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Fizicheskie osnovy stroeniya i evolyucii zvezd

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4.4 Kriticheskaya eddingtonovskaya svetimost'

Iz usloviya sleduet, chto $\left\vert{dP\over dr}\right\vert>\left\vert{dP_r\over dr} \right\vert$ . Voobshe govorya, ne vsegda mozhno differencirovat' neravenstva, no v dannom sluchae netrudno ubedit'sya, chto vse v poryadke. Teper' ochevidno, chto

$\displaystyle L\le{4\pi\,GMc\over\varkappa}.$

Samaya malen'kaya neprozrachnost' -- eto $\varkappa_{\mbox{\sc t}}=0,4\;\mbox{sm}^2/\mbox{g}$ . Poetomu svetimost' zvezdy ne mozhet nikogda prevyshat' velichinu $4\pi\,GMc/0,4$ , t.e.

$\displaystyle L\le 6,3\cdot 10^4M=3\cdot 10^4L_{\odot}\,\left({M\over M_{\odot}}\right)=L_c,$

-- velichina, nazyvaemaya eddingtonovskim predelom svetimosti.

Otmetim, chto dlya Solnca $L_{\odot}/M_{\odot}=2$ erg/gs, t.e. vydelyaetsya energii primerno stol'ko zhe, skol'ko pri gnienii opavshih list'ev, i bol'shaya svetimost' opredelyaetsya tol'ko bol'shoi massoi, no vse ravno $L_{\odot}\ll L_c$ .

Podschitaem eddingtonovskii predel eshe odnim prostym sposobom. Pust' na nekotorom rasstoyanii ot zvezdy so svetimost'yu imeetsya odin elektron. Potok izlucheniya cherez 1 sm raven

$\displaystyle H={L\over 4\pi\,r^2}=\int h\,\nu\,\cos\Theta\cdot\varphi\,(\nu,\;\Theta)\,d\Theta \,d\nu,$

gde $\varphi$ -- chislo kvantov v edinichnom intervale chastot, proletayushih cherez 1 sm

v napravlenii $\Theta$ za odnu sekundu.

Pri stolknovenii s elektronom odin kvant otdaet impul's $h\nu/c$ , i sila, deistvuyushaya na elektron so storony izlucheniya (impul's, peredavaemyi v edinicu vremeni),

$\displaystyle f=\int {h\nu\over c}\,\cos\Theta\cdot\varphi\,\sigma_T\,d\Theta \,d\nu\,.$

Dal'neishii raschet prost. Tak kak $\sigma_T$ ne zavisit ot chastoty, a indikatrissa rasseyaniya hotya i zavisit ot ugla, no takova, chto veroyatnost' rasseyaniya na ugol $\pi-\Theta$ , poluchim

$\displaystyle f={\sigma\over c}\,H.$

(4.4)

Takim obrazom, pri podschete ne vazhno raspredelenie funkcii $\varphi$ po uglu. Odin i tot zhe rezul'tat (4.4) poluchitsya i vnutri zvezdy, gde $\varphi$ pochti simmetrichno, i vne zvezdy, gde kvanty letyat v uzkom telesnom ugle. Priravnivaya eto vyrazhenie dlya

sile prityazheniya, deistvuyushei na odin proton, poluchim

$\displaystyle f={\sigma\over c}\,H={\sigma\over c}\,{L\over 4\pi\,r^2}={GMm_p\over r^2}.$

My podstavili , tak kak sila prityazheniya protonov mnogo bol'she sily elektronov. V stacionarnoi kartine voznikaet elektrostaticheskoe pole, uderzhivayushee elektrony. Takim obrazom, u zvezdy voznikaet zaryad. (Vychislite velichinu i znak etogo zaryada.)

Itak,

$\displaystyle L\le{GMm_pc\over\sigma_T}=L_c.$

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Astrometriya - Astronomicheskie instrumenty - Astronomicheskoe obrazovanie - Astrofizika - Istoriya astronomii - Kosmonavtika, issledovanie kosmosa - Lyubitel'skaya astronomiya - Planety i Solnechnaya sistema - Solnce