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Structure and Evolution of Early Cosmological HII Regions

T. Kitayama (Toho 　 University)with

N. Yoshida, H. Susa, M. Umemura

IntroductionFeedback from the 1st stars in Pop III objects - Radiation - SN explosions

⇒ Formation of HII regions (Yorke 1986) Dissociation of molecules 　 (Omukai & Nishi 1999) Blow-away of gas (Ferrara 1998) Metal enrichment (Gnedin & Ostriker 1997) etc.

Great impacts on - reionization history - galaxy formation

Key questions

Essential physical processes hydrodynamics　 radiative transfer, non-equilibrium chemistry　 heating/cooling….

- How large are the HII regions?- How do they evolve? - How much photons can escape from halos? - What happens after the star dies? blown-away by SN?, next SF? - Depend on Mhalo, Mstar….?

⇒ 　 1D model, useful ingredients to 3D simulations

HII regions in a uniform medium (1)

HII

# of photons emitted = # of recombination ⇒ 　 Stroemgren sphere (1939)

Static solution


Dynamical evolution

Two phases!

1. ionization/heating → pressure gap2. shock → expansion of the HII region

105yr107yr

Rst

Nγ=3×1050 1/s


R-type front D-type front

rion < Rst

vion >> vshock

rion > Rst

vion ～ vshock

HIIHII

shock formation

Highly dynamical !Rst

Model1. Collapsed cloud in a ΛCDM universe zc=10, Mhalo → size Rvir

gas: n r∝ -2, Ti ～ 1000K, Xe=10-4, XH2=10-4

DM: NFW profile (fixed)

2. Radiation from a central massive star zero-metallicity (Schaerer 2002) 　 e.g. M=200 Msun Nγ(>13.6eV) = 2.6×1050 1/s Teff = 105 K, τ= 2.2 Myr

3. Solve 1D hydro, radiative transfer of UV photons, chemical reactions (e, H, H+, H-, H2, H2

+,)

& cooling/heating self-consistently

Mhalo, Mstar free

Mhalo= 106 Msun

Mstar =200 Msun

1. high central density →confined I-front →sweep-out of gas by shock2. prompt ionization

D-type →R-type(opposite to the uniform medium)

Structure of HII regions (1)

106yr

105yr

Mhalo= 108 Msun

Mstar =200 Msun

higher mass→ confined I-front→ no further ionization 　　

D-type only

Structure of HII regions (2)

105yr

106yr

ｎ

ｒ

ｎ

ｒ

ｎ∝ Rs3/2

ｎ∝n r∝ -w

w<3/2

n r∝ -w

w>3/2n R∝ st-3/2

n R∝ st-3/2

Density profile and I-front types

R-type →　 D-type D-type →　 R-type

r<Rst → 　 r>Rstr>Rst → 　 r<Rst

※ D-type front can propagate ～ 10pc within 106 yr → 　 R-type is crucial for ionizing the whole halo !

Final HI and H2 fractions

Critical massesionization ～ 107 Msun

H2 dissociation ～ 108 Msun

H2 fraction positive feedback near Mcrit

HI

H2

Escaping fractions of photons

Critical masses >13.6 eV ～ 107 Msun

11.2-13.6 eV ～ 108 Msun

11.2-13.6 eV (x 103)

>13.6 eVfesc sensitive to Mhalo

～ 1 for Mhalo<Mcrit

Fate of collapsed clouds (1)

HII

HI & H2

HI H2 dissociated

Estimated threshold for R-type front Mhalo∝ Nγ

3/4(1+z)-3/2

Threshold for transition from D- to R-type

ｎ

ｒ

ｎ n R∝ st-3/2 R∝ s

3/2

n r∝ -w

w>3/2

rcross

1. Virialzized cloud with n r∝ -w

→ rcross N∝ γ

-1/(2w-3)

×( nvir Rvirw)2/(2w-3)

2. D-type front propagation rD ～ cs tage

～ 17 pc for T=104K, t=Myr

3. rD > rcross

→ Mhalo < f(w) Nγ3/2w

×(1+z)-3(3-w)/w 　　D-type → R-type


HII

HI & H2

HI H2 dissociated

n r∝ -w

Estimated threshold for R-type front

Feedback from SN explosions

1. Energy injection at the death of the central star ESN = 1051 erg ～ 1053 erg

2. Prompt heating of surrounding gas with Mgas ～　 Mstar 　

3. Propagation of shock & energy dissipation by radiative cooling

⇒ How far can it travel?

zc=10

SN feedback (1)

Mhalo= 3×107Msun

Mstar = 200 Msun

ESN =1053 erg

blown-away!

104yr107yr

SN feedback (2)

Mhalo= 3×107Msun

Mstar = 200 Msun

ESN =1051 erg

Energy dissipationby cooling

104yr107yr

SN feedback (3)

Mhalo= 3×107Msun

Mstar = 200 Msun

Bulk of the energy radiated in ～ 105 yr

ESN=1053 erg

ESN=1051 erg


large:blown-away

1053 erg

1051 erg

ESN

Conclusions1. Radiative feedback from the 1st massive stars → 　 complete ionization (Mhalo<107 Msun at z ～ 10)

& H2 dissociation (Mhalo<108 Msun at z ～ 10)

sweep-out of gas down to n ～ 1 cm-3 　　　　　　　　

　　※　 Highly dynamical ※ 　 R-type front is crucial in ionizing the whole halo　　　　　　 w<1.5 : R-type → D-type 　　　 w>1.5 : D-type → R-type (n r∝ -w) 　

2. Subsequent SN feedback → blow-away of clouds with Mhalo<106 Msun (ESN=1051 erg), 107Msun (ESN=1053 erg)

Future work

- Escape of photons from r<<1 pc- Instability in SN shocks

- Effects of dust & metal

etc.