Primordial black k holes s in light of LIGO/Virgo obse serva - PowerPoint PPT Presentation

Primordial black k holes s in light of LIGO/Virgo obse serva vations Ville Vaskonen vvaskonen@ifae.es Based on work done in collaboration with M. Raidal, C. Spethmann and H. Veermäe.

Co Conte tent 1. Introduction 2. PBH binary formation 3. Survival of the binaries 4. Constraints from LIGO/Virgo 5. Summary

Intr Introduction oduction

Motiva vations s to st study y PBHs Are LIGO/Virgo BHs How did supermassive What is dark matter? astrophysical? BHs form?

B. J. Carr and S. Hawking, Black holes in the early Universe (1974) LIGO

PBH const straints All DM in LIGO/V LIGO/Virgo o PBHs allowed const straints microlensing �� � �� � Hawking �� � ��� > � evaporation � accretion � � ���� �� ����������� �� ���� ��� ��� �� - � ��� �� ���� ��� ���� �� - � ��� � �� - � � ��� ������ �� - � �� - � fraction of �� - � DM in PBHs �� - � �� - � �� - � � > �� � > � � �� - �� � �� - �� �� - �� �� - �� �� - �� �� - � �� � � � � / � �

<latexit sha1_base64="IV5XpljB6Lo93JVsf9mq3tgBnXI=">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</latexit> PBH fo PBH forma rmatio tion High-amplitude overdensities can collapse to BHs at horizon re-entry: M PBH ∼ M H ≈ 0 . 05( T/ GeV) − 2 � ( � ) 𝜏 ! ∝ the amplitude <latexit sha1_base64="SR3nJxaw1DwyCfQOwSQv9R92xOI=">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</latexit> ρ PBH Z of the curvature d δ P ( δ ) ∼ power spectrum ρ tot δ c � PBHs are formed from the tail of the probability distribution. � � > � �

Inflaton potential: � � ��� � ( � )/ � ��� �� - � �� - � formation of PBHs �� - � � �� - � �� - � � �� - � ��� � �� ��� � / � � ��� � � � ( � = � * )= � �� - � formation of GWs �� - � �� - � �� - � �� - � Scalar � �� ( � )/ � � � � �� - � �� - � perturbations � = � * �� - � source tensor �� - � perturbations at �� - � second order. �� - � �� - � CMB �� - � �� - � ��� � �� �� - � � �� � �� � �� � �� � � / � * � / ��� - �

PBH formation can be probed with future GW observatories: ��� �� [ � � * / � � ] �� �� � � - � - �� - �� - �� - �� ��� ���� �� - � ���� ���� �� - � ��� �� ���� ���� / ����� � �� - � ���� / ����� � �� - � ����� � �� - � � < � � � < �� amplitude of the �� - � curvature power ����� - ���� � spectrum �� - � ����� - ���� � � �� �� - � ������ �� - � �� - � � �� � �� � �� � �� � �� �� �� �� �� �� �� �� �� �� �� �� �� �� � * [ ��� - � ] [V. Vaskonen and H. Veermäe, in preparation]

NANOGrav 12.5 year data analysis found “strong evidence of a stochastic process, modeled as a power-law, with common amplitude and spectral slope across pulsars “ (2009.04496). �� - � �������� � � � �� ( � = ��� ��� ) �������� � � �� - � ���� ��������� �� - �� - ��� - ��� - ��� ��� ��� ��� �

Did NANOGrav see a signal from PBH formation? [Vaskonen & Veermäe, 2009.07832] NANOGrav signal is consistent with formation of a non-negligible abundance of PBHs. The signal can be from formation of SMBH seeds: � � ��� � � � �� � �� � �� � �� �

PBH binary y formation

• Two mechanisms for PBH binary formation: 1. close encounters of PBHs at late times, 2. tidally perturbed two body systems before matter-radiation equality. [Nakamura, Sasaki, Tanaka and Thorne, astro-ph/9708060.] • The second one dominates, and implies that less than 𝒫(1%) of DM can be in 𝒫(10𝑁 ⊙ ) PBHs. [Sasaki, Suyama, Tanaka, and Yokoyama, arXiv:1603.08338] [Raidal, Vaskonen, and Veermäe, arXiv:1707.01480] [Ali-Haïmoud, Kovetz, and Kamionkowski, arXiv:1709.06576] • Highly eccentric binaries ⟹ coalescence times may be significantly increased by interactions with surrounding PBHs ⟹ suppression of the merger rate. [Raidal, Spethmann, Vaskonen, and Veermäe, arXiv:1812.01930] [Vaskonen, and Veermäe, arXiv:1908.09752]

Initial st state PBHs are formed with uniform random spatial distribution and zero peculiar velocities. close pairs that decouple from the expansion much before matter radiation equality

<latexit sha1_base64="l5yEBSH01yTZSGQr2kL9oyxPhcQ=">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</latexit> Decoupling from exp xpansi sion Force acting on a BH pair: r /r 2 F /µ = r ¨ a/a M ˆ + (ˆ r · T · r )ˆ + ( r × ( T · r )) × (ˆ r /r ) r − |{z} | {z } | {z } | {z } Hubble flow self-gravity radial tidal forces tidal torque separation of the pair: angular momentum of the pair:

<latexit sha1_base64="gYrlVwqZDegBmL10rEZ7XH/u8W4=">ACG3icbVC7SgNBFJ31bXxFLW0Gg2ChYdcHphFC20EBaOBbBLuTmZ1dPbBzF0xLPsfNv6KjYUiNgoWVv6Kk0eh0QMXzpxzL3Pv8WIpNr2pzUwODQ8Mjo2npuYnJqeyc/OnekoUYyXWSQjVfFAcylCXkaBkldixSHwJD/3rvfb/vkNV1pE4Sm2Yl4L4CIUvmCARmrk1yEhG5T1fA0vUsLW1m1F3pPlUD6htZ6nIEelRfbxtX9a1GvmAX7Q7oX+L0SGF35+vtdrV0cNzIv7vNiCUBD5FJ0Lrq2DHWUlAomORZzk0j4FdwWvGhpCwHUt7dyW0SWjNKkfKVMh0o76cyKFQOtW4JnOAPBS93t8T+vmqBfqUijBPkIet+5CeSYkTbQdGmUJyhbBkCTAmzK2WXYGJBE2fOhOD0n/yXnK0Vnc2ifWLS2CNdjJEFskiWiUO2yC45JMekTBi5Iw/kiTxb9aj9WK9dlsHrN7MPkF6+MbCh+jLA=</latexit> Coalesc scence time The binary loses energy by emitting GWs: length of semimajor axis r 4 τ = 3 η M 3 j 7 a angular momentum 85 total mass symmetric mass ratio The PBH merger rate follows from 1. distribution of PBH masses 2. distribution of initial binary separations 𝑠 # 3. distribution of initial binary angular momenta 𝑘

Me Merge rger r ra rate Accounting for torques from all PBHs and other matter inhomogeneities: [Y. Ali-Haïmoud, E. D. Kovetz and M. Kamionkowski, 1709.06576.] �� � � � � = �� � � �� � � = ��� � = � �� � ��� - � �� - � �� � ���� �� � ��� Effect of other matter �� - � �� - � �� - � ��� � inhomogeneities. � ��� Assumes that all binaries survive until they merge. 𝜐 ∝ 𝑘 ! ⟹ even small increase in 𝑘 increases 𝜐 significantly.

Survi viva val of the binaries

N-body y si simulation 𝑂 − 2 randomly distributed bodies inside a sphere A central PBH pair that will form a binary with lifetime 𝜐 = 𝑢 " The expansion of the universe is accounted by including a Hubble 𝑠 = ̈ 𝑏𝑠/𝑏 . acceleration, ̈ The gravitational attraction of PBHs outside the sphere is approximated by a uniform mass density. We simulated 𝑂 = 70 bodies from 𝑏 = 0.001𝑏 #$ to 𝑏 = 3𝑏 #$ .

Resu sults from 𝒫 1000 simulatons: Green: binaries that survived until the end of the simulation. Yellow: binaries whose coalescence time at the end of the simulation is 𝜐 > 10𝑢 " . 1.2 1.2 0.5 f PBH = 0.01 f PBH = 0.1 f PBH = 1 1.0 1.0 0.4 N = 0.058 N = 0.46 N = 1.5 � = � 0 � = � 0 � = � 0 0.8 0.8 0.3 j d P / d j j d P / d j j d P / d j 0.6 0.6 0.2 0.4 0.4 0.1 0.2 0.2 0.0 0.0 0.0 0.001 0.01 0.1 1 0.001 0.01 0.1 1 0.01 0.1 1 j j j Many binaries get disrupted especially if 𝑔 %&' is large.