Radiative Regulation of Population III Star Formation...Radiative Regulation of Population III Star Formation Kenji Hasegawa (University of Tsukuba)collaborators Masayuki Umemura (University
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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
Result:MM**=25M=25M, D=14pc, 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
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.
Summary of Numerical Runs○○ Collapses, Collapses, △△Collapses with the aid of ionizing radiationCollapses with the aid of ionizing radiation、、××failed collapsefailed collapse
☆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
Summary of Numerical Runs○○ Collapses, Collapses, △△Collapses with the aid of ionizing radiationCollapses with the aid of ionizing radiation、、××failed collapsefailed collapse
Susa 2007
KH+ 2009KH+ 2009
Model B(Low TC,)
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)
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
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
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
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