A New Simulation of 21-cm Signal
in the Epoch of the First Stars:
The model of escape fraction
名古屋大学C研 田中 俊行
共同研究者: 長谷川賢二（名古屋大学）

Introduction
初代星の星質量関数には不定性がある
Susa, Hasegawa+2014

SKAによる空間分解21-cm線観測の見込み©SKA Organisation

星質量関数に関する情報を取り出せないか？
Hirano+ 2015

Mesinger+ 2011

Informationon the IMF

1

21cmFAST

Mesinger+ 2011

問題点：初代星質量依存性を持つパラメータが定数として扱われている。
・21cmFASTでは、

z ~ 20, Lbox = 1Gpc

21-cm線の空間分布を計算できる凖数値的計算コード

電離の判定にイオン化効率という定数を用いている:

fcoll (x, z, R)⇣ 1

fcoll：半径Rの球内の全質量に<latexit sha1_base64="YbIUb/Q+MXtei/XN8pA807MZ0+4=">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</latexit><latexit sha1_base64="PREyUKmmAikslIp8P880lEqa7Yw=">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</latexit>

対する崩壊した割合
・しかし本来、このイオン化効率は電離光子脱出率に比例する。
また、電離光子脱出率は初代星質量に依存するはず。

⇣ / fesc (Mstar )<latexit sha1_base64="efgha9ALC+PE5UOqvrG1fgwEi4k=">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</latexit>

本研究では、電離光子脱出率の初代星質量依存性に着目して初代星質量関数の依存性込みの21-cm線空間分布を計算する。

2

Modeling method for fesc

1

• 個々のmini-haloに対する電離光子脱出率

fesc (Mstar , Mhalo )mini-halo<latexit sha1_base64="oCsBNTHy7FeoP7lngYeu/DIpFOc=">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</latexit>

3• 個々の計算グリッド内mini-haloesの平均の電離光子脱出率
a gridsimulation grids

モデル化したいのは、
グリッドのHMFで重み付き平均したもの:

fesc (IMF, local HMF( )) 2
<latexit sha1_base64="PqeIs10/wmp4qCoCMJFyR/uDNwc=">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</latexit>

この先、簡単のため、・全ての初代星は単一のある星質量 Mstar
・赤方偏移 z = 20を考える。
3<latexit sha1_base64="2dMl+B5HzfnvXgwnJmq7gqaJF3U=">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</latexit>

Step1: 個々のmini-haloに対する電離光子脱出率<latexit sha1_base64="R9yeNBb1iqIUP5ep8KnziZLqYWk=">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</latexit>

rvir<latexit sha1_base64="fKkOL3Xy23K3aWJhNEP/Lpv9S6w=">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</latexit><latexit sha1_base64="5iNovs4HWccvrnnc+SJEgEqn4iQ=">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</latexit><latexit sha1_base64="CAaN9D2uW806olDS5PsOjXS0rdw=">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</latexit>

fesc<latexit sha1_base64="JUen89jOTI5uuQV8O7e0Y2yKISc=">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</latexit>L⌫⌧⌫ (rvir )ed⌫⌫HI,L h⌫R 1 L⌫d⌫⌫HI,L h⌫log(fHII )fesc =

R1<latexit sha1_base64="IYXwolNus/UQ7cqlIxXQ4Veqivg=">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</latexit>⇢gas / r 2.2

log(ngas [/cc])• 1次元球対称輻射流体計算

rvir<latexit sha1_base64="fKkOL3Xy23K3aWJhNEP/Lpv9S6w=">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</latexit>

tage [Myr]<latexit sha1_base64="8qMoY1PW7tJ4cNh0Y146r3aaJkA=">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</latexit>

log(r[kpc])<latexit sha1_base64="k52SyJBKCoTWpbVBGjwRM+1aMJk=">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</latexit>

4

Step1: 個々のmini-haloに対する電離光子脱出率• 時間平均した電離光子脱出率のハロー質量依存性

fesc =

Z tlife

dtfesc (t)/tlife

0<latexit sha1_base64="kWyGFrDXr/jpjkqEpwWdftU2EMI=">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</latexit>

Mstar = 500M

<latexit sha1_base64="MgxiYB4945+eEwJ3v2G3awD5y5Y=">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</latexit>

fesc<latexit sha1_base64="WgWme83x5zjUWpcuvQDooiFC30U=">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</latexit>

Mstar = 40M<latexit sha1_base64="fstNVYhF8WLzu/VhCNlUTBLsuZI=">AAADCHichVG/axRBFP6y8Udy/sipTcDm8IhIiuNdFCKCErCxEfLDy0XuwjG7N3cZsju7zM4dJMs1NkL+AQuxULAQC7USW9NYaGmRIn9ASBnBxsK3extEg8kss/Pme+/75ns8N/JVbIl2RpzRU6fPnB0bL5w7f+HiRPHS5eU47BlP1rzQD82KK2LpKy1rVllfrkRGisD1Zd1dv5/m631pYhXqR3YjkquB6GrVUZ6wDLWKs01XdpVOhK+6enpQeNhqBsKumSCJrTCD0t3SLWIsbIe20JS6fVjYKpapQtkqHQ2qeVBGvubD4i6aaCOEhx4CSGhYjn0IxPw1UAUhYmwVCWOGI5XlJQYoMLfHVZIrBKPr/O/yrZGjmu+pZpyxPX7F522YWcIUfac3dEBf6C3t0a//aiWZRuplg093yJVRa2JrcunniayAT4u1P6xjPVt0cDvzqth7lCFpF96Q3998drB0Z3EquU6vaJ/9v6Qd2uYOdP+H93pBLj4/xo/LXjKVx9PyaaNOmrnvmLt/Qh+HHRjOdnhnGk8+pBo87Oq/oz0aLM9UqjcrtDBTnruXj30MV3ENN3i2s5jDA8yjxm++wDa+4puz5bx3PjqfhqXOSM65gr+W8/k36r28fA==</latexit>log(Mhalo )<latexit sha1_base64="ovMqIEuyae7Ys7mnPtAinX7IWC4=">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</latexit>

5

Step2: local halo mass function• N-body simulation data Ishiyama+ 2016
ボックスサイズ (16Mpc/h)^3
粒子数 = (4096)^3

dn/[Mpc 3 M 1 h4 ]dMhalo◆最小ハロー質量 = 10^5.21 [Msun/h]z = 20<latexit sha1_base64="N4PnSvPnMrpog9I/U6/iGI+T29U=">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</latexit>

log✓<latexit sha1_base64="2CE6RazMid8OaCrtfkNXO5v6RUU=">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</latexit>log(Mhalo /[M h 1 ])<latexit sha1_base64="iujlvWzYNT7eHuxK4hAeRS/KQyc=">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</latexit>

6

Step2: local halo mass function• 計算ボックスを(1Mpc/h)^3の小領域に分割。
• 各小領域の

ビンの小領域に存在するハローを用いてHMFを計算。

<latexit sha1_base64="vz75+cQMfXD3ehOaZ3vMhI59xOE=">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</latexit>dn/[Mpc 3 M 1 h4 ]dMhalohistogram of◆<latexit sha1_base64="vz75+cQMfXD3ehOaZ3vMhI59xOE=">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</latexit><latexit sha1_base64="N4PnSvPnMrpog9I/U6/iGI+T29U=">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</latexit>

log<latexit sha1_base64="vz75+cQMfXD3ehOaZ3vMhI59xOE=">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</latexit>✓• 各を計算し、4つのビンに分割。

<latexit sha1_base64="vz75+cQMfXD3ehOaZ3vMhI59xOE=">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</latexit>log(Mhalo /[M h1])<latexit sha1_base64="iujlvWzYNT7eHuxK4hAeRS/KQyc=">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</latexit>

7

Step3: local HMFで重み付き平均
Mstar = 500M
<latexit sha1_base64="WgWme83x5zjUWpcuvQDooiFC30U=">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</latexit>

fesc

fesc (Mstar , local HMF( ))<latexit sha1_base64="MgxiYB4945+eEwJ3v2G3awD5y5Y=">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</latexit><latexit sha1_base64="7AjP3Q4nsee0vFTPY8oly5BkXRs=">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</latexit>

Mstar = 40M<latexit sha1_base64="fstNVYhF8WLzu/VhCNlUTBLsuZI=">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</latexit>

Mstar = 500M
<latexit sha1_base64="WgWme83x5zjUWpcuvQDooiFC30U=">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</latexit>+log(Mhalo )dn/[Mpc 3 M 1 h4 ]dMhalo◆<latexit sha1_base64="ovMqIEuyae7Ys7mnPtAinX7IWC4=">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</latexit>

Mstar = 40M<latexit sha1_base64="fstNVYhF8WLzu/VhCNlUTBLsuZI=">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</latexit><latexit sha1_base64="N4PnSvPnMrpog9I/U6/iGI+T29U=">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</latexit>

log✓<latexit sha1_base64="vz75+cQMfXD3ehOaZ3vMhI59xOE=">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</latexit>log(Mhalo /[M h 1 ])<latexit sha1_base64="iujlvWzYNT7eHuxK4hAeRS/KQyc=">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</latexit>

8電離度分布のテスト計算• 各計算グリッドにて電離平衡の仮定のもと、以下の式を解く<latexit sha1_base64="NAZBKYVJQD298OaexBCtujgwgw4=">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</latexit>

dfHI
=
dt
<latexit sha1_base64="i442fmAEoREeWXg0pGyGWP2rrEs=">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</latexit>ṅion ( )2
+ ↵B nH ( )fHII
nH ( )

ṅion ：単位時間、単位体積あたりに放射される電離光子数nH ：水素原子の数密度
fHII ：電離水素割合
fHI ：中性水素割合↵B ：再結合率 (case B)<latexit sha1_base64="tryWDR0Mboj3dd29PqGXokCc8As=">AAAC+XichVE9TxtBEH0cH3GcACZpIqVBsYgQhTWGIojKUhpKPmJMZCPr7lible/2TndrS3ByQ4OUIm0KKpAi5aOIotAmTZr8gRQU+QERJUg0FMydDyFAwJz2dvbNvrdvNJbvyFATHfYZ/QODQw8yD7OPHg+PjObGnqyEXjuwRdn2HC9YtcxQOFKJspbaEat+IEzXckTFar2O65WOCELpqTd60xdrrtlUsiFtUzNUz03WLNGUKjId2VRT3ayq11xTbwRuNN/N1oRav6jUc3kqUBLjN5NimuSRxoKX+4ca1uHBRhsuBBQ05w5MhPxVUQTBZ2wNEWMBZzKpC3SRZW6bbwm+YTLa4n+TT9UUVXyONcOEbfMrDq+AmeOYoL/0mY7pD32l/3R2q1aUaMReNnm3elzh10ffPVs+vZfl8q6xccm607NGA7OJV8ne/QSJu7B7/M7Wh+PluaWJ6CXt0xH736ND+s0dqM6J/XFRLO3e4cdiL4nK2ymxU62QYu435h7d08dFBwFXG7wSje3vsQYPu3h9tDeTlelCcaZAi9P50lw69gye4wUmebavUMI8FlDmN9/jAD/xy4iMPeOT8aV31ehLOU9xJYwf57fHtvI=</latexit><latexit sha1_base64="JbTGYUo5BUOAFJ56zTJ4bLjjMN8=">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</latexit><latexit sha1_base64="6mHzCnabRpeDGAZSK/E38bc+/98=">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</latexit><latexit sha1_base64="PLBQQN2QRE/oExVbBt97qKsdhVw=">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</latexit>• 密度分布は公開コードのMUSICを用いる
ボックスサイズ (32 comoving Mpc/h)^3
グリッド数 32^3z=20

9

電離度分布のテスト計算
ṅion = ⇢˙ ? ( )Nion (Mstar )fesc (Mstar , )<latexit sha1_base64="NAZBKYVJQD298OaexBCtujgwgw4=">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</latexit>ṅion：単位時間、単位体積あたりに放射される電離光子数⇢˙ ? ：星形成率密度
Nion：単位星質量あたり生成される電離光子数 (Schaerer 2002)<latexit sha1_base64="5zQpT6HD+3fykTbcS4w1J8jR4KM=">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</latexit><latexit sha1_base64="Ex+GotOvfUwQM95r32iUPki7j0c=">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</latexit>• 星形成率密度はハローの数に比例すると仮定<latexit sha1_base64="ycgxDQCQ6H9PAO/7p5SfSxYyqaA=">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</latexit><latexit sha1_base64="YlydZl+dY9XwJROWfTq0RRuwJ8M=">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</latexit>⇢˙ ? ( ) / Nhalo ( )log(Nhalo )<latexit sha1_base64="Tgd+i1I7dvMj5fqX2RERE70oIIg=">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</latexit><latexit sha1_base64="vz75+cQMfXD3ehOaZ3vMhI59xOE=">AAAC83ichVK/TxRREP5YFeFUOLQhsSFcMIbiMoeFhgpjQ8mv4yB35LK7N3e+8O7tZvfdJXghMTYS/wELKgkUxoixkp7Gf8CCgj/AUGJiY+Hs3hGCRJjN2zfvm/nmfZN5XqhVbImO+pwbN2/13x4YzNy5e29oODtyfzkOWpHPRT/QQbTiuTFrZbholdW8EkbsNj3NJW/9RRIvtTmKVWCW7EbIa023YVRd+a4VqJodr3jcUKbjatUwk5uZSo21dTMVNrUzrJrNUZ5SG7vsFHpODj2bC7LHqKCGAD5aaIJhYMXXcBHLV0YBhFCwNXQEi8RTaZyxiYxwW5LFkuEKui7/hpzKPdTIOakZp2xfbtGyImGOYYJ+0Ec6pe/0iX7Sn//W6qQ1Ei0bsntdLofV4Xeji7+vZTVlt3h5zrpSs0Udz1KtSrSHKZJ04Xf57VfvTxenFyY6j2iHTkT/BzqiQ+nAtH/5e/O8sH2FHk+0pFVWJ/ltuURGuF+Ee3JNH2cdRBKty0prvPma1JBhF/4d7WVneSpfeJKn+anczPPX3bEP4CHG8Vhm+xQzmMUcinLnFvbxDQdOy9l2dpzdbqrT13sqD3DBnM9/AXegtLE=</latexit>

10電離度空間分布: 一様fescと\delta依存fescの比較
X
Box全体で電離に効く電離光子数(⇢˙ ? = 5 ⇥ 10 4 [M<latexit sha1_base64="YTlaMnNdVUbZmjcjvwQvTAsBTA0=">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</latexit>ṅion (xi ) )を固定。

i

yr 1 Mpc 3 ] ,500Msun<latexit sha1_base64="ahYwM3WgtHPCqpluRFySAyEVlis=">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</latexit>

fesc(delta)

空間的に一様 fesc = 0.84

<latexit sha1_base64="YiascgFGpN744JaoxCLeWJMGs54=">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</latexit>

fHII = 0.273%<latexit sha1_base64="YiascgFGpN744JaoxCLeWJMGs54=">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</latexit>

fHII = 0.276%

電離光子脱出率のdelta依存性が小さいため、見た目には変わらない。
計算ボックス全体での空間平均電離度もほぼ同じ。

11

log(度数)

電離度のヒストグラム

fesc(delta)
homogeneous fesclog(電離度)
ヒストグラムもそれほど変わらない。

12

電離度空間分布: 40Msunと500Msun starの比較⇢˙ ? = 5 ⇥ 10

4

[M

yr

1

Mpc

3

]

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500Msun

40Msun<latexit sha1_base64="jaWCR7OTBoPUwDlcwaShf5ogufY=">AAADB3ichVE9axRRFD0ZNcZVk9U0gk1wSZAUy90IKoISsLHMh5uN7IRlZnJ388jMm2Hm7UIctrGR+AdSxEbBQiyCjdiqjaCtRQp/gKSMkMbCO7MTRIPJG968+86957xzuW7kq8QQ7Q5Zp06fGT47cq50/sLF0bHypctLSdiNPa57oR/Gy66TsK80140yPi9HMTuB63PDXb+f5Rs9jhMV6odmI+KVwOlo1VaeYwRqlW/aLneUTh1fdfR0v2SHUp2Jpe2WHThmLQ5STrx+/27JZr16WNcqV6hK+Zo4GtSKoIJizYXl77CxihAeugjA0DAS+3CQyNdEDYRIsBWkgsUSqTzP6KMk3K5UsVQ4gq7LvyO3ZoFquWeaSc725BVfdizMCUzSN3pN+/SZ3tAP+vVfrTTXyLxsyOkOuBy1xp5dWTw4kRXIabD2h3WsZ4M2budelXiPciTrwhvwe4+39hfvLEymU/SS9sT/C9qlT9KB7v30Xs3zwvYxflzxkqs8muanzQZp4e4Id++EPg47iCXblp1rPHmbaciwa/+O9miwNFOt3ajS/Exl9l4x9hFcxTVcl9newiweYA51efM5PuILvlqb1o71zno/KLWGCs44/lrWh98TyL1i</latexit><latexit sha1_base64="undNVMdx3LV3HfLmYD2X0kr4aYU=">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</latexit>

fesc = 0.26

<latexit sha1_base64="jaWCR7OTBoPUwDlcwaShf5ogufY=">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</latexit>

fHII = 0.14%

0.5
0.5
fHII / ṅion / fesc

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dfHI
=
dt
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fesc = 0.87
fHII = 0.28%ṅion ( )2
+ ↵B nH ( )fHII
nH ( )

ṅion = ⇢˙ ? ( )Nion (Mstar )fesc (Mstar , )13

log(度数)

fhii histogram

40Msun
500Msunlog(電離度)星質量が大きいと電離光子脱出率が大きくなり、
電離度が大きくなる。

14

まとめ
• 初代星質量依存性を考慮した電離光子脱出率モデルを作成した• 電離度空間分布の見積もりを行なった• Local overdensity依存性の効果は、電離度にあまり強く影響しないことがわかった: 電離度の平均値はほぼ変わらない。
• 一方、星質量依存性の電離度分布に対する影響はある: 電離度の空間平均 = 0.14 for 500Msun, 0.28 for 40Msun.
（ ⇢˙ ? = 5 ⇥ 10

4

[M

yr

1

Mpc

3

]）

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Future works• fescのモデルを拡張: 異なるMstarやIFM。赤方偏移依存性。
• 21cmFASTに組み込み、21-cm線分布を計算。
• Power spectrum等、統計量を見積もりIMFがどのように影響するかを考察する。

15