Ionization fronts in HII regions

Transcription

1 Ionzaton fronts n HII regons Intal expanson of HII onzaton front s supersonc, creatng a shock front. Statonary frame: front advances nto neutral materal In frame where shock front s statonary, neutral gas flows nto front at velocty υ, wth densty, and leaves as onzed gas wth velocty υ 0 and densty ρ 0. shock

2 Jump condtons To derve jump condtons across front, assume transton regon s very narrow (a good approxmaton). Apply mass, momentum and energy conservaton to get densty jump. Conservaton of mass: Mass flow nto the front must equal the mass flow out: υ = ρ o υ o Conservaton of Momentum: Forces must balance on both sdes of statonary front n reference frame of shock. Include momentum due to bulk flow, and pressure due to random motons: P + υ = P o + ρ o υ o where P and P 0 are the thermal pressures on the two sdes.

3 Conservaton of Energy Normally, would also need to consder energy conservaton. For an onzaton front, can just assume that temperatures (hence sound speeds) n both neutral and onzed gas are fxed: P = a P o = ρ o a o where a, a o are the sothermal sound speeds, gven by a = kt m H a o = kt o m H

4 As HII regon develops, velocty υ of front depends on number of onzng photons reachng t (.e. on the optcal depth to the front and number of recombnatons nsde HII regon) So solve for the densty jump n terms of υ. the pressures: ( ) = ρ ( o a o + υ ) o a + υ Substtutng for Usng mass conservaton we get: υ o = Substtutng we get a quadratc equaton for the densty jump, ρ o υ a o ρ o ( ) ρ o a + υ + υ = 0

5 a o ρ o Ths has solutons, a + υ ( ) ρ o + υ = 0 ρ 0 = υ υ 0 = 1 a o {( a + υ ) ± ( a + υ ) 4a o υ } The temperature n the onzed gas s ~ 10 4 K, whereas the temperature of the neutral gas s ~ 10 K. Thus, a 0 ~ 100 a Letʼs explore the quantty n the square root; negatve no physcal solutons.

6 The quantty n the square root s: Graphcally, ths looks lke: There are two crtcal veloctes where ths functon passes through zero: υ R = a o + υ D = a o where we have used a 0 >> a a o a a o a o a a a o n the approxmatons. f (υ ) = ( a + υ ) 4a o υ No physcal soluton

7 Two possble physcal solutons: υ υ R - R (rarefed) - type onzaton front υ υ D - D (dense) - type front Fnally wrte the jump condtons as: ρ o = υ υ o = 1 a o {( υ R υ D + υ ) ± ( υ υ )( R υ υ )} D If velocty s exactly υ R front s sad to be R-crtcal; f exactly υ D, D-crtcal. Otherwse thereʼs a choce of + or - sgn. Choce that gves smaller densty contrast s weak, the larger strong.

8 Relaton to the physcal pcture of the expanson of an HII regon: If gas s rarefed, or onzng flux s large, expect front to move rapdly. Expect an R-type onzaton front durng ntal expanson of an HII regon, when there are few recombnatons n the nteror and nearly all stellar photons reach the front. If gas s dense, or onzng flux small, front moves more slowly. D-type fronts occur n late evoluton of HII regons. In ether case, the post-onzaton gas may move ether subsoncally or supersoncally wth respect to the front.

9 Strong and weak R fronts Strong R-type front: velocty of onzed gas behnd front s subsonc wth respect to the front and the densty rato s large (does not exst n nature because dsturbances n onzed gas contnually catch up wth the front and weaken t). So durng ntal growth of HII regon a weak R-type front expands supersoncally nto the HI, leavng onzed gas only slghtly compressed and movng out subsoncally n a fxed reference frame.

10 Development of an HII regon (1) Early rapd expanson, weak R-type onzaton front separates rarefed HI gas from rarefed HII gas. () Expanson slows because of geometrcal dluton and recombnatons n nteror. υ decreases untl υ = υ R.,.e. onzaton front becomes R-crtcal, (velocty approaches sound speed and densty contrast s ) (3) Shock wave breaks off from onzaton front and moves nto HI ahead of t. Ionzaton front becomes D-crtcal, because the shock compresses the HI gas to hgher denstes before the gas s onzed. Detaled solutons show that the regon between the shock and the onzaton front remans farly thn, (a small fracton of the radus of the HII regon).

11 Young HII regons are deeply embedded n gas and dust need to go to the rado (freefree emsson) or IR to observe them. The green colour n ths false colour mage denotes a compact HII regon. Small HII regons (called compact or ultracompact HII regons), wth szes of pc, or smaller, sometmes have roughly sphercal shapes. However, there s a wde range of morphology, wth some sources beng cometary or rregular n appearance. Observatons (Credt:

12 Possble explanatons (1) Densty dstrbuton around the young star s not sphercally symmetrc. HII regon expands quckest towards low denstes. Can escape the cloud entrely a `champagne' flow. () Neutral gas s nether at rest nor unform, but nstead has a turbulent or chaotc structure on scales of a few parsec.

13 Turbulent ISM Supernovae drven turbulent densty O stars near md-plane Ionzng photons reach large heghts due to 3D densty structure But, may need B felds Wood et al. 010, ApJ, 71, 1397

14 Lecture 16 revson quz Assumng P = ρ a on both sdes of a shock, where a s the sothermal sound speed, show that the densty jump s gven by a o ρ o ( ) ρ o a + υ Solve the quadratc and plot the quantty nsde the square root sgn as a functon of nflow speed v for the case where a o =100a. Show how the jump condton can be reexpressed as ρ o = υ υ o = 1 a o + υ = 0 {( υ R υ D + υ ) ± ( υ υ )( R υ υ )} D