Sunyaev-Zel‘dovich effectinduced by First Star Supernova
Nagoya Uni. Cosmology Lab. Katsuya T. Abe
Collaborator: Hiroyuki Tashiro
Arxiv:1911.XXXXX

Motivation

z=20-30

Motivation
First stars are important in Astrophysics & Cosmology

It’s difficult to observe them
Really?
We might already catch the signal from First Stars
Oh et al. 2013

Motivation
First stars are important in Astrophysics & Cosmology

It’s difficult to observe them
Really?
We might already catch the signal from First Stars
Oh et al. 2013

First Star Supernova

First Star SNM⇤ ⇠ 100M

The mass of First Stars is large<latexit sha1_base64="AHYkaJ6z8n/DxCb3i70ZnSuuUhE=">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</latexit>

Density・Temperature
1.0

0.5

Shock Shell

1.5

0.5

∼ 0.1kpc
1.0

1.5

2.0

2.5

3.0

Distance from explosion point©NASA／ESA／JPL／Arizona State Univ.

Generation mechanism of CMB anisotropy
Ionized & hightemperature

1.0

0.5

Shock Shell

1.5

0.5

Inverse Compton
Scattering

CMB
photon∼ 0.1kpc
1.0

1.5

2.0

2.5

3.0

Distance from explosion point

ElectronGeneration mechanism of CMB anisotropy
Doppler effect
CMB
photonElectron𝒗Generation mechanism of CMB anisotropy
CMB anisotropy

Ionized & hightemperature

1.0

0.5

Shock Shell

1.5

0.5

Inverse Compton
Scattering

CMB
photonElectron∼ 0.1kpc
1.0

1.5

2.0

2.5

3.0

Distance from explosion point

PlanckThe First Star SN shell model
Pair-instability explosion

ESN = 1046 J<latexit sha1_base64="Vl9d3HQnTsvvVHEay4kxNHVwf3A=">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</latexit>

Heger & Woosley 2002

Other

M⇤ = 100M= 5/3<latexit sha1_base64="9EXvtLVgpHp4TtEu7GDHAN1xHGA=">AAACbXichVHLSsNAFD2Nr1pfVREERcTiY1VvfKAIQtGNy1atig8kiWMNzYskLdTiD7gWXIiCgoj4GW78ARd+grhwoeDGhbdpQFTUO8zMmTP33DkzozqG7vlEDxGpprauviHaGGtqbmlti7d3rHh2wdVEVrMN211TFU8YuiWyvu4bYs1xhWKqhlhV8/OV/dWicD3dtpb9kiO2TCVn6bu6pvhMrW/mFNNUZidHx7fjCUpSEP0/gRyCBMJI2/ErbGIHNjQUYELAgs/YgAKP2wZkEBzmtlBmzmWkB/sCB4ixtsBZgjMUZvM85ni1EbIWrys1vUCt8SkGd5eV/Rike7qmF7qjG3qk919rlYMaFS8lntWqVjjbbYfdS2//qkyefex9qv707GMX04FXnb07AVO5hVbVF/ePX5ZmFgfLQ3RBT+z/nB7olm9gFV+1y4xYPEGMP0D+/tw/wcpYUqaknJlIpObCr4iiBwMY4feeQgoLSCPL51o4winOIs9Sl9Qr9VVTpUio6cSXkIY/AM37jQ0=</latexit><latexit sha1_base64="Qks/xO+K9IPHeOE6QBYtPGueiMo=">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</latexit>

Linear perturbation theory

Hu 2000⇢SN =<latexit sha1_base64="J3fa7h9d3lVlYl6H1nfySDXuUHk=">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</latexit>2
vrms(z) ' 5.8 ⇥ 10 6 (1 + z) 1
<latexit sha1_base64="OwsQcj2D5ofUwdOhMtslQlEEjoE=">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</latexit>

+1
⇢out
1

xe = 1<latexit sha1_base64="kDFTzi9tsTCAnbY3qD8Y/zJO8Lg=">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</latexit>
sha1_base64="bs8QlLljyYde7WbNFuyzJJm+ZMk=">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</latexit>
sha1_base64="ZEKIIhVnWW/2eGZ0DgnheN0ahDk=">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</latexit>
sha1_base64="lgb9QfYzkwX+6Rvo3mDXFpXK26s=">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</latexit>

Sedov-Taylor self similar solution◆
1/5
ESN ⇣ n ⌘ 1
RSN (t) = 12.5 [pc]104 yr1044 J
106 m 3✓◆ 3/5 ✓
◆⇣
1/5
t
ESN
n ⌘ 1
VSN (t) = 490[km/s]
104 yr1044 J
106 m 3✓
◆ 6/5 ✓◆⇣⌘ 1 2/5t
En
SN
TSN (t) = 3.34 ⇥ 106 [K]104 yr1044 J
106 m 3<latexit sha1_base64="chQ9FIAdQKczrBx8Jb6Td1k106o=">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</latexit><latexit sha1_base64="uC5wtHM2iox/mdEffSDIywyV0O8=">AAADQXichZHNihNBEMdrxq81fmzUi+AlGFayB2ONxk8QlhVBPMjuxmQXMkmYaTvJkPmypxOITb+AL+DBk4KI+Bh78QU8LPgCixdxBQ96sGYy7kYX1x6mu+rf9auq7nZj30sk4pZhHjp85OixueOFEydPnZ4vnjnbTKKRYLzBIj8SG66TcN8LeUN60ucbseBO4Pp83R3eS/fXx1wkXhQ+lpOYtwOnH3o9jzmSpG7xU7OrbBGo+iOtK3Lxbu02tuzAkQPShoEuXSn99hLdtn3ekxW7JxympFYWdlRN7wZMhNa28PoDudhRl68Rel1nRGuWu0/1ciCtmWeZSfNwN8ssFk4Db+zFBTqtMlvSyu12R1lZ9W6xjFXMRmm/YeVGGfKxEhXfgg1PIAIGIwiAQwiSbB8cSOhrgQUIMWltUKQJsrxsn4OGArEjiuIU4ZA6pLlPXitXQ/LTnElGM6ri0y+ILMECfsR3uIMf8D1u489/5lJZjrSXCa3ulOVxd/75+fr3/1IBrRIGe9SBPUvowa2sV496jzMlPQWb8uNnL3bqd9YW1CV8jZ+p/1e4hZt0gnD8jb1Z5WsvoUAPYP193fuN5tWqhVVrtVZeWs6fYg4uwEWo0H3fhCV4ACvQAGYsGwPjqSHMTXPb/GJ+nYaaRs6cgz+G+eMXMU3fcg==</latexit><latexit sha1_base64="gu30BOPT8wgO7GM2QATWFWIvj9s=">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</latexit>✓t◆2/5 ✓Generation mechanismof CMB anisotropy

Electron

CMB
photonØ Thermal Sunyaev-Zel’dovich (TSZ) effectT⌫<latexit sha1_base64="5lwNaptUJ0CbFwtbIV4KcTFNNgY=">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</latexit>

✓

◆

h⌫
h⌫
1
(b) = g(⌫)y(b) =
tanh
y(b)
TCMB
kB TCMB
2kB TCMBy(b) =<latexit sha1_base64="9erZYJ1ZxoC5gs3SZKHnGHVUz+k=">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</latexit>

Z

dx

p

p
b2 + x 2 )kB Tgas ( b2 + x2 )me c

T nH x e (Ø Kinetic Sunyaev-Zel’dovich (KSZ) effectZT(n̂) = T d⌘ e ⌧ (⌘) anH xe n̂ · v
TCMB<latexit sha1_base64="8NuLqTwsfo1m54MIWIC6ZiueMs0=">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</latexit>

Effect from First Star SNs on the CMB spectrum
Goal:
Calculate the angular power spectrumof the CMB temperature induced by the SNs？

Effect from First Star SNs on the CMB spectrum
The distribution of the halo hosting the first star :AnisotropyCalculation setup• Apply the Press-Schechter Theory• Assume all of the First stars have 100𝑀⊙
and explode like pair-instability• Neglect the secondary effectfrom the radiation emitted by the SN shell• Use the data summarized in below table
From N-body simulation
logMvir [M ]
6.5
7.0
7.5
8.0
8.5
<latexit sha1_base64="a+owZMLt2rfKXfvBC+vmKm2VhCo=">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</latexit>fhost
2.4 ⇥ 10 4
0.052
0.28
0.90
1.0

logM⇤ [M ]
3.41
3.59
3.88
4.60
5.74

John H. Wise et al. 2014

Angular power spectrum of
the CMB temperature
C`T SZ = g(⌫)2<latexit sha1_base64="WfmsQHUa6BPNN2uLGJxfwpwE/Tc=">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</latexit>Zh⌫g(⌫) =
tanh 1
kB Tgas<latexit sha1_base64="2+EUMZCEWPfZJIQJw9voZ4UrAKY=">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</latexit>✓

C`KSZ = ( T n̄H0 )2<latexit sha1_base64="/nL0l9EjWnmZhDsG2RDCrnudG+g=">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</latexit>q? (k) =<latexit sha1_base64="YO/lPCBtAPc0oGtkdhqzbhdTGEE=">AAADJHichVFNb9NAEB0bCqVAE+CCxCUiKnUOjcYtEggJqYILx36QtlI2tWx3k6zij2W9iQiu/wB/gAMnkEBC/AwuCHFDPfQCZ9RjK3HhwNixVEHVMpa9b9/Mm33r8WQgEo24b5jnzk9duDh9aebylauzleq16xtJPFQ+b/lxEKstz014ICLe0kIHfEsq7oZewDe9weM8vzniKhFx9FSPJe+Ebi8SXeG7miinOmZeWHvmMMmVtHI8aDxkItKsq1w/3dleKrj5LLUWmRSN7aWMBbyr26zv6pRyKeWyBRYO54+ZLGNK9Pq6M7LKisZzh1u7RauFScPdhlOtYxOLqJ0EdgnqUMZKXP0CDHYgBh+GEAKHCDThAFxI6GmDDQiSuA6kxClCoshzyGCGtEOq4lThEjugb4927ZKNaJ/3TAq1T6cE9CpS1mAO9/ADHuJn/Ig/8fepvdKiR+5lTKs30XLpVF7eXP/1X1VIq4b+sepMzxq6cL/wKsi7LJj8Fv5EP3rx6nD9wdpcegff4gH5f4P7+IluEI2O/HerfO31GX488nL6H8vzivCAsIaMxmj/O7STYGOxaWPTXr1bX35UDnQabsFtsGhq92AZnsAKtOiUH8aUMWtUzPfmV/ObuTcpNY1ScwP+CvP7HxfExh8=</latexit>Z

d3 k 0 h 0
k̂
3
(2⇡)

dV
dz
Pyy (k, z)
dzd⌦h⌫
2kB Tgas

Z

◆

dz
H(z)
i

y(n̂, z) =<latexit sha1_base64="sNhZ2hawum3fQuRZirf9/3scHCE=">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</latexit>✓(1 + z)r(z)µ k̂ v(k0 )xe (|k
0

Z

2

k0 |)

kB Tgas (rn̂, z)drnH (r, z)xe (rn̂, z)
me c 2◆2

Pq? (`/r(z), z)

Result

South Pole TelescopeSummarise & Future work
We calculate the angular power spectrum induced by the SNs
We show that a certain scenario about the SNs
can be excluded by the SPT data.
We might use this spectrum
to know more information of the First Star
50
0

δTb [mK]

We can consider the secondary-effectfrom the radiation emitted by the SNs
Considering this effect,
we can also calculate the 21-cm signal-50
t = 10 3yr-100

t = 10 4yr
t = 10 5yr-150

t = 10 6yr

-200
-250

10

100

1000

comoving R [kpc]

10000

Fin.

BACK UP

Physics around a SN shell[1] Meiksin & Whalen, 2013

Density・Temperature
1.5

1.0

衝
撃
波
シ

Ø
Ø

熱制動放射
シンクロトロン放射0.5

ル ∼ 0.1kpc
0.5

1.0

1.5

2.0

2.5

3.0

Distance from explosion point©NASA／ESA／JPL／Arizona State Univ.

Dens., Temp.
1.5

1.0

0.5

衝
撃
波
シ
ル
0.5

1.0

Physics around a SN shell

Distance
1.5

2.0

2.5

3.0

Ionization・temperature Inverse Compton
Scattering
衝
撃ElectronCMB
波シphotonル∼ 1kpc

爆発中⼼からの距離

Dens., Temp.
1.5

1.0

0.5

衝
撃
波
シ
ル
0.5

1.0

Physics around a SN shell

Distance
1.5

2.0

2.5

3.0

Ionization・temperature Inverse Compton
Scattering
衝
撃ElectronCMB
波シphotonル∼ 1kpc

爆発中⼼からの距離But the synchrotron radiaHon
is emiIed by...
ØMagnetic fieldØRelativistic electrons

There’re many uncertaintity

But the synchrotron radiation
is emitted by...
ØMagnetic fieldØRelativistic electrons

There’re many uncertaintity

Bremsstrahlung emissioinPhysics around a SN shell
Spectrum of CMB photon
Black-body
spectrum
SZ effect
Ø Thermal Sunyaev-Zel’dovich (TSZ) effectØ Kinetic Sunyaev-Zel’dovich (KSZ) effectFrequency

Physics around a SN shell
Spectrum of CMB photon
SN explosion

Black-body
spectrum→Wide region (〜0.1kpc)
is ionized and heated

SZ effect→The distortion of the CMB
spectrumØ Thermal Sunyaev-Zel’dovich (TSZ) effectØ Kinetic Sunyaev-Zel’dovich (KSZ) effectFrequencyEffect from SNs on the CMB spectrum
Goal:
Calculate the angular power spectrumof the CMB temperature induced by the SNs

Effect from SNs on the CMB spectrum
Goal:
Calculate the angular power spectrumof the CMB temperature induced by the SNs✅

Mo & White 1996

bSN = 1 +<latexit sha1_base64="2V5fLyv3CdMySx3lDWHxJjh0b1g=">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</latexit>

2
2
( c/
c

1)

Effect from SNs on the CMB spectrum
The distributionof the halo hosting the first star :Matter Power spectrum × Bias

Anisotropy