a few more introductory subjects : equilib. vs non-equil. ISM sources and sinks : matter replenishment, and exhaustion Galactic Energetics

Transcription

1 Today : a few more introductory subjects : equilib. vs non-equil. ISM sources and sinks : matter replenishment, and exhaustion Galactic Energetics photo-ionization of HII assoc. w/ OB stars ionization fraction thickness of I-front ionization parameter (determines state of ionization)

2 very different physics in stars(*) vs equilib. ISM non-equilib. l = mean free path (m.f.p.) = 1/nσ for neutral atoms σ ~ cm -2 è in ISM, l ~ cm (n ~ 1) > distances over which conditions change in *, l ~ 10-5 cm (n ~ ) << distances over which conditions change in *, photon m.f.p. l ν << l ρ,p,t è radiation in T.E w/ gas called LTE (L= local) è Planck rad. field & Maxwellian velocity distrib. in gas and T rad. = T BB = T kinetic = T k

3 for reference : Planck black body radiation : (energy/sec/hz/ster) I! = B! = 2h!3 1 c 2 h! e kt "1 Maxwellian thermal velocity distribution : f ( v) = " $ # m 2!kT % ' & 3/2 e (mv2 /2kT v rms =! v = v = 8kT "m 3kT m c=sound speed= #kt m = 5kT 3m T (K) ,000 c (km/s)

4 in ISM, m.f.p. of ν >~ l cloud è radiation field not Planck in shape or energy density dilution factor out from *, w ~ (R * / d) 2 ~ ==> expect T e,k << T *, but not so!! in fact, in ISM we will encounter many different T s : T k, T R, T e, T x, T d, T bg,t B, T dop kinetic, radiation, electron, excitation, dust, background, brightness, doppler

5 thermal equilibrium above other equilibriums : pressure and hydrostatic equilibrium ionization/dissociation equilibrium statistical equilibrium (for microscopic processes, e.g. excitation of atoms, ions and molecules) ionization equilibrium w/i HII region? yes pressure equilibrium in HII regions? no pressure equilibrium on gal. scales? sometimes yes

6 ISM sources and sinks : for Milky Way, M HI ~ 4x10 9 M M H2 ~ 2x10 9 M minus : star formation (SF) ~ 3 M yr -1 (τ ISM ~ 6x10 9 /3 = 2Gyr) plus : mass return from stellar evol. AGB & planetary nebulae ~ M yr -1 OB star winds ~ M yr -1 SN ~ 0.03 M yr -1 nova ~ M yr -1 high vel. HI clouds < 1 M yr -1 è ISM exhausted on ~ 2 Gyr timescale must be an unseen replenishment e.g. HII accretion??

7 Galactic Energetics : L B ~ 1-2x10 10 L L IR ~ 1-2x10 10 L mechanical energy : SN = ergs / 50 yr ~ 6x10 41 erg/s ~ 1.7x10 8 L OB* winds = ergs / 50 yr ~ 1.6x10 7 L ISM ionization ~ 2x10 8 L [ for reference M = 2x10 33 gr R = 6.9x10 10 cm, ρ ~ 6.5 gc/cc T = 6700 K L = 3.8x10 33 erg/s black body emission w/ L = 4πR 2 σt 4 (σ=5.6x10-5 cgs) other *s : 0.1 to 50 M, K, L ]

8 HII Regions ioniz. of HI requires 13.6 ev (λ < 912Å) 13.6 ev = 2.17x10-11 ergs è T ~ 10 5 K OB* -- photo-ion (PI) planetary nebulae -- PI SN -- PI + collisional ioniz. AGN -- PI w/i HI bound levels, permitted transitions w/ A~ 10 6 sec -1 è neutral H will typically in n = 1

9 Photo-ionization of HII regions e.g. Orion nebula M42 (d ~ 410 pc) ionized by Trapezium cluster 4 primary OB stars most luminous Θ 1 c (O6) only OB * are hot enough w/i HII region, T ~ 8000K n p,e ~ cm -3 1 pc (determined from line ratios & radio free-free continuum) T ~ 10 4 K maintained by excess KE of ejected photo-electrons balanced by cooling due to O +,O ++,N +,...

10 ionization equilibrium : rate of ioniz. = rate of recombination rate of ioniz. : flux of UV photons cross section for ioniz. number of HI rate of recomb. : number density of e -, p + cross section for recomb.

11 ioniz. rate = recomb. rate $ 4!J n % " H h" a d" = n n # " e p " 0 # = recombination rate coef. = ' % v& n n = ' % v& n n ' n = < &v > ( v)f ( v)4!v 2 dv ( v) 4! ( * ) & recomb. ~ 10. ( ) ( v + * 0 - ) v, m 2kT 2 + -, cm 2 3/2.mv 2 2kT e v 2 dv J " = mean intensity = ergs cm.3 hz.1 ster.1 a " = photo. ioniz. cross section caution : Tielens uses α for a ν not a good choice

12 recombination rate coeff s tables and figs from : Osterbrock & Ferland 2006

13 most important : (will see later) α tot = recombination rate coef. 1/ 2 T = 4.2x cm 3 sec α B = recombination rate coef. to n 1 1/ 2 T = 2.6x cm 3 sec how long for e - to recombine? τ rec = 1/ n p α = 1/ (n p 4.2x10-13 ) = 8x10 4 / n yrs ~ 800 yrs at n ~ 100, i.e << expansion time of HII

14 Photo-ioniz. cross sections : #! & for : 1 2 S HI a! = 6.3x10 "18 % 0 ( $! ' 3 cm 2 w / h! 0 = 13.6ev #! & 1 2 S He a! = 8x10 "18 % 1 ( $! ' 3 cm 2 w / h! 1 = 24.6ev #! & He + a! = 1.6x10 "18 % 2 ( $! ' 3 cm 2 w / h! 2 = 54.4ev

15 J ν : at surface of *, I ν = B ν for each cm -2 on star, how much is radiated? #/2 2# $ 0 " $ d!ds = dscos % 0 #/2 0 2# $ 0 $ ( ) sin (%)d%d& = 2# ds sin 2 % / 2 = #ds è πb ν per unit area (called astrophys. flux) total from * = 4πR 2 πb ν at distance d, flux = (4πR 2 / 4πd 2 ) πb ν = w B ν = 4π J ν ==> ioniz. rate per cc = n H w $!B " a h" " d" w / dilution factor w % R 2 # " 0 d 2

16 only care about # of ioniz. photons (Lyman cont.) emitted by star per sec : Q * = 4π R * 2 q q! # of Ly c photons per sec per cm 2 = $ "B % # d# h# # 0 for O6 * (Ori θ1c), T=43,600K, R * = 7x10 11 cm è Q = 2.2x10 49 sec -1 Sp Type T* (10 3 K) Q (10 49 sec -1 ) O O O B ?? ioniz. rate 1 pc from O6 *

17 What is the fractional ioniz. w/i HII? $ % n H w!b " h" a d" = n " H " 0 Q * a " 4!d 2 = n e n p # let x = n e n i.e. n e = xn, n H = (1& x)n then (1-x) Q * a " 4!d 2 = x 2 n# 1 pc from O6 *, (1-x) 1.1x10-6 = x 2 4.2x10-13 n for n = 100, (1-x)/x 2 = 3.8x10-5 = n HI / n è ioniz. nearly complete

18 thickness of transition HII to HI (ionization front)?? m.f.p. of Ly c photon : Δr = 1 / (n H σ ν ) = 1 / (6x10-18 n H ) = 1.7x10 17 / n H << 1 pc for n H ~ 100 è very thin ioniz. front compared to size of HII region What have we ignored in the foregoing analysis of the ionization equilibrium??

19 Two aspects left out : 1) radiative transfer of ionizing photons 2) Ly c photons from recomb. to n = 1 (diffuse Ly c) di ν ds = n H a ν I ν + j ν where j ν = emission coef. from recomb. to n = 1 separate radiation field into 2 terms : I ν = I ν * ( ) + I ν ( diffuse) R for *, 4πJ ν (*) 2 * = πb ν d 2 e τν J ν (*) = B ν ( T * ) πr 2 * 4πd 2 e τν w / τ ν = d r * n H a νdr

20 for the diffuse radiation (Ly cont. recomb.) : let j ν = emission rate of diffuse Ly cont. per unit vol per radian j ν 4π dν = np n e α 1 ν0 hν integrating over HII region, 4π j ν hν dvol = 4π n a ν J vd H hν dvol assume this holds locally, J νd = j ν n H a ν (on the spot approx.)

21 n H 4π J + J ν * ν d a ν dν = n p n e α hν ( ) πb n ν T * H hν R * 2 4πj e τν a d 2 ν dν + n ν a ν H dν n H a ν hν = n e n p α n e n p α 1 2 ( ) R n * πb ν T H * e τ ν a d 2 ν dν = n p n e α B hν [ NB: this is called : case B when all ioniz. photons are absorbed w/i HII and Lyman lines are optically thick. Case A when the later is not true is almost never used in analyzing observations. ]

22 back to ioniz. equilib. : n H 4! J + J " * " d # a h" " d" = n p n e $ ( ) 2!B " T * n H # R * h" d 2 e%& " 4!j a " d" + n " a " H # d" n H a " h" = n e n p $ n e n p $ 1 ( ) 2 R!B n * " T H # * e %& " d 2 h" a d" = n n $ " p e B integrating over vol. of HII region, d& " = n H a " dr ==> d& " n H a " = dr # R * 2!B " h" ' d" # d %e%& = # n e n p $ B r 2 dr 0 ( ) Q * 4! = R 3 3 n n $ ==> Q = 4!R 3 p e B * 3 R 0 n e n p $ B

23 è fresh * ioniz. photons only destroyed by recomb. to n > 1!! # R s = 3 % $ 4! = # % % $ Q * n p n e " B & ( ' 1/3 3x2.2x ! 2.6x10 *13 ( 100) 2 ) Q * 1/3 n e *2/3 R s is called the Stromgren radius of the HII region Sp type & ( ( ' 1/3 = 1.26x10 19 = 4.1pc R s / R s (O6) O5 1.1 O6 1 O B0 0.40

24 other issues/effects : 1) should include coupled ioniz. of H & He (see Osterbrock & Ferland) 2) ionizing radiation becomes harder at edge of HII region since Ly c absorption cross section highest at threshold and those photons absorbed first 3) collisional ionization important in SN and AGN σ elastic varies as v -4 è large m.f.p. for high E particles when collisional ioniz. important, p + /n H varies as n 0

25 Ionization structure of H & He for hotter * s ionization dominated by ν s at > 24.6 ev è He + ~ H + zone T * =40,000K for cooler * s, few ν s at > 24.6 ev è He + much smaller than H + zone T * =30,000K

26 Ionization Parameter : from earlier : è level of ionization, (especially the degree of ioniz. of heavier atoms) depends on the ratio : U = number density of ioniz. photons / gas density (1-x) Q * a! 4"d 2 = x 2 n# where x = n e n & n H ( ) x 2 1$ x = Q / 4"d 2 c * a! n # ( 2 c) 2 n e % n e = Q / 4"d * nn H n H n = (1$ x)n U ' ionization parameter = n e n H = U & 7x10 5 c & 7x10 5 #Ly! per cc #part. per cc HI ionized when U > 10-6 (in AGN, U s get to ~0.1!)