katsuyaabe - 京都大学resonance/pdf_workshop/katsuya_abe.… · katsuyaabe arxiv:1901.06809 in...

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2 day mini-workshop: Axion Cosmology Thermal Sunyaev-Zel’dovich anisotropy due to Primordial black holes Katsuya Abe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

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Page 1: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

2 day mini-workshop: Axion Cosmology

Thermal Sunyaev-Zel’dovich anisotropydue to Primordial black holes

Katsuya Abe

arXiv:1901.06809

in collaboration with Hiroyuki Tashiro (Nagoya Univ.)Toshiyuki Tanaka (Nagoya Univ.)

Page 2: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

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We detected primordial black holes !?

2

Primordial black hole?

Page 3: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

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What’s? How? Conclusion

�Primordial black hole�Thermal Sunyaev-Zel’dovich effect

�Method�Set up

�Anisotropy spectrum�PBH abundance

Page 4: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

/264

What’s? How? Conclusion

�Primordial black hole�Thermal Sunyaev-Zel’dovich effect

�Method�Set up

�Anisotropy spectrum�PBH abundance

Page 5: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

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Horizon scale

threshold

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PBHcollapse

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5

(in the early universe)

BH which forms from collapse of the cosmic fluid in the early universe

What’s primordial black holes (PBH)?

Gaussian fluctuation

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BTWthis fluctuation is…

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Event Horizon Telescope M87What’s happening around a BH?

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Event Horizon Telescope M87

"This brightness comes from hot plasma"(maximum temperature is )6.0⇥ 109K

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What’s happening around a BH?

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PBH is at some point Release of gravitational energyWhat’s happening around a PBH?

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PBH is at some point Release of gravitational energy

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

What’s happening around a PBH?

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

distortion of CMB energy spectrum

Inte

nsity

frequency

shift

CMBElectron

Scattering CMB photons and electron in hot plasma

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

distortion of CMB energy spectrum

Inte

nsity

frequency

shift

CMBElectron

Scattering CMB photons and electron in hot plasma

→Compton y-parameter

y =c�T

mec2

Zdt nHxekBTgas

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The extent of the shift

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What’s? How? Conclusion

�Primordial black hole�ThermalSunyaev-Zel’dovich effect

�Method�Set up

�Anisotropy spectrum�PBH abundance

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PBH

Anisotropy of the distribution of PBHs

PBH

Hot plasma

How does the anisotropy yield?

tSZ effect

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PBH

Anisotropy of the distribution of PBHs

PBH

Hot plasma

tSZ effect

How does the anisotropy yield?

tSZ anisotropy!

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Equations:

Time: z=[10,200]Initial condition : the profiles of Intergalactic medium at z=200Parametrize the luminosity from (around) PBHas a free parameter "epsilon”,

Calculation set up

dxHI

dt= �kHI,� + ↵BnHxexHII

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Ionized rate Recombination rate

dT

dt= (� � 1)

µmp

kB⇢

✓kBT

µmp

d⇢

dt+ �� ⇤

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Heating rate

Cooling rate

y =c�T

mec2

Zdt nHxekBTgas

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LPBH = ✏LEdd<latexit sha1_base64="DpswQPIb3QASv+GYt2pRsOQu/lA=">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</latexit><latexit sha1_base64="DpswQPIb3QASv+GYt2pRsOQu/lA=">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</latexit><latexit sha1_base64="DpswQPIb3QASv+GYt2pRsOQu/lA=">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</latexit><latexit sha1_base64="DpswQPIb3QASv+GYt2pRsOQu/lA=">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</latexit>

Page 16: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

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The profiles of gas around a PBH

MPBH = 10[M�]

✏ = 10�4<latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit><latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">AAACmnichVHPaxNBFP669UeN1qT1IughGBq8NLyVSkuhUOKlIkL6I20hm4bd7SQO2d1ZdieBdtl/wH/AQ08KIuJfIV5Ezx76J4jHCl48+HazIFq0b5iZ9773vjffzDihJ2NNdDplTF+6fOXqzLXS9RuzN8uVufndWI0iV7Rd5alo37Fj4clAtLXUntgPI2H7jif2nOGjLL83FlEsVbCjj0LR9e1BIPvStTVDvcrD+tNeYkV+0mpupOmaSZ0syDB1qHSadi2rblUtEcbSUwHnD5LFpbRXqVGDcqued8zCqaGwlqq8gYVDKLgYwYdAAM2+Bxsxjw5MEELGukgYi9iTeV4gRYm5I64SXGEzOuR1wFGnQAOOs55xznb5FI9nxMwqFugLvaUz+kjv6Cv9/GevJO+RaTni3ZlwRdgrP7+9/eNCls+7xrPfrP9q1uhjJdcqWXuYI9kt3Al/fPzibHt1ayGp0yv6xvpf0il94BsE4+/u602xdYISf4D593Ofd3YfNExqmJtLtfVm8RUzuIN7uM/vvYx1bKCFNp97gvf4hM/GXaNpPDaeTEqNqYJzC3+YsfMLO1md1Q==</latexit><latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit><latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit>

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The profiles of gas around a PBH

MPBH = 10[M�]

✏ = 10�4<latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit><latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit><latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit><latexit sha1_base64="r5F65wEwUDrC8aHZcg2g8A0PJ2U=">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</latexit>

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

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

tSZ angular power spectrum

One-PBH term

Two-PBH term

Cyy(1P )

l =

Zdz

dV

dzd⌦nPBH(M, z)⇥ (yl(M, z))2

<latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit><latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit><latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit><latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit>

Cyy(2P )

l =

Zdz

dV

dzd⌦P (k =

l

dM(z))

⇥ (nPBH(M, z)yl(M, z))2<latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit><latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit><latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit><latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit>

CTTl = g(x)2Cyy

l = g(x)2(Cyy(1P )l + Cyy(2P )

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y<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">AAACZHichVHLSsNAFD2Nr1ofrRZBEEQsFVflRgTFVdGNyz5sFaqUJI4amiYhSQu1+AO6VVy4UhARP8ONP+CiPyCISwU3LrxNA6JFvcPMnDlzz50zM6pt6K5H1ApJPb19/QPhwcjQ8MhoNDY2XnStmqOJgmYZlrOlKq4wdFMUPN0zxJbtCKWqGmJTray19zfrwnF1y9zwGrbYqSr7pr6na4rHVLZRjiUoRX7MdAM5AAkEkbFiN9jGLixoqKEKARMeYwMKXG4lyCDYzO2gyZzDSPf3BY4QYW2NswRnKMxWeNznVSlgTV63a7q+WuNTDO4OK2eQpEe6pVd6oDt6po9fazX9Gm0vDZ7VjlbY5ejxZP79X1WVZw8HX6o/PXvYw7LvVWfvts+0b6F19PXD89f8Si7ZnKMremH/l9Sie76BWX/TrrMid4EIf4D887m7QXEhJVNKzi4m0qvBV4QxhVnM83svIY11ZFDgcwVOcIqz0JM0LMWliU6qFAo0cXwLafoT+EyJ+Q==</latexit><latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit><latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit><latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">AAACZHichVHLSsNAFD2Nr1ofrRZBEEQsFVflRgTFVdGNyz5sFaqUJI4amiYhSQu1+AO6VVy4UhARP8ONP+CiPyCISwU3LrxNA6JFvcPMnDlzz50zM6pt6K5H1ApJPb19/QPhwcjQ8MhoNDY2XnStmqOJgmYZlrOlKq4wdFMUPN0zxJbtCKWqGmJTray19zfrwnF1y9zwGrbYqSr7pr6na4rHVLZRjiUoRX7MdAM5AAkEkbFiN9jGLixoqKEKARMeYwMKXG4lyCDYzO2gyZzDSPf3BY4QYW2NswRnKMxWeNznVSlgTV63a7q+WuNTDO4OK2eQpEe6pVd6oDt6po9fazX9Gm0vDZ7VjlbY5ejxZP79X1WVZw8HX6o/PXvYw7LvVWfvts+0b6F19PXD89f8Si7ZnKMremH/l9Sie76BWX/TrrMid4EIf4D887m7QXEhJVNKzi4m0qvBV4QxhVnM83svIY11ZFDgcwVOcIqz0JM0LMWliU6qFAo0cXwLafoT+EyJ+Q==</latexit>

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: Fourier component of �T

Tcmb'

✓x

tanh(x/2)� 4

◆y ⌘ g(x)y

<latexit sha1_base64="VffqGDcfdzhpF0eAtcl7Cj4HpAY=">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</latexit><latexit sha1_base64="VffqGDcfdzhpF0eAtcl7Cj4HpAY=">AAACyHichVHLbhMxFL0dXiU8GmCD1M2IqChZkHqqSiBWVWFRddVH0laqq8hjnMSq51GPEzodecOSH2DRVSshhPgMNvABLPoJVRcsigRIXfTOZCQEFXBHYx+fe8/1se3HSiaGkKMx59LlK1evjV+v3Lh56/ZE9c7dtSQaaC7aPFKR3vBZIpQMRdtIo8RGrAULfCXW/e1neX59KHQio7Bl0lhsBawXyq7kzCDVqXLa1Yxn9LlQhrktm7U6GdVBxgPfWksTGYgdlyrRNfVR5a4t8oaFfVun0iAxnRMztmEfzVIte33TSKnYGcih26vvNtJKp1ojTVKEexF4JahBGUtR9R1QeAERcBhAAAJCMIgVMEjw2wQPCMTIbUGGnEYki7wACxXUDrBKYAVDdhvHHq42SzbEdd4zKdQcd1H4a1S6MEW+kPfklHwiH8gxOftrr6zokXtJcfZHWhF3Jl7fX/3+X1WAs4H+L9U/PRvowpPCq0TvccHkp+Aj/XDvzenq05Wp7CE5JCfo/4AckY94gnD4jb9dFiv7kD+A9+d1XwRrM02PNL3l2drcfPkU4zAJD6CO9/0Y5mABlqCN+36Gr/ADfjqLTuy8dNJRqTNWau7Bb+G8OgelvLKk</latexit><latexit sha1_base64="VffqGDcfdzhpF0eAtcl7Cj4HpAY=">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</latexit><latexit sha1_base64="VffqGDcfdzhpF0eAtcl7Cj4HpAY=">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</latexit>

Page 19: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

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

x = cp/kBTe<latexit sha1_base64="mRjZ+unA52cs60T4xh0oU3044nQ=">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</latexit><latexit sha1_base64="mRjZ+unA52cs60T4xh0oU3044nQ=">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</latexit><latexit sha1_base64="mRjZ+unA52cs60T4xh0oU3044nQ=">AAACfnichVHLSsNAFD3GV62vqhvFjVha3FhvRFAEQXTj0ldVsKUkcdTQvEjSYg3BvT/gwpWCiAj6EW78ARd+grhUcOPC2zQgKuodZubMmXvunJlRHUP3fKLHJqm5pbWtPdGR7Ozq7ulN9fVveHbF1UResw3b3VIVTxi6JfK+7htiy3GFYqqG2FTLi/X9zapwPd221v2aI4qmsmfpu7qm+EyVUkMHc5ozUS4FBdcMFsJwvYFEGJZSacpRFCM/gRyDNOJYtlOXKGAHNjRUYELAgs/YgAKP2zZkEBzmigiYcxnp0b5AiCRrK5wlOENhtszjHq+2Y9bidb2mF6k1PsXg7rJyBBl6oCt6oXu6pid6/7VWENWoe6nxrDa0win1Hg+uvf2rMnn2sf+p+tOzj13MRF519u5ETP0WWkNfPTx5WZtdzQRZOqdn9n9Gj3THN7Cqr9rFilg9RZI/QP7+3D/BxmROppy8MpWeX4i/IoFhjGKM33sa81jCMvJ87hEucINbCVJWGpcmGqlSU6wZwJeQZj4AwumT0w==</latexit><latexit sha1_base64="mRjZ+unA52cs60T4xh0oU3044nQ=">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</latexit>

tSZ angular power spectrum

One-PBH term

Two-PBH term

Cyy(1P )

l =

Zdz

dV

dzd⌦nPBH(M, z)⇥ (yl(M, z))2

<latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit><latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit><latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit><latexit sha1_base64="/02Jc29Q6py8s2kwJOpjokNxqsg=">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</latexit>

Cyy(2P )

l =

Zdz

dV

dzd⌦P (k =

l

dM(z))

⇥ (nPBH(M, z)yl(M, z))2<latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">AAAC5nichVFNa9RAGH4Tv+pq7aqggpfg0iUBWSaLoAiF0l56Kaatuy102pCP2d1h80Uyu5CEHLx68CY9eFFBRPwZXvwDHvoLRDxW8OLBNx8gWtQ3ZOaZZ97nfZ+ZsSOPJ4KQY0k+c/bc+QsLF1uXLi9eWWpfvTZMwlnssIETemG8Z1sJ83jABoILj+1FMbN822O79nS93N+dszjhYfBYpBE78K1xwEfcsQRSZvvJupl7xWGepmrf0IoVygOhuFmXjmLLyd1hkbuZSx/5bGwVhjpdqXkPaTOnsZ9vFoWaaYWmUNrqUoUK7rOEemwk1KDOMNY2MGfzbqalZasK0ZiPJ0I7zPtFy2x3SI9UoZwGegM60IQRtt8CBRdCcGAGPjAIQCD2wIIEv33QgUCE3AHkyMWIeLXPoIAWameYxTDDQnaK4xhX+w0b4LqsmVRqB7t4+MeoVGCZfCLvyAn5SN6TL+THX2vlVY3SS4qzXWtZZC49vbXz/b8qH2cBk1+qf3oWMIIHlVeO3qOKKU/h1Pp5dnSy83B7Oe+S1+Qr+n9FjskHPEEw/+a82WLbL6B8AP3P6z4Nhv2eTnr61r3O6lrzFAtwG+6Aivd9H1ZhAwwYYN/P0qJ0Q7opT+Rn8nP5qE6VpUZzHX4L+eVPwkW5pg==</latexit><latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">AAAC5nichVFNa9RAGH4Tv+pq7aqggpfg0iUBWSaLoAiF0l56Kaatuy102pCP2d1h80Uyu5CEHLx68CY9eFFBRPwZXvwDHvoLRDxW8OLBNx8gWtQ3ZOaZZ97nfZ+ZsSOPJ4KQY0k+c/bc+QsLF1uXLi9eWWpfvTZMwlnssIETemG8Z1sJ83jABoILj+1FMbN822O79nS93N+dszjhYfBYpBE78K1xwEfcsQRSZvvJupl7xWGepmrf0IoVygOhuFmXjmLLyd1hkbuZSx/5bGwVhjpdqXkPaTOnsZ9vFoWaaYWmUNrqUoUK7rOEemwk1KDOMNY2MGfzbqalZasK0ZiPJ0I7zPtFy2x3SI9UoZwGegM60IQRtt8CBRdCcGAGPjAIQCD2wIIEv33QgUCE3AHkyMWIeLXPoIAWameYxTDDQnaK4xhX+w0b4LqsmVRqB7t4+MeoVGCZfCLvyAn5SN6TL+THX2vlVY3SS4qzXWtZZC49vbXz/b8qH2cBk1+qf3oWMIIHlVeO3qOKKU/h1Pp5dnSy83B7Oe+S1+Qr+n9FjskHPEEw/+a82WLbL6B8AP3P6z4Nhv2eTnr61r3O6lrzFAtwG+6Aivd9H1ZhAwwYYN/P0qJ0Q7opT+Rn8nP5qE6VpUZzHX4L+eVPwkW5pg==</latexit><latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit><latexit sha1_base64="WG0N2ftLcRRB8+rPgGW5E6OWYJ4=">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</latexit>

CTTl = g(x)2Cyy

l = g(x)2(Cyy(1P )l + Cyy(2P )

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y<latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit><latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit><latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">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</latexit><latexit sha1_base64="AuLdew5jpKTPI6dy3LbA+v6AZWo=">AAACZHichVHLSsNAFD2Nr1ofrRZBEEQsFVflRgTFVdGNyz5sFaqUJI4amiYhSQu1+AO6VVy4UhARP8ONP+CiPyCISwU3LrxNA6JFvcPMnDlzz50zM6pt6K5H1ApJPb19/QPhwcjQ8MhoNDY2XnStmqOJgmYZlrOlKq4wdFMUPN0zxJbtCKWqGmJTray19zfrwnF1y9zwGrbYqSr7pr6na4rHVLZRjiUoRX7MdAM5AAkEkbFiN9jGLixoqKEKARMeYwMKXG4lyCDYzO2gyZzDSPf3BY4QYW2NswRnKMxWeNznVSlgTV63a7q+WuNTDO4OK2eQpEe6pVd6oDt6po9fazX9Gm0vDZ7VjlbY5ejxZP79X1WVZw8HX6o/PXvYw7LvVWfvts+0b6F19PXD89f8Si7ZnKMremH/l9Sie76BWX/TrrMid4EIf4D887m7QXEhJVNKzi4m0qvBV4QxhVnM83svIY11ZFDgcwVOcIqz0JM0LMWliU6qFAo0cXwLafoT+EyJ+Q==</latexit>

yl<latexit sha1_base64="5WgkXwquuxh8fKJcu44pZPARHHM=">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</latexit><latexit sha1_base64="5WgkXwquuxh8fKJcu44pZPARHHM=">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</latexit><latexit sha1_base64="5WgkXwquuxh8fKJcu44pZPARHHM=">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</latexit><latexit sha1_base64="5WgkXwquuxh8fKJcu44pZPARHHM=">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</latexit>

: Fourier component of �T

Tcmb'

✓x

tanh(x/2)� 4

◆y ⌘ g(x)y

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What’s? How? Conclusion

�Primordial black hole�Thermal Sunyaev-Zel’dovich effect

�Method�Set up

�Anisotropy spectrum�PBH abundance

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/2621

tSZ angular power spectrum(MPBH[M�], ✏, fPBH) = (10, 10�4, 10�2)

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SPTCMB

Page 22: KatsuyaAbe - 京都大学resonance/pdf_workshop/Katsuya_Abe.… · KatsuyaAbe arXiv:1901.06809 in collaboration with Hiroyuki Tashiro (Nagoya Univ.) Toshiyuki Tanaka (Nagoya Univ.)

/2622

tSZ angular power spectrum(MPBH[M�], ✏, fPBH) = (10, 10�4, 10�2)

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SPTCMB

Flat spectrum

→the suggestion of the existence of PBHs

~10^5

c.f. tSZ anisotropy by clusters

Komatsu & Kitayama 1999

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/2623

Constraint of PBH abundance from this work

fPBH < 10�3

⇣ ✏

10�2

⌘�1

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Compared this signal to the SPT data,we can get…

However, in the previous work about the CMB optical depth induced by PBHs,

fPBH < 10�9

⇣ ✏

10�2

⌘�1

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The unfortunate constraint of PBH abundance

Y. Ali-Ha ı̈moud and M. Kamionkowski (2017)

→This work does not give a new constraint onthe PBH abundance

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Future work (Discussion)

� In axion cosmology, Are there some mechanisms tochange the thermal history of Universelike this work?

� Let’s discuss the relationbetween PBH and axion.

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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 spectrumgives useful information about the existence of PBHs.

Unfortunately, tSZ anisotropy induced by PBHsdoes not give a new constraint on the PBH abundance.

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Fin.