2 day mini-workshop: Axion Cosmology

arXiv:1901.06809

Thermal Sunyaev-Zel’dovich anisotropy
due to Primordial black holes

Katsuya Abein collaboration with
Hiroyuki Tashiro (Nagoya Univ.)
Toshiyuki Tanaka (Nagoya Univ.)We detected primordial black holes !?

Primordial black hole?
2

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What’s?
Primordial black hole
ThermalSunyaev-Zel’dovich eﬀect

How?

Conclusion

MethodSet up

Anisotropy spectrum
PBH abundance

3 /26

What’s?
Primordial black hole
ThermalSunyaev-Zel’dovich eﬀect

How?

Conclusion

MethodSet up

Anisotropy spectrum
PBH abundance

4 /26

What’s primordial black holes (PBH)?
BH which forms from collapse of the cosmic fluid in the early universe= ⇢/⇢ (in the early universe)<latexit sha1_base64="feRB6kHL56NKJdIXkAGyfbeGN6Y=">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</latexit>
sha1_base64="bs8QlLljyYde7WbNFuyzJJm+ZMk=">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</latexit>
sha1_base64="QKtSlsvWdjdtO9+T/JizoAbn97U=">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</latexit>
sha1_base64="9Dkjg6L8mPm1UuYh79ZW3XpRDtU=">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</latexit>

thresholdx

BTW
this fluctuation is…

<latexit sha1_base64="T5eNG1t/rh/1LJqdf1tI18J36qA=">AAACZHichVHLSsNAFD2Nr1pf1SIIghRLxVW5EUFxJbpxaa19QC0liVMNpklI0qIWf0C3igtXCiLiZ7jxB1z0BwRxWcGNC2/TgKiod5iZM2fuuXNmRrUN3fWImiGpq7unty/cHxkYHBoeiY6O5Vyr5mgiq1mG5RRUxRWGboqsp3uGKNiOUKqqIfLq3mp7P18Xjqtb5qZ3YItSVdkx9YquKR5T6f1yNEEp8iP+E8gBSCCIdSt6gy1sw4KGGqoQMOExNqDA5VaEDILNXAkN5hxGur8vcIQIa2ucJThDYXaPxx1eFQPW5HW7puurNT7F4O6wMo4kPdItteiB7uiZ3n+t1fBrtL0c8Kx2tMIujxxPZN7+VVV59rD7qfrTs4cKFn2vOnu3faZ9C62jrx+etzJLG8nGDF3RC/u/pCbd8w3M+qt2nRYbF4jwB8jfn/snyM2lZErJ6fnE8krwFWFMYhqz/N4LWMYa1pHlcwVOcIqz0JM0KMWk8U6qFAo0MXwJaeoD9kyJ+A==</latexit><latexit

P( )collapse<latexit sha1_base64="Vh3epkxfozh3KVZLPT0uQYT1vSs=">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</latexit>

PBH

Horizon scale<latexit sha1_base64="KFwmTAe5Sb/OILCC87BFaj1VD/Y=">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</latexit>

Gaussian fluctuation

5

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What’s happening around a BH?

Event Horizon Telescope M87

6 /26

What’s happening around a BH?

Event Horizon Telescope M87"This brightness comes from hot plasma"(maximum temperature is 6.0 ⇥ 109 K )<latexit sha1_base64="sj2Dvy6FSi47LIP1TxH4A0ILmf0=">AAACfHicSyrIySwuMTC4ycjEzMLKxs7BycXNw8vHLyAoFFacX1qUnBqanJ+TXxSRlFicmpOZlxpaklmSkxpRUJSamJuUkxqelO0Mkg8vSy0qzszPCympLEiNzU1Mz8tMy0xOLAEKxQuIm+kZxJRk5qYWKxgaxFVb1irEFOVWe9fGCygb6BmAgQImwxDKUGaAgoB8geUMMQwpDPkMyQylDLkMqQx5DCVAdg5DIkMxEEYzGDIYMBQAxWIZqoFiRUBWJlg+laGWgQuotxSoKhWoIhEomg0k04G8aKhoHpAPMrMYrDsZaEsOEBcBdSowqBpcNVhp8NnghMFqg5cGf3CaVQ02A+SWSiCdBNGbWhDP3yUR/J2grlwgXcKQgdCF180lDGkMFmC3ZgLdXgAWAfkiGaK/rGr652CrINVqNYNFBq+B7l9ocNPgMNAHeWVfkpcGpgbNZuACRoAhenBjMsKM9AwN9AwDTZQdnKBRwcEgzaDEoAEMb3MGBwYPhgCGULC9ixnWMKxl/MekwqTNpAtRysQI1SPMgAKYzACWVpJN</latexit>

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What’s happening around a PBH?
PBH is at some point

Release of gravitational energy

8 /26

What’s happening around a PBH?
PBH is at some point

Release of gravitational energy

Heat up and emit UV, X-ray, etc.

9 /26

What’s thermal Sunyaev-Zel’dovich (tSZ)?

Intensity

Scattering CMB photons
and electron in hot plasma
distortion of
CMB
CMB energy spectrum
Electronshiftfrequency
10

10 /26

What is thermal Sunyaev-Zel’dovich (tSZ)?

The extent of the shift→Compton y-parameter

c T
y=
me c2
<latexit sha1_base64="pBWN6h3orhoJTjjNUkvn7EUKVj8=">AAACwXichVHNalQxGD29/rSOPx11I7gZHCquhtxSUApCaTdd9memLfTWITfNjGHuH7mZodOQPkBfwIUrBRHxLXTjC7joGyiutIIbF35z70XRon4hycnJd76cJGEWqdwwdjLlnTt/4eL0zKXa5StXr83Wr9/YytOhFrIj0ijVOyHPZaQS2THKRHIn05LHYSS3w8HKZH97JHWu0qRtxpnci3k/UT0luCGqWw/GD4Oe5sKKIFf9mHdtoGPbds7ZuMTSOfHIzjsXqMQ09s1RUvKrzh38zBiUaNm5don6PHeuW2+yFiuicRb4FWiiirW0/hIB9pFCYIgYEgkM4QgcObVd+GDIiNuDJU4TUsW+hEONtEPKkpTBiR3Q2KfVbsUmtJ7UzAu1oFMi6pqUDcyx9+wVO2Xv2Gv2kX3/ay1b1Jh4GdMcllqZdWePb21++68qptng8S/VPz0b9PCg8KrIe1Ywk1uIUj86fHK6ubgxZ++y5+wT+X/GTthbukEy+iperMuNp6jRB/h/PvdZsDXf8lnLX19oLi1XXzGD27iDe/Te97GEVayhQ+e+wQd8xhdvxVNe5uky1ZuqNDfxW3j2B/kMsuc=</latexit>

Z

Intensity

Scattering CMB photons
and electron in hot plasma
distortion of
CMB
CMB energy spectrum
Electrondt nH xe kB Tgas

shiftfrequency
11

11 /26

What’s?
Primordial black hole
ThermalSunyaev-Zel’dovich effectHow?

Conclusion

MethodSet up

Anisotropy spectrum
PBH abundance

12 /26

How does the anisotropy yield?
PBH
tSZ eﬀect

Anisotropy of the
distribution of PBHs
PBH

Hot plasma

13 /26

How does the anisotropy yield?
PBH
tSZ eﬀect

Anisotropy of the
distribution of PBHs
PBH

Hot plasmatSZ anisotropy!
14 /26

Calculation set up
Time: z=[10,200]
Initial condition : the profiles of Intergalactic
medium at z=200
Parametrize the luminosity from (around) PBH
as a free parameter "epsilon”, LPBH = ✏LEdd
Equations:<latexit sha1_base64="DpswQPIb3QASv+GYt2pRsOQu/lA=">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</latexit>

dxHI Ionized rate Recombination rate
= kHI, + ↵B nH xe xHII
dt✓◆
Heating ratedT
µmp kB T d⇢
=(
1)
+
⇤
dt
kB ⇢ µmp dt
Cooling rateZc T
y=dt nH xe kB Tgas2
me c<latexit sha1_base64="Z4DItOjeDmbAaeJhQ5CpTMqJWTU=">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</latexit>
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sha1_base64="iwB39RMSvSMe+kmbs5cOw+Bbt1I=">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</latexit><latexit sha1_base64="pBWN6h3orhoJTjjNUkvn7EUKVj8=">AAACwXichVHNalQxGD29/rSOPx11I7gZHCquhtxSUApCaTdd9memLfTWITfNjGHuH7mZodOQPkBfwIUrBRHxLXTjC7joGyiutIIbF35z70XRon4hycnJd76cJGEWqdwwdjLlnTt/4eL0zKXa5StXr83Wr9/YytOhFrIj0ijVOyHPZaQS2THKRHIn05LHYSS3w8HKZH97JHWu0qRtxpnci3k/UT0luCGqWw/GD4Oe5sKKIFf9mHdtoGPbds7ZuMTSOfHIzjsXqMQ09s1RUvKrzh38zBiUaNm5don6PHeuW2+yFiuicRb4FWiiirW0/hIB9pFCYIgYEgkM4QgcObVd+GDIiNuDJU4TUsW+hEONtEPKkpTBiR3Q2KfVbsUmtJ7UzAu1oFMi6pqUDcyx9+wVO2Xv2Gv2kX3/ay1b1Jh4GdMcllqZdWePb21++68qptng8S/VPz0b9PCg8KrIe1Ywk1uIUj86fHK6ubgxZ++y5+wT+X/GTthbukEy+iperMuNp6jRB/h/PvdZsDXf8lnLX19oLi1XXzGD27iDe/Te97GEVayhQ+e+wQd8xhdvxVNe5uky1ZuqNDfxW3j2B/kMsuc=</latexit>

15 /26

The profiles of gas around a PBH
MPBH = 10[M ]<latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit>✏ = 10 4

16 /26

The profiles of gas around a PBH

MPBH = 10[M ]<latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit>✏ = 10 4
17 /26

tSZ angular power spectrum

Sunyaev & Zel’dovich 1969
Cole & Kaiser 1988
Komatsu & Kitayama 1999

yy(1P )yy(2P )TT2 yy
2Cl = g(x) Cl = g(x) (Cl+ Cl)<latexit sha1_base64="pIGL85WjYZnwrQbQ/AprMbId2uk=">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</latexit>

One-PBH termyy(1P )
Cl=
<latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit>

Z

dV
2
dz
nPBH (M, z) ⇥ (yl (M, z))
dzd⌦

Z

dV
l
dz
P (k =)dzd⌦
dM (z)

Two-PBH termyy(2P )
Cl=

<latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit>⇥ (nPBH (M, z)yl (M, z))2yl : Fourier component of y<latexit sha1_base64="5WgkXwquuxh8fKJcu44pZPARHHM=">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</latexit>

T<latexit sha1_base64="VffqGDcfdzhpF0eAtcl7Cj4HpAY=">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</latexit>

Tcmb

'

✓

◆
4 y ⌘ g(x)y<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit>xtanh(x /2)

x = cp/kB Te<latexit sha1_base64="mRjZ+unA52cs60T4xh0oU3044nQ=">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</latexit>

18 /26

tSZ angular power spectrum

Sunyaev & Zel’dovich 1969
Cole & Kaiser 1988
Komatsu & Kitayama 1999

yy(1P )yy(2P )TT2 yy
2Cl = g(x) Cl = g(x) (Cl+ Cl)<latexit sha1_base64="pIGL85WjYZnwrQbQ/AprMbId2uk=">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</latexit>

One-PBH termyy(1P )
Cl=
<latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit>

Z

dV
2
dz
nPBH (M, z) ⇥ (yl (M, z))
dzd⌦

Z

dV
l
dz
P (k =)dzd⌦
dM (z)

Two-PBH termyy(2P )
Cl=

<latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit>⇥ (nPBH (M, z)yl (M, z))2yl : Fourier component of y<latexit sha1_base64="5WgkXwquuxh8fKJcu44pZPARHHM=">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</latexit>

T<latexit sha1_base64="VffqGDcfdzhpF0eAtcl7Cj4HpAY=">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</latexit>

Tcmb

'

✓

◆
4 y ⌘ g(x)y<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit>xtanh(x /2)

x = cp/kB Te<latexit sha1_base64="mRjZ+unA52cs60T4xh0oU3044nQ=">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</latexit>

19 /26

What’s?
Primordial black hole
ThermalSunyaev-Zel’dovich effectHow?

Conclusion

MethodSet up

Anisotropy spectrum
PBH abundance

20 /26

tSZ angular power spectrum(MPBH [M ], ✏, fPBH ) = (10, 10 4 , 10 2 )<latexit sha1_base64="OwElqDtkGTZ0EmpDqzcX5ZjKKrQ=">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</latexit>

CMB

SPT

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c.f. tSZ anisotropy by clusterstSZ angular power spectrum(MPBH [M ], ✏, fPBH ) = (10, 10 4 , 10 2 )<latexit sha1_base64="OwElqDtkGTZ0EmpDqzcX5ZjKKrQ=">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</latexit>

CMB

SPT
Komatsu & Kitayama 1999

Flat spectrum~10^5→the suggestion of the existence of PBHs
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Constraint of PBH abundance from this work
Compared this signal to the SPT data,
we can get…
⇣ ✏ ⌘ 1
fPBH < 10 3
10 2
However, in the previous work
about the CMB optical depth induced by PBHs,<latexit sha1_base64="e4k+zw4EwU9zLNeO0M9fBWo93FU=">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</latexit>⇣ ✏ ⌘ 1
9
fPBH < 10
10 2<latexit sha1_base64="YYDVoUcBNldBusQfGX4AdLFg3sY=">AAACpXichVHLahRBFD1pX3F8ZNSN4KZxiMaFw+0gmAQXQ9xkI0weMwmkY9PdqZ4UqX5QXTOQNP0D/oALVwoq4me4ceE2Qj5BXEZw48I7PQ2iQb1FVd177j23TlUFmZK5ITqess6cPXf+wvTFxqXLV67ONK9d7+fpUIeiF6Yq1VuBnwslE9Ez0iixlWnhx4ESm8H+43F+cyR0LtNkwxxkYif2B4mMZOgbhrxmJ/IKV8d2d3mltB/ZDj0t7i+WtqtEZObcSPth4YoslypNyqLKzpelq+Vgz9zjwCm9ZovaVJl92nFqp4XaumnzLVzsIkWIIWIIJDDsK/jIeWzDASFjbAcFY5o9WeUFSjSYO+QqwRU+o/u8DjjartGE43HPvGKHfIriqZlpY5aO6B2d0Ed6T1/ox197FVWPsZYD3oMJV2TezLOb69//y4p5N9j7xfqnZoMIC5VWydqzChnfIpzwR4fPT9aX1maLO/SKvrL+l3RMH/gGyehb+HpVrL1Agz/A+fO5Tzv9+bZDbWf1QauzXH/FNG7hNub4vR+igxV00eNz3+ATjvDZums9sTas/qTUmqo5N/CbWd5Pa7ShrQ==</latexit>

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The unfortunate constraint of PBH abundance→This work does not give a new constraint on
the PBH abundance
Y. Ali-Ha ı̈ moud and M. Kamionkowski (2017)24 /26

Future work (Discussion) In axion cosmology,
Are there some mechanisms tochange the thermal history of Universe
like this work?
 Let’s discuss the relation
between PBH and axion.
25 /26

Summary
We calculate the tSZ angular power spectrumof CMB temperature induced by PBHs.
In future SZ anisotropy measurements,
the detection or non-detection of the flat spectrum
gives useful information about the existence of PBHs.
Unfortunately, tSZ anisotropy induced by PBHs
does not give a new constraint on the PBH abundance.

26 /26Fin.

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