Prepared for submission to JCAP

Solving puzzles of GW150914 byprimordial black holes
S. Blinnikov,a,b,c,d,1 A. Dolgov,b,a N.K. Poraykoe,a and K.Postnovc,a,f
a ITEP, Bol. Cheremushkinsaya ul., 25, 117218 Moscow, Russia
b Novosibirsk State University, Novosibirsk, 630090, Russia
c Sternberg Astronomical Institute, Moscow M.V. Lomonosov State University,

Universitetskij pr., 13, Moscow 119234, Russia
d Kavli IPMU (WPI), Tokyo University, Kashiwa, Chiba, Japane Max-Planck-Institut für Radioastronomie, Bonn, Germanyf Faculty of Physics, Moscow M. V. Lomonosov State University, 119991 Moscow, Russia

E-mail: Sergei.Blinnikov@itep.ru, dolgov@fe.infn.it,
nporayko@mpifr-bonn.mpg.de, kpostnov@gmail.com

Abstract. The black hole binary properties inferred from the LIGO gravitational wave signal
GW150914 posed several serious problems. The high masses and low effective spin of blackhole binary can be explained if they are primordial (PBH) rather than the products of thestellar binary evolution. Such PBH properties are postulated ad hoc but not derived fromfundamental theory. We show that the necessary features of PBHs naturally follow from theslightly modified Affleck-Dine (AD) mechanism of baryogenesis. The log-normal distributionof PBHs, predicted within the AD paradigm, is adjusted to provide an abundant populationof low-spin stellar mass black holes. The same distribution gives a sufficient number of quickly
growing seeds of supermassive black holes observed at high redshifts and may comprise anappreciable fraction of Dark Matter which does not contradict any existing observational
limits. Testable predictions of this scenario are discussed.

1

Corresponding author.

Contents
1 Introduction

1

2 The model: Affleck-Dine scenario

2

3 An upper limit on ADBD PBH.

54 Black hole growth.

6

5 Massive PBH as galaxy seeds.

7

6 LIGO GW150914 as ADBD PBH event.

7

7 Discussion and conclusions.

101Introduction

The recent discovery of gravitational waves (GWs) by LIGO [1] not only opened a new
window into high redshift universe but simultaneously presented several problems. The firstobserved signal GW150914 nicely fits the hypothesis of the coalescence of two heavy black+4
holes (BHs) which form a binary system with masses M1 = 36+5
−4 M and M2 = 29−4 M .
While the individual spins of coalescing BH components are poorly constrained, the effective
spin χeff turns out to be close to zero, suggesting either low spins of the components or theiropposite direction, which is difficult to explain by the standard evolution from a massive
binary system. The parameter χeff has been determined to be within [0.19, 0.17] from its
effect on the inspiral rate of the binary [2]. The final BH mass is M = 62+4
−4 M and its spin
+0.05
is substantial, a = 0.65−0.07 , as expected from the orbital angular momentum of the colliding
BHs.
The first problem with GW150914 is a possible origin of so heavy BHs. One of the
proposed mechanisms involves highly rotating massive (from 50M up to 100M ) stars inclose binary systems [3–5]. The rapid rotation of the stars, achieved due to strong tidal
interaction, provides effective mixing of nuclear burning products, thus avoiding significant
post-main-sequence expansion and subsequent mass exchange between the components. To
form so heavy BHs within this mechanism, the progenitors should have low metal abundance
to avoid heavy mass loss during the evolution. Unfortunately, due to poor observational
statistics, there is no strong observational confirmation of the rates of binary systems, undergoing such chemically homogeneous evolution [3]. Moreover, the LIGO collaboration [2]has shown that if both spins need to be aligned with orbital momentum, the individual spinswith 90% probability have quite low values a < 0.3. The second reliable LIGO detection,
GW151226, turned out to be closer to the standard binary BH system [6], which can be
explained by classical binary system evolution.
The misaligned BH spins and low values of effective inspiral spin parameter χeff detected
in GW150914 may strongly constrain astrophysical formation from close binary systems [7].
However, the dynamical formation of double massive BHs with misaligned spins in dense
stellar clusters is still possible [8, 9].

–1–

0.003
U(χ)

0.002

Ф>>Ф1

Im χ



0.001

0

-0.001Ф=Ф1-0.002

χ-0.003-0.001-0.000500.0005

0.001

 χ
Re

Figure 1. Left: behavior of the effective potential of χ for different values of the inflaton field Φ. The
upper blue curve corresponds to Φ  Φ1 which gradually decreases to Φ = Φ1 , the red curve. Thenthe potential returns back to an almost initial shape, as Φ → 0. The evolution of χ in such a potential
is similar to the motion of a point-like particle (shown as the colored ball) in Newtonian mechanics.
First, due to quantum initial fluctuations, χ left the unstable extremum of the potential at χ = 0 and“tried” to keep pace with the moving potential minimum and later starts oscillating around it withdecreasing amplitude. The decrease of the oscillation amplitude is due to the cosmological expansion.
In mechanical analogy, the effect of the expansion is equivalent to the liquid friction term, 3H χ̇. When
Φ < Φ1 , the potential recovers its original form with the minimum at χ = 0, and χ ultimately returns
to zero, but before that it could give rise to a large baryon asymmetry [20]. Right: The evolutionof χ in the complex [Reχ, Imχ]-plane [20]. One can see that χ “rotates” in this plane with a large
angular momentum, which exactly corresponds to the baryonic number density of χ. Later χ decays
into quarks and other particles creating a large cosmological baryon asymmetry.

Mechanisms of BH formation from PopIII stars and subsequent formation of BH binaries
are analyzed in [10]. The scenario proposed in [11] is found to be the most appropriate.
However, the contribution of PopIII stars to the formation of BH binaries with masses ∼30 + 30M can be negligible, contradicting the population synthesis results [12, 13].
A binary system of massive BHs like LIGO GW150914 could be formed from primordial
black holes (PBH) [14–16]. Here we propose a specific model of PBH formation which bothnaturally reproduce the extreme properties of GW150914, the rate of binary BH merging
events as inferred from the first LIGO science run 9-240 Gpc−3 yr−1 [17], and provide seeds
for early supermassive BH formation in galaxies. The model is based on the modified AffleckDine [18] scenario for baryogenesis. It was suggested in 1994 [19], discussed in more details
in ref. [20], applied to an explanation of the early supermassive BH (SMBH) observations
at high redshifts [21], and to a prediction and study of the properties of possible antimatterstellar-like objects in the Galaxy [22, 23].

2

The model: Affleck-Dine scenario

Our model of early formation of heavy primordial black holes is based on the supersymmetricscenario of baryogenesis (Affleck and Dine mechanism) [18] slightly modified by an additionof general renormalizable coupling of the scalar baryon field χ to the inflaton field Φ, see–2–

figure 1. The potential of the interacting fields Φ and χ are taken in the form:
U (χ, Φ) = UΦ (Φ) + Uχ (χ) + λ1 (Φ − Φ1 )2 |χ|2 ,(2.1)

where the first term UΦ (Φ) is the potential of the inflaton field which ensures sufficient
inflation, Uχ (χ) is the potential of the scalar field with non-zero baryonic number. According
to the suggestion of ref. [18], this potential possesses flat directions along which the χ could
travel away from the origin accumulating a large baryonic number density. The last term ineq. (2.1), introduced in ref. [19], closes the flat directions when the inflaton field Φ is awayfrom some constant value Φ1 . The latter is chosen such that Φ passes through Φ1 during
inflation, close to its end when the remaining number of e- foldings was about 30-40. This
number depends upon the model can can be adjusted if necessary to comply with specificobservational requirements.
The potential (2.1) allows for an open window to the flat directions only during a
relatively short period of time. Correspondingly, the probability of the scalar baryon, χ, toreach a large value is small because the initial evolution of χ from the unstable minimumat χ = 0 is a slow stochastic one, similar to the Brownian motion. Most of χ would remain
small, and in these regions of the universe the baryon asymmetry would have its normal
value, β = 6 × 10−10 . However, there would be some small bubbles where the asymmetry
might be huge, even of order unity. With properly chosen parameters of the model these
bubbles would have astrophysically interesting sizes but occupy a relatively small fraction of
the whole volume of the universe. Despite that, due to large baryonic number, they could
make a noticeable contribution to the total cosmological energy density. The shape of themass distribution of these high-B bubbles is determined by inflation and thus it is virtuallymodel independent (except for the unknown values of the parameters) and has the log-normal
form:


dn
= µ2 exp −γ ln2 (M/M0 ) ,(2.2)
dM
where µ, γ, and M0 are some unknown, model dependent constant parameters. An interesting
feature of this distribution is that a power-of-mass, M q , factor instead of µ2 does not change
the log-normal shape after the redefinition of parameters.
Originally, the induced small scale fluctuations of the baryonic number lead predominantly to isocurvature fluctuations, but after the QCD phase transition at the temperature
T = 100 − 200 MeV, when the massless quarks turn into heavy nucleons, the isocurvaturefluctuations transformed into large density perturbations at astrophysically large but cosmologically small scales.
Depending upon the history of their formation, the high-B bubbles could be either
primordial black holes, compact stellar-like objects, or even rather dense primordial gas
clouds. In particular at the high mass tail of the distribution superheavy PBHs might becreated. Their emergence at redshifts of order 10 is highly mysterious and even their existencein each large galaxy is in serious tension with the conventional mechanisms of their formation.
An early formation of superheavy black holes which later serve as seeds for galaxy formation
looks more probable. For a review of the problems with rich evolved population in the early
universe see sec. 5 of ref. [24] or more recent review in the lecture [25]. The accumulated
data of the last few years suggest an early SMBH formation.
We can fit the parameters of the distribution (2.2) using the following three sets of data
and/or assumptions:

–3–

0.12

ρPBH (0.1−1 rM sun )/ρ DM

0.11
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.2

0.4

0.6

0.8

γ

1

1.2

1.4

1.6

Figure 2. Fraction of PBH density ρ(0.1 − 1)/ρDM in the mass range 0.1 − 1M
parameter γ. See Eq. (2.2).

as a function of

A The fraction of dark matter in MACHOs is f ≈ 0.1 for the mass range (0.1 − 1)M(see, e.g. [26]).
B All primordial black holes make the whole cosmological dark matter
C The number density of the primordial black holes with masses above 103 M
to the number density of the observed large galaxies.

is equal(A) The MACHO group has concluded that compact objects with masses
0.15M < M < 0.9M have a fraction f in the Galactic halo in the range 0.08 < f < 0.50
(95% CL). Therefore, based on the results of MACHO group, it is recognized that a population of compact lensing objects really exists [26]. There were some contradicting results
based on microlensing observations of Andromeda galaxy M31, see reviews in [23, 27]. A recent study of M31 [28] has discovered 10 new microlensing events and the authors conclude:“statistical studies and individual microlensing events point to a non-negligible MACHO population, though the fraction in the halo mass remains uncertain”. To fit this constraint, theparameter M0 and γ of the distribution 2.2 should be related as M0 = M (γ + 0.1γ 2 − 0.2γ 3 )(see figure 2).
(B) Condition B is not obligatory and can (must) be diminished in accordance with thebound on the BH dark matter. Condition C should be fulfilled if all large galaxies were seededby a superheavy PBH. The initially formed superheavy PBH might have much smaller masses(around 103 − 105 M ) which subsequently grow to 109 M because of an efficient accretionof matter and mergings. This mass enhancement factor is much stronger for heavier BH
and thus their mass distribution may be different from (2.2). However, we assume that theoriginal BHs were created with the distribution (2.2). Note that the accepted lower mass
limit M > 103 M is rather arbitrary and is used here only for the sake of simple parameter
estimates.
Conditions A,B, and C can be crudely satisfied if the parameters in the initial PBH
mass distribution (2.2) are γ = 0.5, Mmax = M , and µ = 10−43 Mpc−1 in the natural
system of units ~ = c = 1. Here the value of µ is fixed by the condition that all Dark Matter–4–

is described by objects with the distribution (2.2). The energy density of black holes with
masses above 10M in this case would be close to the energy density of the cosmologicaldark matter.
Let us note that the B-bubbles are formed predominantly spherically symmetric becausesuch configurations minimizes the bubble energy. Their angular momentum should be zero
because they are formed as a result of phase transition in cosmological matter with vanishingangular momentum due to absence of the cosmological vorticity perturbations. This is in
striking contrast to BHs formed through the matter accretion, when the angular momentum
must be substantial.

3

An upper limit on ADBD PBH.

Let us discuss what could be the maximum mass of PBH in the AD scenario. The massof the bubbles with high baryonic number density, or High B Bubbles (HBB), after theirformation at the inflationary stage was equal to:
Minfl =

4π 3
ρl ,
3

(3.1)

where l ∼ (1/H) exp(H(t − tin )), H is the Hubble parameter during inflation, tin is themoment when the window to the flat direction became open, i.e. the inflaton filed Φ started
to approach Φ1 from above.
The cosmological energy density at this stage wasρ=3H 2 m2P l= const .
8π

(3.2)

Thus we obtain for the maximum value of the HBB mass at the end of inflation at t = te :
(max)

Minfl

=

m2P l 3H(te −t1 )
e
.
2H

(3.3)

In the instant heating approximation, when the universe was heated up to temperature Th ,one findsπ2ρ=g∗ Th4 ,(3.4)
30
where g∗ ∼ 100 is the number of particle species in thermal equilibrium plasma after the
inflaton decay.
Taking all factors together, we find for the maximum value of the HBB mass at the endof inflation:1/2 3mP l 3H(te −t1 )90(max)
Minfl =e.
(3.5)
332π g∗
Th2
After the end of inflation the HBBs were filled by relativistic matter and thus their masses
dropped down as T /Th because the density of relativistic matter decreased as 1/a4 , while
the HBB size rose as a, i.e. its volume grew up as a3 , where a is the cosmological scale
factor. After the QCD phase transition at TM D ∼ 100 MeV the matter inside HBBs turns
into nonrelativistic one, and the total mass of HBB becomes constant. A reasonable value of
Th is about 1014 GeV, but the exact magnitude is of minor importance because the necessary
duration of inflation to create HBB with the present day value of the mass Mtoday depends–5–only logarithmically on the temperature. So we find for the maximum value of the HBB mass
today:
1/2 3mP l TMD 3H(te −t1 )90
Mtoday =
e
.
(3.6)
3
32π g∗
Th2 ThTherefore, for the duration of inflation after the HBB formation which is necessary to create(max)
PBH with the mass MBH we find:
3H(te −t1 )e37+5−10+15

= 10



Th
14
10 GeV

3

(max)

MBH
104 M

100 MeV
.
TMD

(3.7)

Thus, finally we need H(te − t1 ) = 36 to create a PBH distribution with the mass cut-off of104 M , if all other factors are taken to be unity. Such a duration of inflation after Φ = Φ1
looks very reasonable. In these estimates the Planck mass was taken to be mP l = 10−5 g =1019 GeV.
In principle, we can turn equation (3.6) another way around to find the high mass cut-off
for fixed duration of inflation after the HBB formation.

4Black hole growth.

The very first estimations of the accretion growth of PBHs in radiation-dominated epoch weredone by Zel’dovich and Novikov [29]. Using non-relativistic Bondi-Hoyle accretion analysis
the authors have shown that the masses of the formed at t = t0 BHs change as
M=

M0
,
KM0
1 − t0 (1 − tt0 )

(4.1)

√
where K = 9 3G/2c3 . According to this formula, a PBH grows at the same rate as the
Universe if its initial size is comparable to the cosmological horizon, and at the end ofradiation-dominated epoch the predicted masses of the resultant BHs would become unrealistically high. Zel’dovich & Novikov method was generalized for the relativistic case in[30], [31]. However, while accounting for cosmological decrease of the density of the accreted
substance, the previous simplified analyses ignored the influence of cosmological expansion
on the dynamics of accretion itself. This effect can be significant in the case of massive PBHs
in the early Universe when the BHs’ radius can approach the Universe horizon. In our case,the mass of PBH is
M0 ≈ 105 M t(4.2)
for t in seconds, that is the Schwarzschild radius of PBHt
rg ' ct = 3 × 1010 cm
s

(4.3)

is comparable to the size of horizon rH ' 2ct = 6 × 1010 (t/s) cm. Carr and Hawking [32]were the first who had drawn attention to downsides of estimations based on the BondiHoyle formula. Their results were analytically confirmed in [33], [34]. According to CarrHawking mechanism of accretion, the growth of very massive PBHs in Zel’dovich & Novikov
analysis is significantly overestimated [35]. However, Lora-Clavijo et al [36] numericallyshowed substantial growth of relatively smalM0 = M (γ + 0.1γ 2 − 0.2γ 3 )l PBHs (rg  rH )during the leptonic era (up to 100 sec).

–6–

5

Massive PBH as galaxy seeds.

The state-of-the-art SMBH growth paradigm, see e.g. resent EAGLE results [37], assumes adelta-like initial BH seed masses of about 105 M , which formed in DM halos at z ∼ 15 andrapidly grow through gas accretion and host galaxy mergings by z ∼ 5. In the DM halos lessmassive than ∼ 1012 M , virtually no growth of the seed BH mass is observed, while at larger
halo masses the BH mass increases rapidly until a self-regulating BH mass – DM halo mass
relation (MBH − M200 ) is established. The seed SMBH masses increase up to 108 M , after
which their growth is linearly proportional to the surrounding DM halo mass. Importantly,
the shape of the SMBH mass function almost does not change after z ∼ 5, exhibiting only
the normalization increase by an order of magnitude by z = 0. These finding are independent
on the assumed seed BH mass for Mseed & 104 M .
However, if there is a population of primordial SMBHs, they can serve as seeds forgalaxy formation. Guided by analogy with numerical simulations discussed above, we canassume that
1) seed BH masses . 105 M do not substantially evolve, i.e. in the low mass interval
the observed SMBH mass function has the primordial shape;2) seed BH masses in the range 105 − 108 M rapidly grow up to ∼ 108 M ;3) seed BH masses exceeding 108 M at z = 0 scale linearly with DM halo mass;
4) the rapid SMBH growth is completed by z = 5 after which the SMBH mass function(for M > 106 ) linearly increases up to the present-day values.
Points (2) and (3) imply that the actual shape of the primordial SMBH mass function
is not very important for seed BH masses & 105 M , since these BHs rapidly grow to reachself-regulation in the surrounding DM halos.
Therefore, fitting the PBH mass function normalization in the 10 − 100 M range tothe BH+BH merging rate derived from the LIGO BH+BH detections (9 − 240 events a year
per cubic Gpc), we should only take care that the mass density of primordial SMBHs does
not contradict the existing SMBH mass function as inferred from observations of galaxies,
dN/(d log M dV ) ' 10−2 − 10−3 Mpc−3 (see figure 3).

6

LIGO GW150914 as ADBD PBH event.

Fixing the parameters µ, γ, and M0 in (7.1) we can satisfy all existing constraints, understandthe origin and properties of the merging BBHs, and explain other exciting puzzles. We
have found that the model parameters µ = (2 − 3) · 10−43 Mpc−1 , γ = 0.4 − 1.0, and M0 =M (γ + 0.1γ 2 − 0.2γ 3 ) are suitable to explain most of DM as ADBD BHs, do not contradict
all existing constraints on PBHs [38] and give sufficient amount of massive PBHs as seeds
for early galaxy formation (see figure 4). Note that CMB constraints from early accretion
onto PBH shown in the analogous plot [39] are model-dependent and should be treated withcaution.
Assuming the fraction of binaries among the PBH to be 10−3 , the present-day merging
rate of binary BPH can be estimated as the space density divided by the Hubble time
(1010 years) (see figure 5). Clearly, this can be easily made compatible with the binary
BH merging rate as inferred from LIGO observations (the purple rectangle in figure 5) byassuming the parameters of the initial ADBD PBH distribution which are consistent with
MACHO and SMBH constraints discussed above.

–7–

dn
−3
[ Mpc /d log (M / M sun )]dlog(M / M sun )log 10( M / M sun )Figure 3. Space density of PBH (per Mpc−3 per d log M ), to be compared to those derived fromobservations of SMBH in large galaxies (purple rectangle).

Binary systems from PBHs started forming already at the radiation-dominated epoch[41]. Assuming the population of PBHs with the same mass MBH , on the stage of matterradiation equality with radiation density ρeq the average distance between BHs can be defined
as:

1
MBH 3
x̄ =
,
(6.1)
f ρeq
where f is the fraction of DM in MACHOs. Two PBHs separated by the co-moving distancex form a binary system and decouple from cosmological expansion when the absolute value ofmean gravitational energy of the PBH binary becomes higher than the energy of the universe
within horizon:
Leq  x 3
a>
,
(6.2)
f
x̄
where a is the scale factor, and Leq ∼ (3c2 /8πGρeq )1/2 is the horizon scale at matter-radiation
equality [41]. Along with mean fluctuation field and angle dependence of the tidal force, theauthors of [42], have accounted for an important mechanism of 3-body interaction. The tidal
interactions with neighboring PBHs provide the almost born binary system with sufficientangular momentum to prevent the two components of the binary from merging even if PBHs
are assumed to be born with negligibly small relative velocities. All these effects should be
accurately taken into consideration, since ignoring them leads to a 50% uncertainty in the
PBH binary merging rate estimates [42].

–8–

HR

FL

MACHO
EROS

NS-C

ER II

DF

FIRAS

PBH

WMAP

Figure 4. Constraints on PBH fraction in DM, f = ρPBH /ρDM , where the PBH mass distribution is taken as ρPBH (M ) = M 2 dN/dM (see [38]). The existing constraints (extragalactic γ-rays
from evaporation (HR), femtolensing of γ-ray bursts (F), neutron-star capture constraints (NS-C),
MACHO, EROS, OGLE microlensing (MACHO, EROS) survival of star cluster in Eridanus II (E),dynamical friction on halo objects (DF), and accretion effects (WMAP, FIRAS)) are taken from [38]and reference therein. The PBH distribution is shown for ADBD parameters µ = 10−43 Mpc−1 ,M0 = γ + 0.1 × γ 2 − 0.2 × γ 3 with γ = 0.75 − 1.1 (red solid lines), and γ = 0.6 − 0.9 (blue solid lines).

These estimates can be easily generalized for the non-monochromatic mass spectrum of
PBHs presented in (2.2). For PBHs with the mass 30M the predicted event rate of GW
bursts [15] matches the one observed by LIGO only for f ' 7 × 10−4 − 7 × 10−3 . Taking into
account the tidal forces from adiabatic density perturbation of dark matter [43], the valid
range of f shifts to f ' 2 × 10−3 − 2 × 10−2 . These limits on f can be satisfied assuming
different ranges of parameter γ of log-normal distribution: γ ' 0.75 − 1.1 and γ ' 0.6 − 0.9
in the first and second case, respectively (see figures 3 and 5).
Binary PBHs can also form later in the matter-dominated epoch. Driven by dynamical
friction with collisionless particles, PBHs can form gravitationally bounded pair in the centersof DM halos. However, the effectiveness of this mechanism is poorly known and considerablymodel dependent [44].

–9–log (R [ Gpc−3 dlog ( M / M sun )−1 yr −1 ])γFigure 5. Merging rate of binary BH R (1/Gpc3 /yr) per logarithmic mass interval over the universe
age. The observed LIGO event rate is shown by the purple rectangle [40].

7Discussion and conclusions.

We have summarized the basic features of the HBB formation mechanism in figure 1. In this
scenario [19, 20] cosmologically small, but possibly astronomically large, bubbles with highbaryon density β could be created in the early universe, occupying a small fraction of theuniverse volume, while the rest of the universe has the standard β ≈ 6 · 10−10 .
The mass distribution of the high baryon density bubbles has the log-normal form:dN= µ2 exp [−γ ln2 (M/M0 )],
dM

(7.1)

where µ, γ, and M0 are constant parameters.1 The shape of the spectrum is practicallymodel-independent, it is determined by inflation. There is an intrinsic high-mass cut-off inthe spectrum set by duration of inflation that can be ∼ 104 M or even higher (see Section 4).
The constants in Eq. (7.1) are not predicted by the theory, they can be fixed from comparison
with observations. For example, the parameter µ can be determined by the normalization to
the total number of high-B bubbles (i.e. BD-stars and black holes) per comoving volume.
The formation of PBHs from the high-B bubbles proceeded in the following way. After
the QCD phase transition in the early universe at T = 100 - 200 MeV and t ∼ 10−5 − 10−4
seconds, quarks combined forming nonrelativistic baryons (protons and neutrons), thus large
density contrast arose between the bubble filled by heavy baryons and the relativistic plasma
in the bulk of the universe. When the bubble radius reenters the cosmological horizon, thedensity contrast could easily be large, δρ/ρ & 1, and thus the bubble would turn into a BH.
This mechanism is strongly different from those traditionally considered in the literature (e.g.
[45] and references therein).
1Though the log-normal mass distribution is quite common for the usual stars, the considered here mechanism is the only one known to us for creation of such mass distribution of primordial black holes.

– 10 –

The promising constraints on PBHs density in several tens of solar masses range canbe made with pulsar timing arrays through investigation of third-order Shapiro delay [46].
However, upper limit based on today’s timing sensitivity will be within Eridanus and Firas
estimates (figure 4).
Thus, the PBHs formed in the AD-BD scenario possess the following properties:
1. They have negligible angular momenta (vorticity perturbations are practically absent).
2. They have tiny peculiar velocities in the cosmological frame.
3. They could be easily captured, forming binaries, due to dynamical friction in the dense
early universe.
4. Their number density can be high enough to create an avalanche of GW observations,especially with the higher sensitivity of the advanced LIGO and new GW detectors.
5. At the high-mass end of the universal log-normal PBH spectrum, they can seed an early
SMBH formation in galaxies and even seed the galaxy formation.
Measurement of BH mass and spin distribution from LIGO GW observations can beused to check the prediction of the ADBD model presented here.
Note added. S.B. is grateful to H.Niikura, M.Takada for valuable discussions on PBHs.
Additional historical and modern references are found in papers [47–53].

Acknowledgments
A.D. acknowledges support of the Grant of President of Russian Federation for the leading
scientific Schools of Russian Federation, NSh-9022-2016.2. S.B., N.P., K.P. acknowledge support from RSF grant 14-12-00203 (analysis of PBH constraints from existing observations and
LIGO GW150914 event). The work of S.B. on manuscript was supported by World PremierInternational Research Center Initiative (WPI Initiative), MEXT, Japan. N.P. acknowledges
the support from IMPRS Bonn/Cologne and Bonn-Cologne Graduate School(BCGS).

References[1] B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley et al.,Observation of Gravitational Waves from a Binary Black Hole Merger, Physical Review Letters
116 (Feb., 2016) 061102, [1602.03837].
[2] B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley et al.,Properties of the Binary Black Hole Merger GW150914, Physical Review Letters 116 (June,2016) 241102, [1602.03840].
[3] I. Mandel and S. E. de Mink, Merging binary black holes formed through chemicallyhomogeneous evolution in short-period stellar binaries, MNRAS 458 (May, 2016) 2634–2647,[1601.00007].
[4] P. Marchant, N. Langer, P. Podsiadlowski, T. M. Tauris and T. J. Moriya, A new route
towards merging massive black holes, A&A 588 (Apr., 2016) A50, [1601.03718].
[5] S. E. de Mink and I. Mandel, The chemically homogeneous evolutionary channel for binary
black hole mergers: rates and properties of gravitational-wave events detectable by advanced
LIGO, MNRAS 460 (Aug., 2016) 3545–3553, [1603.02291].
[6] B. P. Abbott, R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley et al.,GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole
Coalescence, Physical Review Letters 116 (June, 2016) 241103, [1606.04855].

– 11 –

[7] D. Kushnir, M. Zaldarriaga, J. A. Kollmeier and R. Waldman, GW150914: spin-based
constraints on the merger time of the progenitor system, MNRAS 462 (Oct., 2016) 844–849,[1605.03839].
[8] S. F. Portegies Zwart and S. L. W. McMillan, Black Hole Mergers in the Universe, ApJL 528(Jan., 2000) L17–L20, [astro-ph/9910061].
[9] C. L. Rodriguez, C.-J. Haster, S. Chatterjee, V. Kalogera and F. A. Rasio, Dynamical
Formation of the GW150914 Binary Black Hole, ApJL 824 (June, 2016) L8, [1604.04254].
[10] I. Dvorkin, E. Vangioni, J. Silk, J.-P. Uzan and K. A. Olive, Metallicity-constrained merger
rates of binary black holes and the stochastic gravitational wave background, ArXiv e-prints(Apr., 2016) , [1604.04288].
[11] C. L. Fryer, K. Belczynski, G. Wiktorowicz, M. Dominik, V. Kalogera and D. E. Holz,
Compact Remnant Mass Function: Dependence on the Explosion Mechanism and Metallicity,
ApJ 749 (Apr., 2012) 91, [1110.1726].
[12] T. Kinugawa, K. Inayoshi, K. Hotokezaka, D. Nakauchi and T. Nakamura, Possible indirectconfirmation of the existence of Pop III massive stars by gravitational wave, MNRAS 442(Aug., 2014) 2963–2992, [1402.6672].
[13] T. Kinugawa, A. Miyamoto, N. Kanda and T. Nakamura, The detection rate of inspiral andquasi-normal modes of Population III binary black holes which can confirm or refute the generalrelativity in the strong gravity region, MNRAS 456 (Feb., 2016) 1093–1114, [1505.06962].
[14] S. Bird, I. Cholis, J. B. Muñoz, Y. Ali-Haı̈moud, M. Kamionkowski, E. D. Kovetz et al., Did
LIGO Detect Dark Matter?, Physical Review Letters 116 (May, 2016) 201301, [1603.00464].
[15] M. Sasaki, T. Suyama, T. Tanaka and S. Yokoyama, Primordial black hole scenario for thegravitational wave event GW150914, ArXiv e-prints (Mar., 2016) , [1603.08338].
[16] K. Hayasaki, K. Takahashi, Y. Sendouda and S. Nagataki, Rapid merger of binary primordial
black holes: An implication for GW150914, PASJ 68 (Aug., 2016) 66, [0909.1738].
[17] B. P. A. et al. (LIGO Scientific Collaboration and V. Collaboration), GW151226: Observationof Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence, LIGO Document
P1600088 116 (June, 2016) .
[18] I. Affleck and M. Dine, A new mechanism for baryogenesis., Nuclear Physics B 249 (1985)
361–380.
[19] A. Dolgov and J. Silk, Baryon isocurvature fluctuations at small scales and baryonic dark
matter, Phys. Rev. D 47 (May, 1993) 4244–4255.
[20] A. D. Dolgov, M. Kawasaki and N. Kevlishvili, Inhomogeneous baryogenesis, cosmic
antimatter, and dark matter, Nuclear Physics B 807 (Jan., 2009) 229–250, [0806.2986].
[21] A. D. Dolgov and S. I. Blinnikov, Stars and black holes from the very early universe, Phys. Rev.
D 89 (Jan., 2014) 021301, [1309.3395].
[22] C. Bambi and A. D. Dolgov, Antimatter in the Milky Way, Nuclear Physics B 784 (Nov.,
2007) 132–150, [arXiv:astro-ph/0702350].
[23] S. I. Blinnikov, A. D. Dolgov and K. A. Postnov, Antimatter and antistars in the Universe andin the Galaxy, Phys. Rev. D 92 (July, 2015) 023516, [1409.5736].
[24] A. D. Dolgov, Early astrophysical objects and cosmological antimatter, in Gravitation,
Astrophysics, and Cosmology (J.-P. Hsu and et al., eds.), pp. 168–175, 2016. [1508.07398].
[25] A. D. Dolgov, Beasts in Lambda-CDM Zoo, ArXiv e-prints (May, 2016) , [1605.06749].
[26] D. P. Bennett, Large Magellanic Cloud Microlensing Optical Depth with Imperfect Event
Selection, ApJ 633 (Nov., 2005) 906–913, [astro-ph/0502354].

– 12 –

[27] S. I. Blinnikov, Mirror matter and other dark matter models, Physics Uspekhi 57 (Feb., 2014)
183–188.
[28] C.-H. Lee, A. Riffeser, S. Seitz, R. Bender and J. Koppenhoefer, Microlensing Events from the
11 Year Observations of the Wendelstein Calar Alto Pixellensing Project, ApJ 806 (June,2015) 161, [1504.07246].
[29] Y. B. Zel’dovich and I. D. Novikov, The Hypothesis of Cores Retarded during Expansion andthe Hot Cosmological Model, Sov. Astron. 10 (Feb., 1967) 602.
[30] T. Harada and B. J. Carr, Growth of primordial black holes in a universe containing a masslessscalar field, Phys. Rev. D 71 (May, 2005) 104010, [astro-ph/0412135].
[31] E. Babichev, V. Dokuchaev and Y. Eroshenko, Black Hole Mass Decreasing due to Phantom
Energy Accretion, Physical Review Letters 93 (July, 2004) 021102, [gr-qc/0402089].
[32] B. J. Carr and S. W. Hawking, Black holes in the early Universe, MNRAS 168 (Aug., 1974)
399–416.
[33] G. V. Bicknell and R. N. Henriksen, Self-similar growth of primordial black holes. I - Stiff
equation of state, ApJ 219 (Feb., 1978) 1043–1057.
[34] D. K. Nadezhin, I. D. Novikov and A. G. Polnarev, The hydrodynamics of primordial black holeformation, Sov. Astron. 22 (Apr., 1978) 129–138.
[35] B. J. Carr, T. Harada and H. Maeda, BRIEF REVIEW: Can a primordial black hole orwormhole grow as fast as the universe?, Classical and Quantum Gravity 27 (Sept., 2010)
183101, [1003.3324].
[36] F. D. Lora-Clavijo, F. S. Guzmán and A. Cruz-Osorio, PBH mass growth through radialaccretion during the radiation dominated era, J. Cosmol. Astropart. Phys. 12 (Dec., 2013) 015,
[1312.0989].
[37] Y. Rosas-Guevara, R. G. Bower, J. Schaye, S. McAlpine, C. Dalla-Vecchia, C. S. Frenk et al.,Supermassive black holes in the EAGLE Universe. Revealing the observables of their growth,
ArXiv e-prints (Mar., 2016) , [1604.00020].
[38] B. Carr, F. Kuhnel and M. Sandstad, Primordial Black Holes as Dark Matter, ArXiv e-prints(July, 2016) , [1607.06077].
[39] M. Ricotti, J. P. Ostriker and K. J. Mack, Effect of Primordial Black Holes on the Cosmic
Microwave Background and Cosmological Parameter Estimates, ApJ 680 (June, 2008)
829–845, [0709.0524].
[40] The LIGO Scientific Collaboration, the Virgo Collaboration, B. P. Abbott, R. Abbott, T. D.
Abbott, M. R. Abernathy et al., The Rate of Binary Black Hole Mergers Inferred from
Advanced LIGO Observations Surrounding GW150914, ArXiv e-prints (Feb., 2016) ,[1602.03842].
[41] T. Nakamura, M. Sasaki, T. Tanaka and K. S. Thorne, Gravitational Waves from Coalescing
Black Hole MACHO Binaries, ApJL 487 (Oct., 1997) L139–L142, [astro-ph/9708060].
[42] K. Ioka, T. Chiba, T. Tanaka and T. Nakamura, Black hole binary formation in the expanding
universe: Three body problem approximation, Phys. Rev. D 58 (Sept., 1998) 063003,[astro-ph/9807018].
[43] Y. N. Eroshenko, Formation of PBHs binaries and gravitational waves from their merge, ArXiv
e-prints (Apr., 2016) , [1604.04932].
[44] J. Binney and S. Tremaine, Galactic dynamics. 1987.
[45] T. Nakama, T. Harada, A. G. Polnarev and J. Yokoyama, Identifying the most crucial
parameters of the initial curvature profile for primordial black hole formation, J. Cosmol.
Astropart. Phys. 1 (Jan., 2014) 037, [1310.3007].

– 13 –

[46] K. Schutz and A. Liu, Pulsar timing can constrain primordial black holes in the LIGO mass
window, ArXiv e-prints (Oct., 2016) , [1610.04234].
[47] M. Y. Khlopov, P. D. Nasel’skij and A. G. Polnarev, Primordial black holes and observational
restrictions on quantum gravity, in Quantum Gravity (M. A. Markov, V. A. Berezin and V. P.
Frolov, eds.), p. 690, 1985.
[48] M. Y. Khlopov, S. G. Rubin and A. S. Sakharov, Strong Primordial Inhomogeneities andGalaxy Formation, ArXiv Astrophysics e-prints (Feb., 2002) , [astro-ph/0202505].
[49] S. Clesse and J. Garcı́a-Bellido, Massive primordial black holes from hybrid inflation as dark
matter and the seeds of galaxies, Phys. Rev. D 92 (July, 2015) 023524, [1501.07565].
[50] K. Belczynski, D. E. Holz, T. Bulik and R. O’Shaughnessy, The first gravitational-wave sourcefrom the isolated evolution of two stars in the 40-100 solar mass range, Nature 534 (June,2016) 512–515, [1602.04531].
[51] L. Chen, Q.-G. Huang and K. Wang, Constraint on the abundance of primordial black holes indark matter from Planck data, ArXiv e-prints (Aug., 2016) , [1608.02174].
[52] A. M. Green, Microlensing and dynamical constraints on primordial black hole dark matterwith an extended mass function, Phys. Rev. D 94 (Sept., 2016) 063530, [1609.01143].
[53] S. Wang, Y.-F. Wang, Q.-G. Huang and T. G. F. Li, Stochastic gravitational-wave backgroundfrom primordial black hole scenario after GW150914 and GW151226, ArXiv e-prints (Oct.,2016) , [1610.08725].

– 14 –