Heavy primordial black holes from strongly clustered light black holes

2025-05-06 0 0 694.03KB 6 页 10玖币

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Valerio De Luca,

1, ∗

Gabriele Franciolini,

2, 3, †

and Antonio Riotto

4, ‡

Center for Particle Cosmology, Department of Physics and Astronomy,

University of Pennsylvania 209 S. 33rd St., Philadelphia, PA 19104, USA

Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185, Roma, Italy

INFN, Sezione di Roma, Piazzale Aldo Moro 2, 00185, Roma, Italy

Département de Physique Théorique and Gravitational Wave Science Center (GWSC),

Université de Genève, CH-1211 Geneva, Switzerland CH-1211 Geneva, Switzerland

We show that heavy primordial black holes may originate from much lighter ones if the latter are

strongly clustered at the time of their formation. While this population is subject to the usual

constraints from late-time universe observations, its relation to the initial conditions is diﬀerent from

the standard scenario and provides a new mechanism to generate massive primordial black holes even

in the absence of eﬃcient accretion, opening new scenarios, e.g. for the generation of supermassive

black holes.

Introduction. Multiple detections of gravitational waves

(GWs) coming from black hole binary mergers [

–

]

have revived the interest in the physics of Primor-

dial Black Holes (PBHs) [

–

]. Indeed, some of the

LIGO/Virgo/KAGRA data may be of primordial origin

[

–

] and future GW experiments will shed light on the

possible existence of PBHs [17–22].

PBHs in the early universe are commonly born in the

radiation-dominated phase (see Ref. [

] for a review on

the various formation mechanisms). Given our ignorance

of the production mechanism giving rise to PBHs, if any,

we do not know if they are born randomly distributed or

with a strong correlation among them. In the standard

scenario where PBHs are generated by the collapse of large

overdensities created during inﬂation on small scales [

PBHs are Poisson distributed in space [

–

]. However,

large initial correlations are conceivable and not ruled out,

unless the PBH abundance in the universe (normalised to

the dark matter)

fPBH

is larger than

1) in the stellar

mass range [27].

In this Letter we propose a new mechanism to generate

heavy PBHs from light ones making use of the large initial

PBH clustering, a mechanism that we dub “clusteringen-

esis”. The idea is quite simple: if PBHs are born close to

each other, the strong gravitational interactions among

them may result in the collapse of this clump into a more

massive PBH, even in the radiation dominated phase

of the early universe. This mechanism provides a novel

way to increase the mass of light PBHs in the primordial

epochs, which is alternative to the more standard process

relying on baryonic mass accretion, which is eﬃcient only

for PBHs with mass larger than

(10)

M

[

] at lower

redshifts.

In the following we will describe the basics of this idea

and discuss some of its possible implications.

Collapse of large overdensities in the radiation-dominated

era. Independently from the formation mechanism and be-

ing discrete objects, the most generic initial two-point cor-

relator for the PBH density contrast

δPBH

δρPBH/ρPBH

acquires the form [23]

hδPBH(~r)δPBH(0)i=1

nPBH

δD(r) + ξPBH(r),(1)

in terms of their distance r, where

nPBH '30fPBH MPBH

M−1

kpc−3(2)

is the average PBH number density per comoving volume

for a monochromatic PBH population with mass MPBH .

We suppose that, at the time of formation, such two-

point correlator is dominated by the reduced correlation

function

ξPBH

(

)up to some comoving clustering scale

rcl

while on larger scales the Poisson shot noise, arising from

the discrete nature of PBHs, dominates. For simplicity

and for the sake of the argument, we assume an approx-

imately constant in space and large reduced two-point

correlation function up to rcl,

ξPBH(r)'(ξ01 for r∼

<rcl,

0 otherwise.(3)

We will be agnostic in the following regarding the origin

of such correlations. Let us just point out that large

clustering appears if the local properties of the PBH

overdensity ﬁeld are space dependent. This eﬀect might

either come from an actual ﬁeld diﬀerent from the over-

density ﬁeld, or from a long wavelength modulation of the

overdensity ﬁeld itself, resulting from a self-coupling of

long and short scales as happens, e.g., in local models of

non-Gaussianity [

]. Alternatively, large correlation may

arise if PBHs are formed by bubble collisions in ﬁrst-order

phase transitions [

–

] or for PBHs generated thanks

to long-range scalar forces [

]. These models can be used

to construct explicit realisations of the scenario proposed

in this work. Once rescaled to the total dark matter den-

sity

δρPBH/ρDM ≡

'ξ0fPBH

, the corresponding density

contrast is suppressed by the PBH abundance, which we

will assume to be tiny in the following in order to avoid

arXiv:2210.14171v2 [astro-ph.CO] 15 Apr 2023

PBH formation Clusteringenesis HPBH formation

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rcl

<latexit sha1_base64="shKe+3Ok1jn43qZ4RuHfAqehsLE=">AAAB/HicbVDLSsNAFL3xWesr2qWbYBHcWBJRdFl002UF+4A2lslk0g6dTMLMRAgh/oobF4q49UPc+TdO0yy09cCFwzn3zp17vJhRqWz721hZXVvf2KxsVbd3dvf2zYPDrowSgUkHRywSfQ9JwignHUUVI/1YEBR6jPS86e3M7z0SIWnE71UaEzdEY04DipHS0sisDYs3MkH8PGs9ZGdOno/Mut2wC1jLxClJHUq0R+bX0I9wEhKuMENSDhw7Vm6GhKKYkbw6TCSJEZ6iMRloylFIpJsVi3PrRCu+FURCF1dWof6eyFAoZRp6ujNEaiIXvZn4nzdIVHDtZpTHiSIczxcFCbNUZM2SsHwqCFYs1QRhQfVfLTxBAmGl86rqEJzFk5dJ97zhXDbsu4t686aMowJHcAyn4MAVNKEFbegAhhSe4RXejCfjxXg3PuatK0Y5U4M/MD5/ABvnlQ8=</latexit>

H1

<latexit sha1_base64="92/EFT8r0Q72C6svge2a00VIt7Y=">AAAB/3icbVBNS8NAEN34WetXVPDiZbEInkoiRT1J0UuPFewHtKFstpt26WYTdidiiT34V7x4UMSrf8Ob/8ZtmoO2Phh4vDfDzDw/FlyD43xbS8srq2vrhY3i5tb2zq69t9/UUaIoa9BIRKrtE80El6wBHARrx4qR0Bes5Y9upn7rninNI3kH45h5IRlIHnBKwEg9+7AL7AHSWv26huMoTkSmT3p2ySk7GfAicXNSQjnqPfur249oEjIJVBCtO64Tg5cSBZwKNil2E81iQkdkwDqGShIy7aXZ/RN8YpQ+DiJlSgLO1N8TKQm1Hoe+6QwJDPW8NxX/8zoJBJdeymWcAJN0tihIBIYIT8PAfa4YBTE2hFDFza2YDokiFExkRROCO//yImmeld3zcuW2Uqpe5XEU0BE6RqfIRReoimqojhqIokf0jF7Rm/VkvVjv1sesdcnKZw7QH1ifPyfvljI=</latexit>

HPBH population

<latexit sha1_base64="cStL19mA0HAJJmSH9IDZ4N+IM0A=">AAAB+XicbVBNS8NAEN3Ur1q/oh69LBbBU0lE1JMUvHisYD+gCWGz3bRLN5uwOymG0H/ixYMiXv0n3vw3btsctPXBwOO9GWbmhangGhzn26qsrW9sblW3azu7e/sH9uFRRyeZoqxNE5GoXkg0E1yyNnAQrJcqRuJQsG44vpv53QlTmifyEfKU+TEZSh5xSsBIgW2rwAP2BIUHXOY4nAZ23Wk4c+BV4pakjkq0AvvLGyQ0i5kEKojWfddJwS+IAk4Fm9a8TLOU0DEZsr6hksRM+8X88ik+M8oAR4kyJQHP1d8TBYm1zuPQdMYERnrZm4n/ef0Mohu/4DLNgEm6WBRlAkOCZzHgAVeMgsgNIVRxcyumI6IIBRNWzYTgLr+8SjoXDfeqcflwWW/elnFU0Qk6RefIRdeoie5RC7URRRP0jF7Rm1VYL9a79bForVjlzDH6A+vzB/L2k9w=</latexit>

FIG. 1. Pictorial representation of the clusteringenesis mechanism. The red line denotes the growing cosmological horizon

H−1

bounds coming from CMB anisotropies on isocurvature

perturbations [34–36].

The key point is the subsequent evolution of such large

density PBH clumps during the radiation phase. The com-

mon lore is that they do not grow till the matter-radiation

equality epoch is reached, because of the counteraction

of the radiation pressure [

]. However, this is true only

at the linear level. In the full non-linear theory, the self

gravity of these large non-linear ﬂuctuations may become

important before the equality time, and consequently give

rise to their collapse and production of very dense clus-

ters, after they decouple from the general expansion and

virialize [38].

Adopting the spherical collapse model, one can write

down the evolution equation for the parameter

, de-

scribing the deviation of the motion of each collapsing

shell from the uniform Hubble ﬂow of the background

Friedmann universe [38]

x(1+x)d2R

dx2+1 + 3

2xdR

dx+1

21+Φ

R2−R= 0,(4)

as a function of the rescaled scale factor

a/aeq

, in

terms of the one at the epoch of matter-radiation equality

aeq

. This equation assumes that the statistical distribu-

tion of the initial overdensities (or clumps) is determined

by the correlation function

ξPBH

; see the appendices of

Ref. [

] for details on the relation between the proﬁle of

initial clumps and the correlation function. In particular,

at scales smaller than the clump separation, the density

proﬁle of the clusters is directly related to the correla-

tion function and its evolution depends on its amplitude

ξ0[39].

An analytic approximation for the solution can be ob-

tained with a power expansion in the rescaled scale factor

x, giving [38]

R'1−Φx

2−Φ2x2

8+O(x3),(5)

from which one can show that the decoupling occurs ap-

proximately at

acl

aeq/

Φ. The corresponding timescale

is approximately given by the free-fall time [40]

τcl =r3π

32Gρcl

'1.2·104Φ−2C

200−1/2

yr,(6)

expressed in terms of the average density of such clusters

after relaxation

ρcl

Cρrad

(

acl

) =

Cρeq

[

], where

)is a constant that describes the overdensity

amplitude. Their mass and physical radius are given

by [27]

Mcl '1.3·102Φrcl

kpc3

M,

rb'4·10−5Φ−1C

200−1/3rcl

kpckpc.(7)

Notice that the mass of the cluster

Mcl

does not depend on

the individual PBH mass

MPBH

because of two competing

eﬀects that cancel out. Indeed, for a given correlation

function, a ﬁxed PBH abundance may either result into

heavier PBHs with a smaller number density, or into

lighter and more abundant ones.

Formation of heavy PBHs by initial clustering. The key

point of this Letter is that the PBH clusters may collapse

into PBHs of mass

≈Mcl

if the ﬁnal halo is more compact

than a BH, giving rise to a population of heavy PBHs.

These objects are initially Poisson distributed on scales

larger than

rcl

, as the perturbation of their number density

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HeavyprimordialblackholesfromstronglyclusteredlightblackholesValerioDeLuca,1,GabrieleFranciolini,2,3,yandAntonioRiotto4,z1CenterforParticleCosmology,DepartmentofPhysicsandAstronomy,UniversityofPennsylvania209S.33rdSt.,Philadelphia,PA19104,USA2DipartimentodiFisica,SapienzaUniversitàdiRoma,PiazzaleAl...

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Heavy primordial black holes from strongly clustered light black holes

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