHULQ RUWDODPD \|UQJH
DoÕVDOPRPHQWXPXQGDQçok daha büyük ELU|]DoÕVDOPRPHQWXPGH÷HULQHVDKLSWLU
%LU FLYDUÕQGDNL NWOH RUDQODUÕ LoLQ H÷HU D\UÕODQ PDGGH DNÕPÕQÕQ DoÕVDO PRPHQWXPX RQXQ VLVWHPGHNL JHUoHN
için birlikte dönme bunu VD÷ODU
bu durumda L2QRNWDVÕQGDNL|]DoÕVDOPRPHQWXP|]\|UQJHDoÕVDOPRPHQWXPXQXQ\DNODúÕNRODUDNNDWÕROXU
\HULQHLOLúNLQDoÕVDOPRPHQWXPGH÷HULQHHúLWROGX÷XNDEXOHGLOLUVH|UQH÷LQ/2
64
-
ùHNLO6WDQGDUGNWOHOL; ÕúÕQoLIWOHULQLQHYULPLGH/RRUHYH'H*UHYH
Böylece
dJ
J
= 4( )
dM
M
(18.6)
J ≈ M (M, sistemin toplam kütlesi)
(18.7)
ya da
olur.
Bu evre süresince kütle
r.%X \ROODED]Õ;-ÕúÕQ YH:5oLIWOHULQLQ&HQ ;-3, SMC X-1, CX Cep (P = 1.6
6RQXoRODUDN ¶GHQ NoN NWOH RUDQOÕ VLVWHPOHU ELU RUWDN ]DUI HYUHVLQH HYULPOHúLUOHU
YHDoÕVDOPRPHQWXP ND\EHGLOL
g), CQ Cep (P
J NÕVD \|UQJH G|QHPOHUL DoÕNODQDELOLU %LU FLYDUÕQGD NWOH RUDQOÕ VLVWHPOHU NRUXQXPOX
65
RODUDN HYULPOHúHELOLUOHU YH EX GD JQ \D GD GDKD X]XQ \|UQJH G|QHPOL VSHUQRYD VRQUDVÕ oLIWOHULQ RUWD\D
oÕNPDVÕQD\RODoDU
- ve B-WU WD\IVDO oLIWOHULQ \DOQÕ]FD ¶ ¶WHQ NoN NWOH RUDQODUÕQD
sahiptir. dRN NÕVDG|QHPOL:5YH;-ÕúÕQoLIWOHULQLQ ROXúDELOPHVLLoLQEXVLVWHPOHUGHNWOHYHDoÕVDOPRPHQWXP
(YULPOHúPHPLú NÕVD G|QHPOL 2
ND\ÕSODUÕQÕQ PH\GDQD JHOPHVL EHNOHQLU 6LVWHPOHULQ oRN E\N ELU NÕVPÕ NRUXQXPOX RODUDN HYULPOHúLU YH EX GD
-
VSHUQRYDSDWODPDVÕQGDQVRQUDJQGHQGDKDX]XQG|QHPOL; ÕúÕQoLIWOHULQLQROXúPDVÕQD\RODoDU
Problem 18.4: Denklem 18.5’e uygun olarak kütle kaybedenEDúODQJÕoG|QHPLJQYHNWOHVL 25 M+ 20 M
RODQ ELU =$06 VLVWHPL LoLQ KHO\XP \ÕOGÕ]Õ NDOÕQWÕVÕQÕQ NWOH DNWDUÕPÕQGDQ VRQUD Wolf-5D\HW \ÕOGÕ]ÕQÕQ
U]JDUODUÕQHGHQL\OH0 GDKDNWOHND\EHWWL÷LQLYDUVD\DUDNVRQXoG|QHPGH÷HULQLKHVDSOD\ÕQÕ].
ùHNLO%DúODQJÕoG|QHPLJQRODQELU0
+ 10 MVLVWHPLQLQHú]DPDQOÕHYULPL(YULPDúDPDODUÕD\UÕN\DUÕ-D\UÕN
NWOHOL ELU KHO\XP \ÕOGÕ]Õ LOH 20.5 M kütleli bir
YH GH÷HHQ úHNLOGH EHOLUWLOPLúWLU +HVDSODPDODUÕQ VRQXQGD VLVWHP 0
NWOHOL ELOHúHQ LoHUPHNWHGLU 6LVWHPLQ G|QHPL JQGU %\N NWOHOL ELOHúHQ \ÕOGÕ] U]JDUODUÕ\OD NWOH ND\EHWPHNWHGLU
ama
KHO\XP \ÕOGÕ]Õ GDKD GD HYULPOHúLU YH VRQXQGD SDWOD\DUDN JHUL\H ELU Q|WURQ \ÕOGÕ]Õ NDOÕQWÕVÕ EÕUDNÕU 6LPHWULN SDWO
durumunda dönem 81 gün olur (de Loore ve ark. 1984).
18.6.3. Be X-,ù,1dø)7/(5ø1ø125ø-ø1ø
Bu tür X-ÕúÕQND\QDNODUÕ NoNEDúODQJÕo NWOHOL 20MVLVWHPOHUWDUDIÕQGDQROXúWXUXOXUODU Bir örnek olarak,
EDúODQJÕo G|QHPL JQ RODQ ELU 5 M + 10 M VLVWHPLQLQ Hú ]DPDQOÕ HYULPL ùHNLNO ¶WH J|VWHULOPLúWLU GH
Loore ve ark. 1984). 6LVWHP \DNODúÕN PLO\RQ \ÕO VRQUD \DUÕ-D\UÕN GXUXPD JHOLU YH \DNODúÕN \ÕO VRQUD
GH÷HQ HYUHVLQH HYULPOHúLU 6LVWHPGHQ NWOH DWÕOÕU VLVWHP \HQLGHQ \DUÕ-D\UÕN GXUXPD JHoHU YH \ÕO VRQUD
KHO\XPXQ\DQPD\DEDúODPDVÕ\ODLNLELOHúHQGH÷HQGXUXPDJHOLUOHU Sonuç sistem, -3.42 M NWOHOLELUEDú\ÕOGÕ]
ile 20.5 M NWOHOL ELU \ROGDú- 68 günlük bir yörünge dönemine sahiptir. 10 M¶GHQ EDúOD\DQ \Õ÷ÕúPD ELOHúHQL
sonunda 20.5 M¶H XODúÕU EX ELOHúHQ =$06¶D SDUDOHO ELU \RO ER\XQFD HYULPOHúLU <DYDú NWOH DNWDUÕP HYUHVL
EDúODGÕ÷ÕQGD HYULP \ROX =$06¶DGR÷UX NÕYUÕOÕU EXQGDQ VRQUD \ÕOGÕ]WÕSNÕ 0
NWOHOLELU =$06 \ÕOGÕ]Õ JLEL
HYULPOHúLU%XVÕUDGDEDú\ÕOGÕ]ÕQKHO\XPNDOÕQWÕVÕHYULPLQLVUGUUYHSDWODU%XHYUHGHVLVWHP\DNODúÕN0
kütleli bir Be-ELOHúHQL LOH 0 NWOHOL ELU Q|WURQ \ÕOGÕ]Õ ELOHúHQLQGHQ ROXúDQ ELU %H-X-ÕúÕQ oLIWL ROXúWXUPXú
olur.(YULPLQúHPDWLNELUJ|VWHULPLùHNLO¶WHYHULOPLúWLU
66
Be X-ÕúÕQoLIWOHULQLQROXúXPX
ùHNLO
18.7. Kütleli X-ÕúÕQoLIWOHULQLQNRUXQXPVX]HYULPOHUL
'DKD |QFH GH÷LQLOGL÷L ]HUH NRUXQXPOX YDUVD\ÕPÕ \DNÕQ oLIW VLVWHPOHULQ HWNLOHúLPOL HYULPOHULQL
yeterli bir
úHNLOGHWDQÕPOD\DELOPHN EDNÕPÕQGDQ EDVLW NDOPDNWDGÕU YH NWOH DNWDUÕP HYUHVL ER\XQFD |QHPOL RUDQGD NWOH YH
DoÕVDOPRPHQWXPND\EÕPH\GDQDJHOL\RURODELOLU'DKDVÕ\ÕOGÕ]U]JDUODUÕ\ODNWOHND\EÕGDGLNNDWHDOÕQPDOÕGÕU
q = 0.8 –¶GDQGDKDNoNNWOHRUDQODUÕLoLQVHQHU\RoRNGH÷LúPH]YHNRUXQXPOXGXUXPGDNLQe benzer evrim
örnekleri elde ederiz. $QFDNNWOHRUDQÕQÕQFLYDUÕQGDNLGH÷HUOHULQGHGXUXPIDUNOÕGÕU Böylesi bir durumda, her
LNLELOHúHQLQHYULPVHO ]DPDQ|OoH÷LSUDWLN RODUDN D\QÕGÕU E|\OHFH HYULPOHúPLú EDú \ÕOGÕ]SDWODGÕ÷ÕQGD, \ROGDúÕQ
kalan ömrü çokNÕVDGÕUùHNLO¶GHNWOHRUDQODUÕq = 0.75 ve q = 0.925 olan iki sistemin evrimiJ|VWHULOPLúWLU
øNLQFL GXUXPGD LNL :5 \ÕOGÕ]OÕ ELU HYUH ROXúXU YH EXQX ELU NÕVD :5 NDoDN HYUHVL WDNLS HGHU %Dú \ÕOGÕ]
-
SDWODPDGDQ|QFH\ROGDúELOHúHQ]DWHQ5RFKHOREXQXWDúPD\DEDúODPÕúROXUE|\OHFH2%NDoDNDúDPDVÕLOH; ÕúÕQ
ve
kabul ediOPLúWLU EX GXUXPXQ G|QHP ]HULndeki etkisi
DúDPDVÕ J|]OHQPH] %X |UQHNWH EDú \ÕOGÕ] WDUDIÕQGDQ DNWDUÕODQ PDGGHQLQ ¶VLQLQ VLVWHPL WHUN HWWL÷L
EHUDEHULQGH GH DoÕVDO PRPHQWXPXQ ¶VLQL J|WUG÷
son derece güçlüdür.
18.8. Kütleli X-ÕúÕQoLIWOHULQLQVRQXoHYULPOHUL
d(.ø06(/(ù=$0$1/,/,.9(d(.ø06(/.$5$56,=/,.
<HWHULQFH NÕVD G|QHPOHU LoLQ oHNLPVHO NXYYHWOHU VSHUQRYD ROD\ÕQGDQ VRQUDNL ELU NDo PLO\RQ \ÕO LoHULVLQGH
yörüngeQLQ oHPEHUOHúPHVLQH YH Hú]DPDQOÕ G|QPH\H QHGHQ ROXUODU Hemen hemen çember yörüngelere sahip
olan X-ÕúÕQND\QDNODUÕ60&;-1, Cen X-3 ve Her X-oHPEHUVHOOHúPHROD\ÕQÕQ|UQHNOHULGLUOHUdHPEHUVHOOHúPH
VUHFL LoLQ EHOLUOH\LFL HWNHQ \ÕOGÕ]ODUÕQ Lo NÕVÕPODUÕQÕQ DNÕúNDQOÕ÷Õ YLVNR]LWH¶GÕU Zahn (1977)’ye göre, dinamik
ER]XOPDQÕQ úLGGHWLQLQ ÕúÕQÕP \ROX\OD D]DOWÕOPDVÕ kütleli X-ÕúÕQ oLIWOHUL LoLQ JHUHNOL RODQ NÕVD ]DPDQ |OoHNOHULQL
DoÕNOD\DELOLU
67
Darwin (1908) ve Counselman (1973), (çHPEHUOHúPH YH Hú]DPDQOÕ G|QPeden sonraki) yörünge ve dolanma
DoÕVDOPRPHQWXPODUÕRUDQÕQÕQ
J orb
≤3
J rot
(18.8)
ROPDVÕ GXUXPXQGD VLVWHPLQ oHNLPVHO RODUDN NDUDUVÕ] RODFD÷ÕQÕ
ve
VÕNÕúÕN ELOHúHQLQ KHOH]RQLN ELU \|UQJH LOH
ELOHúHQLQH\DNODúDFD÷ÕQÕLVSDWODPÕúODUGÕU'RODQPDDoÕVDOPRPHQWXPX
J rot = k 2 MωR 2
(18.9)
ile verilir, burada M ve R
QRUPDO \ÕOGÕ]ÕQ NWOH YH \DUÕoDSÕ
ω RQXQ DoÕVDO KÕ]Õ YH k ise gyration (dönme)
\DUÕoDSÕGÕU<|UQJHDoÕVDOPRPHQWXPXLVH
J orb =
ω MmA 2
M +m
ED÷ÕQWÕVÕ\ODYHULOLU EXUDGD
(18.10)
m
VÕNÕúÕNELOHúHQLQ NWOHVL YH
A
LVH ELOHúHQOHU DUDVÕQGDNL X]DNOÕNWÕU
LIDGHOHULQLQED÷ÕQWÕVÕQGDNXOODQÕOPDVÕ\ODG|QPH\DUÕoDSÕ
k2 >
(18.9) ve (18.10)
k için
mA 2
3R 2 ( M + m)
(18.11)
limitini elde ederiz. Kütleleri 15 M < M < 30 M DUDVÕQGD RODQ \ÕOGÕ]ODU LoLQ k2¶QLQ GH÷HUL ∼0.075 (ZAMS)
GH÷HULQGHQPHUNH]LKLGURMHQLQWNHQPHVLGH÷HULQHGúHU'H*UHYHGH/RRUH6XWDQW\R
Problem 18.5: ÇizHOJH¶GHYHULOHQVLVWHPOHULQNULWLNGH÷HUOHULQLKHVDSOD\ÕSVRQXoODUÕk2LoLQ\XNDUÕGDYHULOHQ
GH÷HUOHULOHNDUúÕODúWÕUÕQYHEXVLVWHPOHULQoHNLPVHONDUDUOÕOÕNODUÕQDLOLúNLQVRQXoODUHOGHHGLQL]
dø)7$7$5&$/$5ø/(.$d$.$7$5&$/$5,12/8ù808
P • ¶GHQ ¶H NDGDU RODQ VLVWHPOHUGH 5RFKH OREX WDúPD\D EDúODUEDúODPD] RSWLN \ÕOGÕ]ÕQ ]DUIÕ KÕ]OD JHQLúOHU YH
kütle kayÕS KÕ]Õ ∼10-3 M \ÕO-1 GH÷HULQH XODúÕU 0DGGH LQFH ELU \Õ÷ÕúPD GLVNLQGH ELULNWLULOLU %XQXQOD ELUOLNWH,
Eddington limiti JHUH÷LQFH, aktaUÕODQ NWOHQLQ ∼10-7 M\ÕO-1 GH÷HULQGHQ GDKD E\N NÕVPÕ Q|WURQ \ÕOGÕ]Õ
WDUDIÕQGDQ WXWXODPD] \DQL DNWDUÕODQ NWOHQLQ E\N ELU NÕVPÕ VLVWHPL WHUNH HGHU 'LVNLQ Lo NÕVPÕ (GGLQJWRQ
ÕúÕWPDVÕQD XODúÕU E|\OFH PDGGHQLQ DWÕOPDVÕ ÕúÕQÕP EDVÕQFÕ \ROX\OD YH oR÷XQOXN
GR÷UXOWXGDROXúXU6KDNXUD
la da disk düzlemine dik
ve Sunyayev, 1975)
$WÕODQ PDGGH EHUDEHULQGH E\N PLNWDUGD |] DoÕVDO PRPHQWXP VÕNÕúÕN FLVPLQ \|UQJH DoÕVDO PRPHQWXPX
J|WUU YH E|\OHFH \|UQJH KÕ]OÕ ELU úHNLOGH GDUDOÕU JHULGH \DOQÕ]FD E\N NWOHOL ELOHúHQLQ HYULPOHúPLú
oHNLUGH÷LQLQ NDOGÕ÷Õ VRQD GR÷UX XODúÕOPDN ]HUH \|UQJHQLQ VSLUDO ELoLPLQGHNL GDUDOPDVÕ EHNOHQLU 6RQXQGD
HYULPOHúPLú KHO\XP \ÕOGÕ]Õ ELU VSHUQRYD ROD\Õ LOH SDWODU YH H÷HU oLIW VLVWHPLP WRSODP NWOHVLQLQ \DUÕVÕQGDQ
ID]ODVÕ DWÕOÕUVD oLIW VLVWHP GD÷ÕODELOLU %X VXUHWOH SDWODPD PHUNH]LQGHQ VDQL\HGH ELU NDo \] NLORPHWUH KÕ]OD
X]DNODúDQ LNL DGHW NDoDN UDG\R DWDUFDVÕ ROXúXU %LU oRN UDG\R oLIWL ELOLQPHNWHGLU 2QODUÕQ ELU OLVWHVL ED]Õ
|]HOOLNOHUL\OHELUOLNWHdL]HOJH¶GHYHULOPLúWLU
Çizelge 18.2. Çift atarcalar
øVLP
PSR 0656+64
PSR 0820+02
PSR 1913+16
PSR 1937+215
Pyör
24sa41dk
1100 gün
7sa 75dk
--
Patma (s)
0.196
0.865
0.059
0.0015
'ÕúPHUNH]OLN
0.06
0
0.617
68
a bir atma dönemine ve 108 gauss
12
gauss mertebesindeki daha
PHUWHEHVLQGH ]D\ÕI ELU PDQ\HWLN DODQD VDKLSWLU %LOLQHQ GL÷HU oLIW DWDUFDODU LVH LVLPOL PLOLVDQL\H DWDUFDVÕ PLOLVDQL\HOLN VRQ GHUHFH NÕV
E\N PDQ\HWLN DODQODUD YH GDKD X]XQ G|QHPOHUH VDKLSWLUOHU 0LOLVDQL\H DWDUFDODUÕ PXKWHPHOHQ LNL Q|WURQ
\ÕOGÕ]ÕQÕQELUOHúPHVL\OHROXúPDNWDGÕUODU
dLIW UDG\R DWDUFDVÕ 365 PXKWHPHOHQ NWOHOHUL
∼ 1.4 M RODQ LNL Q|WURQ \ÕOGÕ]Õ LoHUPHNWHGLU
<|UQJHQLQ NoOPHVL JHQHO UHODWLYLWH NXUDPÕQD J|UH oHNLPVHO ÕúÕQÕPÕQ VDOÕQPDVÕ\OD WDKPLQ HGLOGL÷L ELoLPGH
RUWD\DoÕ
kar ve bu durum 3 108\ÕOLoHULVLQGHVLVWHPLQELUOHúPHVLQHQHGHQROXU
69
BÖLÜM 19
7(.YHdø)7<,/',=/$5,1<$3,YH(95ø002'(//(5ø
19.1. <DSÕPRGHOOHUL
%ø567$1'$5'*h1(ù02'(/ø1ø1ød<$3,6,%DKFDOOYHDUN
log Teff = 3.76, log L = 0
Mr, kütle; T ve ρVÕFDNOÕNYH\R÷XQOXNGH÷HUOHULXD÷ÕUOÕNoDKLGURMHQEROOX÷Xdur.HVLNOLoL]JLÕúÕQÕPoHNLUGH÷L
LOHNRQYHNWLIGÕú]DUIDUDVÕQGDNLVÕQÕUÕJ|VWHUPHNWHGLU
Mr
log T
Lr/L
log ρ
R / R
Χ
0
0.0099
0.0385
0.1038
0.1620
0.2100
0.2580
0.3100
0.3900
0.4700
0.5500
0.6900
0.8300
0.9264
0.9602
0.9784
7.1903
7.1703
7.1399
7.0934
7.0569
7.0334
7.0086
6.9822
6.9430
6.9030
6.8615
6.7803
6.6675
6.5315
6.4346
6.3263
0.000
0.079
0.264
0.555
0.718
0.809
0.874
0.921
0.964
0.986
0.996
1.000
1.000
1.000
1.000
1.000
2.194
2.127
2.034
1.897
1.801
1.729
1.660
1.585
1.468
1.344
1.207
0.905
0.455
-0.111
-0.471
-0.772
0.000
0.046
0.076
0.113
0.138
0.156
0.173
0.190
0.217
0.245
0.275
0.336
0.430
0.554
0.641
0.718
0.355
0.417
0.497
0.592
0.641
0.668
0.688
0.702
0.716
0.724
0.728
0.731
0.732
0.732
0.732
0.732
0.9954
1.0000
5.9777
4.2366
1.000
1.000
-1.301
-6.553
0.849
1.000
6&+:$5=6&+ø/'.5ø7(5øø/(+(6$3/$1$10
ød<$3,6,
0.732
0.732
¶/ø.%ø5+202-(1=$0602'(/ø1ø1
log Teff = 4.5941, log L = 5.0418, R = 7.201 R, Mbol = -7.864, X = 0.7, Z = 0.03.
KonvHNWLIoHNLUGH÷LQNWOHVL0¶GLU.HVLNOLoL]JLNRQYHNWLIoHNLUGHNLOHÕúÕQÕPOÕGÕúNDWPDQODUDUDVÕQGDNL
VÕQÕUÕJ|VWHUPHNWHGLU
Mr/M
log Tc
log Lr/L
log ρc
R/R
log (∇rad/∇ad)
0
0.0400
0.0853
0.1542
0.2071
0.2778
0.3215
0.3721
0.4975
0.5749
0.7663
1.0189
7.5526
7.5504
7.5485
7.5462
7.5446
7.5427
7.5416
7.5404
7.5375
7.5359
7.5320
7.5273
........
3.555
3.860
4.093
4.206
4.314
4.367
4.419
4.518
4.565
4.696
4.736
0.473
0.470
0.463
0.458
0.454
0.449
0.447
0.444
0.437
0.433
0.424
0.413
0.000
0.269
0.345
0.421
0.465
0.514
0.541
0.568
0.628
0.694
0.730
0.807
0.950
0.930
0.913
0.884
0.877
0.860
0.850
0.839
0.814
0.784
0.768
0.730
70
1.5532
2.3424
3.0605
5.1221
6.5549
8.3171
12.6712
15.3354
7.5183
7.5062
7.4960
7.4683
7.4496
7.4265
7.3650
7.3221
4.842
4.925
4.967
5.019
5.031
5.038
5.337
5.337
0.392
0.363
0.339
0.280
0.243
0.200
0.067
-0.031
0.937
1.089
1.203
1.469
1.624
1.794
2.173
2.403
0.660
0.573
0.506
0.353
0.272
0.191
0.055
0.006
18.9169
21.9517
25.0006
27.7135
28.5000
30.0000
7.2558
7.1895
7.1015
6.9737
6.9098
4.5900
5.337
5.337
5.337
5.337
5.337
5.337
-0.178
-0.336
-0.596
-0.976
-1.182
-12.000
2.728
3.037
3.533
3.988
4.249
7.201
-0.034
-0.070
-0.093
-0.119
-0.093
........
19.1.36&+:$5=6&+ø/'.5ø7(5øø/(+(6$3/$1$10¶/ø.%ø5+202-(1=$0602'(/ø1ø1
ød<$3,6,
log Teff = 4.627, log L = 5.315, log Tsurf = 4.557, R = 8.487 R, Mbol = -8.548, X = 0.7, Z = 0.03.
.RQYHNWLIoHNLUGH÷LQNWOHVL0 ’dir. Kesikli çizgi, konvekti IoHNLUGHNLOHÕúÕQÕPOÕGÕúNDWPDQODUDUDVÕQGDNL
VÕQÕUÕJ|VWHUPHNWHGLU
Mr/M
log Tc
log Lr/L
log ρc
R/R
log (∇rad/∇ad)
0
0.0400
0.0976
0.2044
0.3175
0.4917
0.6566
0.7581
1.0088
1.5406
2.0342
5.1868
10.8218
15.1384
20.3504
24.2644
7.5687
7.5663
7.5644
7.5616
7.5592
7.5559
7.5531
7.5514
7.5476
7.5405
7.5344
7.5010
7.4470
7.4043
7.3456
7.2928
........
3.702
4.064
4.359
4.526
4.863
4.781
4.782
4.829
5.038
5.107
5.266
5.310
5.315
5.315
5.315
0.396
0.389
0.384
0.376
0.369
0.360
0.352
0.347
0.337
0.318
0.303
0.223
0.104
0.025
-0.121
-0.243
0.000
0.284
0.383
0.492
0.572
0.664
0.734
0.772
0.853
0.991
0.110
1.555
2.099
2.439
2.832
3.145
10.451
9.887
9.387
8.925
8.292
7.902
7.219
6.422
5.833
5.214
3.091
1.583
1.321
1.094
1.050
1.000
30.2375
35.2456
37.2063
38.0860
39.0724
39.7021
39.9600
7.1935
7.0644
6.9808
6.9224
6.8179
6.6658
6.4107
5.315
5.315
5.315
5.315
5.315
5.315
5.315
-0.472
-0.792
-1.110
-1.305
-1.631
-2.148
-2.930
3.688
4.353
4.771
5.047
5.527
6.168
7.013
0.865
0.829
0.789
0.815
0.779
0.808
0.858
71
19.1.4. ROXBURGH .5ø7(5øø/(+(6$3/$1$10¶/ø.%ø5+202-(1=$0602'(/ø1ø1ød
YAPISI
log Teff = 4.59, log L = 5.257, log Tsurf = 4.557, R = 9.416 R, Mbol = -8.40, X = 0.7, Z = 0.03.
.RQYHNWLIoHNLUGH÷LQNWOHVL0
VÕQÕUÕJ|VWHUPHNWHGLU
¶GLU.HVLNOLoL]JLNRQYHNWLIoHNLUGHNLOHÕúÕQÕPOÕGÕúNDWPDQODUDUDVÕQGDNL
Mr/M
0.0000
0.0231
0.1599
1.0666
6.3386
24.4712
31.8283
log Tc
7.5082
7.5066
7.5025
7.4874
7.4324
7.2444
7.0960
log Lr/L
.........
3.383
4.181
4.859
5.223
5.257
5.257
log ρc
0.193
0.189
0.179
0.142
0.027
-0.419
-0.728
R/R
0.000
0.276
0.529
1.012
1.936
3.635
4.415
log (∇rad/∇ad)
15.996
15.990
15.976
15.922
15.729
15.050
14.587
35.9454
39.9900
39.9999
40.0000
6.9791
6.1892
5.4209
4.5123
5.257
5.257
5.257
5.257
-1.065
-3.564
-6.141
-12.000
5.074
8.216
9.188
9.455
14.121
1.0854
7.856
0.000
19.2. 7HN\ÕOGÕ]ODULoLQHYULPPRGHOOHUL
g, çekim; Tc ve ρcVÕFDNOÕNYH\R÷XQOX÷XQPHUNH]GHNLGH÷HUOHULGLU
<DúODUPLO\RQ\ÕOELULPLQGHYHULOPLúWLU
19.2.1. ÖBEK I YILDIZLARI –%h<h.0(5.(=ø),5/$70$l = α.Hp ; α = 1
M = 1.2 M, X = 0.7, Z = 0.02 Chiosi ve ark. (1987)
<Dú
0
801.488
1625.39
2417.61
4287.25
4728.40
4740.35
4768.50
4885.65
4987.07
5030.63
5047.00
5108.61
5122.68
5131.03
5137.13
5138.97
log L/ L
log Teff
log g
log Tc
log ρc
Χc
0.326
0.369
0.416
0.464
0.556
0.768
0.703
0.650
0.900
1.200
1.400
1.500
2.002
2.297
2.599
2.999
3.189
3.816
3.816
3.815
3.810
3.778
3.795
3.754
3.727
3.702
3.690
3.681
3.675
3.645
3.625
3.603
3.573
3.558
4.443
4.402
4.349
4.283
4.063
3.917
3.818
3.766
3.416
3.066
2.829
2.708
2.085
1.710
1.322
0.798
0.549
7.2155
7.2354
7.2586
7.2835
7.3522
7.4987
7.4887
7.5593
7.5492
7.5235
7.5395
7.5518
7.6361
7.6803
7.7334
7.8136
7.8547
1.9794
2.0297
2.0765
2.1173
2.243
3.03334
3.7985
4.2662
4.8958
5.0877
5.1761
5.2163
5.4366
5.5326
5.6335
5.782
5.8627
0.700
0.599
0.501
0.400
0.101
0.000
0
0
0
0
0
0
0
0
0
0
0
M = 1.5 M, X = 0.7, Z = 0.02 Chiosi ve ark. (1987)
<Dú
0
579.907
1150.3
1974.21
2735.46
2738.44
2741.12
2746.38
log L/ L
log Teff
log g
log Tc
log ρc
Χc
0.738
0.791
0.847
0.942
1.205
1.055
1.012
1.099
3.885
3.881
3.872
3.839
3.816
3.749
3.73
3.712
4.404
4.336
4.245
4.017
3.661
3.545
3.511
3.354
7.2754
7.2923
7.3108
7.3435
7.543
7.5388
7.5691
7.6171
1.9211
1.9427
1.9606
2.0057
2.8594
3.5296
3.7613
4.0529
0.7
0.604
0.499
0.3010
0
0
0
0
72
2755.5
2765.95
2771.03
2780.27
2784.53
2790.63
2800.37
2803.44
2804.45
1.402
1.799
2.000
1.854
2.000
2.200
2.611
2.802
2.877
3.694
3.670
3.657
3.667
3.658
3.644
3.614
3.599
3.594
2.976
2.485
2.233
2.419
2.235
1.979
1.450
1.199
1.101
7.7019
7.7935
7.8391
7.9102
7.9066
7.8942
7.8915
7.9024
7.9756
4.4237
4.774
4.9375
5.223
5.3006
5.4002
5.5784
5.6585
5.6804
0
0
0
0
0
0
0
0
0
M = 2 M, X = 0.7, Z = 0.02 Chiosi ve ark. (1987)
<Dú
0
326.237
579.747
960.011
1263.96
1266.42
1268.66
1272.92
1273.49
1274.44
1280.66
1321.98
1374.56
1416.58
1418.71
1418.96
1420.75
1429.74
1443.19
1445.92
1447.9
1448.15
1448.67
1449.03
1449.08
log L/ L
log Teff
log g
log Tc
log ρc
Xc/Yc
1.228
1.298
1.363
1.481
1.656
1.522
1.798
2.465
2.560
2.387
1.810
1.751
1.808
1.997
2.200
2.122
2.047
2.105
2.408
2.608
2.905
3.002
3.200
3.288
3.307
3.98
3.974
3.964
3.921
3.849
3.724
3.691
3.641
3.634
3.648
3.691
3.697
3.697
3.682
3.666
3.672
3.678
3.673
3.649
3.633
3.61
3.602
3.586
3.579
3.578
4.420
4.326
4.220
3.933
3.470
3.104
2.693
1.829
1.704
1.932
2.683
2.767
2.709
2.458
2.192
2.293
2.392
2.317
1.918
1.654
1.265
1.135
0.873
0.757
0.732
7.3256
7.3395
7.353
7.3824
7.5304
7.6338
7.74
7.9653
8.035
8.0425
8.0526
8.0642
8.0986
8.2211
8.2455
8.2015
8.1091
8.1099
8.1468
8.1396
8.0908
8.0773
8.0373
8.0054
8.0005
1.7883
1.7933
1.7988
1.8291
2.262
3.5484
4.0396
4.754
4.793
4.5359
4.4193
4.3396
4.259
4.5591
4.845
4.9289
5.0465
5.1821
5.5317
5.7087
5.9537
5.9967
6.0851
6.1411
6.1475
0.7
0.599
0.501
0.29
0.001
0
0
0.98
0.979
0.972
0.949
0.802
0.404
0.011
0
0
0
0
0
0
0
0
0
0
0
M = 3 M, X = 0.7, Z = 0.02 Chiosi ve ark. (1987)
<Dú
log L/ L
log Teff
log g
log Tc
log ρc
Xc/Yc
0
104.416
227.232
321.77
398.08
424.186
428.629
429.117
429.544
429.844
430.001
430.429
434.237
460.441
463.855
463.863
463.876
463.913
465.175
1.902
1.968
2.072
2.173
2.269
2.316
2.470
2.236
2.595
2.807
2.919
3.005
2.602
2.506
2.718
2.726
2.731
2.694
2.761
4.099
4.094
4.08
4.05
3.982
3.945
4.016
3.707
3.658
3.64
3.632
3.624
3.659
3.679
3.652
3.651
3.651
3.655
3.647
4.400
4.312
4.152
3.932
3.565
3.366
3.500
2.498
1.942
1.657
1.511
1.396
1.940
2.113
1.794
1.783
1.776
1.828
1.733
7.3766
7.3871
7.4041
7.4254
7.4628
7.51
7.6512
7.7485
7.8743
7.963
8.0104
8.0822
8.1022
8.1949
8.338
8.3347
8.3202
8.2959
8.2129
1.5763
1.5703
1.5726
1.5897
1.6632
1.8075
2.4675
3.435
3.8898
4.1685
4.306
4.185
3.992
4.006
4.5301
4.5545
4.5784
4.6308
5.0882
0.7
0.608
0.47
0.31
0.11
0.19
0
0
0
0
0.98
0.97
0.901
0.1
0
0
0
0
0
73
466.92
467.909
468.198
468.498
468.619
468.706
468.733
468.736
3.011
3.327
3.503
3.803
4.001
3.921
4.089
4.100
3.625
3.600
3.586
3.562
3.549
3.554
3.545
3.545
1.396
0.979
0.744
0.349
0.100
0.200
0.005
0.018
8.2536
8.3185
8.3354
8.2942
8.2143
8.1358
8.1068
8.1034
5.3714
5.6757
5.8494
6.1699
6.4017
6.6541
6.7247
8.1034
0
0
0
0
0
0
0
0
M = 5 M, X = 0.7, Z = 0.02 Chiosi ve ark. (1987)
<Dú
log L/ L
log Teff
log g
log Tc
log ρc
Xc/Yc
0
32.6348
60.3164
92.938
119.289
120.591
120.671
120.68
120.729
120.798
120.825
120.888
120.971
123.484
126.624
128.198
128.212
128.216
128.221
128.344
128.515
128.629
128.659
128.673
128.679
2.712
2.789
2.87
3.011
3.184
3.238
3.312
3.272
3.244
3.115
3.401
3.603
3.724
3.405
3.452
3.497
3.527
3.542
3.556
3.699
3.904
4.101
4.222
4.402
4.463
4.236
4.232
4.223
4.193
4.100
4.136
4.171
4.162
4.016
3.667
3.625
3.608
3.598
3.629
3.702
3.622
3.618
3.617
3.615
3.602
3.585
3.569
3.565
3.556
3.554
4.358
4.266
4.147
3.887
3.343
3.431
3.498
3.502
2.947
1.680
1.226
0.954
0.793
1.240
1.482
1.115
1.072
1.051
1.031
0.835
0.563
0.304
0.162
0.052
0.122
7.4308
7.4414
7.4546
7.4806
7.5646
7.6405
7.7304
7.7303
7.7929
7.9032
7.9485
8.0486
8.1348
8.1696
8.2209
8.3761
8.401
8.4074
8.4028
8.4189
8.5101
8.5914
8.5634
8.4149
8.3387
1.2975
1.2928
1.2874
1.3055
1.5124
1.7308
2.2045
2.3533
2.8427
3.2947
3.449
3.7669
3.7512
3.5317
3.5617
4.0079
4.1124
4.171
4.2189
4.8225
4.3841
6.0799
6.51
6.8788
7.0239
0.7
0.599
0.486
0.296
0.021
0.001
0
0
0
0
0
0
0.972
0.701
0.223
0.001
0
0
0
0
0
0
0
0
0
M = 9 M, X = 0.7, Z = 0.02 Chiosi ve ark. (1987)
<Dú
log L/ L
log Teff
log g
log Tc
log ρc
Xc/Yc
0
8.64708
16.8651
26.5255
34.5502
35.0071
35.0247
35.0273
35.0299
35.0557
35.9597
36.5093
36.9585
36.9733
36.9742
36.9908
36.9992
37.0154
37.0195
3.577
3.654
3.746
3.898
4.101
4.129
4.101
4.004
4.352
4.524
4.282
4.337
4.350
4.393
4.401
4.498
4.584
4.690
4.707
4.378
4.376
4.369
4.342
4.243
4.247
3.799
3.627
3.587
3.575
3.601
3.784
3.59
3.586
3.585
3.577
3.572
3.566
3.565
4.315
4.23
4.111
3.852
3.253
3.241
1.476
0.887
0.376
0.157
0.503
1.162
0.392
0.331
0.32
0.191
0.085
0.044
0.064
7.4852
7.4954
7.5086
7.5348
7.6212
7.8961
8.0422
8.0638
8.0855
8.1952
8.2383
8.2770
8.4120
8.4746
8.4863
8.5728
8.6183
8.7388
8.8343
0.996
0.99
0.9872
1.0052
1.2131
2.3793
2.9697
3.0441
3.1163
3.2652
3.16
3.2245
3.6037
3.8043
3.8468
4.3552
4.5916
5.2874
5.8423
0.7
0.607
0.494
0.302
0.022
0
0
0
0.98
0.969
0.514
0.214
0.004
0
0
0
0
0
0
74
19.2.2. ÖBEK I YILDIZLARI –g1(0/ø.219(.7ø)FIRLATMA: l = α.Hp ; α = 1.5 -1 1.75; Roxburgh
M = 6 M, X = 0.7, Z = 0.03 Doom (1987)
<Dú
M/M
- M
log L/L
log Teff
Χat
Mcc
Χc/Yc
0.0000
1.1903
2.0266
3.2399
4.8807
6.9954
9.6120
12.7389
16.6400
21.3344
26.4344
31.1333
35.5172
39.0643
42.3994
45.3914
48.1764
50.7548
55.4573
59.0801
62.3067
65.2278
67.9515
69.0181
69.5051
69.7308
69.8946
69.9393
69.9460
69.9560
69.9626
69.9829
69.9895
69.9962
69.9995
70.0062
70.0128
70.0228
70.0295
6.0000
NML (kütle
2.9730
2.9730
2.9750
2.9810
2.9890
3.0050
3.0140
3.0310
3.0530
3.0790
3.1090
3.1380
3.1690
3.1930
3.2180
3.2410
3.2610
3.2800
3.3170
3.3460
3.3720
3.3950
3.4200
3.4360
3.4490
3.4610
3.4870
3.5270
3.5450
3.5310
3.4950
3.4840
3.4880
3.4870
3.4850
3.4770
3.4650
3.4420
3.4220
4.2660
4.2660
4.2650
4.2650
4.2640
4.2630
4.2620
4.2600
4.2570
4.2530
4.2490
4.2440
4.2380
4.2320
4.2260
4.2190
4.2120
4.2050
4.1880
4.1710
4.1540
4.1360
4.1200
4.1180
4.1210
4.1260
4.1430
4.1680
4.1750
4.1690
4.1490
4.0610
4.0270
3.9900
3.9910
3.9270
3.8770
3.7780
3.6700
0.7000
2.4000
2.3300
2.3400
2.3400
2.3200
2.31
2.2800
2.2600
2.2000
2.1800
2.1000
2.0500
1.9700
1.9200
1.8600
1.7800
1.7300
1.7100
1.6000
1.4800
1.3900
1.3200
1.2100
1.1700
1.1600
1.1600
1.1600
1.0300
0.7600
0.7600
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.7000
0.6960
0.6930
0.6790
0.6690
0.6560
0.6400
0.6180
0.5910
0.5580
0.5270
0.4990
0.4580
0.4250
0.3940
0.3940
0.3340
0.2710
0.2140
0.1600
0.1070
0.0480
0.0230
0.0110
0.0050
0.0010
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
ND\EÕ\RN
6.0000
0.7000
75
M = 10 M, X = 0.7, Z = 0.03 Doom (1987)
<Dú
M/M
0.0000
0.2276
0.4305
0.7491
1.2134
1.8398
2.6461
3.6429
4.8322
6.8142
8.9101
10.8589
12.6354
14.2517
17.0242
19.2400
20.1640
22.3847
23.5933
25.0516
25.8907
27.0125
27.2854
27.3565
27.3642
27.3672
27.3688
27.3704
27.3736
27.3767
27.3791
27.3815
27.3839
27.3863
27.3887
27.3895
10
10
-M
NML
log L/L
3.7160
3.7160
3.7100
3.7130
3.7190
3.7280
3.7400
3.7550
3.7730
3.8050
3.8400
3.9750
3.9090
3.9410
3.9970
4.0530
4.0730
4.1320
4.1650
4.2070
4.2320
4.2730
4.2940
4.3210
4.3400
4.3560
4.3690
4.3690
4.3360
4.3090
4.3040
4.3060
4.3090
4.3080
4.3020
4.0640
log Teff
4.3870
4.3870
4.3970
4.3870
4.3970
4.3870
4.3860
4.3850
4.3830
4.3800
4.3770
4.3740
4.3700
4.3650
4.3550
4.3410
4.3340
4.3120
4.2950
4.2690
4.2510
4.2270
4.2290
4.2540
4.2680
4.2770
4.2810
4.2800
4.2590
4.2150
4.1680
4.1080
4.0310
3.9260
3.7510
3.5930
Χat
Mcc
Χc/Yc
0.7000
4.9300
4.7700
4.8700
4.8700
4.8600
4.8400
4.8200
4.7600
4.7500
4.6300
4.5800
4.4600
4.4100
4.2800
4.1800
4.0000
3.8900
3.7200
3.5900
3.4300
3.3300
3.1600
3.1300
3.0600
2.9100
2.2900
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.7000
0.6980
0.6960
0.6930
0.6880
0.6800
0.6700
0.6570
0.6410
0.6130
0.5800
0.5470
0.5140
0.4810
0.4190
0.3540
0.3240
0.2440
0.1940
0.1270
0.0840
0.0220
0.0050
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.7000
76
M = 20 M, X = 0.7, Z = 0.03; α = 1.5 Prantzos ve ark. (1987)
<Dú
M/M
-M
log L/L
log Teff
Χat
Mcc
Χc/Yc
0.0000
0.1546
0.4541
0.6944
1.0039
1.8443
2.6067
3.5196
4.3706
5.1230
5.7840
6.3970
6.9527
7.4351
7.8351
8.1843
8.7780
9.2394
9.9342
10.0730
10.1986
10.3160
10.7062
11.0719
11.2561
11.2834
11.2969
11.3101
11.3104
11.3118
11.3138
11.3150
11.3160
20.0000
19.9900
19.9700
19.9500
19.9200
19.8400
19.7600
19.6500
19.5300
19.4000
19.2800
19.1500
19.0200
18.8900
18.7700
18.6500
18.4200
18.2100
17.7200
17.6300
17.5400
17.1800
16.7300
16.4500
16.4000
16.3800
16.3600
16.3600
16.3600
16.3600
16.3500
16.3500
16.3500
7.72E-8
7.61E-8
7.90E-8
8.25E-8
8.68E-8
9.99E-8
1.14E-8
1.33E-7
1.55E-7
1.77E-7
2.01E-7
2.20E-7
2.52E-7
2.82E-7
3.14E-7
3.48E-7
4.19E-7
4.94E-7
6.66E-7
7.15E-7
7.61E-7
8.10E-7
1.03E-6
1.42E-6
1.67E-6
1.64E-6
1.62E-6
1.66E-6
1.68E-6
1.83E-6
2.29E-6
2.69E-6
3.31E-6
4.5730
4.5740
4.5790
4.5870
4.5970
4.6270
4.6550
4.6890
4.7240
4.7560
4.7840
4.8090
4.8340
4.8570
4.8770
4.8960
4.9280
4.9550
4.9980
5.0070
5.0150
5.0230
5.0520
5.0820
5.1040
5.1090
5.1140
5.1340
5.1370
5.1550
5.1800
5.1820
5.1780
5.5200
4.5200
4.5180
4.5170
4.5160
4.5160
4.5140
4.5050
4.5000
4.5000
4.4900
4.4860
4.4780
4.4710
4.4630
4.4550
4.4380
4.4210
4.3840
4.3730
4.3640
4.3660
4.3150
4.2580
4.2380
4.2490
4.2590
4.2790
4.2910
4.2730
4.2300
4.1750
4.0970
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
12.7200
12.9100
12.9100
12.9100
12.8900
12.8800
12.6800
12.4700
12.2500
11.9100
11.1600
11.6300
11.6300
11.4500
11.2100
11.1400
11.0700
10.8000
10.3310
10.2710
10.2130
0.7000
0.6960
0.6870
0.6790
0.6690
0.6390
0.6100
0.5720
0.5340
0.4970
0.4620
0.4270
0.3930
0.3620
0.3340
0.3080
0.2610
0.2220
0.1560
0.1420
0.1290
0.1170
0.0740
0.0300
0.0070
0.0040
0.0020
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
77
M = 40 M, X = 0.7, Z = 0.03; α = 1.5 Prantzos ve ark. (1987)
<Dú
M/M
-M
log L/L
log Teff
Χat
Mcc
Χc/Yc
0.0000
0.1537
0.2499
0.3917
0.5680
0.7865
1.1048
1.4842
2.0537
2.5516
2.9816
3.3591
3.6630
3.9588
4.1702
4.3708
4.6966
4.8516
4.9890
5.1114
5.2257
5.4254
5.5168
5.6967
5.8970
6.0244
6.2314
6.3157
6.3886
6.4002
6.4010
6.4016
6.4024
6.4028
6.4040
6.4061
6.4063
6.4085
6.4101
6.4192
6.4277
6.4348
6.4412
6.4486
6.4925
6.5208
6.5528
6.5923
6.6077
6.6401
6.6605
6.6955
6.7074
6.7822
6.7870
40.0000
39.9300
39.8800
39.8200
39.7300
39.6100
39.4600
39.1800
38.7800
38.3800
37.9900
37.5900
37.2300
36.8700
36.5400
36.2300
35.6500
35.3400
35.0400
34.7500
34.4600
33.9000
33.6100
32.9900
32.1800
31.6200
30.6500
30.2400
29.8900
29.8400
29.8300
29.8200
29.8200
29.8100
29.8000
28.3600
28.2900
28.1600
28.0700
27.5200
27.0100
26.5800
26.2000
25.7600
23.1200
21.4200
19.5000
17.1300
16.2100
14.2600
13.0400
10.9400
10.2300
5.7400
4.0000
4.68E-7
4.68E-7
4.84E-7
5.02E-7
5.28E-7
5.61E-7
5.99E-7
6.48E-7
7.59E-7
8.52E-7
9.90E-7
1.10E-6
1.25E-6
1.36E-6
1.50E-6
1.64E-6
1.93E-6
2.09E-6
2.27E-6
2.44E-6
2.63E-6
3.03E-6
3.25E-6
3.73E-6
4.31E-6
4.50E-6
4.88E-6
4.87E-6
4.56E-6
6.49E-6
7.56E-6
8.03E-6
8.67E-6
9.41E-6
1.66E-5
5.43E-4
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
5.2730
5.2720
5.2760
5.2830
5.2920
5.3050
5.3200
5.3410
5.3720
5.4010
5.4280
5.4530
5.4730
5.4930
5.5110
5.5270
5.5540
5.5670
5.5790
5.5910
5.6010
5.6220
5.6310
5.6520
5.6750
5.6910
5.7180
5.7340
5.7510
5.8370
5.8590
5.8680
5.8770
5.8810
5.8970
5.9110
5.9150
5.9310
5.9450
5.8960
5.8190
5.7980
5.7770
5.7670
5.7070
5.6590
5.5750
5.5220
0.4800
5.3980
5.3350
5.2080
5.1560
4.6580
4.4700
4.6110
4.6110
4.6100
4.6090
4.6080
4.6060
4.6040
4.6170
4.5960
4.5930
4.5860
4.5810
4.5730
4.5670
4.5610
4.5540
4.5390
4.5310
4.5220
4.5140
4.5060
4.4900
4.4810
4.4670
4.4570
4.4670
4.4900
4.5140
4.5620
4.5540
4.5310
4.5220
4.5070
4.4850
4.3110
4.2950
4.6130
4.6170
4.6040
4.7060
4.7190
4.7220
4.7220
4.7220
4.7100
4.6990
4.6820
4.6700
4.6610
4.6430
4.6300
4.6000
4.5890
4.4720
4.4000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.6990
0.6890
0.6680
0.6080
0.5750
0.5400
0.5390
0.5390
0.5380
0.5380
0.3700
0.5360
0.3810
0.3730
0.3560
0.3360
0.2630
0.2070
0.1400
0.0040
0.0040
0.7800
0.7190
0.7170
0.6320
0.6020
0.5420
0.5090
0.4530
0.4360
0.3490
0.3360
31.6600
31.9300
31.8400
31.7400
31.6200
31.2500
31.0700
30.8800
30.3000
29.9100
29.4200
29.1300
28.8100
28.5200
28.2600
28.0600
27.6900
275300
27.3700
27.2300
27.1000
26.8700
26.7800
26.5800
26.3400
26.1900
25.8900
25.7500
25.7100
0.0000
0.0200
3.1400
9.8800
13.6900
22.6500
23.7800
23.9700
23.1500
23.8800
24.6000
25.0100
24.7500
24.7700
24.3500
21.7600
20.0800
18.2000
15.7800
14.8600
12.9500
11.7400
9.6000
8.8800
4.4400
3.1800
7.0000
0.6920
0.6860
0.6770
0.6650
0.6510
0.6320
0.6000
0.5550
0.5130
0.4740
0.4380
0.4060
0.3750
0.3480
0.3240
0.2820
0.2610
0.2420
0.2240
0.2070
0.1760
0.1620
0.1310
0.0970
0.0740
0.0340
0.0170
0.0020
0.0000
0.0000
0.9700
0.9700
0.9700
0.9690
0.9660
0.9660
0.9630
0.9610
0.9430
0.9230
0.9140
0.8990
0.8820
0.8480
0.7810
0.6540
0.5790
0.5520
0.4980
0.4660
0.4180
0.4030
0.3300
0.3000
78
M = 60 M, X = 0.7, Z = 0.03; α = 1.5 Prantzos ve ark. (1987)
<Dú
M/M
-M
log L/L
log Teff
Χat
Mcc
Χc/Yc
0.1256
0.3215
0.4665
0.6465
0.8615
1.6434
2.0141
2.3233
2.5968
2.8898
3.0756
3.4525
3.6088
4.0021
4.2543
4.4367
4.5687
4.7614
4.8953
5.0004
5.0084
5.0099
5.0116
5.0126
5.0143
5.0252
5.0296
5.0357
5.0433
5.0472
5.0557
5.0764
5.0901
5.1197
5.1461
5.1823
5.2392
5.2899
5.3325
5.3826
5.4253
5.4624
5.4905
5.5139
5.5160
59.8700
59.6400
59.4600
59.2300
58.9400
57.7000
57.0200
56.3800
56.7500
55.7490
54.4500
53.2100
52.6200
50.8900
49.5900
48.5500
47.7800
46.6200
45.7900
45.1400
45.0900
45.0800
45.0300
44.9700
44.8700
44.2200
43.9600
43.5900
43.1400
42.9000
42.3900
41.1500
40.3300
38.5500
36.9700
34.7900
31.3800
28.3400
25.7800
22.7800
20.2200
17.9900
16.3100
14.9000
14.7700
1.11E-6
1.20E-6
1.26E-6
1.32E-6
1.42E-6
1.71E-6
1.96E-6
2.17E-6
2.41E-6
2.77E-6
3.03E-6
3.62E-6
3.94E-6
4.81E-6
5.55E-6
5.81E-6
5.90E-6
6.15E-6
6.22E-6
5.90E-6
5.74E-6
6.54E-6
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
5.6200
5.6300
5.6390
5.6490
5.6650
5.7120
5.7390
5.7630
5.7790
5.8070
5.8220
5.8560
5.8690
5.9090
5.9460
5.9630
5.9810
6.0080
6.0290
6.0530
6.0920
6.1520
6.1760
6.1810
6.1420
6.1170
6.1110
6.1060
6.1030
6.1000
6.0930
6.0830
6.0750
6.0470
6.0330
5.9960
5.9530
5.8890
5.8390
5.7850
5.7000
5.6390
5.5860
5.5530
5.5690
4.6490
4.6460
4.6440
4.6420
4.6400
4.6350
4.6290
4.6250
4.6180
4.6100
4.6040
4.5930
4.5870
4.5840
4.5890
4.6040
4.6240
4.6530
4.6830
4.7360
4.7960
4.8270
4.7350
4.7280
4.7550
4.7750
4.7790
4.7840
4.7880
4.7900
4.7910
4.4900
4.7900
4.7840
4.7820
4.7750
4.7650
4.7550
4.7450
4.7340
4.7170
4.7040
4.6960
4.6930
4.6980
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.6990
0.6990
0.6540
0.6040
0.5540
0.4700
0.4140
0.3420
0.2890
0.2850
0.2840
0.2810
0.2770
0.2690
0.2250
0.0230
0.1650
0.1060
0.0660
0.0000
0.8760
0.8580
0.7810
0.7120
0.6070
0.4610
0.3470
0.2600
0.1970
0.1160
0.0760
0.0420
0.0230
0.0210
52.0500
51.7590
51.3040
51.1420
51.9340
49.3040
48.4230
47.8410
47.8410
47.4030
46.6930
46.2940
45.7050
45.3910
44.5810
43.8870
43.4170
43.2190
42.8060
42.4580
27.9650
0.0930
25.1000
39.2480
41.7150
42.0050
42.0130
41.9290
41.7630
41.6510
41.1830
39.9530
39.0970
37.4490
35.8030
33.7460
30.2180
27.2770
24.7030
21.6940
19.1840
16.8310
15.1000
13.2740
10.8520
0.6910
0.6740
0.6620
0.6450
0.6250
0.0544
0.5020
0.4640
0.4290
0.3890
0.3620
0.3050
0.2790
0.2110
0.1630
0.1260
0.0990
0.0560
0.0260
0.0020
0.0000
0.0000
0.9690
0.9680
0.9650
0.9470
0.9370
0.9210
0.8980
0.8860
0.8600
0.8000
0.7600
0.6790
0.6090
0.5190
0.3910
0.2900
0.2150
0.1490
0.0860
0.0470
0.0210
0.0010
0.0000
79
M = 80 M, X = 0.7, Z = 0.03; α = 1.5 Prantzos ve ark. (1987)
<Dú
M/M
-M
log L/L
log Teff
Χat
Mcc
Χc/Yc
0.0000
0.1142
0.1900
0.2925
0.4246
0.5865
0.7852
1.4952
1.7614
2.0253
2.3109
2.5306
2.7320
2.9547
3.2032
3.4022
3.8650
4.1352
4.3768
4.3817
4.3830
4.3855
4.3865
4.3899
4.3917
4.4046
4.4127
4.4307
4.4707
4.5076
4.5635
4.6007
4.6360
4.6851
4.7282
4.7596
4.8005
4.8045
4.8050
4.8060
80.0000
79.7900
79.6500
79.4400
79.1600
78.8000
78.3300
76.3900
75.5600
74.6600
73.5600
72.6200
71.6700
70.5000
69.0600
67.8000
64.6300
62.5400
60.5100
60.4300
60.3500
60.2000
60.1400
59.9700
59.8800
59.1100
58.6200
57.5400
55.1400
52.9200
49.5700
47.3400
45.2200
42.2700
39.6900
37.8000
35.2100
35.1100
35.0800
35.0200
1.89E-6
1.91E-6
1.98E-6
2.06E-6
2.15E-6
2.15E-6
2.45E-6
2.96E-6
3.27E-6
3.59E-6
4.11E-6
4.49E-6
4.91E-6
5.57E-6
6.05E-6
6.61E-6
7.05E-6
8.10E-6
7.37E-6
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
6.00E-5
5.8480
5.9480
5.8500
5.8560
5.8630
5.8730
5.8890
5.9370
5.9570
5.9730
5.9950
6.0160
6.0350
6.0560
6.0850
6.1050
6.1570
6.2000
6.2490
6.3700
6.3960
6.4110
6.3740
6.2580
6.3010
6.2970
6.2930
6.2890
6.2700
6.2520
6.2330
6.2090
6.1840
6.1600
6.1296
6.1080
6.0940
6.1010
6.1080
6.1280
406670
4.6660
4.6680
4.6660
4.6640
4.6610
4.6590
4.6530
4.6490
4.6440
4.6360
4.6320
4.6310
4.6270
4.6340
4.6390
4.6880
4.7140
4.8130
4.7830
4.7530
4.8160
4.8120
5.0120
4.8230
4.8300
4.8310
4.8310
4.8300
4.8260
4.8260
4.8200
4.8180
4.8130
4.8090
4.8080
4.8110
4.8150
4.8180
4.8260
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.7000
0.6870
0.6570
0.6210
0.5810
0.4060
0.2850
0.1510
0.1450
0.1390
0.1300
0.1280
0.1220
0.1180
0.0590
0.0000
0.9070
0.8230
0.7040
0.5320
0.4320
0.3850
0.2340
0.1700
0.1040
0.1510
0.0430
0.0410
0.0400
71.9000
71.6630
71.6670
71.4410
71.0330
70.6030
69.7680
67.7370
66.8680
66.2150
65.3680
64.7470
64.1890
63.5770
62.8630
62.1550
60.7490
59.2960
58.3610
37.1730
45.3360
52.5240
56.5870
59.1570
58.1090
57.8080
57.3740
56.2930
53.9340
51.7670
48.4050
46.3280
44.2570
41.2340
38.7740
36.7930
34.1190
33.1140
32.1400
0.0000
7.000
0.6900
0.6820
0.6720
0.6580
0.6400
0.6180
0.5300
0.4930
0.4560
0.4130
0.3780
0.3440
0.3050
0.2590
0.2190
0.1250
0.0610
0.0000
0.0000
0.0000
0.9590
0.9560
0.9520
0.9480
0.9090
0.8810
0.8200
0.8740
0.5820
0.4320
0.3440
0.2680
0.1740
0.1050
0.0580
0.0060
0.0010
0.0000
0.0000
80
19.2.3.ÖBEK I YILDIZLARI –.hdh.0(5.(=øFIRLATMA I=aHP; α=0.25
M = 1 M€; X = 0.7; Z = 0.02; Maeder ve Meynet (1988)
<$ù
M/M
− M
log L/L
log Teff
7.000+06
3.249+09
5.670+09
7.277+09
8447+09
9.197+09
9.701+09
1.039+10
1.098+10
1.158+10
1.173+10
1.191+10
1.197+10
1.195+10
1.226+10
1.235+10
1.243+10
1.248+10
1.253+10
1.257+10
1.260+10
1.263+10
1.265+10
1.267+10
1.268+10
1.270+10
1.271+10
1.273+10
1.274+10
1.274+10
1.275+10
1.275+10
1.276+10
1.276+10
1.276+10
1.277+10
1.277+10
1.277+10
1.277+10
1.277+10
1.277+10
1.277+10
1.277+10
1.000
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
I
1
l
1
1
0.999
0.999
0.998
0.998
0.997
0.996
0.994
0.993
0.992
0.99
0.988
0.985
0.982
0.969
0.962
0.953
0.941
0.926
0.905
0.877
0.837
0.784
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
NML
-10.968
-10.813
-10.658
-10.5
-10.343
-10.108
-10.19
-9.862
-9.704
-9.536
-9.373
-9.197
-9.043
-8.876
-8.45
-8.28
-8.095
-7.918
-7.744
-7.746
-7.342
-7.145
-6.945
-0.207
-0.075
0.006
0.069
0.118
0.156
0.186
0.234
0.080
0.322
0.327
0.321
0.319
0.318
0.428
0.517
0.622
0.712
0.820
0.921
1.023
1.122
1.221
1.321
1.42
1.564
1.517
1.717
1.815
1.915
2.015
2.115
2.215
2.315
2.56
2.66
2.76
2.86
2.96
3.06
3.16
3.26
3.346
3.739
3.751
3.757
3.759
3.759
3.758
3.757
3.755
3.750
3.734
3.725
3.710
3.704
3.700
3.678
3.676
3.673
3.671
3.668
3.666
3.663
3.66
3.656
3.653
3.648
3.639
3.643
3.631
3.626
3.617
3.612
3.602
3.598
3.590
3.563
3.555
3.540
3.529
3.520
3.501
3.481
3.468
3.446
Xat
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.698
0.696
0.692
0.689
0.686
0.684
0.682
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
0.681
Mcc
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Xc/Yc
0.700
0.472
0.279
0.143
0.031
0.002
0.000
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.18
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
M = 1.3 M€; X = 0.7; Z = 0.02; α = 0.25; Maeder ve Meynet (1988)
<$ù
2.000+007
4.510+009
6.777+009
7.630+009
8.038+009
8.114+009
8.123+009
8.128+009
8.153+009
M/M
1.300
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
− M
NML
NML
NML
NML
NML
NML
NML
NML
NML
log L/L
0.401
0.477
0.579
0.611
0.631
0.709
0.781
0.763
0.763
log Teff
3.816
3.797
3.791
3.776
3.764
3.778
3.79
3.777
3.755
Xat
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
0.700
Mcc
0.075
0.2054
0.1664
0.1404
0.1131
0.0962
0.0546
0
0
Xc/Yc
0.682
0.473
0.28
0.143
0.03
0.002
0
0.98
0.98
81
8.179+009
8.193+009
8.206+009
8.219+009
8.235+009
8.283+009
8.315+009
8.343+009
8.368+009
8.393+009
8.414+009
8.433+009
8.449+009
8.459+009
8.470+009
8.474+009
8.478+009
8.484+009
8.491+009
8.497+009
8.503+009
8.507+009
8.511+009
8.514+009
8.517+009
8.519+009
8.521+009
8.523+009
8.524+009
8.524+009
8.527+009
8.527+009
8.528+009
8.529+009
8.529+009
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.299
1.299
1.299
1.298
1.298
1.297
1.297
1.297
1.296
1.295
1.295
1.294
1.293
1.291
1.29
1.287
1.285
1.281
1.278
1.273
1.266
1.258
1. 247
1.234
1.216
1.193
1.168
NML
NML
NML
NML
NML
-11.545
-11.384
-11.232
-11.077
-10.914
-10.753
-10.601
-10.435
-10.277
-10.117
-10.029
-9.984
-10.082
-9.917
-9.758
-9.592
-9.426
-9.269
-9.097
-8.932
-8.763
-8.608
-8.435
-8.262
-8.091
-7.911
-7.732
-7.531
-7.346
-7.21
0.737
0.713
0.684
0.658
0.646
0.744
0.845
0.942
1.041
1.144
1.246
1.344
1.448
1.547
1.646
1.7
1.729
1.67
1.768
1.867
1.967
2.066
2.166
2.266
2.366
2.466
2.56
2.66
2.76
2.86
2.96
3.06
3.16
3.26
3.331
3.74
3.73
3.72
3.71
3.7
3.685
3.68
3.677
3.673
3.67
3.665
3.662
3.658
3.653
3.648
3.645
3.643
3.647
3.639
3.634
3.627
3.622
3.615
3.605
3.598
3.589
3.582
3.572
3.561
3.551
3.539
3.527
3.505
3.492
3.481
0.700
0.700
0.700
0.700
0.700
0.698
0.695
0.692
0.69
0.687
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0.685
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
1.5M€ X = 0.7 - Z = 0.02 - α=0.25 - Maeder ve Meynet, 1988
•
<$ù
M
Log( M )
Log L
Log Teff
Xat
Mcc
Xc-Yc
8.500+006
1.5
NML
0.577
3.821
0.314
0.699
0.700
3.338+009
1.5
NML
0.758
3.835
0.258
0.474
0.700
4.586+009
1.5
NML
0.845
3.818
0.2025
0.282
0.700
5.076+009
1.5
NML
0.872
3.795
0.1725
0.143
0.700
5.333+009
1.5
NML
0.891
3.78
0.1335
0.028
0.700
5.390+009
1.5
NML
0.976
3.801
0.114
0.002
0.700
5.397+009
1.5
NML
1.037
3.817
0.0675
0
0.700
5.404+009
1.5
NML
1.021
3.783
0
0.98
0.700
5.415+009
1.5
NML
1.002
3.76
0
0.98
0.700
82
5.425+009
1.5
NML
0.968
3.745
0
0.98
0.700
5.432+009
1.5
NML
0.92
3.729
0
0.98
0.700
5.437+009
1.5
NML
0.883
3.719
0
0.98
0.700
5.441+009
1.5
NML
0.855
3.709
0
0.98
0.700
5.445+009
1.5
NML
0.848
3.703
0
0.98
0.700
5.460+009
1.5
NML
0.94
3.688
0
0.98
0.698
5.470+009
1.5
NML
1.046
3.683
0
0.98
0.695
5.480+009
1.5
-10.99
1.147
3.679
0
0.98
0.691
5.489+009
1.5
-10.839
1.242
3.675
0
0.98
0.688
5.498+009
1.5
-10.684
134
3.67
0
0.98
0.686
5.507+009
1.5
-10.52
1.443
3.666
0
0.98
0.685
5.515+009
1.499
-10.365
1.541
3.662
0
0.98
0.684
5.523+009
1.499
-10.203
1.642
3.656
0
0.98
0.683
5.530+009
1.498
-10.04
1.741
3.649
0
0.98
0.683
5.535+009
1.498
-9.96
1.791
3.647
0
0.98
0.683
5.538+009
1.497
-9.878
1.841
3.644
0
0.98
0.683
5.542+009
1.497
-9.803
1.888
3.641
0
0.98
0.683
5.547+009
1.496
-10.058
1.734
3.651
0
0.98
0.683
5M€ X = 0.7- Z = 0.02- Maeder ve Meynet, 1988
<$ù
M
•
Log( M )
Log L
Log Teff
Xat
Mcc
Xc-Yc
1.250+06
5.000
NML
2.720
4.244
0.700
1.520
0.697
4.900+07
5.000
NML
2.851
4.219
0.700
1.310
0.476
7.565+07
5.000
NML
2.958
4.188
0.700
1.025
0.280
8.868+07
5.000
NML
3.019
4.155
0.700
0.840
0.140
9.636+07
5.000
NML
3.065
4.130
0.700
0.705
0.032
9.842+07
5.000
NML
3.110
4.159
0.700
0.635
0.002
9.881+07
5.000
NML
3.156
4.191
0.700
0.390
0.000
9.886+07
5.000
NML
3.117
4.159
0.700
0.000
0.000
9.898+07
5.000
NML
3.166
4.057
0.700
0.000
0.000
9.907+07
5.000
NML
3.131
3.946
0.700
0.000
0.000
9.912+07
5.000
NML
3.084
3.862
0.700
0.000
0.000
9.916+07
5.000
NML
3.023
3.766
0.700
0.000
0.981
9.918+07
5.000
NML
2.979
3.707
0.700
0.000
0.981
9.920+07
5.000
NML
2.924
3.662
0.700
0.000
0.981
9.920+07
5.000
NML
2.924
3.662
0.700
0.000
0.981
9.950+07
4.997
-7.793
3.454
3.588
0.690
0.300
0.973
1.045+08
4.952
-8.314
3.160
3.631
0.690
0.406
0.859
83
1.054+08
4.948
-8.324
3.168
3.641
0.690
0.416
0.790
1.063+08
4.944
-8.302
3.214
3.666
0.690
0.420
0.749
1.068+08
4.941
-8.315
3.248
3.698
0.690
0.425
0.740
1.073+08
4.939
-8.365
3.272
3.740
0.690
0.430
0.754
1.212+08
4.837
-7.960
3.445
3.674
0.690
0.624
0.309
1.235+08
4.810
-7.891
3.460
3.651
0.690
0.635
0.186
1.243+08
4.798
-7.850
3.453
3.625
0.690
0.662
0.104
1.250+08
4.788
-7.816
3.455
3.610
0.690
0.661
0.050
1.260+08
4.769
-7.635
3.553
3.586
0.690
0.095
0.000
9M€ X = 0.7 - Z = 0.02 - α=0.25 - Maeder ve Meynet, 1988
<$ù
•
M
Log(- M )
Log L
Log Teff
Xat
Mcc
Xc-Yc
7.301+005
9.000
NML
3.603
4.390
0.700
3.438
0.692
1.360+007
9.000
NML
3.756
4.369
0.700
2.970
0.472
2.089+007
8.999
-9.691
3.873
4.342
0.700
2.484
0.285
2.494+007
8.997
-9.252
3.949
4.310
0.700
2.132
0.148
2.808+007
8.995
-3.894
4.015
4.279
0.700
1.718
0.024
2.861+007
8.994
-8.905
4.048
4.312
0.700
1.664
0.001
2.870+007
8.994
-8.921
4.079
4.338
0.700
1.007
0.000
2.872+007
8.994
-8.850
4.061
4.303
0.700
0.000
0.000
2.874+007
8.994
-8.239
4.093
4.147
0.700
0.000
0.000
2.875+007
8.994
-7.936
4.069
3.995
0.700
0.000
0.000
2.876+007
8.993
-7.669
4.026
3.842
0.700
0.000
0.000
2.876+007
8.993
-7.450
3.992
3.743
0.700
0.000
0.981
2.877+007
8.993
-7.175
3.910
3.633
0.700
0.000
0.981
2.877+007
8.993
-7.149
3.876
3.616
0.700
0.000
0.981
2.877+007
8.993
-7.149
3.876
3.616
0.700
0.000
0.981
2.880+007
8.995
-6.535
4.321
3.539
0.686
0.773
0.975
3.007+007
8.705
-6.762
4.127
3.574
0.686
1.149
0.776
3.020+007
8.681
-6.771
4.176
3.611
0.686
1.163
0.750
3.022+007
8.679
-6.824
4.190
3.649
0.686
1.163
0.744
3.050+007
8.663
-7.526
4.232
3.899
0.686
1.195
0.636
3.091+007
8.656
-7.878
4.260
4.001
0.686
1.264
0.562
84
3.225+007
8.628
-7.699
4.298
3.981
0.686
1.493
0.268
3.309+007
8.578
-6.717
4.294
3.694
0.686
1.535
0.055
3.312+007
8.571
-6.633
4.287
3.636
0.686
1.534
0.048
3.315+007
8.563
-6.604
4.247
3.573
0.686
1.533
0.038
3.331+007
8.518
-6.451
4.339
3.539
0.686
0.009
0.000
20M€ X = 0.7 - Z = 0.02 - α=0.25 - Maeder, 1990
<$ù
•
M
-log(- M )
Log L
Log Teff
Qcc
Xat
Xc
logTc
Log ρc
0.016
19.993
7.387
4.639
4.552
0.543
0.7
0.695
7.564
0.709
0.156
19.93
7.303
4.69
4.544
0.522
0.7
0.622
7.562
0.679
0.295
19.853
7.214
4.743
4.537
0.499
0.7
0.541
7.565
0.668
0.416
19.771
7.123
4.795
4.527
0.476
0.7
0.46
7.572
0.470
0.516
19.686
7.028
4.843
4.516
0.45
0.7
0.382
7.58
0.678
0.604
19.593
6.929
4.89
4.499
0.425
0.7
0.301
7.591
0.695
0.68
19.492
6.821
4.935
4.477
0.401
0.7
0.219
7.603
0.721
0.729
19.409
6.74
4.967
4.456
0.382
0.7
0.159
7.615
0.750
0.772
19.323
6.657
4.997
4.429
0.362
0.7
0.1
7.629
0.791
0.799
19559
6.6
5.017
4.409
0.349
0.7
0.061
7.645
0.736
0.827
19.183
6.542
5.040
4.392
0.335
0.7
0.018
7.679
0.939
0.839
19.149
6.532
5.055
4.41
0.329
0.7
0.002
7.736
1.109
0.H42
19.141
6.537
5.088
4.461
0.227
0.7
0
7.89
1.607
0.842
19.14
6.535
5.084
4.454
0.052
0.7
0.981
7.934
1.786
0.843
19.138
6.34
5.114
4.316
0
0.7
0.981
8.107
2.450
0.843
19.135
6.103
5.134
4.155
0.109
0.7
0.979
8.206
2.748
0.844
19.132
5.777
5.151
4.007
0.19
0.7
0.978
8.215
2.749
0.844
19.123
5.435
5.168
3.86
0.208
0.7
0.977
8.218
2.748
0.845
19.078
5.234
5.184
3.7
0.212
0.7
0.972
8.225
2.762
0.847
18.956
5.461
5.153
3.557
0.229
0.7
0.956
8.247
2.821
0.847
18.947
5.452
5.161
3.552
0.218
0.7
0.954
8.248
2.823
85
0.847
18.937
5.444
5.168
3.55
0.219
0.7
0.950
8.253
2.837
0.851
18.809
5.432
5.177
3.549
0.228
0.7
0.901
8.258
2.843
0.856
18.633
5.421
5.183
3.549
0.237
0.7
0.850
8.253
2.819
0.861
18.439
5.414
5.187
3.548
0.244
0.7
0.802
8.262
2.838
0.869
18.128
5.402
5.195
3.548
0.256
0.7
0.752
8.262
2.824
0.882
17.588
5.379
5.206
3.547
0.277
0.7
0.699
8.265
2.816
0.892
17.151
5.357
5.217
3.546
0.295
0.7
0.649
8.272
2.823
0.903
16.684
5.345
5.224
3.546
0.312
0.7
0.600
8.276
2.822
0.908
16.424
5.334
5.230
3.546
0.324
0.7
0.552
8.282
2.832
0.913
16.196
5.329
5.233
3.546
0.335
0.7
0.500
8.287
2.839
0.918
15.952
5.313
5.241
3.545
0.353
0.7
0.452
8.299
2.868
0.925
15.638
5.302
5.246
3.545
0.367
0.7
0.401
8.305
2.878
0.929
15.424
5.296
5.248
3.545
0.378
0.7
0.351
8.311
2.890
0.936
15.043
5.282
5.255
3.545
0.393
0.7
0.301
8.319
2.902
0.939
14.900
5.278
5.257
3.545
0.401
0.7
0.268
8.324
2.914
0.945
14.557
5.263
5.262
3.546
0.417
0.7
0.200
8.338
2.947
0.950
14.288
5.251
5.267
3.546
0.430
0.7
0.150
8.351
2.982
0.955
14.026
5.252
5.272
3.543
0.441
0.693
0.100
8.367
3.027
0.973
12.984
5.200
5.289
3.547
0.479
0.653
0.051
8.402
3.115
0.975
12.840
5.187
5.295
3.546
0.484
0.642
0.031
8.423
3.174
0.978
12.667
5.159
5.307
3.546
0.489
0.618
0.010
8.462
3.291
0.980
12.486
5.072
5.348
3.542
0
0.571
0
8.606
3.731
0.980
12.457
4.992
5.377
3.54
0
0.554
0
8.701
4.052
0.981
12.415
4.971
5.389
3.539
0
0.550
0
8.801
4.527
0.981
12.402
4.962
5.396
3.541
0
0.547
0
8.840
4.861
0.981
12.400
4.926
5.410
3.54
0
0.545
0
8.889
5.132
0.981
12.400
4.921
5.412
3.54
0
0.544
0
8.942
5.32
0.981
12.400
4.893
5.412
3.54
0
0.544
0
8.957
5.39
0.981
12.400
4.904
5.401
3.539
0
0.544
0
8.972
5.525
0.981
12.400
4.884
5.400
3.539
0
0.543
0
9.027
5.823
86
40M€ X = 0.7 - Z = 0.02 - α=0.25 – Maeder, 1990
<$ù
0.01
0.079
0.145
0.206
0.261
0.308
0.350
0.378
0.405
0.421
0.443
0.446
0.449
0.449
0.449
0.450
0.450
0.450
0.450
0.450
0.450
0.452
0.453
0.454
0.458
0.459
0.463
0.466
0.467
0.469
0.471
0.474
0.476
0.479
0.482
0.485
0.489
0.493
0.498
0.505
0.508
0.511
0.514
0.514
0.515
0.515
0.515
0.515
0.515
0.515
0.515
•
M
39.981
39.859
39.693
39.482
39.208
38.85
38.356
37.877
37.237
36.732
35.888
35.771
35.658
35.653
35.643
35.636
35.626
35.604
35.525
35.474
34.111
26.703
23.642
22.735
22.407
22.303
20.786
19.467
18.657
17.333
15.938
14.161
12.489
11.191
10.148
9.23
8.42
7.693
6.986
6.288
6.009
5.748
5.572
5.534
5.497
5.492
5.489
5.488
5.488
5.487
5.487
-log(- M )
6.835
6.679
6.538
6.390
6.213
6.038
5.844
5.694
5.553
5.475
5.388
5.387
5.403
5.401
5.317
5.145
4.743
4.21
3.882
3.788
3.419
3.407
3.493
4.71
5.188
4.398
4.398
4.398
4.142
4.222
4.008
4.138
4.276
4.396
4.502
4.606
4.705
4.803
4.908
5.023
5.072
5.122
5.157
5.164
5.172
5.173
5.174
5.174
5.174
5.174
5.174
Log L
5.369
5.414
5.458
5.5
5.539
5.576
5.61
5.634
5.658
5.674
5.697
5.702
5.725
5.723
5.726
5.735
5.739
5.739
5.717
5.724
5.812
5.827
5.827
5.827
5.824
5.819
5.762
5.695
5.669
5.628
5.575
5.49
5.405
5.33
5.263
5.198
5.136
5.075
5.011
4.942
4.914
4.893
4.942
5.008
5.127
5.147
5.167
5.17
5.173
5.178
5.195
Log Teff
4.652
4.643
4.643
4.623
4.606
4.584
4.553
4.519
4.470
4.427
4.362
4.374
4.444
4.439
4.311
4.167
4.000
3.855
3.713
3.681
3.669
3.688
3.717
4.044
4.351
4.433
4.75
4.83
4.724
4.748
4.647
4.686
4.726
4.759
4.788
4.814
4.839
4.862
4.887
4.914
4.927
4.945
4.991
5.024
5.043
5.045
5.047
5.048
5.048
5.049
5.057
60M€ X = 0.7 - Z = 0.02 - α=0.25 - Maeder, 1990
Qcc
0.705
0.677
0.651
0.624
0.593
0.566
0.542
0.523
0.505
0.493
0.481
0.48
0.388
0.271
0.222
0.226
0.297
0.329
0.37
0.378
0.397
0.522
0.605
0.628
0.659
0.667
0.742
0.788
0.786
0.782
0.793
0.75
0.733
0.719
0.701
0.688
0.676
0.666
0.649
0.636
0.632
0.624
0
0
0
0
0
0
0
0
0
Xat
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.653
0.581
0.536
0.327
0.322
0.322
0.227
0.001
0
0.981
0.697
0.559
0.482
0.456
0.425
0.391
0.354
0.319
0.278
0.23
0.209
0.191
0.176
0.173
0.171
0.17
0.17
0.17
0.17
0.169
0.169
Xc
0.695
0.62
0.542
0.462
0.381
0.301
0.221
0.162
0.101
0.061
0.007
0.002
0
0.981
0.981
0.98
0.98
0.98
0.979
0.979
0.975
0.95
0.927
0.898
0.802
0.781
0.7
0.626
0.599
0.55
0.494
0.452
0.4
0.349
0.3
0.25
0.2
0.15
0.1
0.05
0.031
0.01
0
0
0
0
0
0
0
0
0
logTc
7.606
7.602
7.605
7.611
7.619
7.628
7.640
7.650
7.665
7.680
7.740
7.779
7.992
8.049
8.149
8.200
8.228
8.235
8.239
8.239
8.246
8.287
8.295
8.3
8.305
8.299
8.312
8.318
8.318
8.32
8.321
8.321
8.322
8.324
8.327
8.331
8.337
8.345
8.357
8.379
8.394
8.427
8.571
8.701
8.8
8.824
8.877
8.899
8.91
8.922
9.053
Log ρc
0.487
0.460
0.452
0.456
0.468
0.488
0.517
0.547
0.593
0.640
0.823
0.940
1.596
1.792
2.131
2.299
2.387
2.408
2.417
2.417
2.433
2.551
2.573
2.585
2.591
2.568
2.602
2.624
2.637
2.662
2.69
2.726
2.77
2.812
2.853
2.897
2.946
3.001
3.071
3.173
3.235
3.347
3.802
4.261
4.778
4.945
5.23
5.282
5.343
5.536
6.223
87
•
<$ù
M
0.080
0.562
1.070
1.532
1.971
2.338
2.722
2.956
3.169
3.331
3.453
3.473
3.491
3.492
3.494
3.495
3.495
3.496
3.497
3.498
3.499
3.499
3.556
3.586
3.616
3.646
3.667
3.682
3.701
3.727
3.75
3.776
3.801
3.829
3-862
3.895
3.933
3.976
4.025
4.087
4.116
4.154
4.182
4.187
4.192
4.193
4.194
4.194
4.194
4.194
4.194
59.966
59.784
59.491
59.070
58.409
57.489
55.753
54.018
51.948
50.177
48.373
47.978
47.697
47.687
47.65
47.644
46.243
45.394
44.239
41.695
39.783
39.771
37.495
36.291
35.089
33.887
33.061
32.460
27.561
20.486
17.152
14.720
13.009
11.574
10.330
9.376
8.509
7.735
7.050
6.361
6.090
5.779
5.580
5-544
5.507
5.502
5.498
5.498
5.498
5.497
5.497
-log(- M )
6.514
6.338
6.151
5.939
5.12
5.497
5.219
5.065
4.979
4.932
4.701
4.746
4.826
4.814
4.894
4.768
2.375
3.282
2.611
2.738
2.926
4.398
4.398
4.398
4.398
4.398
4.398
4.398
3.392
3.732
3.928
4.095
4.231
4.356
4.481
4.587
4.693
4.797
4.898
5.011
5.058
5.115
5.155
5.163
5.170
5.171
5.172
5.172
5.172
5.172
5.172
Log L
Log Teff
Qcc
Xat
Xc
logTc
Log ρc
5.729
5.766
5.803
5.838
5.872
5.900
5.931
5.951
5.971
5.989
6.006
6.010
6.022
6.026
6.030
6.032
6.046
6.058
6.063
6.113
6.120
6.151
6.130
6.119
6.091
6.044
6.036
6.031
5.935
5.746
5.63
5.519
5.436
5.357
5.278
5.212
5.146
5.081
5.019
4.953
4.927
4.898
4.942
5.005
5.124
5.145
5.167
5.171
5.173
5.177
5.178
4.693
4.683
4.673
4.658
4.638
4.612
4.558
4.499
4.404
4.279
4.136
4.158
4.208
4.202
4.234
4.162
4.007
3.781
3.746
3.811
3.828
4.416
4.572
4.687
4.789
4.829
4.872
4.895
4.446
4.561
4.624
4.674
4.714
4.749
4.783
4.810
4.837
4.861
4.885
4.913
4.925
4.944
4.992
5.024
5.044
5.046
5.049
5.05
5.05
5.051
5.056
0.773
0.750
0.726
0.696
0.664
0.638
0.616
0.605
0.600
0.595
0.598
0.601
0.584
0.549
0.394
0.370
0.405
0.452
0.485
0.574
0.550
0.531
0.679
0.721
0.767
0.810
0.832
0.840
0.826
0.805
0.784
0.756
0.739
0.726
0.707
0.690
0.679
0.666
0.651
0.638
0.636
0.63
0
0
0
0
0
0
0
0
0
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.7
0.648
0.647
0.583
0.543
0.499
0.364
0.329
0.211
0.207
0.193
0.192
0.186
0.083
0
0.639
0.586
0.552
0.515
0.479
0.45
0.413
0.379
0.344
0.308
0.271
0.229
0.21
0.188
0.171
0.168
0.165
0.165
0.165
0.165
0.165
0.165
0.165
0.695
0.622
0.542
0.463
0.379
0.3
0.209
0.148
0.087
0.038
0.003
0.001
0
0.981
0.981
0.981
0.98
0.98
0.98
0.979
0.977
0.977
0.905
0.853
0.803
0.753
0.699
0.656
0.61
0.552
0.501
0.45
0.4
0.351
0.299
0.251
0.2
0.149
0.101
0.05
0.031
0.01
0
0
0
0
0
0
0
0
0
7.623
7.621
7.623
7.629
7.636
7.645
7.658
7.669
7.686
7.71
7.777
7.828
7.973
8.019
8.149
8.165
8.21
8.234
8.243
8.249
8.252
8.255
8.305
8.3 13
8.316
8.321
8.33
8.333
8.328
8.324
8.323
8.323
8.323
8.325
8.328
8.332
8.338
8.346
8.358
8.381
8.396
8.428
8.575
8.7
8.8
8.824
8.879
8.905
8.913
8.925
9.037
0.374
0.355
0.348
0.353
0.368
0.389
0.427
0.464
0.516
0.591
0.796
0.948
1.388
1.527
1.954
2.006
2.151
2.228
2.256
2.274
2.281
2.288
2.43
2.448
2.454
2.469
2.496
2.509
2.539
2.619
2.671
2.718
2.761
2.804
2.85
2.894
2.944
3.001
3.07
3.173
3.235
3.349
3.812
4.247
4.767
4.937
5.24
5.313
5.371
5.522
6.236
85M€ X = 0.7 - Z = 0.02 - α=0.25 – Maeder, 1990
<$ù
0.7001
0.4574
0.8801
0.127
•
M
84.917
84.544
83.861
82.821
-log(- M )
6.122
5.913
5.694
5.462
Log L
6.004
6.034
6.065
6.092
Log Teff
4.719
4.709
4.969
4.68
Qcc
0.819
0.793
0.767
0.744
Xat
0.7
0.7
0.7
0.7
Xc
0.695
0.622
0.54
0.46
logTc
7.635
7.635
7.636
7.642
Log ρc
0.283
0.271
0.266
0.274
88
0.162
0.1936
0.2229
0.2381
0.2639
0.2778
0.2855
0.2955
0.2993
0.2994
0.2996
0.2997
0.2999
0.3
0.3011
0.3016
0.3026
0.3041
0.3079
0.3106
0.3122
0.3146
0.3153
0.3173
0.3192
0.3213
0.3236
0.3261
0.3288
0.3317
0.335
0.3386
0.3426
0.3471
0.3522
0.3587
0.3614
0.3651
0.3686
0.3691
0.3696
0.3697
0.3697
0.3697
0.3698
0.3698
0.3698
81.169
78.489
74.163
71.013
65.094
61.912
60.098
56.089
54.582
54.534
54.455
54.416
54.352
54.29
53.879
53.658
53.279
52.648
51.128
50.077
49.431
48.461
43.481
29.358
23.076
19.065
16.205
14.031
12.397
11.102
9.969
9.017
8.187
7.463
6.802
6.145
5.909
5.628
5.392
5.36
5.33
5.325
5.321
5.321
5.32
5.32
5.32
5.207
4.959
4.73
4.654
4.631
4.652
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
3.11
3.218
3.346
3.606
3.81
3.989
4.147
4.283
4.402
4.519
4.629
4.734
4.836
4.937
5.049
5.091
5.145
5.192
5.198
5.205
5.206
5.207
5.207
5.207
5.207
5.208
6.117
6.14
6.161
6.174
6.199
6.213
6.221
6.228
6.243
6.256
6.292
6.307
6.321
6.327
6.33
6.332
6.333
6.326
6.29
6.275
6.272
6.268
6.208
5.971
5.82
5.697
5.59
5.484
5.4
5.324
5.25
5.18
5.114
5.051
4.988
4.923
4.9
4.875
4.924
4.991
5.104
5.127
5.148
5.152
5.156
5.157
5.167
4.654
4.618
4.559
4.511
4.546
4.577
4.555
4.641
4.761
4.784
4.711
4.645
4.571
4.449
4.426
4.394
4.565
4.717
4.867
4.909
4.923
4.39
4.428
4.432
4.52
4.586
4.643
4.688
4.728
4.761
4.791
4.819
4.845
4.868
4.892
4.918
4.93
4.948
5.005
5.032
5.05
5.053
5.055
5.056
5.05d
5.057
5.061
0.719
0.703
0.705
0.713
0.731
0.741
0.748
0.775
0.769
0.665
0.673
0.688
0.694
0.705
0.719
0.729
0.741
0.765
0.823
0.848
0.86
0.869
0.864
0.835
0.811
0.795
0.782
0.747
0.73
0.718
0.701
0.683
0.671
0.658
0.645
0.632
0.629
0.623
0
0
0
0
0
0.022
0.034
0
0
0.7
0.7
0.7
0.692
0.523
0.436
0.394
0.295
0.254
0.253
0.25
0.249
0.247
0.246
0.245
0.243
0.216
0.201
0.157
0.088
0.051
0.001
0
0.672
0.636
0.598
0.558
0.52
0.483
0.456
0.419
0.384
0.347
0.312
0.274
0.233
0.216
0.197
0.177
0.174
0.172
0.171
0.171
0.171
0.171
0.171
0.171
Qcc
Xat
0.38
0.301
0.221
0.177
0.097
0.053
0.029
0.002
0
0.981
0.98
0.979
0.978
0.977
0.972
0.97
0.964
0.95
0.899
0.851
0.801
0.722
0.701
0.651
0.602
0.551
0.502
0.451
0.4
0.349
0.299
0.25
0.2
0.15
0.101
0.049
0.031
0.01
0
0
0
0
0
0
0
0
0
7.648
7.657
7.667
7.675
7.694
7.712
7.729
7.803
8.047
8.17
8.25
8.255
8.258
8.26
8.277
8.286
8.296
8.306
8.316
8.329
8.336
8.341
8.336
8.327
8.324
8.322
8.321
8.321
8.322
8.324
8.326
8.33
8.336
8.344
8.356
8.38
8.395
8.428
8.602
8.71
8.799
8.825
8.889
8.923
8.955
8.954
9.024
0.291
0.317
0.354
0.379
0.441
0.497
0.552
0.782
1.519
1.893
2.148
2.166
2.174
2.179
2.227
2.256
2.284
2.309
2.335
2.375
2.4
2.417
2.429
2.517
2.581
2.636
2.684
2.729
2.773
2.815
2.859
2.904
2.954
3.01
3.08
3.184
3.243
3.36
3.914
4.311
4.792
4.972
5.263
5.344
5.457
5.55
6.195
120M€ X = 0.7 - Z = 0.02 - α=0.25 - Maeder, 1990
<$ù
0.0700
0.3981
0.7522
ø
1.3872
1.5460
1.9403
2.1383
2.2475
2.4323
2.5522
2.6521
•
M
119.727
118.596
116.534
113.364
108.306
104.231
93.500
88.366
85.475
78.086
73.287
69.288
-log(- M )
5.585
5.356
5.136
4.916
4.658
4.537
4.590
4.582
4.398
4.398
4.398
4.398
Log L
6.252
6.275
6.295
6.313
6.329
6.337
6.362
6.377
6.387
6.401
6.408
6.408
Log Teff
4.739
4.727
4.712
4.693
4.663
4.044
4.665
4.675
4.636
4.674
4.711
4.780
0.854
0.825
0.802
0.782
0.775
0.780
0.802
0.810
0.814
0.844
0.872
0.904
0.694
0.62
0.54
0.461
0.382
0.338
0.222
0.159
0.123
0.059
0.021
0.001
Xc
0.700
0.700
0.700
0.700
0.700
0.692
0.506
0.424
0.378
0.252
0.164
0.091
logTc
7.649
7.647
7.648
7.652
7.659
7.663
7.677
7.688
7.696
7.718
7.748
7.834
Log ρc
0.206
0.194
0.192
0.204
0.227
0.244
0.297
0.335
0.361
0.438
0.535
0.805
89
2.6955
2.6971
2.6981
2.6996
2.7007
2.7007
2.7027
2.7038
2.7053
2.7234
2.7356
2.7477
2.7598
2.774
2.7772
2.8136
2.8346
2.8565
2.8806
2.9088
2.9425
2.9787
3.0149
3.06
3.1126
3.1701
3.2409
3.316
3.3558
3.3987
3.4448
3.4516
3.4575
3.4584
3.459
3.459
3.4591
3.4592
3.4593
67.555
67.493
67.452
67.390
67.348
67.348
67.266
67.225
67.163
66.438
65.952
65.467
64.982
64.415
59.673
26.266
20.919
17.537
15.067
13.074
11.379
10.071
9.086
8.146
7.309
6.608
5.941
5.395
5.152
4.920
4.698
4.667
4.64
4.636
4.634
4.634
4.633
4.633
4.633
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
4.398
2.8008
2.5768
3.4602
3.7114
3.8999
4.0673
4.2192
4.3673
4.5024
4.6159
4.7347
4.8527
4.9637
5.0819
5.1884
5.2386
5.2902
5.3416
5.3493
5.3554
5.3567
5.3574
5.3575
5.3575
5.3576
5.3577
6.415
6.423
6.430
6.430
6.429
6.429
6.429
6.429
6.429
6.436
6.434
6.433
6.432
6.431
6.39
5.899
5.754
5.639
5.537
5.432
5.335
5.248
5.174
5.097
5.019
4.946
4.871
4.807
4.777
4.753
4.79
4.883
5.024
5.051
5.069
5.071
5.073
5.076
5.091
4.878
4.903
4.925
4.930
4.931
4.931
4.932
4.933
4.934
4.951
4.955
4.959
4.962
4.278
4.158
4.47
4.554
4.613
4.665
4.708
4.748
4.748
4.812
4.84
4.866
4.889
4.913
4.936
4.949
4.966
5.023
5.057
5.072
5.072
5.072
5.072
5.072
5.072
5.078
0.849
0.881
0.849
0.878
0.880
0.880
0.876
0.876
0.875
0.868
0.876
0.883
0.885
0.891
0.860
0.825
0.806
0.785
0.769
0.738
0.717
0.698
0.682
0.667
0.652
0.636
0.622
0.609
0.605
0.599
0
0
0
0
0
0
0
0
0
0
0.981
0.98
0.979
0.978
0.978
0.977
0.976
0.975
0.95
0.902
0.852
0.803
0.747
0.738
0.651
0.6
0.551
0.502
0.449
0.399
0.349
0.303
0.251
0.200
0.151
0.100
0.051
0.030
0.010
0
0
0
0
0
0
0
0
0
0.060
0.058
0.058
0.057
0.056
0.056
0.055
0.054
0.053
0.040
0.031
0.019
0.009
0.001
0.000
0.676
0.637
0.6
0.563
0.525
0.483
0.445
0.414
0.382
0.346
0.311
0.268
0.231
0.215
0.198
0.179
0.175
0.175
0.175
0.175
0.175
0.174
0.174
0.174
8.076
8.164
8.246
8.262
8.264
8.264
8.267
8.268
8.271
8.333
8.339
8.342
8.345
8.348
8.336
8.324
8.321
8.319
8.318
8.318
8.318
8.32
8.322
8.326
8.331
8.339
8.352
8.374
8.392
8.424
8.583
8.703
8.797
8.829
8.878
8.895
8.904
8.909
9.036
1.535
1.799
2.046
1093
2.099
2.099
2.109
2.114
2.123
2.312
2.330
2.339
2.348
2.358
2.341
2.542
2.604
2.655
2.701
2.746
2.794
2.839
2.882
2.931
2.985
3.045
3.121
3.223
3.292
3.407
3.917
4.380
4.901
5.130
5.369
5.416
5.462
5.574
6.338
g%(.,,<,/',=/$5,ødø1(95ø002'(//(5ø
1.2M€ X = 0.7 - Z = 0.001 – Chiosi ve ark., 1987
L / L€
<$ù
Log Teff
Log g
logTc
Log ρc
Xc
0
0.553
3.914
4.607
7.2513
2.024
0.7
555.693
0.606
3.92
4.578
7.2736
2.0796
0.602
697.646
0.656
3.925
4.552
7.2955
2.144
0.507
1569.73
0.74
3.935
4.505
7.3424
2.3156
0.305
2108.44
0.828
3.931
4.401
7.396
2.3661
0.203
2552.08
2709.94
0.907
1.032
3.911
3.953
4.244
4.288
7.4539
7.5543
2.4783
3.0288
0.045
0
2723.76
1.103
3.900
4.004
7.4905
3.8369
0
2767.8
1.127
3.848
3.773
7.4833
4.1519
0
2804.98
1.141
3.801
3.568
7.5321
4.3584
0
2910.06
1.203
3.732
3.230
7.6148
4.9439
0
90
2923.97
1.253
3.729
3.168
7.6143
4.994
0
2935.75
1.301
3.726
3.111
7.6147
5.0349
0
2956.45
1.401
3.722
2.994
7.6189
5.1062
0
2973.5
1.500
3.718
2.877
7.6264
5.1669
0
2987.74
1.601
3.713
2.759
7.6366
5.2217
0
3009.13
1.806
3.704
2.517
7.6627
5.3197
0
3049.08
2.598
3.665
1.569
7.7991
5.686
0
1.5M€ X = 0.7 - Z = 0.001 – Chiosi ve ark., 1987
L / L€
<$ù
Log Teff
Log g
Log ρc
logTc
Xc
0
0.959
4.002
4.653
7.3158
2.0076
0.7
293.582
1.012
4.007
4.62
7.3377
2.0590
0.601
547.091
1.066
4.011
4.583
7.3635
2.1152
0.498
705.535
1.106
4.012
4.545
7.3807
2.1376
0.442
832.289
1.141
4.011
4.506
7.3936
2.1464
0.4
1054.11
1.201
4.004
4.417
7.4168
2.1773
0.3
1244.24
1.265
3.988
4.291
7.4406
2.2020
0.196
1476.49
1.366
3.955
4.057
7.5011
2.3408
0.03
1500.74
1.389
3.961
4.058
7.5284
2.4279
0.01
1512.56
1.503
3.990
4.059
7.6331
3.4367
0
1518.2
1.553
3.800
3.249
7.7367
4.2307
0
1523.7
1.505
3.732
3.026
7.8484
4.6625
0
1531.76
1.705
3.718
2.771
7.9014
5.0090
0
1539.77
1.903
3.708
2.533
7.8981
5.1935
0
1550.78
2.200
3.693
2.176
7.8862
5.3845
0
1553.88
2.300
3.688
2.056
7.8860
5.4391
0
1559.02
2.500
3.678
1.814
7.8926
5.5417
0
1563.19
2.600
3.673
1.694
7.9122
5.6426
0
1564.03
2.645
3.671
1.641
7.9941
5.6472
0
2M€ X = 0.7 - Z = 0.001 – Chiosi ve ark., 1987
<$ù
0
193.737
352.181
478.935
599.759
774.84
788.153
788.291
788.807
789.79
790.298
790.638
L / L€
1.442
1.514
1.587
1.660
1.747
1.931
2.056
1.992
2.092
2.023
2.198
2.305
Log Teff
4.102
4.104
4.102
4.096
4.082
4.015
4.089
4.060
3.948
3.731
3.708
3.702
Log g
4.693
4.630
4.551
4.454
4.310
3.858
4.027
3.977
3.429
2.632
2.365
2.230
logTc
7.3853
7.4056
7.4241
7.4411
7.4617
7.5414
7.6903
7.6813
7.7255
7.8290
7.8846
7.9194
Log ρc
1.9397
1.9591
1.9714
1.9826
1.9972
2.1600
2.8480
3.1107
3.5543
4.0270
4.2238
4.3426
Xc
0.7
0.6
0.503
0.409
0.293
0.029
0
0
0
0
0
0
91
791.247
792.358
804.946
819.858
844.926
857.503
858.403
863.483
865.034
865.45
866.297
866.628
866.791
2.487
2.503
2.205
2.301
2.400
2.500
2.436
2.696
2.908
3.001
3.302
3.500
3.616
3.691
3.690
3.717
3.748
3.792
3.698
3.706
3.683
3.670
3.664
3.646
3.634
3.626
2.006
1.987
2.390
2.418
2.497
2.019
2.118
1.764
1.500
1.385
1.011
0.763
0.617
7.9811
8.0566
8.0794
8.0951
8.1412
8.3172
8.1772
8.1994
8.2366
8.2499
8.2691
8.2493
8.2144
4.5404
4.4064
4.1913
4.1149
4.0649
4.6474
4.9542
5.3233
5.5082
5.5850
5.8396
6.0248
6.1596
0.999
0.990
0.884
0.707
0.271
0
0
0
0
0
0
0
0
3M€ X = 0.7 - Z = 0.001 – Chiosi ve ark., 1987
<$ù
L / L€
Log Teff
Log g
Log ρc
logTc
Xc
0
53.5686
136.195
191.156
265.255
299.64
302.514
302.684
2.082
2.136
2.239
2.329
2.503
2.636
2.679
2.740
4.215
4.215
4.211
4.203
4.165
4.116
4.149
4.182
4.681
4.627
4.511
4.388
4.060
3.732
3.821
3.890
7.4481
7.4571
7.4744
7.4904
7.5294
7.6004
7.6774
7.7546
1.7613
1.7587
1.7547
1.7564
1.7841
1.9468
2.1750
2.6359
0.7
0.637
0.518
0.412
0.191
0.02
0.001
0
302.845
302.999
303.051
2.780
2.805
2.792
4.049
3.855
3.745
3.320
2.519
2.095
7.8017
7.8747
7.9010
3.2706
3.6051
3.7030
0
0
0
303.161
303.233
303.445
304.259
310.493
320.455
320.860
320.892
321.26
321.979
322.247
2.904
3.001
3.169
3.100
3.004
3.101
3.093
3.134
3.206
3.498
3.704
3.689
3.682
3.671
3.675
3.749
3.803
3.686
3.684
3.672
3.632
3.64
1.755
1.630
1.418
1.506
1.894
2.015
1.556
1.509
1.387
1.016
0.759
7.9581
7.9936
8.1001
8.1065
8.1381
8.2804
8.3656
8.3346
8.3041
8.3779
8.4375
3.8986
4.0177
4.0831
3.9571
3.7704
3.9864
4.3434
4.4357
4.9459
5.4445
5.7513
0
0
0.994
0.96
0.705
0.017
0
0
0
0
0
322.403
322.505
322.565
322.581
3.900
4.102
4.301
4.100
3.627
3.618
3.612
3.619
0.514
0.276
0.052
0.281
8.4465
8.3367
8.1926
8.1609
6.0751
6.4434
6.7712
6.8695
0
0
0
0
322.592
4.204
3.614
0.158
8.1399
6.9185
0
5M€ X = 0.7 - Z = 0.001 – Chiosi ve ark., 1987
<$ù
0
L / L€
2.848
Log Teff
4.336
Log g
4.622
logTc
7.5050
Log ρc
1.5021
Xc
0.7
92
29.3855
2.947
4.335
4.52
7.5191
1.4918
0.588
45.0853
3.012
4.332
4.443
7.5291
1.4863
0.512
76.3984
94.3404
3.205
3.404
4.308
4.242
4.154
3.689
7.5631
7.6346
1.4950
1.6277
0.288
0.041
96.5833
3.508
4.298
3.812
7.8220
2.2850
0
96.6807
3.603
3.886
2.067
8.0047
3.4284
0
96.6997
3.563
3.681
1.288
8.0465
3.5709
0.999
96.7099
3.712
3.663
1.068
8.0697
3.6429
0.999
96.7633
3.845
3.653
0.893
8.1481
3.6394
0.991
96.931
3.800
3.657
0.953
8.1530
3.5705
0.962
97.7112
3.727
3.670
1.081
8.1678
3.4770
0.858
100.676
3.796
4.061
2.573
8.2375
3.4663
0.217
101.612
3.829
3.827
1.603
8.3578
3.7987
0.006
101.658
3.793
3.670
1.013
8.4168
4.0307
0
101.672
3.849
3.665
0.938
8.4029
4.1823
0
101.854
4.104
3.639
0.577
8.5514
5.3091
0
101.904
4.200
3.633
0.457
8.6189
5.7773
0
101.939
101.943
4.306
4.415
3.626
3.627
0.326
0.221
8.6415
8.5773
6.639
6.8791
0
0
101.945
4.433
3.627
0.200
8.5377
6.9641
0
9M€ X = 0.7 - Z = 0.001 – Chiosi ve ark., 1987
L / L€
<$ù
Log Teff
Log g
Log ρc
logTc
Xc
0
3.720
4.460
4.501
7.5674
1.2057
0.7
13.2998
18.7534
26.4075
30.4512
30.5095
30.5181
30.5311
30.6063
31.6887
32.0844
32.1000
32.1030
32.1296
32.1337
3.822
3.908
4.091
4.252
4.301
4.354
4.311
4.500
4.510
4.534
4.544
4.567
4.685
4.708
4.457
4.450
4.413
4.377
4.332
4.203
3.663
3.643
4.164
3.801
3.643
3.641
3.632
3.631
4.388
4.272
3.944
3.638
3.409
2.839
0.722
0.455
2.527
1.051
0.408
0.377
0.226
0.198
7.5819
7.5959
7.6336
7.7655
8.0232
8.0966
8.1998
8.2065
8.2782
8.4230
8.4905
8.5012
8.6362
8.6646
1.2000
1.2000
1.2412
1.5963
2.7171
3.0138
3.2395 .
3.1574
3.1747
3.5854
3.8178
3.9115
4.6741
4.8172
0.523
0.418
0.196
0.003
0
0.999
0.995
0.95
0.244
0.004
0
0
0
0
$1$.2/g1&(6ø(95ø0
1 M€.h7/(/ø%ø5<,/',=,1$QDNRO|QFHVLHYULPL)LJXHLUHGRXQSXEOLVKHG
=DPDQ\ÕO
Log Teff
Log L/L€
R/R€
Log Tc
Log ρc
1.11595e+4
3.5777
1.3879
11.3560
5.8350
-2.1947
2.05936e+4
3.5796
1.3442
10.7100
5.8596
-2.1208
93
2.56673e+4
3.5805
1.3231
10.4130
5.8714
-2.0854
3.800676+4
4.48850e+4
6.07290e+4
6.54482e+4
8.03167e+4
9.09827e+4
1.16655e+5
1.58I41e+5
1.89778e+5
2.01401e+5
3.01187e+5
4.15419e+5
3.5823
3.5832
3.5849
3.5853
3.5865
3.5872
3.5887
3.5904
3.5914
3.5917
3.5937
3.5949
1.2775
1.2549
1.2086
1.1962
1.1601
1.1366
1.0869
1.0210
0.9792
0.9652
0.8665
0.7838
9.8040
9.5170
8.9590
8.8160
8.4140
8.1640
7.6620
7.0510
6.6920
6.5770
5.8220
5.2660
5.8963
5.9094
5.9349
5.9417
5.9614
5.9742
6.0011
6.0363
6.0585
6.0659
6.1177
6.1605
-2.0093
-1.9717
-1.8952
-1.8748
-1.8156
-1.7773
-1.6968
-1.5912
-1.5247
-1.5025
-1.3472
-1.2189
5.01631e+5
6.94507e+5
7.92080e+5
9.05225e+5
1.03750e+6
1.60251e+6
2.06874e+6
2.95811e+6
3.22337e+6
3.54167e+6
4.75824e+6
5.25140e+6
3.5955
3.5961
3.5963
3.5963
3.5962
3.5954
3.5944
3.5923
3.5917
3.5910
3.5884
3.5875
0.7335
0.6443
0.6075
0.5697
0.5306
0.4039
0.3284
0.2206
0.1943
0.1655
0.0749
0.0446
4.9580
4.4640
4.2770
4.0950
3.9170
3.4010
3.1330
2.7950
2.7190
2.6400
2.4070
2.3350
6.1861
6.2309
6.2492
6.2678
6.2867
6.3472
6.3822
6.4307
6.4417
6.4534
6.4876
6.4985
-1.1419
-1.0075
-0.9528
-0.8970
-0.8399
-0.6584
-0.5529
-0.4056
-0.3695
-0.3299
-0.2032
-0.1597
5.843 19e+6
3.5864
0.0120
2.2600
6.5099
-0.1124
6.44960e+6
8.05052e+6
8.94532e+6
1.00191e+7
1.13076e+7
1.63394e+7
2.09588e+7
3.27097e+7
4.03184e+7
5.76286e+7
7.90291e+7
9.01548e+7
1.04564e+8
3.5854
3.5832
3.5822
3.5811
3.5801
3.5784
3.5791
3.5875
3.5964
3.6251
3.6687
3.6901
3.7089
-0.0182
-0.0846
-0.1158
-0.1485
-0.1823
-0.2769
-0.3303
-0.3890
-0.3910
-0.3270
-0.1771
-0.1071
-0.0910
2.1930
2.0530
1.9910
1.9260
1.8610
1.6830
1.5780
1.4190
1.3590
1.2820
1.2460
1.2240
1.1430
6.5204
6.5430
6.5536
6.5648
6.5766
6.6134
6.6407
6.6998
6.7353
6.8176
6.9308
6.9941
7.0619
-0.0676
0.0342
0.0843
0.1390
0.1985
0.3910
0.5332
0.8252
0.9850
1.3113
1.6537
1.7811
1.8646
1.09508e+8
3.7116
-0.0980
1.1050
7.0765
1.8753
1.197636+8
3.7123
-0.1620
1.0370
7.0936
1.8840
(95ø0
M€+ 8.1 M€ - P=3.133 g (Packet, 1988)
Evre
6
<Dú \ÕO
M1
Log L1
Log Teff 1
M2
Log L2
Log Teff 2
P (g)
ZAMS
0.00
9.00
3.58
4.46
5.40
2.82
4.24
1.62
ZAMS
Red point prim.
Blue point prim.
Begin RLOFI->2
0.00
2.61
2.72
2.73
9.00
9.00
9.00
9.00
3.58
3.85
3.91
3.92
4.36
4.27
4.31
4.26
8.10
8.10
8.10
8.10
3.43
3.65
3.66
3.66
4.33
4.26
4.26
4.26
3.13
3.13
3.13
3.13
94
Mass ratio reversal
Min.Lumimosity
Max.Lumimosity
He ignition prim.
End RLOF-min R
0.18
0.50
0.55
2.03
2.71
8.55
4.06
3.25
1.73
1.51
3.75
2.54
2.77
3.76
3.93
4.22
3.84
3.84
3.91
3.92
8.55
13.03
13.84
15.37
15.58
3.88
4.38
4.40
4.40
4.43
4.29
4.44
4.46
4.47
4.48
3.11
8.16
13.28
64.61
92.81
Max.Luminosity
Min.Lum- min. R
2.76
2.91
1.51
1.51
3.95
3.07
4.07
4.73
15.58
15.58
4.43
4.49
4.48
4.47
92.81
92.81
End He burn. prim.
Min L- Min R
Begin RLOFl->2
3.32
3.33
3.36
1.51
1.51
1.51
3.67
3.54
4.08
4.82
4.83
3.95
15.58
15.58
15.58
4.62
4.63
4.64
4.42
4.41
4.41
92.81
92.81
92.81
Xat=0
3.36
1.43
4.12
3.95
15.85
4.67
4.42
107.58
(95ø0
M€+ 5.4 M€ - P=2.983 g (Packet, 1988)
Evre
6
<Dú \ÕO
M1
Log L1
Log Teff 1
M2
Log L2
Log Teff 2
P (g)
ZAMS
0.00
9.00
3.58
4.36
5.40
2.82
4.23
2.98
Red point prim.
2.68
9.00
3.85
4.27
5.40
2.91
4.21
2.98
Blue point prim.
2.93
9.00
3.91
4.31
5.40
2.92
4.21
2.98
Begin RLOF1->2
2.93
9.00
3.92
4.26
5.40
2.92
4.21
2.98
Begin contact
2.941
7.97
3.22
4.11
6.42
4.06
4.35
2.55
Mass ratio rev.
2.945
7.20
2.91
4.04
7.20
4.15
4.36
2.46
End contact
2.949
5.95
1.71
3.77
8.45
4.33
4.39
2.69
MinL
2.951
5.52
1.71
3.76
8.87
4.33
4.40
2.91
He ignition prim.
1.69
1.71
3.77
4.01
12.68
4.12
4.45
33.11
End RLOF
2.33
1.52
3.95
4.03
12.87
4.14
4.45
45.34
Min luminosity
3.09
1.52
3.08
4.73
12.87
4.18
4.45
45.34
End He bur.prim.
3.50
1.52
3.68
4.82
12.87
4.28
4.43
45.34
Begin RLOF1->2
3.54
1.52
4.08
4.06
12.87
4.29
4.43
45.34
End computations
3.57
1.21
4.15
4.00
13.19
4.37
4.45
84.31