merger rate distribution of primordial-black-hole binaries€¦ · 10-7 10-6 frequency [hz] gw...

Merger Rate Distribution of Primordial-Black-HoleBinaries

Zu-Cheng ChenDone with Fan Huang and Prof. Qing-Guo HuangBased on arXiv:1801.10327 and a work in progress

Institute of Theoretical Physics

May 25, 2018

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Introduction Merger Rate Distribution of PBH Binaries Stochastic Gravitational-Wave Background

Outline

1 Introduction

2 Merger Rate Distribution of PBH Binaries

3 Stochastic Gravitational-Wave Background

Zu-Cheng Chen Merger Rate Distribution of PBH Binaries May 25, 2018

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https://www.ligo.caltech.edu


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What we know after LIGO/Virgo

There are many BH binaries.

They do have mass distribution.

They can merge within Hubble time,

The merger rate is 12 ∼ 213Gpc−1yr−1. PRL 118, 221101 (2017)

What we don’t know after LIGO/Virgo

Where do these BHs come from?

What is the mechanism of the binary formation?


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Maybe, primordial BHs!

All PBHs with mass 30M⊙ and the torque from the nearestthird BH. PRL 117, 061101 (2016)

General mass function, but the torque from the nearest thirdBH. PRD 96, 123523 (2017)

A monochromatic mass function, and the torques from allother BHs. PRD 96, 123523 (2017)


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Outline

1 Introduction




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Merger Rate Distribution of PBH Binaries

PBHs have a general mass function.

PBHs distributed randomly in the early Universe.

Torques from all other BHs and linear density perturbations.


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Merger Rate Density

R(t,mi,mj) ≈ 3.9 · 106 ×(

t

t0

)− 3437

f2(f2 + σ2eq)

− 2174

×min

(P (mi)

mi,P (mj)

mj

)(P (mi)

mi+

P (mj)

mj

)×(mimj)

337 (mi +mj)

3637

The fraction of PBHs in DM is fpbh ≡ Ωpbh/ΩDM ≈ f/0.85.

P (m) is the mass function (PDF)∫ ∞

0P (m)dm = 1.

σeq is the variance of density perturbations of the rest of DM.


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Power-law: α = 1.5, M = 1M⊙

P (m) ≈ α− 1

M

(m

M

)−α

Lognormal: σ = 1, mc = 40M⊙

P (m) =1√

2πσme−

log2(m/mc)

2σ2

Power-law

Lognormal

20 40 60 80

0.01

0.02

0.03

0.04

m [M⊙]

PD

F[M

⊙-

1]


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Constrains on fpbh: 5M⊙ ≤ m1,m2 & m1 +m2 ≤ 100M⊙

Power-law

Lognormal

0.001 0.010 0.100 10.01

1

100

104

fpbh

Ev

en

tra

te[G

pc-

3y

r-1]

Power-law: 0.0036 ≲ fpbh ≲ 0.021

Lognormal: 0.0021 ≲ fpbh ≲ 0.011

Consistent with other observations.Zu-Cheng Chen Merger Rate Distribution of PBH Binaries May 25, 2018

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1D merger rate distribution

RH(t0,mH) =

∫ mH

mmin

R(t0,m,mH)dm

Power-law

Lognormal

5 10 50 10010-4

0.001

0.010

0.100

1

10

mH [M⊙]

Ev

en

tra

te[G

pc-

3y

r-1]


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2D merger rate distribution

GW150914

GW151226

LVT151012

GW170104

GW170608

GW170814

6 8 11 15 19 26 34 45 60 80

80

60

45

34

26

19

15

11

8

6

m1 [M⊙]

m2[M

⊙]

Power-law

1

2

3

4

5

6

GW150914

GW151226

LVT151012

GW170104

GW170608

GW170814

6 8 11 15 19 26 34 45 60 80

80

60

45

34

26

19

15

11

8

6

m1 [M⊙]

m2[M

⊙]

Lognormal

1

2

3

4

5

6

7

Merger rate distributions are quite sensitive to P (m).

P (m) could be reconstructed from merger rate distributions.

Understand the origin of BHs detected by LIGO/Virgo.


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Outline

1 Introduction




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Events observed by LIGO/Virgo

Events Primary mass Secondary mass Source Redshift

GW150914 36.2+5.2−3.8M⊙ 29.1+3.7

−4.4M⊙ 0.09+0.03−0.04

LVT151012 23+18−6 M⊙ 13+4

−5M⊙ 0.20+0.09−0.09

GW151226 14.2+8.3−3.7M⊙ 7.5+2.3

−2.3M⊙ 0.09+0.03−0.04

GW170104 31.2+8.4−6.0M⊙ 19.4+5.3

−5.9M⊙ 0.18+0.08−0.07

GW170608 12+7−2M⊙ 7+2

−2M⊙ 0.07+0.03−0.03

GW170814 30.5+5.7−3.0M⊙ 25.3+2.8

−4.2M⊙ 0.11+0.03−0.04


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Constraints for lognormal PDF

P (m) =1√

2πσmexp

(− log2(m/mc)

2σ2

)with (mc, σ) = (20.82M⊙, 0.58)

-1 0 1 2 30.0

0.5

1.0

1.5

2.0

2.5

log10(mc/M⊙)

σ


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Fractional energy density ΩGW(ν)

The energy-density spectrum of a GW background is characterizedby the dimensionless quantity

ΩGW(ν) =ν

ρc

dρGW

dν,

which represents the contribution of GW to the critical energydensity of the Universe, ρc = 3H2

0/(8πG), and can be expressed as

ΩGW(ν) =ν

ρc

∫dz dmi dmj

R(z,mi,mj)

(1 + z)H(z)

dEGW

dνs

∣∣∣∣νs=(1+z)ν

.


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O2

O3

Design

LISA

10-5 10-4 10-3 10-2 10-1 100 101 102 103 10410-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

Frequency [Hz]

ΩG

W

Several times larger than that from astrophysical BBHs as inPRL 120, 091101 (2018)

Can be detected by LIGO/Virgo and LISA.


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Signal-to-Noise Ratio (SNR) for LISA

1σ

3σ

5σ

0.5 1 5 10 50 100 5000.1

0.5

1

5

10

50

100

Observation time (hours)

SN

R


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Conclusions and Discussions

We derive the merger rate distribution of PBH binaries with ageneral mass function by taking into account the torques byall primordial black holes and linear density perturbations.

It will help us to settle down the formation mechanism ofBBHs observed by LIGO/Virgo.

The SGWB can be detected by LIGO/Virgo and LISA if BBHsare of primordial orgin.


merger rate distribution of primordial-black-hole binaries€¦ · 10-7 10-6 frequency [hz] gw...

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