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Ãëàâà 10 Âðàùåíèå ïåðèàñòðîâ òåñíûõ çâ¼çäíûõ ïàð 10.1 Âðàùåíèå àïñèä òåñíûõ ïàð çâ¼çä Âðàùåíèå ëèíèé àïñèä â òåñíûõ äâîéíûõ çâ¼çäíûõ ñèñòåìàõ åñòü ðåçóëüòàò îòêëîíåíèÿ äâèæåíèÿ ýòèõ çâ¼çä îò çàêîíîâ Êåïëåðà, ïðîèñõîäÿùåãî èç-çà íåñôåðè÷íîñòè ðàñïðåäåëåíèÿ âåùåñòâà âíóòðè íèõ. Ãëàâíîé ïðè÷èíîé âîçíèêíîâåíèÿ íåñôåðè÷íîñòè ÿâëÿåòñÿ ñîáñòâåííîå âðàùåíèå çâ¼çä. Âïåðâûå òåîðèÿ ýòîãî ýôôåêòà áûëà ñîçäàíà À.Êëåðî (A.Clairault) â íà÷àëå XVIII âåêà. Â íàñòîÿùåå âðåìÿ èçâåñòíî îêîëî ïîëóñîòíè òåñíûõ äâîéíûõ çâ¼çä, âðàùåíèå ïåðèàñòðîâ êîòîðûõ èçìåðåíî. Ïðè ýòîì, ñîãëàñíî òåîðèè, áàçèðóþùåéñÿ íà âû÷èñëåíèÿõ Êëåðî, îêàçûâàåòñÿ, ÷òî, åñëè áû âåùåñòâî âíóòðè çâ¼çä áûëî áû ðàñïðåäåëåíî ðàâíîìåðíî, òî âðàùåíèå ïåðèàñòðîâ ýòèõ çâ¼çä äîëæíî áûëî áû ïðîèñõîäèòü ïðèìåðíî â ñòî ðàç áûñòðåå. Íàîáîðîò, åñëè áû âñå âåùåñòâî çâ¼çä áûëî áû ñîñðåäîòî÷åíî â èõ öåíòðàõ, òî âðàùåíèå ïåðèàñòðîâ âîîáùå îòñóòñòâîâàëî. Ñîãëàñîâàòü òåîðèþ ñ íàáëþäåíèÿìè ìîæíî, åñëè ïðåäïîëîæèòü, ÷òî ïëîòíîñòü çâ¼çäíîãî âåùåñòâà âîçðàñòàåò ïî ìåðå ïðèáëèæåíèÿ ê öåíòðó è äîñòèãàåò òàì âåëè÷èíû ïðèìåðíî â ñòî ðàç áîëüøåé, ÷åì óñðåäíåííàÿ ïëîòíîñòü ïî âñåìó îáúåìó çâåçäû. Èìåííî òàêîå âîçðàñòàíèå ïëîòíîñòè ñëåäóåò èç ñòàíäàðòíûõ ìîäåëåé çâ¼çäíîãî èíòåðüåðà, è ïîýòîìó ñ÷èòàåòñÿ, ÷òî âðàùåíèå àïñèä òåñíûõ çâ¼çäíûõ ïàð êà÷åñòâåííî äîêàçûâàåò èõ ïðàâèëüíîñòü. Îäíàêî êîëè÷åñòâåííîãî ñîîòâåòñòâèÿ äëÿ êîíêðåòíûõ çâ¼çä ìîæíî äîñòèãíóòü òîëüêî ïóòåì ïîäáîðà ïàðàìåòðîâ èõ âíóòðåííåãî ñòðîåíèÿ èíäèâèäóàëüíî äëÿ êàæäîé ïàðû. Ðàññìîòðèì ýòó çàäà÷ó ñ ó÷åòîì ýëåêòðè÷åñêîé ïîëÿðèçàöèè. Ïðè ýòîì ðîëüþ àòìîñôåðû, èìåþùåé ìàëóþ ïëîòíîñòü, ìîæíî ïðåíåáðå÷ü. Èç-çà çíà÷èòåëüíîé 83
êîíöåíòðàöèè âåùåñòâà âíóòðè ÿäðà çâåçäû ìîæíî ñ÷èòàòü, ÷òî îïðåäåëÿþùóþ ðîëü â ðàññìàòðèâàåìîì ýôôåêòå áóäåò èãðàòü èçìåíåíèå ôîðì ÿäåð çâ¼çä, âðàùàþùèõñÿ âîêðóã ñâîèõ îñåé. Çà ñ÷åò ñâîåãî âðàùåíèÿ âîêðóã îñè ÿäðî çâåçäû ïðèîáðåòàåò ôîðìó ñïëþñíóòîãî ýëëèïñîèäà âðàùåíèÿ, è ýòî âûçûâàåò äîïîëíèòåëüíûå ñèëû, ïðèâîäÿùèå ê èçìåíåíèþ åå ñêîðîñòè ïî ýëëèïòè÷åñêîé îðáèòå. Â ñîîòâåòñòâèè ñ [7],[17] îòíîøåíèå óãëîâîé ñêîðîñòè âðàùåíèÿ ïåðèàñòðà ω, âîçíèêàþùåãî çà ñ÷åò äåéñòâèÿ ýòîãî ìåõàíèçìà, ê óãëîâîé ñêîðîñòè âðàùåíèÿ âîêðóã îñè Ω ðàâíî: ω Ω = 3 (I A − I C) . (10.1) 2 Ma 2 Çäåñü I A è I C - ìîìåíòû èíåðöèè îòíîñèòåëüíî ãëàâíûõ îñåé ýëëèïñîèäà. Èõ ðàçíîñòü I A − I C = M 5 (a2 − c 2 ), (10.2) çäåñü a è c - ýêâàòåðèàëüíûé è ïîëÿðíûé ðàäèóñû çâåçäû. Â ðåçóëüòàòå ïîëó÷àåòñÿ ω Ω ≈ 3 (a 2 − c 2 ) . (10.3) 10 a 2 10.2 Ðàâíîâåñíàÿ ôîðìà ÿäðà âðàùàþùåéñÿ çâåçäû Â îòñóòñòâèè âðàùåíèÿ óðàâíåíèå ðàâíîâåñèÿ ïëàçìû â ÿäðå áûëî ïîëó÷åíî ðàíåå (6.4). Ïåðåïèøåì åãî â âèäå γg G + ρ GE G = 0, (10.4) ïðèïèñàâ èíäåêñ G ñîîòâåòñòâóþùèì âåëè÷èíàì, ÷òîáû îòìåòèòü, ÷òî èõ ïðîèñõîæäåíèå âûçâàíî äåéñòâèåì ãðàâèòàöèè, èìåÿ â âèäó ïðè ýòîì, ÷òî div g G = 4π G γ, div E G = 4πρ G è ρ G = √ Gγ. Ìîæíî ïðåäïîëîæèòü, ÷òî ïðè âðàùåíèè ïîä äåéñòâèåì öåíòðîáåæíîãî óñêîðåíèÿ g Ω, ìîãóò â ïëàçìå âîçíèêíóòü äîïîëíèòåëüíûå ýëåêòðè÷åñêèå çàðÿäû ñ ïëîòíîñòüþ ρ Ω è äîïîëíèòåëüíîå ýëåêòðè÷åñêîå ïîëå E Ω. Â ýòîì ñëó÷àå óðàâíåíèå ðàâíîâåñèÿ ïðèîáðåòåò âèä: (γ G + γ Ω)(g G + g Ω) = (ρ G + ρ Ω)(E G + E Ω), (10.5) çäåñü div (E G + E Ω) = 4π(ρ G + ρ Ω) (10.6) 84
Page 3 and 4:
Á.Â.Âàñèëüåâ ÀÑÒÐÎÔ
Page 5 and 6:
4
Page 7 and 8:
5 Ýëåêòðè÷åñêàÿ ïîë
Page 9 and 10:
8
Page 12 and 13:
Ãëàâà 1 Òåîðèÿ è ýêñ
Page 14 and 15:
1.2 Î ñïåöèôèêå ðàáî
Page 16 and 17:
1.4 Õàðàêòåðíûå ñâîé
Page 18 and 19:
Ãëàâà 2 Î ïñåâäî-òåî
Page 20 and 21:
log T/T o 1.0 0.9 0.8 0.7 0.6 measu
Page 22 and 23:
Ðèñ. 2.3: (a) Ñïåêòð ñî
Page 24 and 25:
Log L Ðèñ. 2.4: Èçìåðåíí
Page 26 and 27:
2.4 Ôèçèêà ýëåìåíòàð
Page 28 and 29:
Ãëàâà 3 Ââåäåíèå 3.1
Page 30 and 31:
ñîáñòâåííàÿ, îñîáå
Page 32 and 33:
Òàêèì îáðàçîì ìîæí
Page 34 and 35: Ñëåäóþùèå ãëàâû áó
Page 36 and 37: Ãëàâà 4 Ýíåðãåòè÷åñ
Page 38 and 39: ( ) I µe ≈ e kT 3 (kT ) 5/2 Γ 2
Page 40 and 41: ñëàãàåìûìè ìîæíî ï
Page 42 and 43: Ãëàâà 5 Ýëåêòðè÷åñê
Page 44 and 45: ò.å. P 2 = 3GMr 2πr ne ( A Z mp
Page 46 and 47: Ãëàâà 6 Âíóòðåííåå
Page 48 and 49: ðàññìàòðèâàòü êàê
Page 50 and 51: Ãëàâà 7 Ìàññà çâåçä
Page 52 and 53: 7.2 Òåìïåðàòóðà ÿäðà
Page 54 and 55: èçìåðåíèÿìè. Íà ðèñ
Page 56 and 57: 40 N 35 30 10 9 8 7 6 5 4 3 2 1 A/Z
Page 58 and 59: 7.3.3 Ñðàâíåíèå ñ íàá
Page 60 and 61: 2.10 log (TR/R o T o ) 1.55 1.00 me
Page 62 and 63: Ãëàâà 8 Òåðìîäèíàìè
Page 64 and 65: çäåñü W - ýíòàëüïèÿ
Page 66 and 67: log R/R o 1.5 1.3 1.1 0.9 measured
Page 68 and 69: Òàáëèöà(8.2)(ïðîäîëæ
Page 70 and 71: Òàáëèöà(8.2)(ïðîäîëæ
Page 72 and 73: 8.3 Ñîîòíîøåíèÿ ìàññ
Page 74 and 75: äîëæíà ñîãëàñíî (8.19
Page 76 and 77: Ðèñ. 8.4: Ñõåìàòè÷åñê
Page 78 and 79: Ãëàâà 9 Ìàãíèòíûå ï
Page 80 and 81: 45 µ/L=G 1/2 /c Log µ 35 25 Mercu
Page 82 and 83: 100 90 H,kOe 80 70 V 901 Ori 60 50
Page 86 and 87: èëè div E Ω = 4πρ Ω. (10.7)
Page 88 and 89: 10.4 Ñðàâíåíèå âû÷èñ
Page 90 and 91: Ãëàâà 11 Ñïåêòð ñîáñ
Page 92 and 93: íàáëþäàòåëüíûõ äàí
Page 94 and 95: Ðèñ. 11.2: (a) Ñïåêòð ñî
Page 96 and 97: Ïðè T = T ⋆ è n e = n ⋆ è
Page 98 and 99: δE = N⋆ 6 Ââåäÿ îáîçí
Page 100 and 101: Ãëàâà 12 Äîïîëíåíèå:
Page 102 and 103: Èíòåãðèðóÿ ýòî âûð
Page 104 and 105: Ýòî äèôôåðåíöèàëüí
Page 106 and 107: Ïîëó÷åííûå ôîðìóëû
Page 108 and 109: Ãëàâà 13 Äîïîëíåíèå:
Page 110 and 111: ñèñòåìàòèêîé ñâîéñ
Page 112 and 113: Çäåñü E kinetic - êèíåòè
Page 114 and 115: N 10 9 8 7 6 5 4 3 2 1 0 1.0 1.1 1.
Page 116 and 117: Òàê êàê ðàâíîâåñíà
Page 118 and 119: Âíóòðè íåãî òàêèì î
Page 120 and 121: Ãëàâà 14 Çàêëþ÷åíèå
Page 122 and 123: èõ ÿðêîñòè, ñ÷èòàÿ,
Page 124 and 125: Ëèòåðàòóðà [1] Vasiliev B
Page 126 and 127: Appendix Ñâîäíàÿ òâáëè
Page 128 and 129: Ëèòåðàòóðà [1] Khaliulili
Page 130 and 131: [19] Popper D.M. Rediscussion of ec
Page 132 and 133: [41] Andersen J., Garcia J.M., Gime
Page 134 and 135:
[64] Wolf M. and Saronova L., Aspid
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