7.2
Òåìïåðàòóðà ÿäðà çâåçäû
7.2.1
Ýíåðãèÿ ÷åðíîãî èçëó÷åíèÿ
Ýíåðãèÿ ÷åðíîãî èçëó÷åíèÿ â ÿäðå E? (br) =
π2 kT? 15
kT? ~c
3
(7.14)
V? .
Ýíåðãèÿ ÷åðíîãî èçëó÷åíèÿ â àòìîñôåðå Z
R0
Ea (br) = 4π R?
π2 kT? 15
kT? ~c
3
R? r
16
r2 dr =
3 π2 kT? 13 15
kT? ~c
3 V? .
(7.15)
Ïîëíàÿ ýíåðãèÿ ÷åðíîãî èçëó÷åíèÿ 16 π 2 E(br) = E? (br) + Ea (br) = kT? 13 15 7.2.2
3
kT? ~c
π2 V? = 1.23 kT? 15
kT? ~c
3
V? . (7.16)
Ïîëíàÿ ýíåðãèÿ çâåçäû
 ñîîòâåòñòâèè ñ (7.3) ïîëíàÿ ýíåðãèÿ çâåçäû (7.17)
E star = −E kinetic + E(br),
òî åñòü E star = −
15 16 π 2 kT? N? + kT? 7 13 15
kT? ~c
3 V? .
(7.18)
Óñòîé÷èâîå ñîñòîÿíèå çâåçäû îïðåäåëÿåòñÿ ìèíèìóìîì åå ýíåðãèè
dE star dT?
= 0,
(7.19)
N=const,V=const
÷òî ñîîòâåòñòâóåò óñëîâèþ −
64π 2 15 N? + 7 13 · 15
kT? ~c
3 V? = 0,
(7.20)
èç êîòîðîãî ñ ó÷åòîì (4.18) îïðåäåëÿåì ðàâíîâåñíóþ òåìïåðàòóðó ÿäðà T? =
25 · 13 28π 4
1/3
~c kaB
51
Z ≈ Z · 2.13 · 107 K.
(7.21)