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2.3 Ostatki sverhnovyh i ih vzaimodeistvie s mezhzvezdnoi sredoi

Sbroshennaya pri vspyshke sverhnovoi obolochka rasshiryaetsya so sverhzvukovoi skorost'yu v mezhzvezdnuyu sredu i obrazuet udarnuyu volnu. Razlichayut neskol'ko stadii vzaimodeistviya obolochki s okruzhayushei sredoi.

Stadiya 1. Svobodnyi razlet.

Na etoi stadii obolochka dvizhetsya po inercii tak, kak esli by vneshnei sredy ne bylo voobshe, $R(t)\propto t$ . Izluchenie obolochki ne igraet roli v ee dinamike. Staliya zakanchivaetsya pri sgrebanii massy okruzhayushego veshestva, ravnoi masse rasshiryayusheisya obolochki $M_0=4\pi/3 \rho_0 R^3$ . Dlya $\rho_0=2 10^{-24}$ g/sm³ i $M_0=1M_\odot$ etot moment nastupaet pri $R\approx 2$ pk, primerno cherez 100 let posle nachala rasshireniya.

Stadiya 2. Adiabaticheskoe rasshirenie.

Radiacionnye processy po-prezhnemu dinamicheski nevazhny (otsyuda nazvanie - adiabaticheskaya stadiya), tak kak temperatura gaza za frontom udarnoi volny ochen' vysokaya. Kineticheskaya energiya obolochki rashoduetsya na nagrev gaza za frontom sil'noi udarnoi volny i na uskorenie sgrebennogo mezhzvezdnogo gaza. Kogda massa sgrebennogo gaza mnogo bol'she M₀, dvizhenie obolochki dovol'no tochno opisyvaetsya avtomodel'nym resheniem L.I. Sedova (1946) dlya sil'nogo vzryva v srede. Mozhno poluchit' zavisimost' povedeniya radiusa obolochki ot vremeni iz prostyh fizicheskih soobrazhenii (L. Spitcer, Fizicheskie processy v mezhzvezdnoi srede, M.: Mir, 1981). Pust' teplovaya energiya gaza sostavlyaet dolyu K₁ ot polnoi energii E₀, a davlenie neposredstvenno za frontom UV p₂ v K₂ raz bol'she srednego davleniya vnutri obolochki. Dlya ideal'nogo gaza s pokazatelem adiabaty $\gamma$ $p=(\gamma-1)\epsilon$ , gde $\epsilon$ - plotnost' energii. Togda

$\begin{displaymath} p_2=K_2 (\gamma-1) \frac{K_1E_0}{4\pi/3 R_s(t)^3} \end{displaymath}$

(8)

No v sluchae sil'nyh udarnyh voln spravedlivo sootnoshenie

$\begin{displaymath} p_2=\frac{2\rho_1u_1^2}{\gamma+1} \end{displaymath}$

(9)

mezhdu davleniem srazu za frontom p₂, plotnost'yu $\rho_1$ i skorost'yu vtekaniya nevozmushennogo gaza v UV u₁. Kombiniruya eti uravneniya i uchityvaya, chto u₁=dR_s/dt, poluchaem

$\begin{displaymath} \left(\frac{dR_s}{dt}\right)^2=\frac{4\pi}{3}K_1K_2 \frac{(\gamma^2-1)}{2}\left(\frac{E_0}{\rho_1 R_s^3}\right) \end{displaymath}$

(10)

Tochnyi dinamicheskie raschet daet dlya $\gamma=5/3$ K₁=0.72, K₂=2.13, tak chto K₁K₂=1.53.

Integriruya poslednee uravnenie, poluchaem dlya skorosti rasprostraneniya UV v etom rezhime

$\begin{displaymath} R_s(t)\propto \left(\frac{E_0}{\rho_1}\right)^{1/5}t^{2/5} \... ...\right)^{1/5}\left(\frac{t}{\hbox{gody}}\right)^{2/5}\hbox{pk} \end{displaymath}$

(11)

Zdes' v poslednem ravenstve $E_{51}\equiv (E_0/10^{51}$ erg/s) - nachal'naya energiya vzryva, n₁ - koncentraciya atomov v nevozmushennoi mezhzvezdnoi srede ( $\sim 1-100$ sm^-3 v razlichnyh astrofizicheskih situaciyah), $\rho_1=1.26 m_Hn_1$ dlya harakternogo Solnechnogo himicheskogo sostava mezhzvezdnoi sredy.

Poskol'ku temperatura za frontom sil'noi udarnoi volny dlya ideal'nogo gaza s $\gamma=5/3$

$\begin{displaymath} T_s=\frac {3\mu (dR_s/dt)^2}{16k_B}=1.8\times 10^5 \left(\frac{R/\hbox{pk}}{t/\hbox{gody}}\right)^2\hbox{keV} \end{displaymath}$

(k_B - postoyannaya Bol'cmana, $\mu$ - molekulyarnyi ves) padaet so vremenem kak $T\propto R_s^{-3}\propto t^{-6/5}$ , nachinaya s nekotorogo momenta vremeni (radiusa obolochki) stanovyatsya vazhnymi processy radiativnogo ohlazhdeniya UV i adiabaticheskoe priblizhenie narushaetsya.

Zametim, chto uzhe v konce stadii svobodnogo razleta voznikaet obratnaya udarnaya volna, rasprostranyayushayasya vnutr' obolochki (v sisteme koordinat, svyazannoi s frontom UV), no dvizhushayasya naruzhu v laboratornoi sisteme (t.e. gaz vtekaet v obratnuyu udarnuyu volnu iznutri obolochki). Poskol'ku izluchenie plazmy proporcional'no kvadratu plotnosti, imenno obratnaya UV daet naibol'shii vklad v rentgenovskoe izluchenie molodyh ostatkov sverhnovyh (sm. noveishie nablyudeniya rentgenovskimi kosmicheskimi observatoriyami Chandra i HMM "N'yuton"). Eti nablyudeniya okazalis' ochen' horoshee soglasie s teoreticheskimi modelyami ostatkov sverhnovyh umerennyh vozrastov.

Stadiya 3. Stadiya snegoochistitelya (angl. "snow-plow").

Nastupaet posle katastroficheskogo ohlazhdeniya gaza obolochki, kogda temperatura padaet nizhe $\approx 6\times 10^5$ K i plazma nachinaet intensivno vysvechivat' zapasennuyu teplovuyu energiyu. UV pri etom stanovitsya izotermicheskoi ( $\gamma=1$ ). Obolochka stanovitsya tonkoi i holodnoi, poskol'ku skorost' gaza, proshedshego cherez udarnuyu volnu, men'she skorosti dvizheniya fronta po srede i gaz, podzhimaemyi davleniem obolochki iznutri, dolgo ostaetsya vblizi fronta UV. Perehod k etomu rezhimu proishodit pri radiuse obolochki

$\begin{displaymath} R_c=24 \left(\frac{E_{51}}{n_0}\right)^{1/3}\;\hbox{pk} \end{displaymath}$

Dvizhenie UV podderzhivaetsya za schet zapasennogo v obolochke impul'sa ( M(dR_s/dt)=const, $M=4\pi/3\rho_1R_s^3$ ), UV sgrebaet okruzhayushii gaz i peredaet emu svoi impul's, i situaciya pohozha na sgrebanie snega snegoochistitelem. V etom rezhime rasshirenie obolochki zamedlyaetsya, t.k. iz sohraneniya impul'sa sleduet $dR_s/dt\propto R_s^{-3}$ (a ne R_s^-3/2 kak v sluchae adiabaticheskogo razleta, sm. (10)). Neslozhno pokazat' (sm. naprimer, S.I. Blinnikov, Astrophysics of exploding objects, Osaka, 2000), chto pri etom $R_s\propto (R_ct)^{2/7}$ . Tak kak radius smeny rezhimov R_c zavisit ot nachal'noi energii, izmeryaya skorost' dvizheniya obolochki u na radiativnoi stadii (naprimer, po opticheskim liniyam), mozhno poluchit' ocenku energii nachal'nogo vzryva E₀:

$\begin{displaymath} E_0\approx 0.8\times 10^{51} n_0 \left(\frac{u}{10^3\hbox{km... ...ight)^{1.2}\left(\frac{R}{10\,\hbox{pk}}\right)^3 \,\hbox{erg} \end{displaymath}$

Razrezhennyi goryachii gaz vnutri obolochki prakticheski ne ostyvaet i yavlyaetsya dopolnitel'nym istochnikom rasshireniya obolochek na pozdnih radiativnyh stadiyah. Po proshestvii $\sim 10^4$ let posle nachala rasshireniya mery emissii obolochek sverhnovyh umen'shayutsya nastol'ko, chto oni stanovyatsya prakticheski nerazlichimymi na fone srednego izlucheniya mezhzvezdnoi sredy.

V deistvitel'nosti znachitel'naya neodnorodnost' plotnosti mezhzvezdnoi sredy, magnitnye polya, razlichnye neustoichivosti (teplovye neustoichivosti, neustoichivost' Releya-Teilora pri rasshirenii goryachego gaza v holodnom, neustoichivost' fronta UV Rihtmaiera-Meshkova i t.d.) i prochie astrofizicheskie faktory znachitel'no uslozhnyayut obrisovannuyu vyshe shematicheskuyu kartinu evolyucii ostatkov sverhnovyh. V nekotoryh tipah ostatkov (t.n. pleriony) osnovnaya energiya v obolochku postupaet v vide relyativistskih chastic, rozhdennyh bystrovrashayusheisya neitronnoi zvezdoi s sil'nym magnitnym polem - pul'sarom, obrazuyushimsya v rezul'tate kollapsa. Horosho izvestnyi primer molodogo ostatka sverhnovoi s pul'sarom - Krabovidnaya tumannost', ostatok vspyshki SN 1054 g. v sozvezdii Tel'ca. Bolee detal'noe izlozhenie i sopostavlenie s nablyudatel'nymi dannymi sm. v upomyanutoi monografii T.A. Lozinskoi.

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