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Dvizhushiesya obolochki zvezd << 1.1 Osnovnye uravneniya | Oglavlenie | 1.3 Otnositel'nye intensivnosti linii >>

1.2 Stepen' vozbuzhdeniya i ionizacii

Dlya resheniya sistemy (9) neobhodimo znat' znachenie funkcii C_i i B_icρ_ic^* dlya dannogo atoma. Dlya atoma vodoroda eti funkcii imeyut vid (sm. citirovannuyu rabotu Cillie):

$\begin{eqnarray} C_i(T)=\frac{2^9\pi^6}{(6\pi)^{3/2}}\frac{e^{10}}{m^2c^3h^3}\left(\frac{m}{kT}\right)^{\frac{3}{2}}\frac{1}{i^3}e^{\frac{h\nu_{ic}}{kT}}E_i\left(\frac{h\nu_{ic}}{kT}\right),\nonumber \end{eqnarray}$ (13)

$\begin{eqnarray} B_{ic}\rho_{ic}^*=4\pi\int\limits_{\nu_{ic}}^{\infty} \alpha_{i\nu}\frac{J_\nu^* d\nu}{h\nu},\nonumber \end{eqnarray}$ (14)

$\begin{eqnarray} \alpha_{i\nu}=\frac{2^6\pi^4}{3\sqrt{3}}\frac{me^{10}}{ch^6i^5}\frac{1}{\nu^3},\nonumber \end{eqnarray}$ (15)

gde m i e - massa i zaryad elektrona; h - postoyannaya Planka i k - postoyannaya Bol'cmana.

Legko videt', chto esli sistema (9) reshena dlya vodoroda, to poluchennye rezul'taty mogut byt' ispol'zovany dlya ionizovannogo geliya. V samom dele, my imeem: spektral'nye termy He⁺ v 4 raza bol'she termov N, koefficienty spontannyh perehodov dlya He⁺ v 16 raz bol'she, chem dlya N, a statisticheskie vesa sostoyanii sovpadayut (sm. rabotu V. A. Ambarcumyana [2]). Poetomu iz rassmotreniya sistemy (9) my prihodim k sleduyushemu vyvodu: chisla $\frac{n_i}{n_en^+}$ dlya ionizovannogo geliya budut v 8 raz men'she sootvetstvuyushih chisel dlya vodoroda, esli prinyat' temperaturu v 4 raza bol'shuyu.

Sistemu (9) my reshili chislenno dlya vodorodnogo atoma. Pri etom my schitali, chto temperatura sredy sovpadaet s temperaturoi zvezdy. Esli eti temperatury razlichny, to v uravneniyah (9) velichiny B_icρ_ic^* budut funkciyami ot T_∗, a velichiny C_i - funkciyami ot T_e. Odnako iz rassmotrennyh nami sluchaev legko sdelat' perehod k drugim sluchayam. Eto svyazano s tem, chto otnositel'nye znacheniya velichin C_i ochen' malo menyayutsya s izmeneniem T_e. Poetomu i otnositel'nye znacheniya velichin n_i budut takzhe slabo zaviset' ot T_e. Tak, naprimer, pri T_e=10000°; vse velichiny n_i budut priblizitel'no v 2 raza bol'she, chem pri T_e=20000°; .

My rassmotreli sleduyushie sluchai: T = 20000°; , x = 0; 0,01; 0,1; 1,0; T=50000°; ; h = 0; 0,1; 1,0; 10. Rezul'taty vychislenii privedeny v tablicah I, II i III.

Tablica I
$\frac{n_en^+}{Wn_1}\cdot 10^{-20}$

T\x 0 0.01 0.1 1.0 10 ∞

20000 0.027 0.022 0.015 0.014 - 0.014

50000 11.8 - 9,4 7.3 6.8 6.8

Tablica II
$100\frac{n_k}{n_1}$ (T=20000^o)

k\x 0 0.01 0.1 1.0

2 1.06 0.97 0.29 0.036

3 0.64 0.33 0.030 0.00056

4 0.60 0.20 0.0085 0.000058

5 0.61 0.16 0.0037 0.000012

6 0.65 0.14 0.0021 0.000004

Tablica III
$100\frac{n_k}{n_1}$ (T=50000^o)

k\x 0 0.1 1.0 10

2 0.30 0.18 0.046 0.0067

3 0.26 0.13 0.019 0.00095

4 0.28 0.12 0.012 0.00030

5 0.31 0.11 0.009 0.00015

6 0.34 0.10 0.007 0.00010

Iz tabl. I vidno, chto stepen' ionizacii slabo zavisit ot parametra h. Mozhno schitat', chto pri lyubyh znacheniyah h stepen' ionizacii opredelyaetsya obychnoi ionizacionnoi formuloi (s mnozhitelem W v pravoi chasti).*

Naprotiv, stepen' vozbuzhdeniya, malo otlichayushayasya ot bol'cmanovskoi, pri x = 0, chrezvychaino bystro ubyvaet s vozrastaniem velichiny h. Eto znachit, chto dlya nahozhdeniya stepeni vozbuzhdeniya v dvizhushihsya obolochkah zvezd ni v koem sluchae nel'zya pol'zovat'sya formuloi Bol'cmana. Ubyvanie stepeni vozbuzhdeniya s uvelicheniem velichiny h (osobenno bystroe dlya vysokih urovnei) privodit k tomu, chto pri dostatochno bol'shih znacheniyah h sreda stanovitsya prozrachnoi dlya izlucheniya v liniyah dannoi serii. K takim sluchayam rezul'taty, poluchennye v etom paragrafe, neprimenimy. Eti sluchai podrobno rassmatrivayutsya v § 4.

* Eto svyazano s nashim predpolozheniem o malosti opticheskoi tolshiny sredy za granicei osnovnoi serii. Esli eta opticheskaya sreda velika, to, kak budet pokazano v glave IV , izmenenie stepeni ionizacii s opticheskoi glubinoi sil'no zavisit ot parametra h.

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T\x	0	0.01	0.1	1.0	10	∞
20000	0.027	0.022	0.015	0.014	-	0.014
50000	11.8	-	9,4	7.3	6.8	6.8

k\x	0	0.01	0.1	1.0
2	1.06	0.97	0.29	0.036
3	0.64	0.33	0.030	0.00056
4	0.60	0.20	0.0085	0.000058
5	0.61	0.16	0.0037	0.000012
6	0.65	0.14	0.0021	0.000004

k\x	0	0.1	1.0	10
2	0.30	0.18	0.046	0.0067
3	0.26	0.13	0.019	0.00095
4	0.28	0.12	0.012	0.00030
5	0.31	0.11	0.009	0.00015
6	0.34	0.10	0.007	0.00010