Dynamical formation of black hole binaries in dense star clusters Rapid cluster evolution code Konstantinos Kritos1Vladimir Strokov1Vishal Baibhav2and Emanuele Berti1

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Dynamical formation of black hole binaries in dense star clusters: Rapid cluster

evolution code

Konstantinos Kritos,

1, ∗

Vladimir Strokov,

1, †

Vishal Baibhav,

2, ‡

and Emanuele Berti

1, §

Department of Physics and Astronomy, Johns Hopkins University,

3400 N. Charles Street, Baltimore, Maryland, 21218, USA

Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy,

Northwestern University, 1800 Sherman Avenue, Evanston, Illinois 60201, USA

(Dated: August 20, 2024)

Gravitational-wave observations have just started probing the properties of black hole binary

merger populations. The observation of binaries with very massive black holes and signiﬁcantly

asymmetric masses motivates the study of dense star clusters as astrophysical environments which can

produce such events dynamically. In this paper we present

Rapster

(for “Rapid cluster evolution”),

a new code designed to rapidly model binary black hole population synthesis and the evolution

of massive star clusters based on simple, yet realistic prescriptions. We also perform a thorough

comparison with the Cluster Monte Carlo code and ﬁnd generally good agreement. The code can be

used to generate large populations of dynamically formed binary black holes.

CONTENTS

I. Introduction 1

II. Dynamical model 2

A. Star cluster evolution 2

B. Black holes in star clusters 4

1. Remnant-mass prescription 4

2. BH spins 5

3. Natal kicks 5

4. BH segregation, velocities, and core radius 6

C. Binary–single interactions 7

1. Encounter timescale 7

2. Binary hardening 7

3. Interaction recoil 8

4. BBH–BH exchanges 8

5. BH ejections 9

D. Dynamical assembly channels of BBHs 9

1. Original binary stars 9

2. Three-body binary formation 10

3. Two-body captures 10

4. Binary–single GW capture mergers 11

5. BBHs from exchanges in binary stars 12

6. Binary-binary interactions 13

E. Our simulation algorithm 15

1. Code input parameters 15

2. Global simulation timestep 15

3. Local BBH evolution algorithm 15

III. Comparison with the Cluster Monte Carlo 16

A. Global evolution of the star cluster 18

1. Cluster mass 18

2. Half-mass radius 18

∗kkritos1@jhu.edu

†vstrokov1@jhu.edu

‡vishal.baibhav@northwestern.edu

§berti@jhu.edu

3. BH subsystem evaporation 19

B. Binary black hole merger properties 19

1. Fraction of merger channels 20

2. Primary mass and mass ratio 22

3. Merger times 23

4. Orbital properties of ejected merging pairs 24

IV. Conclusions 25

Acknowledgments 26

A. BH core radius 27

B. Three-body binary rate 28

C. Contribution of BH-BH-star three-body

encounters to BBH formation 29

D. Gravitational captures 30

References 30

I. INTRODUCTION

The detection of gravitational waves (GWs) in 2015 [

]

ushered in a major revolution in modern astrophysics

and cosmology. The GW transient catalogs published

by the LIGO-Virgo-KAGRA collaboration can be used

to carry out population studies and infer the properties

of neutron stars (NSs) and black holes (BHs) [

]. The

intrinsic characteristics predicted by astrophysical models

can also be compared with those of the observed events

to learn about the environments that host these mergers.

A key question concerns the origin of the observed

binary black hole (BBH) mergers. There are currently two

main astrophysical scenarios proposed for the formation

of BBHs, which involve either isolated binaries in the ﬁeld

or dynamical assembly in star clusters [

–

]. In turn, each

scenarios could consist of multiple sub-channels, such as

arXiv:2210.10055v3 [astro-ph.HE] 19 Aug 2024

common envelope evolution [

], stable mass transfer [

and chemically homogeneous evolution [

] for the isolated

binaries in the ﬁeld; and formation in young massive star

clusters [

–

], globular clusters [

–

], nuclear star

clusters [

–

], open clusters [

–

], and the disks of

active galactic nuclei [35,36] for the dynamical channel.

At the time of writing, it is highly uncertain how much

each of these channels actually contributes to the intrinsic

astrophysical merger rates and to the overall population

of BBH mergers observed in GWs [

]. Some studies

claim that a single formation channel could still explain all

of the observed events [

] because several poorly con-

strained parameters appear in the astrophysical modeling

of each formation channel, and this leads to large uncer-

tainties in the predicted properties of the single events and

of the overall population. The general consensus is that

a combination of various formation scenarios, including

possibly also primordial BHs [

], is more likely [

–

see e.g. [

] for a recent review. Given a suﬃciently large

number of events, it might be possible to use statistical

methods (such as Bayesian inference) to disentangle iso-

lated and dynamical mergers by comparing the intrinsic

binary parameters measured in GWs (e.g., the compo-

nent masses and spins) with the predictions of population

synthesis models.

In this work, we model and simulate the assembly of

BBHs in dynamical environments with a new open source

Python code, Rapster 1(for “Rapid cluster evolution”).

The development of this code is mainly motivated by the

necessity to simulate a large number of clusters within a

reasonable time. There are several state-of-the-art numer-

ical packages that can provide accurate results (including

direct

-body solvers [

–

] or the

CMC

[

] and

MOCCA

[

] codes, which rely on a Monte Carlo ap-

proach based on Hénon’s method to evolve self-gravitating

million-body systems). New implementations of BBH

mergers and stellar evolution have recently been added

-body codes [

–

]. Despite these advances, it

is computationally expensive to apply these techniques to

produce large BBH populations or to infer astrophysical

hyperparameters, due to the large number of star clusters

that must be simulated. In contrast,

Rapster

can simu-

late the evolution of star clusters within seconds for light

clusters (

Mcl <

6M⊙

), or within a minute for more

massive clusters. The simulation runtime grows for the

heaviest nuclear star clusters—very dense, massive sys-

tems found at the centers of most galaxies and comprising

∼108bodies or more.

A second motivation is the detection of GW events

with asymmetric mass-ratio (e.g., GW190412 [

]

and GW190814 [

]) and of BBH mergers such as

GW190521 [

], in which the binary components have

masses within or above the so-called pair-instability su-

pernova (upper) mass gap [

–

]. These massive BH

The code and documentation are available on

github

at the URL

https://github.com/Kkritos/Rapster.

components could themselves result from hierarchical

mergers [

–

]: in particular, BHs could assemble dy-

namically in a cluster, merge and be retained, so that they

can merge again in the same dense environment [

To obtain the BH population in hierarchical merger scenar-

ios and compare it with GW observations, it is necessary

to simulate their dynamical assembly in multiple clusters

across the Universe. This task is computationally pro-

hibitive for most existing direct or indirect

-body codes.

It should be noted however that there are several proposed

alternatives to repeated BH mergers that could produce

BHs within the upper-mass gap, including runaway stellar

collisions [

], tidal-disruption events [

], or even

primordial BHs [77].

Rapster

is based on a semianalytic approach relying

on a set of simple, yet realistic prescriptions (see Sec. II).

Unlike existing rapid semianalytic codes to evolve BBHs

in star clusters [

–

] which use scaling relations, in our

code we treat all dynamical channels that occur simulta-

neously in the cluster as Poisson processes. Other semian-

alytic codes similar to

Rapster

include

FASTCLUSTER

[

cBHB

[

B-POP

[

], and

QLUSTER

[

]. We compute

the initial single-BH mass spectrum using

SEVN

[

] to

ﬁnd the remnant mass as a function of the zero-age main-

sequence (ZAMS) mass of massive progenitor stars, but

the code is modular, and any other initial mass spectrum

(e.g. from

SSE

[

]) can be used as input. To compute

the properties of merger remnant products, such as mass,

spin and GW kick, we use the

precession

code [

The plan of the paper is as follows. In Sec. II we

summarize the semianalytic prescriptions implemented

in the code. In Sec. III we show comparisons of

Rapster

results with the Cluster Monte Carlo (

CMC

) code. In

Sec. IV we present our conclusions.

Throughout the code and in this text, we use astrophys-

ical units in which we measure masses in

M⊙

, distances

and radii in pc (and occasionally in AU), velocities in

km s

−1

, and time in Myr. In those units the gravitational

constant is approximately G≃(232)−1[88].

II. DYNAMICAL MODEL

This section is dedicated to the physical model under-

lying

Rapster

. We ﬁrst summarize our treatment of star

cluster evolution. Then we describe how we populate clus-

ters with BHs, how we treat binary–single interactions,

and the various dynamical channels that can lead to the

formation of BBHs. We conclude with a ﬂow chart that

illustrates our simulation algorithm.

A. Star cluster evolution

Star clusters are formed from the fragmentation of giant

molecular clouds. The majority of stars (if not all) form

in groups and larger associations [

]. Since all stars

in a cluster form at roughly the same time (with potential

slight time delays resulting in diﬀerent populations), they

have similar chemical composition (or metallicity

) at

formation. Stars will however form with diﬀerent masses,

whose distribution is assumed to follow the Kroupa [

]

initial mass function (IMF)—a broken power law, here

assumed to be universal. The lower end of the initial

stellar masses is assumed to be 0

M⊙

by default. We

implement the mean power law indices from Ref. [

], and

a default power law index of

−

3for stars heavier than

the Sun. For simplicity we ignore all ﬁnite size eﬀects

for stars, and treat all members of the cluster as point

particles. Clusters that avoid infant mortality, surviving

the ﬁrst phase of gas expulsion, collapse and virialize.

The root mean square velocity of stars in the cluster

is determined by the virial theorem, and given by (see

Ref. [92], page 12)

⟨v2

⋆⟩1/2=r0.4GMcl

≃13 km s−1Mcl

105M⊙

2rh

1pc−1

,(1)

where

Mcl

is the total mass of the cluster,

is its half-

mass radius, and

is the gravitational constant. It turns

out that the numerical coeﬃcient of 0.4 in the equation

above depends weakly on the density proﬁle, and it can

vary by a factor of at most 2. The stationarity condition

above is assumed at every moment in time and it is a good

approximation, because the timescale it takes for a star

to cross the size of the cluster (roughly the time to reach

virial equilibrium) is much smaller than the timescale it

takes for the stellar distribution function to change [

also known as the relaxation timescale.

The subsequent evolution of an isolated cluster follow-

ing core collapse is driven by its internal dynamics and

is dominated by two-body relaxation and stellar mass

loss. A fraction of about

ξe≃

0074 [

] of all stars

in an isolated cluster

have velocities in the tail of the

Maxwellian distribution, and escape the cluster’s gravi-

tational potential. The tail is then replenished through

close encounters, and more stars escape. In addition, since

star clusters are not isolated systems, the host galaxy af-

fects the evolution as well. The presence of an external

tidal ﬁeld enhances the mass loss rate from the cluster,

because it creates a ﬁnite tidal boundary through which

stars can escape. The tidal (or Jacobi) radius is given

= (

GMclR2

))

1/3

, where

and

are the

galactocentric radius and circular velocity, respectively.

According to numerical experiments performed in [

] the

dimensionless mass loss rate

ξe

should be modiﬁed by

a multiplicative factor of

≃exp(10rh/rJ)

. As the clus-

ter loses mass, the escape velocity

vesc

= 2

⟨v2

⋆⟩1/2

(see

This result is obtained by integrating the normalized Maxwell-

Boltzmann distribution with one-dimensional velocity dispersion

parameter σfrom 2√3σ(the escape velocity) to inﬁnity.

Ref. [

], page 51) decreases and more stars are likely to

be ejected, so Mcl decreases exponentially.

The timescale on which energy is distributed through-

out a collisional

-body system is controlled by the half-

mass relaxation timescale (see Ref. [

], Eq. (30); and

Ref. [92], page 40)

τrh = 0.138 N1

2G1

2ln Λ

≃128 Myr Mcl

105M⊙

2rh

1pc

20.6M⊙

ln Λ

ψ,(2)

where we have used

Mcl

, and we set Λ

≈

in the Coulomb logarithm. Here,

is the average stellar

mass in the cluster, which is around 0

M⊙

under the

assumption of the Kroupa IMF in the range [0

150]

M⊙

Moreover,

is the dimensionless mass moment factor, de-

ﬁned as

m5/2/m5/2

, and accounts for a cluster composed

of multiple mass components. It has been demonstrated

numerically that multimass systems evolve faster due to

a smaller relaxation timescale [

]. For two-mass models

with a dominant component (such as one that contains

stars and BHs) we can write

= 1 +

, where the symbol

represents the Spitzer parameter, accounting for the

eﬀect of the BH subcluster [

]. The relaxation time is

smaller than the lifetime of collisional systems; in par-

ticular, this criterion is met by star clusters. This is in

contrast to stars in the solar neighborhood, where the

relaxation time is much larger than the Hubble time: this

makes galactic ﬁelds eﬀectively collisionless, so that dy-

namical encounters play no role. Lighter clusters have

smaller relaxation times and evolve faster than massive

systems [97].

We describe the internal and external evolution of star

cluster environments as in Refs. [

]. A code that

simulates the global evolution of star clusters in a manner

similar to ours is

EMACSS

[

100

]. If we write

Mcl

then the rate of change of the cluster’s mass is due to

variations in

(mass loss due to stellar evolution) and

(relaxational loss due to ejections). Since it takes

approximately one half-mass relaxation timescale for the

system to thermalize and for the unbound high-mass tail

of the Maxwellian to be ﬁlled, we model the cluster mass

loss due to relaxation processes as

dM(rlx)

dt ≡mdN

dt =−ξeMcl

τrh

.(3)

Note that we have ignored the factor of 2.5 in

ξe

in the last

equation above (which is accounted for in [

]) because

the eﬀect of a multimass distribution has already been

included through the mass moment

in the expression

for

τrh

(see Eq.

(2)

). Finally, the cluster loses mass as

a consequence of stellar evolution and winds according

to [80,100]:

dM(sev)

dt ≡Ndm

dt =−νMcl

tΘ(t−τsev),(4)

where

= 0

07,

τsev

= 2 Myr and Θ(

)denotes the

Heaviside function. In deriving this previous equation,

we assume the average mass to evolve according to

(

t/τsev

)

−ν

for

t>τsev

[

100

], where

is the

initial average mass. The total rate of change of

Mcl

then determined by adding the relaxation and stellar evo-

lution terms in Eqs.

(3)

and

(4)

, respectively. In

dMBH/dt

we do not include the BH mass loss rate, because the lat-

ter contributes a very small amount in systems that are

dominated by low-mass stars, as is the case in systems

that follow the default Kroupa IMF. In our simulations,

the BH ejection rate is determined by the microphysical

processes (primarily binary–single interactions and rela-

tivistic recoils) that occur in the core of the system and

will be discussed in a later section (Sec. II C 5).

Energy production in the core of the cluster, originat-

ing from the formation of tight binaries and from the

interactions of stars with tight binaries, causes the cluster

to slowly expand. We model the time evolution of the

half-mass radius due to relaxation and stellar evolution

processes by writing [see [80], Eq. (8), (15), and (17)]:

drh

dt ="ζrh

τrh

+ 2dM(rlx)

Mcl #Θ(t−τcc)−dM(sev)

Mcl

(5)

The ﬁrst term in this equation becomes eﬀective for

times

t > τcc

, where

τcc

= 3

τrh,0

is the core collapse

timescale [

] and

τrh,0

is the initial half-mass relaxation

time, because it is only after the core collapses that en-

ergy is generated via binary formation and interactions.

We set the dimensionless constant to an average value of

= 0

08 (for both the whole cluster and the BH subsys-

tem) to match numerical simulations of tidally limited

clusters [

101

102

]. Here,

represents the fraction of

the total energy of the cluster that can be conducted by

way of two-body relaxation through

and shared among

the members of the cluster within one

τrh

. In other words,

the heat ﬂow rate via gravitational encounters in a star

cluster is ≃0.2ζGM2

cl/(rhτrh).

Finally, we implement Eqs. (7) and (8) from [

] to

evolve the galactocentric radius of the cluster under the

eﬀect of dynamical friction. As the cluster inspirals toward

the galaxy’s center because of dynamical friction, it can

be tidally stripped or merge with the central nuclear star

cluster (if present).

In implementing all the above mentioned diﬀerential

equations (along with Eq.

(5)

(4)

, and

(3)

above) we

use a ﬁnite diﬀerence scheme. We update the half-mass

radius and cluster mass by choosing the increment

match the time step of the simulation. (See Sec. II E 2

for a discussion of the adaptive time step used in our

simulations.)

B. Black holes in star clusters

To populate clusters with BHs, we need to introduce

prescriptions for their initial mass (which is related to the

ZAMS mass of the progenitor stars), their spin, the kick

they receive at birth, and their distribution in the cluster.

1. Remnant-mass prescription

Massive stars evolve quickly and produce compact ob-

ject remnants within a few million years. It is expected

that a population of BHs might reside near the centers

of star clusters. This hypothesis is supported by spec-

troscopic and kinematic observational evidence for the

existence of compact objects in dense star clusters [

103

–

107

]. We implement the compact remnant mass–ZAMS

mass prescription based on the Fryer et al. (2012) delayed

model [

108

] as a default option. Other remnant mass mod-

els included are the Fryer et al. (2012) rapid function

based on the

SSE

code [

109

], and the delayed model of

the

SEVN

code [

]. The implementation is not tied to a

speciﬁc stellar evolution code, allowing easy integration

of alternative prescriptions for remnant mass based on

ZAMS mass and metallicity. To enhance ﬂexibility, the

code oﬀers customization through an input option for

users to provide their own list of BH masses retained in

the cluster. For the Fryer et al. (2012) rapid and de-

layed models we use the

updated-BSE

code described in

Ref. [

]. For computational eﬃciency, we create look-up

tables with remnant masses on a 700

700 grid in ZAMS

mass vs. metallicity, and we perform a two-dimensional

interpolation of this grid.

The

SEVN

code allows us to obtain BH masses as a

function of the ZAMS mass and metallicity of the progeni-

tor stars,

mrem

(

mZAMS, Z

). The implementation

of this procedure in

SEVN

works by interpolating stellar

evolutionary tracks from

PARSEC

simulations [

110

], and

it includes the latest stellar wind and pair-instability su-

pernova prescriptions. For the supernovae, we adopt the

delayed core-collapse engine, although the exact details

of the supernova convection eﬃciency aﬀect only the low-

mass end of the BH mass spectrum [

108

]. This choice

gives rise to a number of BHs within the so-called “lower

mass gap” that ranges from

≃

M⊙

≃

M⊙

[

111

]. We

calculate the remnant masses only for stars with ZAMS

masses above 20

M⊙

, because in

SEVN

these stars produce

remnants above

∼

M⊙

regardless of metallicity: see e.g.

Fig. 2 of Ref. [

]. Then, we keep track of only those BHs

that are more massive than 3

M⊙

. This gives us the total

number of BHs originally produced in the cluster,

Ntot

BH,0

The interpolation provided by

SEVN

handles metallicities

in the (absolute) range between 10−4and 0.02.

In environments with metallicity lower than

≈

5% of the

solar metallicity, which we assume to be

Z⊙

= 1

4% ([

112

page 24), very massive stars presumably collapse directly,

avoiding the pair-instability mechanism and producing

BH remnants with masses above the upper mass gap. We

can account for these direct-collapse BHs by extrapolating

the IMF up to stars with a ZAMS mass of 340

M⊙

, which

is the heaviest star the

SEVN

code interpolates based on

simulations [

113

]. This provides one of the possible for-

mation pathways for intermediate-mass BHs (IMBHs):

the direct collapse of low-metallicity stars at high redshift

can generate a few BHs with masses above 100

M⊙

in star

clusters, which can then further grow by mergers [

114

]

or accretion (see e.g. [

115

]). Despite the typically chosen

maximum ZAMS mass of 150

M⊙

employed in theoretical

studies (a value based on observations of stars in the

Arches cluster [

116

]), cosmological simulations provide

numerical support to the idea that zero-metallicity stars

could reach hundreds of solar masses [

117

]. Moreover,

spectroscopic observations and

-body simulations for

the star cluster R136 in the Large Magellanic Cloud sug-

gest the existence of stars more massive than the putative

theoretical limit of 150

M⊙

[

118

] (but see [

119

] for inter-

pretations of those stars as the result of stellar runaway

mergers). Motivated by these considerations, and taking

into account the uncertainty in the IMF for very massive

stars, we set the maximum ZAMS mass to be a free pa-

rameter that can be provided as an input to our code. We

choose the highest possible value for this parameter to

be 340

M⊙

, due to the lack of simulations for more massive

stars. We have checked that varying this parameter from

150

M⊙

to 340

M⊙

changes the number of BH progenitors

at the percent level. The initial number of BHs is expected

to vary even less at low metallicities, because most stars

above 150

M⊙

completely explode through pair-instability

supernova (PISN), leaving behind no BH remnant.

2. BH spins

We consider two prescriptions for the dimensionless

spin parameter

χ1g ∈

1] of “ﬁrst-generation” BHs (i.e.,

those formed by stellar collapse). Some stellar models

favor low natal spins for ﬁrst generation BHs [

120

], but we

opt to keep this parameter as an input, especially because

individual spins are diﬃcult to measure and strongly

constrain with current GW observatories [

121

122

]. One

option is a monochromatic (delta function) distribution at

a given

χ1g

; we also consider another simple option, i.e., a

uniform distribution in the range [0

, χ1g

]. It is possible to

modify the source code to include diﬀerent distributions

for the spin of 1g BHs.

Whenever the spins

of BHs in a binary are nonzero,

we randomize their orientations by sampling

χ·L/|L| ≡

cos θ

uniformly in [

−

1]. Here,

stands for the or-

bital angular momentum of the BBH, and

|L|

denotes

its magnitude. The relative angle ∆

between the spin

projections in the orbital plane is sampled uniformly in

]. Since the spins can undergo precession as the

BBH goes through the inspiral, we assume the angles to

be deﬁned at the last stable circular orbit, just before the

ﬁnal plunge and coalescence of the binary. However, since

an initially isotropic distribution evolves to an isotropic

distribution [

123

–

125

], the frequency at which these an-

gles are deﬁned does not really matter. It is possible for

the user to alter these choices by modifying the function

sample_angles()

in the

functions2.py

ﬁle for a non-

isotropic sampling of the spin directions (such as clusters

with a disklike geometry, that tend to have a preferred

orientation in space [126]).

After the merger of two BHs, we compute the spin of

the merger product (as well as other parameters, such as

the GW-induced recoil and remnant mass) with ﬁtting

formulas implemented in the

precession

code [

Those formulas are ﬁtted to numerical relativity simula-

tions of merging BBHs and based on Refs. [

127

–

132

] for

the GW recoil, Ref. [

133

] for the ﬁnal mass, and Ref. [

134

]

for the ﬁnal spin.

3. Natal kicks

It is believed that BHs and neutron stars generally have

nonzero velocity (receive a “kick”) at birth as a conse-

quence of asymmetric supernova mass ejection and the

conservation of momentum [

135

136

]. If that kick exceeds

the escape velocity of the host environment, the remnant

escapes the gravitational pull of the cluster, and no longer

contributes to internal dynamical processes. This means

that only a fraction

fret

of the BHs is retained in the

cluster. The recoil has been constrained to be a few hun-

dreds of km s

−1

for neutron stars, based on observations

of pulsar proper motions in the Milky Way [

137

138

For BHs, the recoil velocity is highly uncertain [

139

140

It is believed, however, that massive stellar cores that

directly collapse into heavy BHs receive little or no kick

at birth, due to material falling back onto the newly born

compact remnant.

We calculate the fallback (“fb”) fraction

ffb

of the

ejected supernova mass that falls back onto the BH by

implementing Eq. (19) and (16) from Ref. [

108

] in the case

of the delayed and rapid core-collapse engine, respectively.

Whenever required, we use the analytic formulas from

Ref. [

] to determine the carbon/oxygen (CO) core mass

when we use the Fryer et al. (2012) models. When instead

we use

SEVN

, we consistently use the CO core mass output

of the

SEVN

code (see [

]). To speed up the simulations,

we have also precomputed the CO core mass output of

SEVN

using the same grid of ZAMS mass and metallicity

as for the remnant masses (see Sec. II B 1). This output

is saved in look-up tables whose values are later interpo-

lated. The BH kick at birth,

vkick,0

, is originally drawn

from a Maxwellian distribution with one-dimensional root-

mean-square velocity of 265 km s

−1

[

137

] (in our code, the

user can set this parameter to a value diﬀerent from

the default). Due to isotropy, the 3-dimensional natal

kick is obtained by multiplying the sampled velocity by

√3

. The ﬁnal natal kick is then determined by either

vkick

= (1

−ffb

)

vkick,0

in the fallback prescription, or (by

default)

vkick

= (1

M⊙/mBH

)

vkick,0

in the momentum

conservation prescription, where

mBH

is the mass of the

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Dynamicalformationofblackholebinariesindensestarclusters:RapidclusterevolutioncodeKonstantinosKritos,1,∗VladimirStrokov,1,†VishalBaibhav,2,‡andEmanueleBerti1,§1DepartmentofPhysicsandAstronomy,JohnsHopkinsUniversity,3400N.CharlesStreet,Baltimore,Maryland,21218,USA2CenterforInterdisciplinaryExploratio...

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Dynamical formation of black hole binaries in dense star clusters Rapid cluster evolution code Konstantinos Kritos1Vladimir Strokov1Vishal Baibhav2and Emanuele Berti1.pdf

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Dynamical formation of black hole binaries in dense star clusters Rapid cluster evolution code Konstantinos Kritos1Vladimir Strokov1Vishal Baibhav2and Emanuele Berti1

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