6PŨůçÛĸŘz#ŀśŚĈīĭQŎŗŚH" drt'-ĂĘĘėĕĦïġĘïĈīğēĠïĭïñĈīĭòïĢĚġĦġĠïĤēĖěēĦėĖïĘĤġğïĢĤěğġĤĖěēĞïĕĞġħĖïĦġïH" ĘġĤğēĦěġĠïĎĚěĠīēïÿĬēğě ñĐĠěĨėĤĥěĦīïġĘïďĥħĝħĔēòĉēĥēīħĝěïĐğėğħĤēôïĉēĝěĦġ ÿĔėïñĐĠěĨėĤĥěĦīïġĘïďĥħĝħĔēò・Introduction• ăěĤĥĦïġĔĜėĕĦïñ%OòØ ăěĤĥĦïĥĦēĤïēĠĖïĘěĤĥĦïęēĞēĪīïğēĖėïĘĤġğïĢĤěğġĤĖěēĞïęēĥïĕĞġħĖ•ąěĥĦġĤīïġĘïħĠěĨėĤĥė

Observation of super massive black hole (SMBH) at z~7
ƌ # ~10' #⨀ ƍĤėěġĠěĬēĦěġĠ

ĒěĦĚġħĦïğėĦēĞăěĤĥĦïġĔĜėĕĦïõþïĥėėĖïĀąĉėĦēĞïĘġĤğēĦěġĠñĢĤěğġĤĖěēĞïęēĥïĕĞġħĖòĒěĦĚïğėĦēĞï

・Introduction• ăěĤĥĦïġĔĜėĕĦïĘġĤğēĦěġĠïĥĕėĠēĤěġĕġĞĞēĢĥėïġĘïēïĕĞġħĖïġĘïĢĤěğġĤĖěēĞïęēĥ

ĒěĦĚġħĦïğėĦēĞ

ÿĨēěĞēĔĞėïĕġġĞěĠęïěĥïġĠĞīïąïēĠĖïH"•ąïĕġġĞěĠęïİ T*+, ~ 8,000 K•

H" ĕġġĞěĠęïİ T*+, ~ 200 K

H" cooling_week

H" cooling_strong(Omukai 2001)

・Introduction• ďĚėïĤėĞēĦěġĠïĔėĦĩėėĠïĕġġĞěĠęïġĘïĢĤěğġĤĖěēĞïęēĥïēĠĖïĘěĤĥĦïġĔĜėĕĦïñĖěĤėĕĦïĕġĞĞēĢĥėïĥĕėĠēĤěġòï
ČĤěğġĤĖěēĞïęēĥïĕĞġħĖïĕĤėēĦėïĘěĤĥĦïĥĦēĤĥï
ěĘïĦĚėĤėïēĤėïĠġïėĘĘėĕĦïĦġïĖėĥĦĤħĕĦïH"ČĤěğġĤĖěēĞïĕĞġħĖï
ğēĥĥï10123 M⊙ĢĤėĨėĠĦïH" ĘġĤğēĦěġĠH" ĕġġĞěĠęïĥĦĤġĠę

ĩėėĝĐđïĤēĖěēĦěġĠïĘĤġğï
ĠėēĤïĕĞġħĖ
l Destruct 67 , 6 2

ăġĤğēĦěġĠïġĘïĘěĤĥĦïĥĦēĤ
Mass ~8~899 :⨀ĎħĢėĤïğēĥĥěĨėïĥĦēĤï
~89;2< :⨀Direct collapse ĥĕėĠēĤěġFormation seed BH : mass ~89;2< :⨀Lyman-Werner radiation

・ Introduction• ĂĘĘėĕĦïġĘïĈīĭïĢĚġĦġĠïĦġïĢĤėĨėĠĦïH" ĘġĤğēĦěġĠï(Johnson & Dijkstra 2017)• ĉēěĠïĤėēĕĦěġĠïĦġïĘġĤğēĦěġĠïH" ěĠïĢĤěğġĤĖěēĞïĕĞġħĖČĤěğġĤĖěēĞïĕĞġħĖInner

Lyα radiationƌĖėĥĦĤħĕĦïH2ƍ
Photodetachment ėĠėĤęīïüï þ0.76 eVLyα photon üï10.2 eVH cooling radiation

OuterLW radiation(destruct H" , H2)ÿĦïĚěęĚïĖėĠĥěĦīïĤėęěġĠôïěĦïĕēĠïĠġĦïĢĤėĨėĠĦïH" ĘġĤğēĦěġĠïġĠĞīïġħĦėĤïĐđïĤēĖěēĦěġĠôĀħĦïěĠĕĞħĖėïěĠĠėĤïĈīĭïĤēĖěēĦěġĠïĕēĠïĢĤėĨėĠĦïH" ĘġĤğēĦěġĠö

・ IntroductionØ ČĤġĔĞėğïġĘïĈīĭ ĦĤēĠĥĘėĤïěĠïJohnson & Dijkstra 2017ĂĘĘėĕĦïġĘïğħĞĦěĢĞėïĥĕēĦĦėĤěĠęïēĠĖïĦĤēĢĢěĠęïİ ħĥėïĢēĤēğėĦėĤïLuminosity of Lyα : ęĤēĨěĦēĦěġĠēĞïĢġĦėĠĦěēĞïėĠėĤęīEnergy density of Lyα(#> : increase length to escape primordial cloud)ĀïüïėĘĘėĕĦïġĘïĠġĠõħĠěĘġĤğïėĠėĤęīïĖėĠĥěĦīB = 1 ~ 10ĒėïĦĚěĠĝïěĦïĠėėĖïĦġïĦĤėēĦïĈīĭïĦĤēĠĥĘėĤïğġĤėïėĪēĕĦĞīï

・Method•čēĖěēĦěĨėïĦĤēĠĥĘėĤïġĘïĈī? İ ĤēĖěēĦěĨėïĖěĘĘħĥěġĠïėģöØ ċĠėõĖěğėĠĥěġĠïĢĞēĠėïĢēĤēĞĞėĞï@A üïěĠĦėĠĥěĦīôï?A üïėĪĦěĠĕĦěġĠïĕġėĘĘěĕěėĠĦôïBA üïĥġħĤĕėïĦėĤğôïC = cosHĖėĕĤėēĥėěĠĕĤėēĥėĉġğėĠĦïėģħēĦěġĠïñēĨėĤēęėïġĘïĥġĞěĖïēĠęĞėò•ĘěĤĥĦôïĥėĕġĠĖïğġğėĠĦïėģöïóïĂĖĖěĠęĦġĠïēĢĢĤġĪěğēĦěġĠïñěĥġĦĤġĢěĕïĤēĖěēĦěġĠòčēĖěēĦěĨėïĖěĘĘħĥěġĠïėģħēĦěġĠ•ĎġħĤĕėïĦėĤğïüïēĢĢĤġĪěğēĦěġĠïġĘïĤėĖěĥĦĤěĔħĦěġĠïñčīĔěĕĝěïðïĖėĞĞĮÿĠĦġĠěġ øûûúò

ĊġĤğēĞěĬėïĘĤėģħėĠĕī

I=J − JLΔJNJL üïĞěĠėïĕėĠĦėĤïĘĤėģħėĠĕīôïO
ΔJN = RPQ JL üïāġĢĢĞėĤïĩěĖĦĚčēĖěēĦěġĠïĥġħĤĕė

ĒėïĥġĞĨėïĦĚěĥïėģħēĦěġĠïħĥěĠęïĠħğėĤěĕēĞïĥěğħĞēĦěġĠ・ MethodĬ• ĀġħĠĖēĤīïĕġĠĖěĦěġĠ

[ = \, S = STUVØ čēĖěēĦěġĠïĥġħĤĕėïüï
ċĠĞīïĕĞġħĖïĕėĠĦėĤïñS = 0 òēĠĖïĘĤėģħėĠĕīïĞěĠėïĕėĠĦėĤïñĪý÷òï= Y S Y(I)TS = 0 ĥġħĤĕėØ ĘĤėģħėĠĕīïñĪòïïüïĔġħĠĖēĤīïýƎ
S = STUVØ ĎħĤĘēĕėïġĘïĕĞġħĖïñSòïïüïĤēĖěēĦěġĠïěĥïěĥġĦĤġĢěĕïēĠĖïġĠĞīïėĥĕēĢėïĤēĖěēĦěġĠ

@öïČĞēĠėïĢēĤēĞĞėĞôïġĢĦěĕēĞïĖėĢĦĚïSS = STUVSĎěğħĞēĦěġĠïĤėęěġĠ

Ø Symmetry at S = 0S=0I = ITWX

I=0I = ITUVI

・ Method• ĂĠĨěĤġĠğėĠĦïġĘïęēĥïĕĞġħĖØ ĆĥġĦĤġĢěĕïęēĥïĕĞġħĖØ ČēĤēğėĦėĤïġĘïĥěğħĞēĦěġĠ• ĄēĥïĦėğĢėĤēĦħĤėïT
• Optical depth at Lyα line center (S]^_` a`_b`c ò• ĂĥĦěğēĦėïġĘïġĢĦěĕēĞïĖėĢĦĚïτ]^_` a`_b`c = e f \ = gh f ƌĕĞġħĖïĤēĖěħĥïĈƍjk l" 1t 2"
2j1f = ij"= 5.89 × 10mn o ΔJN101

ďġĦēĞïğēĥĥïġĘïęēĥïĕĞġħĖïüïM*+, = 103 #⨀ĖėĠĥěĦīïüïn = 0.1 ~ 10v

τ]^_` a`_b`c üï103 ~ 10j" ñēĥĥħğėïěĥġĦĤġĢěĕïĥĢĚėĤěĕēĞïĕĞġħĖò・Result• ĎĢėĕĦĤēĞïġĘïėĥĕēĢėïĢĚġĦġĠĤėĖƏđġěęĦïĢĤġĘěĞėïüïĠħğėĤěĕēĞïñĦĚěĥïĩġĤĝòĔĞēĕĝƏLorentz profile :analytical

0.08

Voigt
Lorentz

0.35

0.07

0.3

0.012

0.05

0.2

0.04

0.15

0.006
0.004

0.02

0.05

0.002

0.01

-15-10-50510
Standardized frequency x

tau= 101

15200-50

0.01

0.008

0.03

0.1

Voigt
Lorentz

0.014

0.06

0.25

0-20

0.016

Voigt
Lorentzmean intensity of escape photon J(x)0.4mean intensity of escape photon J(x)mean intensity of escape photon J(x)T= 101 K-40-30-20 -1001020Standardized frequency x

tau= 103

3040500-200-150-100-50050100
Standardized frequency x150200tau= 10w

ÿĦïĚěęĚïġĢĦěĕēĞïĖėĢĦĚAgree with Harrington-Neufeld ĥġĞħĦěġĠïñĈġĤėĠĦĬïĢĤġĘěĞėïēĠēĞīĦěĕēĞïĥġĞħĦěġĠòHarrington-Neufeld ĥġĞħĦěġĠ(Harrington 1973, Neufeld 1990)

・Result• ăĤėģħėĠĕīïēĨėĤēęėïğėēĠïěĠĦėĠĥěĦīïñěĠĕěĖėĠĕėïěĠĦėĠĥěĦīïýïøò

T=10| K
T=101 K

Frequency integral mean intensity

x = 89<Optically thinyz{z (S)0

Optical depth (S)103ĆĠĕĤėēĥėïğėēĠïěĠĦėĠĥěĦīïēĦïĕĞġħĖïĕėĠĦėĤïį ėĘĘėĕĦïġĘïğħĞĦěĢĞėïĥĕēĦĦėĤěĠęĲ

・Result• H 2 ĢĚġĦġĖėĦēĕĚğėĠĦ ĤēĦėïġĘïĈīĭïĤēĖěēĦěġĠ

Ä`+_Ø Average rate in gas cloud }~`b+añS]^_` a`_b`c òïüïS]^_` a`_b`c = 101 ~ 10jLmean photodetachment rate [cm-3 s-1]

10-2T=1034 K
T=10 K
fitting T=1034 Kfitting T=10 K

10-3ăěĦĦěĠęïĘħĠĕĦěġĠïēĦïďýï101 ć

10-4

10-5104

105

106

107
total optical depth

108

109

1010

・Result• Compare with H" formation and destruction• ĉēěĠïĤėēĕĦěġĠï• Lyα radiation : H 2 destruction• Outer UV radiation : H" destruction• H" ĘġĤğēĦěġĠïĘġĤğïH 2• H" ĘġĤğēĦěġĠïĤēĦėïM*+, = 103 #⨀ , T*+, = 101 K

H2 + H → H" + e2

optical depth
5.5 × 106

2.5 × 107

1.2 × 108

5.5 × 108

2.5 × 109

1.2 × 1010

5.5 × 1010

}ÑÖ ÜácÄ = 4.0×102' ×t 2L.jâ ×eÑ [ä 2j ](Galli & Palla 1998)

10-4
H2 formation

UV radiation

reaction rate [s-1]10-610Lyα radiationčėĥĦĤěĕĦïH" ĘġĤğēĦěġĠġĠĞīïĈīĭïĤēĖěēĦěġĠïï

-810-101010-12Lya
J21=100
J21=1000
H2 formation-1410-1

100101210-3
number density nH [cm ]103104105

・Conclusion
Ø H 2 ĢĚġĦġĖėĦēĕĚğėĠĦ ĤēĦėïĔīïĈīĭïĖėĥĕĤěĔėïĔėĞġĩïĘġĤğħĞēïěĠïĢĞēĠėïĢēĤēĞĞėĞïĢĤěğġĤĖěēĞïęēĥïĕĞġħĖØ ÿĦïĚěęĚïĖėĠĥěĦīôïĢĤėĨėĠĦïH" ĘġĤğēĦěġĠïġĠĞīïĔīïěĠĠėĤïĈīĭïĤēĖěēĦěġĠØ ĀħĦïēĦïĞġĩïĖėĠĥěĦīôïĠėėĖïĦġïġħĦėĤïĐđïĤēĖěēĦěġĠ