radiative regulation of population iii star formation...radiative regulation of population iii star...

Radiative Regulation ofPopulation III Star Formation

☆Kenji Hasegawa (University of Tsukuba)collaborators

Masayuki Umemura (University of Tsukuba)Hajime Susa (Konan University)

14-16 Jan. 2009, Italo-Japanese Mini-Workshop @ University of Tsukuba

Outline

Introduction Population (Pop) III stars Radiative feedbackMethodologies Simulation code SetupResultsSummary

Pop III starsVery Massive Stars of >100MVery Massive Stars of >100M

e.g., Abel, Bryan & Norman 2000;Bromm, Coppi & Larson 2001;Nakamura & Umemura2001;Yoshida et al. 2006

Not only very massive Pop III stars but alsoless massive Pop III stars are expected to form

Less Massive Star ~10MLess Massive Star ~10M-100M-100M

(eg.,Shapiro & Kang 1987; Susa et al. 1998; Oh & Haiman 2002)Enhanced HEnhanced H22 cooling (via virial shock with cooling (via virial shock with T Tvirvir>10>1044K)K)

(eg.,Nkamura & Umemura 2002; Ngakura & Omukai 2005; Grief & Bromm 2006;Yoshida, Omukai & Hernquist 2007)

HD cooling in fossil HII region (often called Pop III.2 star)HD cooling in fossil HII region (often called Pop III.2 star)

Variation of cosmological density fluctuation Variation of cosmological density fluctuation (O’Shea & Norman 2007)

H2 cooling → T ~ 100K

UV radiation from Pop IIIUV radiation from Pop IIIstars affects star formationstars affects star formationaround the stars.around the stars.

Pop III starsPop III starsare massive !are massive !

Radiative Feedback Effects

Photoionization Photoionization((hhνν>13.6ev) >13.6ev) 　　　　　　

Photodissociation Photodissociation(11.2eV<(11.2eV<hhνν<13.6ev)<13.6ev)

Negative FeedbackNegative Feedback

Increase of electron fraction　H　＋　e-　→　H-　＋　γ　H-　＋　H　→　H2　＋　e-

HH22 formation formationprocessprocess

Positive FeedbackPositive FeedbackLyman-Werner (LW) band radiation Lyman-Werner (LW) band radiation

Shock induced by the ionizationShock induced by the ionizationBlowouts a gas cloud.Blowouts a gas cloud.CompressionCompressionEnhancement of HEnhancement of H22 formation rate formation rate

Gas temperaturereaches ~104K

Destruction of coolants (H2)

Enhancement of H2 formation

Negative feedbackNegative feedback

Positive feedbackPositive feedback

Pop III stars are Massive UV radiation from the stars affects surrounding medium!!

Alvarez, Bromm & Shapiro 2006 Suwa, Umemura & Susa in prep.Pop III minihalosPop III minihalos

One star perhalo

Distancebetween halos~ 200pc

Multiple star

Distancebetween peaks~ 60-70pc

First GalaxiesFirst GalaxiesStars can form from metal-freecomponent in interstellar gas.(e.g., Tornatore, Ferrara & Schneider 2007)

Feedback from Pop IIIstars is important.

(Umemura-san’s talk)

First peak

Second peak

UV feedback by PopIII stars

Ionizing radiation alleviates thenegative effect by LW radiation.

RHD simulationsRHD simulationsSusa & Umemura (2006),Susa & Umemura (2006), Ahn Ahn & Shapiro (2007), Whalen + (2008)& Shapiro (2007), Whalen + (2008)

LW LW

Ionizedregion

I-front

H2 s

hell

The H2 shell can shield the cloudcore from the LW radiation emittedby the source star.

3D RHD simulations

These studies focus on the radiative feedback from a very massivea very massivePop III star with MPop III star with M**=120M=120M..

H　＋　e-　→　H-　＋　γ　H-　＋　H　→　H2　＋　e-

Radiaticve feedback criteion ?

Purpose

Radiative feedback from less massiveRadiative feedback from less massive PopIII PopIII starsstarson neighboring cores have not been investigated inon neighboring cores have not been investigated indetail so far...detail so far...

We perform 3D RHD simulations in order to

Investigate dependence of the radiative feedback onthe mass of source star.Derive the radiative feedback criterion.

The feedback tends to be more negative ?The feedback tends to be more negative ?

Numerical Scheme

€

dρdt

= −ρ∇ ⋅ v

d2rdt 2

= −1ρ∇P −∇φ + f rad

dudt

=Pρ∇ ⋅ v +

Γ − Λρ

P = (γ −1)ρu =kBρbTµmp

Gas Dynamics: SPHGas Dynamics: SPH

Gravity :Tree-GRAPEGravity :Tree-GRAPE

⇒⇒determinesdetermines fractions of speciesfractions of species and radiative cooling rateradiative cooling rate

For e, p, H, H2, H2+, H-,

Radiative transfer (Susa 2006)Radiative transfer (Susa 2006)

: kH2dis=1.13×108FLW0 fsh[s-1 ] 　　　 fsh=min[1,(NH2/1014)-0.75]

€

€

dIvdτ v

= Iv + Sv On the spot approximation

Draine & Bertoldi (1996)€

Γion = dv dΩ (hv − hvL )avIvhv∫

vL

∞

∫

€

kion = dv dΩ avIvhv∫

vL

∞

∫Photoionization rate

Photoheating rate

Photodissociation rate

Non equilibrium chemistry (Kitayama et al.2001)Non equilibrium chemistry (Kitayama et al.2001)

€

dnidt

= k jkn jnkk

6

∑j

6

∑ + klmnnlnmn

6

∑m

6

∑l

6

∑ nn

Setup3D-RHD simulation

1. Purely baryonic primordialcloud

nH=14cm-3 (uniform),M = 8.3×104M, Ti = 100K,350K

We also perform simulations with We also perform simulations with NO ionizing radiationNO ionizing radiation to toinvestigate the effect of ionizing radiation.investigate the effect of ionizing radiation.

50pc

No feedback case

Model A (high Tc)

kH- ∝ T

Model B (low Tc)

2. When the density of cloud coreexceeds a certain value nnonon, thecore is irradiated by the sourcestar with mass of MM**, whichplaced DD pc away from the core.

Gravitationalcontraction

ParametersParametersnon: 30 - 104 cm-3

D : 10-200pcM*: 25, 40, 80, 120M

D pc

non

M*

Result:MM**=80M=80M, D=40pc, non=103cm-3

LW only LW + IONDottedDotted SolidSolid

Time variations of density profilesTime variations of density profilesVarious physical quantities along theVarious physical quantities along thesymmetry axis at 1Myr after the ignitionsymmetry axis at 1Myr after the ignition

Fails to collapse (a hydrostaticcore is formed)

LW : Self-shielding by the core is not sufficient.LW + ION:The H2 shell enhances NH2

The cloud is able to collapse




LW : Self-shielding by the core LW + ION:The H2 shell does NOT enhance NH2

Fails to collapse

The LW flux is the same asthat in the previous case.

Ionizing radiation cannot alleviates the negativefeedback of photodissociation. Fails to collapse

Summary of Numerical Runs○○ Collapses, Collapses, △△Collapses with the aid of ionizing radiationCollapses with the aid of ionizing radiation、、××failed collapsefailed collapse

Model A(High TC)

☆The shielding effect by H2 shell becomes weak as the source star becomesless massive.


☆Resultant critical distance does not so strongly depend on the mass of source star.

Model A(High TC)

☆The shielding effect by H2 shell becomes weak as the source star becomesless massive.

Analytic EstimationLW radiation is mainly shielded at the two part of a cloud

CoreCore HH22 shell shell

€

NH2,core= 4.5 ×1015 FLW,0

5 ×1023ergs−1

−4nc

104 cm−3

4 Tc300K

6

€

yH2 =nHyekH −

kdisH2 column density of the core

Chemical equilibrium

Susa 2007: collapse criterionSusa 2007: collapse criterion ttffff==ttdisdis

€

Dcr,d =147pc LLw5 ×1023erg s−1

1/ 2nc

103cm−3

−7 /16 Tc

300K

−3 / 4

Core radius ~ Jeans scale

€

Dcr,sh =147pc LLw f s,sh5 ×1023erg s−1

1/ 2nc

103cm−3

−7 /16 Tc

300K

−3 / 4

Critical distance (KH, Umemura & Susa 2009)

€

NH2,sh= 5.8 ×1014 N ion

1050s−1

4 LLW5 ×1023ergs−1

−4

strongly depends onstrongly depends on NNionion//LLLwLw !!!!

H2 column density of the shell

€

fs,sh =min{1,(NH2,sh /1014cm−2)−0.75}

Shielding function (Shielding function (Draine Draine && Bertoldi Bertoldi 1996)1996)

Nion: number of ionizing photos emitted per second


Susa 2007

KH+ 2009KH+ 2009

Model B(Low TC,)


Model A(High TC)

Summary (1)We have foundWe have found

ii) H2 column density of the H2 shell sensitively depends on therelative intensity of the ionizing radiation to LW radiation{∝(Nion/LLW)4}.

If If MM** is less than ~25M is less than ~25M, ionizing radiation cannot, ionizing radiation cannotsupresssupress the negative feedback of LW radiation. the negative feedback of LW radiation.

i) The critical distance below which a neighboring cloud cannotcollapse does not so strongly depend on the mass of source star.

Summary (2)We have foundWe have found

iii) The feedback criterion is well expressed as

€

Dcr =147pc LLw f s,sh5 ×1023erg s−1

1/ 2nc

103cm−3

−7 /16 Tc

300K

−3 / 4

where fs,sh is a factor regarding the shielding effect by H2 shell.

Using above formula (fs,sh=1), FLW.cr is given by

€

FLW,cr = 3.01×10−17erg cm−2s−1 fdyn−2 nc103cm−3

7 / 8 Tc

300K

3 / 2

This criterion is available for LW background radiation.

Research InterestsFirst Galaxiesformed via mergers of Pop III minihalosProperties ? (e.g., Metallicity, star formation rate, stellar population)

Radiative FeedbackLocal feedback

Global feedback (LW background radiation)SN Feedback

Mechanical : heating, compression. Chemical : metal enrichment ⇨ cooling function, PopIII→II

RHD simulations including SN feedback.RHD simulations including SN feedback.

Dynamical effect

€

fdyn ≡Dcr,num

Dcr,analy

W:gravitational energy U: internal energy

Low initail temperature

High High initail initail temperaturetemperature

Effects of Dark Matter

Static NFW potential Mvir = 5×Mb = 4.15×105MRvir = 160pc (zc=15), 240pc(zc=10)

€

fdyn ≡Dcr,num

Dcr,analy

W:gravitational energy U: internal energy

Spectrum for source Pop III stars

1.069*101.069*105050

5.938*105.938*104949

1.873*101.873*105959

5.446*105.446*104848

5.34*105.34*102323

3.05*103.05*102323

3.94*103.94*1022221.17*101.17*102323

LLLWLW[erg/s][erg/s] NNionion [s[s-1-1]]

If a sourceIf a sourcestar is lessstar is lessmassive,massive,LLLWLW//NNionionincreases !!increases !!

Based on Schaerer 2002




LW : Self-shielding by the core LW + ION:The H2 shell enhances NH2

Fails to collapse

Fails to collapse

Low Tc case

Positive feedback by shock

In the low core density cases,shocks positively work.

Estimate of the thickness of H2 shell

Shell

D

Thickness of the shell~ the amount of ionizedgas in the envelope.

Dsh

H2 column densityof the shell

H2 fraction in the shell⇨determined by FLW, nsh,and Tsh (chemical equilibrium)

FLW∝LLW/DSH2

LLW

Dependence of the cloud massDependence of the cloud mass

Parameters:Cloud Mb, distance D

nnonon=10=1033cmcm-3-3

DistanceDistance　　DD

M*=120M

TTiniini=350K=350K

Cloud Mb=8.3×104M, 1.6×105M,3.3×105M

Dependence of the cloud massDependence of the cloud mass

Critical distance Critical distance analyticanalytic simulationsimulation~190pc~190pc ~180pc~180pc

~150pc~150pc~130pc~130pc

~60pc~60pc~10pc~10pc

WHYWHY？？？？？？

Dependence of the cloud massDependence of the cloud massMMcloudcloud = 3.32= 3.32××101055MM , , DD=10pc, =10pc, TTi =350K, ni =350K, nonon = 10 = 1033cmcm-3-3

Radiation driven star formation ?Radiation driven star formation ?

QQ：：Can UV photons drive the star formation in mini-Can UV photons drive the star formation in mini-halo which is destined to fail to collapse.halo which is destined to fail to collapse.

MMcloudcloud = 2.77= 2.77××101044MM(Cannot collapse)(Cannot collapse)

100pc, 200pc, 300pc100pc, 200pc, 300pc

Preliminary resultPreliminary result

CollapseCollapse！！！！

Radiation Transfer

Smootihng lengthτn1 Target

n8

n4n5

n6n7

n3

n2

n1

Δτ

€

τ target = τ n1 + Δτ

NH2,target = NH2,n1 + ΔNH2

kion, Γion and kH2 areobtained

Test calculations (Static)

distance

Radiation source Source: Nion =5×1048s-1, Teff = 105KStructure: uniformN =10-3cm-3, T=100KNumber of particles: 643

Test calculations (dynamic)Radiation Source: Nion =5×1048s-1, Teff = 105KStructure: uniformN =10-3cm-3, T=100KNumber of particles: 643

UV feedback by PopIII starsHH22-dissociating radiation (LW radiation)-dissociating radiation (LW radiation)Omukai & Nishi (1999): Uniform virialized halo is assumedOmukai & Nishi (1999): Uniform virialized halo is assumed＊＊HH22 molecules are totally dissociated by LW radiation from a molecules are totally dissociated by LW radiation from asingle massive starsingle massive star Subsequent star formation is NOT feasible in the halo. Subsequent star formation is NOT feasible in the halo.

Ionizing radiation alleviates thenegative effect by LW radiation.

LW + ionizing radiationLW + ionizing radiationSusa & Umemura (2006),Susa & Umemura (2006), Ahn Ahn & Shapiro (2007), Whalen + (2008)& Shapiro (2007), Whalen + (2008)

LW LW

Ionizedregion

I-front

H2 s

hell

The H2 shell can shield the cloudcore from the LW radiation emittedby the source star.

3D Radiation-Hydrodynamicsimulation

Escape fractions

Kitayama et al. 2004

The escapes fraction of LWphotons are larger than thoseof the ionizing radiation.

Dynamical EffectM*=80M, D=40pc, non = 103cm-3

€

yH2= 2.33×10−5 FLw

2 ×10−17cgs

4nc

104cm−3

7 / 2 Tc103K

15 / 2

H2 fraction at the core (Susa 2007)

Intense LW radiation ⇨adiabatic evolutionTc∝nc

2/3 and yyH2H2∝∝nncc17/217/2

Adiabatic phase

HH22 fraction is quickly fraction is quicklyrecovered, and Hrecovered, and H22 column columndensity becomes large.density becomes large.Finally, Finally, t tffff<< ttdisdis is satisfiedis satisfied UVUV

Evolution of Clouds withoutRadiative Feedback

Low Tc model: high initial temperature ⇨ high U/WHigh Tc model: low initial temperature ⇨ low U/W

High Tc model High Tc model

Low Tc modelLow Tc model

radiative regulation of population iii star formation...radiative regulation of population iii star...

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