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

• duction

Motiva vations s to st study y PBHs

What is dark matter? Are LIGO/Virgo BHs astrophysical? How did supermassive BHs form?

LIGO

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

fraction of DM in PBHs

• >

> >

• /
• microlensing

accretion Hawking evaporation All DM in PBHs allowed

PBH const straints

LIGO/V LIGO/Virgo

• const

straints

PBH fo PBH forma rmatio tion

• >
• ()

PBHs are formed from the tail of the probability distribution.

High-amplitude overdensities can collapse to BHs at horizon re-entry:

MPBH ∼ MH ≈ 0.05(T/GeV)−2

ρtot ∼ Z

δc

dδP(δ)

𝜏! ∝ the amplitude

• f the curvature

power spectrum

=* (=*)=

• /-
• formation of PBHs

formation of GWs

• /

()/

• /*

()/

CMB

Scalar perturbations source tensor perturbations at second order.

• Inflaton potential:

• /

/

• <

<

• *[-]
• [*/]

amplitude of the curvature power spectrum

PBH formation can be probed with future GW observatories:

[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?

NANOGrav signal is consistent with formation of a non-negligible abundance of PBHs.

• The signal can be from formation of SMBH

seeds:

[Vaskonen & Veermäe, 2009.07832]

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.
• The second one dominates, and implies that less than 𝒫(1%) of DM can be in

𝒫(10𝑁⊙) PBHs.

[Nakamura, Sasaki, Tanaka and Thorne, astro-ph/9708060.] [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

Decoupling from exp xpansi sion

F/µ = r¨ a/a |{z} Hubble flow − Mˆ r/r2 | {z } self-gravity + (ˆ r · T · r)ˆ r | {z } radial tidal forces + (r × (T · r)) | {z } tidal torque ×(ˆ r/r)

Force acting on a BH pair: separation of the pair: angular momentum of the pair:

Coalesc scence time

The binary loses energy by emitting GWs:

τ = 3 85 r4

a

ηM 3 j7

length of semimajor axis angular momentum 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 acceleration, ̈ 𝑠 = ̈ 𝑏𝑠/𝑏.

The gravitational attraction of PBHs

• utside the sphere is approximated by

a uniform mass density.

We simulated 𝑂 = 70 bodies from 𝑏 = 0.001𝑏#$ to 𝑏 = 3𝑏#$.

Resu sults

1 0.1 0.01 0.001 0.0 0.2 0.4 0.6 0.8 1.0 1.2 j j dP/dj

=0

fPBH = 0.01 N = 0.058 1 0.1 0.01 0.0 0.1 0.2 0.3 0.4 0.5 j j dP/dj

=0

fPBH = 1 N = 1.5 1 0.1 0.01 0.001 0.0 0.2 0.4 0.6 0.8 1.0 1.2 j j dP/dj

=0

fPBH = 0.1 N = 0.46

Many binaries get disrupted especially if 𝑔

%&' is large.

Green: binaries that survived until the end of the simulation. Yellow: binaries whose coalescence time at the end of the simulation is 𝜐 > 10𝑢". from 𝒫 1000 simulatons:

Disr sruption mechanism sms

• 1. A three-body system is formed instead of a binary.
• 2. The binary becomes a part of a dense halo.

Disr sruption by y a third BH

y

Require that the PBH closest to the binary so far that it doesn’t fall into the binary. ⟹ bound on the expected number

• f PBHs inside a sphere of radius 𝑧:

⟹ suppression factor for the merger rate:

R ∝ e− ¯

N(y)

¯ N(y) ' M hmi fPBH fPBH + σM

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 0.0 0.5 1.0 1.5 xNN/aeq/pc dP/dxNN N =0.058 fPBH = 0.01 0.15 0.20 0.25 0.30 2 4 6 8 10 xNN/aeq/pc dP/dxNN N =1.5 fPBH = 1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 xNN/aeq/pc dP/dxNN N =0.46 fPBH = 0.1

Distribution of the distance to the BH nearest to the binary:

Analytical estimate for the bound on $ 𝑂 works well. Significantly higher probability for getting disrupted.

Disr sruption in a sm small halo

Halos with 𝑂 < 𝑂((𝑨) have become unstable before redshift 𝑨:

• These halos experience core collapse where the density increases significantly

⟹ binary-PBH encounters become very likely.

To estimate maximal disruption factor, assume that all binaries in small halos are disrupted. Survival probability:

Pnp ' 1

Nc(z)

X

N=3

¯ pN(zc) X

N 0>Nc(z)

2 4

Nc(z)

X

N=3

˜ pN(zc) 3 5 ¯ pN 0(zc)

0.15 0.20 0.25 0.30 2 4 6 8 10 xNN/aeq/pc dP/dxNN N =1.5 fPBH = 1

𝑨 ≈ 1000:

pN(z) ∝ N −1/2e−N/N ∗(z)

Probability that the binary belongs to a halo of 𝑂 < 𝑂! BHs. Probability that the binary belongs to a subhalo of 𝑂 < 𝑂! BHs inside a halo of 𝑂" > 𝑂! BHs.

• =

= =

• Me

Merge rger r ra rate

disruption by a third PBH and small halos disruption by a third PBH no disruption

Still above the LIGO/Virgo rate for 𝑔

&'( = 1.

• =

= =

• Merger rate of disr

srupted binaries

Disrupted binaries that initially had a very short lifetime can contribute to the present merger rate.

Const straints s from LIGO/Virgo

Const straint from obse serve ved eve vent rate

• =
• /
• 2σ bound assuming

that none of the

• bserved events were

PBH mergers (𝑂 < 3).

N = T Z dR(m1, m2, z)dVc(z) θ(ρ(m1, m2, z) − ρc)

comoving volume signal-to- noise ratio merger rate

• bservation

time threshold for

• bservation

During O1 and O2 LIGO/Virgo

• bserved 𝑂 = 10 events in

𝒰 = 165 days.

Fi Fit t assu ssuming that LIGO/Virgo obse serve ved PBHs

• =
• /
• PBHs can explain these events

with a narrow mass function centered at 𝑁 = 20𝑁⊙ with 𝑔

&'( = 0.003.

Sensi sitivi vities s of future GW exp xperiments

• /
• /
• Sensitivity to individual events:

Non-observation of SGWB:

Separating PBBHs s from ABBHs

• /
• /

Astrophysical and primordial BH merger rates are very different as a function of redshift: e.g. ET can separate astrophysical and primordial origin of the binaries.

• ()/()

/

BH sp spins

Accretion changes the PBH mass distribution, abundance, merger rate, and spins:

[V. De Luca, G. Franciolini, P. Pani, and A. Riotto, arXiv: 2003.02778, 2003.12589 and 2005.05641]

accretion

effective spin mass ratio

Su Summa mmary ry

• =

= =

• =
• /
• A population of PBH binaries is formed

before matter-radiation equality from large Poisson fluctuations.

• Many of these binaries are disrupted by a

nearby PBH or a small cluster of PBHs.

• Yet, the present merger rate for 𝑔

&'( = 1 is

well above the observed one ⟹ the strongest constraint on 𝑔

&'( in the mass

range around 10 − 100𝑁⊙.

• Future GW observatories determine the
• rigin of LIGO/Virgo binaries and probe

formation of PBHs.

Thank you!