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Poverhnostnaya fotometriya galaktik

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7.1 Modeli raspredeleniya pyli

Rassmotrim, sleduya v osnovnom rabote Disneya i dr. [147], raznye modeli raspredeleniya zvezd i pyli. Otmetim, chto v ispol'zuemom dalee prostom podhode rasseyanie izlucheniya otdel'no ne rassmatrivaetsya. Pod poglosheniem budut ponimat'sya summarnye poteri izlucheniya po puti k nablyudatelyu (kak za schet poglosheniya, tak i za schet rasseyaniya).

$\bullet$ Pogloshayushii ekran

Naibolee prostaya model' poglosheniya sostoit v tom, chto mezhdu nablyudatelem i galaktikoi nahoditsya sloi iz pogloshayushego veshestva. Pri otsutstvii rasseyaniya nablyudaemaya poverhnostnaya yarkost' galaktiki budet ravna $I = I^0 e^{-\tau}$ (zakon Bugera), gde -- neiskazhennaya poglosheniem yarkost' diska, a $\tau$ -- opticheskaya tolshina pogloshayushego sloya vdol' lucha zreniya (velichiny yarkostei i $\tau$ otnosyatsya, estestvenno, k fiksirovannoi dline volny). Velichina poglosheniya v zvezdnyh velichinah svyazana s opticheskoi tolshinoi vyrazheniem

$\begin{displaymath} A = -2.5\,{\rm lg}\frac{I}{I^0} = 1.086\,\tau. \end{displaymath}$

(69)

$\bullet$ Odnorodnyi sloi

Rassmotrim ploskii sloi tolshiny , v kotorom ravnomerno peremeshany zvezdy i pyl'. Pust' $\epsilon_*$ -- polnaya svetimost' zvezd diska v edinice ob'ema, a -- srednyaya dlina svobodnogo probega fotonov, idushih ot zvezd, bez ucheta poglosheniya. Togda v polozhenii ''plashmya'' poverhnostnaya yarkost' takogo sloya budet ravna

$\begin{displaymath} I(i=0^{\rm o}) = \int_0^H \epsilon_* e^{-x/l}{\rm d}x = \epsilon_* l \left[1-e^{-\tau}\right], \end{displaymath}$

(70)

gde $\tau = H/l$ -- polnaya opticheskaya tolshina sloya. Pri $\tau << 1$ (opticheski tonkii sloi) iz (70) sleduet, chto $I(i=0^{\rm o})=\epsilon_* H$ , pri $\tau >> 1$ $I(i=0^{\rm o})=\epsilon_* l$ .

Esli sloi raspolozhen pod uglom k nablyudatelyu, to (70) modificiruetsya sleduyushim obrazom:

$\begin{displaymath} I(i) = \epsilon_* l \left[1-e^{-\tau\,{\rm sec}i}\right]. \end{displaymath}$

(71)

Esli sloi opticheski tolstyi ( $\tau >> 1$ ), ego poverhnostnaya yarkost' ne zavisit ot naklona: $I(i) = I(i=0^{\rm o}) = \epsilon_* l$ . Esli zhe sloi (disk galaktiki) yavlyaetsya opticheski tonkim, to ego poverhnostnaya yarkost' dolzhna uvelichivat'sya s rostom

: $I(i)=\epsilon_* H\,{\rm sec}i=I(i=0^{\rm o})\,{\rm sec}i$ . Poslednyuyu formulu mozhno perepisat' kak $\mu_0^{obs}=\mu_0^{face-on}\,-\,2.5\,{\rm lg}\,{\rm sec}i$ (sm. (61)).

Sravnivaya poverhnostnye yarkosti sloya pri nalichii pyli i bez nee, mozhno naiti svyaz' mezhdu opticheskoi tolshinoi i velichinoi poglosheniya v zvezdnyh velichinah:

$\begin{displaymath} A = -2.5\,{\rm lg}\frac{\epsilon_* l \left[1-e^{-\tau}\right]}{\epsilon_* H} = -2.5\,{\rm lg}\frac{1-e^{-\tau}}{\tau}. \end{displaymath}$

(72)

Pri fiksirovannoi opticheskoi tolshine pogloshayushego sloya model' ekrana privodit k gorazdo bol'shemu poglosheniyu, chem model' diska s ravnomerno peremeshannymi zvezdami i pyl'yu. Naprimer, pri $\tau=5$ iz (69) sleduet, chto , a (72) privodit k znacheniyu .

$\bullet$ Model' sandvicha

V etoi modeli v centre zvezdnogo diska tolshinoi nahoditsya sloi s otnositel'noi tolshinoi $\delta$ (polnaya tolshina etogo sloya ravna, sledovatel'no, $\delta H$ ), v kotorom ravnomerno peremeshany zvezdy i pyl' (sm. ris. 29). Pri $\delta=1$ eta model' perehodit v opisannuyu ranee model' odnorodnogo sloya. Polnaya opticheskaya tolshina sandvicha $\tau=\delta\,H/l$ .

ris. 29: Shema modeli sandvicha.

$\begin{figure}\centerline{\psfig{file=sandw.ps,angle=-90,width=12.0cm}}\end{figure}$

Esli my rassmotrim opticheski tolstyi sandvich, to chast' diska galaktiki pod pogloshayushim sloem budet polnost'yu skryta ot nablyudatelya. Oblast' diska nad etim sloem budet vidna bez pomeh i, krome togo, my budem prinimat' izluchenie iz sloya pyli vplot' do glubiny . Sledovatel'no, nablyudaemaya poverhnostnaya yarkost' modeli budet ravna $I(i=0^{\rm o}) \approx \epsilon_* H (1-\delta)/2 + \epsilon_* l$ . Pri otsutstvii poglosheniya ( $\tau=0$ ) $I(i=0^{\rm o})=\epsilon_* H$ . Takim obrazom, $A = -2.5\,{\rm lg}[(1-\delta)/2\,+\,\delta/\tau]$ (pri $\tau >> 1$ ).

Esli rassmotret' model'nuyu galaktiku pod uglom , to integrirovanie vdol' lucha zreniya privodit k sleduyushemu vyrazheniyu dlya nablyudaemoi poverhnostnoi yarkosti [150,151,147]:

$\begin{displaymath} I(i) = \epsilon_* H {\rm sec}i \left[\frac{1-\delta}{2}(1+e^... ...rac{\delta}{\tau\,{\rm sec}i}(1-e^{-\tau\,{\rm sec}i})\right]. \end{displaymath}$

(73)

Dlya opticheski tolstogo sandvicha s $\delta=0.5$ mozhno poluchit', chto $I(i) \approx \epsilon_* H\,{\rm sec}i/4\,=\,I(i=0^{\rm o})\,{\rm sec}i/4$ . Sledovatel'no, harakter izmeneniya poverhnostnoi yarkosti budet takim zhe, kak u opticheski tonkogo odnorodnogo sloya tolshinoi

(oblast' takoi tolshiny nahoditsya nad pogloshayushim sloem).

Esli disk galaktiki viden ''plashmya'', to v modeli sandvicha opticheskaya tolshina i velichina poglosheniya v zvezdnyh velichinah svyazany sleduyushim sootnosheniem (sm. (73)):

$\begin{displaymath} A = -2.5\,{\rm lg}\left[\frac{1-\delta}{2}(1+e^{-\tau})+\frac{\delta}{\tau}(1-e^{-\tau})\right]. \end{displaymath}$

(74)

Modifikaciya modeli, v kotoroi chast' pyli sosredotochena v tonkom sloe v ploskosti simmetrii galaktiki, a drugaya chast' raspredelena po vsemu ee ob'emu, rassmotrena v rabote [152].

Na ris. 30 sravnivayutsya sootnosheniya mezhdu i $\tau$ dlya opisannyh vyshe modelei [147]. Ochevidno, chto v zavisimosti ot raspredeleniya pogloshayushei sredy fiksirovannomu znacheniyu opticheskoi tolshiny pyli mogut sootvetstvovat' sil'no razlichayushiesya znacheniya poglosheniya. Na risunke takzhe horosho vidno, chto bolee shirokoe raspredelenie pyli v napravlenii, perpendikulyarnom ploskosti diska galaktiki, privodit k bol'shemu poglosheniyu.

ris. 30: Zavisimost' velichiny poglosheniya (v zv. vel.) ot opticheskoi tolshiny dlya vidimyh ''plashmya'' modelei: punktir -- pogloshayushii ekran; tochki -- odnorodnyi sloi; nepreryvnye linii -- model' sandvicha s $\delta=0.75$ (tonkaya liniya), $\delta=0.50$ (bolee tolstaya liniya), $\delta=0.25$ (samaya tolstaya nepreryvnaya liniya).

$\begin{figure}\centerline{\psfig{file=absorpt.ps,angle=-90,width=9.5cm}}\end{figure}$

$\bullet$ Troinaya eksponencial'naya model'

V predydushih modelyah raspredeleniya zvezd i pyli ne menyayutsya v radial'nom i vertikal'nom napravleniyah i, sledovatel'no, ih rezul'taty mogut ispol'zovat'sya lish' lokal'no. Troinaya eksponencial'naya model' yavlyaetsya sushestvenno luchshim priblizheniem k opisaniyu struktury real'nyh galaktik.

Predpolozhim, chto radial'nye raspredeleniya zvezd i pyli opisyvayutsya eksponencial'nym zakonom (43) s odinakovym masshtabom . Pust' vertikal'nye raspredeleniya takzhe yavlyayutsya eksponencial'nymi, prichem - masshtab raspredeleniya zvezd v vertikal'nom napravlenii, a $z_d=\delta\,z_*$ -- sootvetstvuyushii masshtab dlya pyli (sm. p. 5.3). Dlya togo, chtoby naiti rezul'tiruyushee raspredelenie poverhnostnoi yarkosti, neobhodimo v kazhdoi tochke diska galaktiki reshit' uranenie perenosa izlucheniya. Esli disk yavlyaetsya tonkim (), to pri $i \leq 80^{\rm o}$ eta zadacha imeet sleduyushee analiticheskoe reshenie [147]:

$\begin{displaymath} I(r) = 2 I(0,0) z_* \frac{\theta}{{\rm cos}i} e^{-r/h}, \end{displaymath}$

(75)

gde

$\begin{displaymath} \theta = e^{-\tau}\left[1+\frac{\tau^2}{(\delta+1)(\delta+2)... ...c{\tau^4}{(\delta+1)(\delta+2)(\delta+3)(\delta+4)}...\right], \end{displaymath}$

(76)

$\begin{displaymath} \delta= z_d/z_* = \left(\frac{ {\rm sin}i} {h} + \frac{{\rm ... .../\left(\frac{ {\rm sin}i} {h} + \frac{{\rm cos}i} {z_d}\right) \end{displaymath}$

(77)

$\begin{displaymath} \tau = \frac{\tau_0}{{\rm cos}i}e^{-r/h} \end{displaymath}$

(78)

( $\tau_0$ -- opticheskaya tolshina centra diska pri $i=0^{\rm o}$ ).

Na ris. 31 izobrazheny model'nye fotometricheskie razrezy, postroennye po formulam (75-78) pri . Pri $\tau_0=0$ poluchaetsya standartnyi eksponencial'nyi disk. Vvedenie umerennogo poglosheniya ( $\tau_0=1$ ) izmenyaet vid profilya v central'noi chasti, delaya ego pohozhim na profil' II tipa (sm. p.6.1) -- s central'noi depressiei yarkosti. Uvelichenie naklona diska k luchu zreniya uvelichivaet ego nablyudaemuyu poverhnostnuyu yarkost' (za schet integrirovaniya izlucheniya zvezd vdol' lucha zreniya).

ris. 31: Fotometricheskie razrezy model'nyh galaktik ( $\mu$ -- otnositel'naya poverhnostnaya yarkost',

-- rasstoyanie ot centra, vyrazhennoe v dolyah radial'nogo masshtaba

). Pryamaya iz tochek -- ''prozrachnaya'' galaktika ( $\tau_0=0$ ) v polozhenii ''plashmya'' ( $i=0^{\rm o}$ ). Tonkaya nepreryvnaya krivaya -- model' s $\tau_0=1.0$ i $i=0^{\rm o}$ ; bolee tolstaya krivaya -- $\tau_0=1.0$ i $i=40^{\rm o}$ ; samaya tolstaya krivaya -- $\tau_0=1.0$ i $i=75^{\rm o}$ .

$\begin{figure}\centerline{\psfig{file=absincl.ps,angle=-90,width=10.0cm}}\end{figure}$

$\bullet$ Bolee realisticheskie modeli

Struktura real'nyh galaktik slozhnee rassmotrennyh vyshe modelei. Pri opisanii vliyaniya pyli na harakteristiki galaktik neobhodimo uchityvat' raznoe radial'noe i vertikal'noe raspredelenie pyli i zvezd, rasseyanie izlucheniya zvezd na pyli, bolee slozhnuyu geometriyu galaktik, nalichie u nih baldzha i t.d. Pri etom zadacha stanovitsya stol' slozhnoi, chto reshat' ee mozhno tol'ko putem chislennogo modelirovaniya.

Na ris. 32 priveden primer modelirovaniya opticheskoi struktury spiral'noi galaktiki NGC 891 s pomosh'yu programmy, opisannoi v [153]. Pri modelirovanii predpolagalos', chto raspredeleniya zvezd i pyli opisyvayutsya dvoinym eksponencial'nym zakonom (58) s radial'nymi masshtabami dlya zvezd i pyli kpk i kpk, sootvetstvuyushie vertikal'nye masshtaby -- kpk, kpk (eti znacheniya polucheny v rabote [154] dlya cvetovoi polosy ). Otnoshenie polnyh svetimostei baldzha i diska prinyato ravnym 0.15, galaktika vidna tochno ''s rebra'', polnaya opticheskaya tolshina vdol' lucha zreniya cherez centr galaktiki pri $i=90^{\rm o}$ vzyata ravnoi 10. (Uchityvaya, chto $\tau_{i=90^{\rm o}}=\tau_0\,h_d/z_d$ , poluchaem, chto $\tau_0(V)=0.3$ .) Nebol'shaya asimmetriya izofot vdol' bol'shoi osi obuslovlena tem, chto v model' galaktiki zalozhena dvuhrukavnaya spiral'naya struktura.

ris. 32: Fotometricheskaya model' galaktiki NGC 891 (sm. ris. 28). Edinicy izmereniya vdol' osei -- kiloparseki.

$\begin{figure}\centerline{\psfig{file=n891dust.ps,angle=-90,width=10.0cm}}\end{figure}$

Pervoe podrobnoe issledovanie vliyaniya pyli na trehmernuyu fotometricheskuyu strukturu galaktik s uchetom poglosheniya i rasseyaniya sveta bylo vypolneno Byunom i dr. [155]. Rassmotrim, kak vliyaet pyl' na raznye harakteristiki soglasno etoi rabote (sm. takzhe [156]).

Izofotnye diametry (diametry, izmerennye po kakoi-libo fiksirovannoi izofote) zavisyat ot soderzhaniya pyli v galaktikah. Odnako dazhe galaktiki s ochen' bol'shim soderzhaniem pyli demonstriruyut uvelichenie svoih diametrov s rostom naklona k luchu zreniya.

Razrezy vdol' bol'shoi osi stanovyatsya bolee pologimi. Pri otnositel'no nebol'shih naklonah ploskosti galaktiki ( $i \leq 30^{\rm o}$ ) i umerennyh opticheskih tolshinah ( $\tau_0(V) \leq 5$ , gde $\tau_0(V)$ -- opticheskaya tolshina centra galaktiki v polose pri $i=0^{\rm o}$ ) etot effekt pochti nezameten (sm. takzhe ris. 31). Pri bol'shih naklonah ( $i \geq 70^{\rm o}$ ) profili sil'no iskazhayutsya dazhe pri nebol'shih znacheniyah opticheskoi tolshiny. Dazhe pri umerennom soderzhanii pyli nablyudaemoe znachenie central'noi poverhnostnoi yarkosti diska ( $\mu_0$ ), opredelyaemoe ekstrapolyaciei vneshnih oblastei razrezov, otnositel'no slabo zavisit ot naklona galaktiki k luchu zreniya. Sledovatel'no, chasto ispol'zuemyi test ''poverhnostnaya yarkost' -- naklon'' yavlyaetsya plohoi diagnostikoi soderzhaniya pyli. Uploshenie razrezov vdol' bol'shoi osi iz-za pyli i naklona privodit k uvelicheniyu izmeryaemogo znacheniya radial'nogo eksponencial'nogo masshtaba diska . U galaktik, v strukture kotoryh dominiruet disk, pyl' privodit k poyavleniyu (v oblasti, gde opticheskaya tolshina vdol' lucha zreniya sostavlyaet $\tau(V) \sim 1$ ) radial'nyh gradientov pokazatelei cveta (galaktiki ''golubeyut'' s udaleniem ot centra), velichina kotoryh korreliruet s opticheskoi tolshinoi pyli i naklonom. Odnako prisutstvie vyrazhennogo baldzha zatrudnyaet ispol'zovanie gradientov pokazatelei cveta dlya ocenki soderzhaniya pyli.

Razrezy vdol' maloi osi pri $i=90^{\rm o}$ yavlyayutsya simmetrichnymi. Pri izmenenii naklona simmetriya narushaetsya, prichem dazhe nebol'shoe otklonenie ot polozheniya ''s rebra'' (na $1^{\rm o}-2^{\rm o}$ ) mozhet privesti k zametnoi asimmetrii raspredeleniya yarkosti vdol' maloi osi. Eto ob'yasnyaetsya tem, chto s odnoi storony ot bol'shoi osi naklonennoi galaktiki izluchenie prihodit v osnovnom iz oblasti nad pyl'yu, a s drugoi storony, obrashennoi k nablyudatelyu, -- ono preterpevaet sil'noe pogloshenie v pylevom sloe. (Eto pozvolyaet ocenivat' prostranstvennuyu orientaciyu galaktiki -- bolee blizkaya storona diska vyglyadit bolee ''krasnoi''.) Pri fiksirovannom naklone galaktiki stepen' asimmetrii zavisit ot tipa galaktiki (ot sootnosheniya svetimostei i razmerov baldzha i diska) i ot soderzhaniya pyli. (V rabote [157] predlozhena sootvetstvuyushaya procedura ocenki opticheskoi tolshiny pyli v centre galaktiki po nablyudaemoi asimmetrii razreza vdol' ee maloi osi (pravda, bez ucheta rasseyaniya). Pervye podobnye raschety byli provedeny Hol'mbergom eshe v 1947 godu [158].) Eshe odin lyubopytnyi effekt -- pogloshenie pyl'yu privodit k smesheniyu vidimogo polozheniya centra galaktiki (nablyudaemogo pika yarkosti) vdol' maloi osi v napravlenii dal'nei ot nablyudatelya poloviny galaktiki. Velichina etogo sdviga zavisit ot opticheskoi tolshiny pyli.

Nablyudaemaya svetimost' galaktiki umen'shaetsya pri povorote ee ploskosti k polozheniyu ''s rebra''. Velichina etogo effekta v modelyah, ne uchityvayushih rasseyanie sveta, mozhet pereocenivat'sya [155,156]. Zavisimost' velichiny popravki za naklon ot dliny volny otlichaetsya ot standartnogo zakona mezhzvezdnogo poglosheniya. Esli pogloshayushaya sreda raspolozhena mezhdu galaktikoi i nablyudatelem (model' ekrana -- sm. vyshe), to pogloshenie, naidennoe v odnoi cvetovoi polose, mozhno pereschitat' v druguyu polosu po standartnomu zakonu mezhzvezdnogo poglosheniya (sm. Prilozhenie). V real'nyh galaktikah pyl' nahoditsya vnutri zvezdnogo diska i peremeshana so zvezdami. V etom sluchae vnutrennee pogloshenie ne yavlyaetsya prostoi funkciei dliny volny. Naprimer, v [155] pokazano, chto, hotya popravka za naklon galaktiki v polose men'she, chem v , odnako ih raznost' men'she, chem eto predskazyvetsya standartnym zakonom poglosheniya (sm. takzhe [159]).

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