structure and evolution of early cosmological hii regions

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

HII regions in a uniform medium (2)

Dynamical evolution

Two phases!

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

105yr107yr

Rst

Nγ=3×1050 1/s

HII regions in a uniform medium (3)

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

Fate of collapsed clouds (2)

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

Fate of collapsed clouds (3)

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.