The LIGO/Virgo detections of gravitational waves from merging black holes of
$\simeq$ 30 solar mass suggest progenitor stars of low metallicity
(Z/Z$_{\odot} \lesssim 0.3$). In this talk I will provide constrains on where
the progenitors of GW150914 and GW170104 may have formed, based on advanced
models of galaxy formation and evolution combined with binary population
synthesis models. First I will combine estimates of galaxy properties
(star-forming gas metallicity, star formation rate and merger rate) across
cosmic time to predict the low redshift BBH merger rate as a function of
present day host galaxy mass, formation redshift of the progenitor system and
different progenitor metallicities. I will show that the signal is dominated by
binaries formed at the peak of star formation in massive galaxies with and
binaries formed recently in dwarf galaxies. Then, I will present what very high
resolution hydrodynamic simulations of different galaxy types can learn us
about their black hole populations.Comment: Proceeding of IAU Symposium 338 : "Gravitational Waves Astrophysics :
  Early results from GW searches and EM counterparts

Lamberts, Astrid

English

arXiv

The LIGO/Virgo detections of gravitational waves from merging black holes of ≃ 30 solar mass suggest progenitor stars of low metallicity (Z/Z⊙ ≲ 0.3). In this talk I will provide constrains on where the progenitors of GW150914 and GW170104 may have formed, based on advanced models of galaxy formation and evolution combined with binary population synthesis models. First I will combine estimates of galaxy properties (star-forming gas metallicity, star formation rate and merger rate) across cosmic time to predict the low redshift BBH merger rate as a function of present day host galaxy mass, formation redshift of the progenitor system and different progenitor metallicities. I will show that the signal is dominated by binaries formed at the peak of star formation in massive galaxies with and binaries formed recently in dwarf galaxies. Then, I will present what very high resolution hydrodynamic simulations of different galaxy types can learn us about their black hole populations

Caltech Authors - Main

Gravitational Wave Astrophysics: Early Results from Gravitational
Wave Searches and Electromagnetic Counterparts
Proceedings IAU Symposium No. 338, 2017
G. Gonza´lez & R. Hynes, eds.
c© International Astronomical Union 2019
doi:10.1017/S1743921318000182
Merging massive black holes
the right place and the right time
Astrid Lamberts
Theoretical Astrophysics, California Institute of Technology,
Pasadena, CA, 91125, USA
email: lamberts@caltech.edu
Abstract. The LIGO/Virgo detections of gravitational waves from merging black holes of  30
solar mass suggest progenitor stars of low metallicity (Z/Z  0.3). In this talk I will provide
constrains on where the progenitors of GW150914 and GW170104 may have formed, based on
advanced models of galaxy formation and evolution combined with binary population synthesis
models. First I will combine estimates of galaxy properties (star-forming gas metallicity, star
formation rate and merger rate) across cosmic time to predict the low redshift BBH merger rate
as a function of present day host galaxy mass, formation redshift of the progenitor system and
diﬀerent progenitor metallicities. I will show that the signal is dominated by binaries formed
at the peak of star formation in massive galaxies with and binaries formed recently in dwarf
galaxies. Then, I will present what very high resolution hydrodynamic simulations of diﬀerent
galaxy types can learn us about their black hole populations.
Keywords. galaxies:abundances, stellar content; stars:binaries, black holes, evolution; gravita-
tional waves
1. Introduction
The detection of gravitational waves (GW) from merging black holes (BH) and neu-
tron stars has opened a new window on our Universe (LIGO/Virgo (2016), LIGO/Virgo
(2017)). More speciﬁcally, it has revived the study of massive stars and their binary inter-
actions (Belczynski et al. (2016), Eldridge & Stanway (2016), Spera & Mapelli (2017)).
While there is a global understanding of binary evolution for ﬁeld binaries, the exact
properties of their mass loss, mass transfer and supernova mechanisms are still unclear
(Belczynski et al. (2010), Dominik et al. (2013)). The high masses of the ﬁrst GW detec-
tion, (30 M BHs for GW150914) were unexpected (but see Belczynski et al. (2010)).
These high masses suggest low-metallicity progenitors, where mass loss due to winds is
reduced. We have limited information on low-metallicity massive stars as massive stars
are short-lived and stars recently formed in the Milky Way have a metallicity at least
as high as the Sun. In this talk, we determine the conditions where the progenitors of
GW150914 may have formed, based on a semi-analytic formalism of galaxy evolution and
a binary population synthesis model. We determine the formation rate of GW150914-
like progenitors based on the mass of the host galaxy and the formation time of the
progenitor. We refer the reader to Lamberts et al. (2016) for a more detailed description
of the method. We then present a preliminary analysis of the merger rates predicted by
cosmological simulations.
2. Forming low-metallicity stars
The ﬁrst step is to determine the conditions for low-metallicity star formation in the
universe. Globally, the metallicity in the Universe increases as successive generations of
40
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Merging massive BH 41
Figure 1. Low-metallicity star formation rate (arbitrary units) as a function of galaxy mass
and lookback time to formation (left) and metallicity (right).
stars progressively enrich the star-forming gas. At a given epoch galaxies follow the mass-
metallicity relation (Kewley & Ellison (2008)), with more massive galaxies being more
metal rich. For each present-day galaxy mass, we determine the mass of the corresponding
dark matter halo using abundance matching by Behroozi et al. (2013). Based on the
model by Behroozi et al. (2013) we then determine the amount of star formation in
each halo in 10 Myr time bins. Based on the redshift-dependent mass-metallicity relation
computed by Ma et al. (2016), we derive the stellar mass formed in 11 metallicity bins
between Z = 0.01Z and Z = 1Z, where Z ≡ 0.02. We include scatter between
diﬀerent galaxies of σ = 0.1 dex, based on observations by Tremonti et al. (2004). We
also include σ = 0.2 scatter of the metallicity within galaxies, according to Berg et al.
(2013). Fig. 1 shows the normalized star formation rate as a function of present-day galaxy
mass and lookback time to formation (left) and metallicity (right). The ﬁgure only shows
subsolar metallicity star-formation, which is relevant to binary BH formation. However,
particularly in massive galaxies, a large fraction of the stars form at higher metallicities.
We ﬁnd a slightly bimodal distribution, with most of the low-metallicity stars forming
in massive (Milky-Way like) galaxies around the peak of cosmic star-formation (between
6 and 10 Gyrs ago). More recent low-metallicity star formation also occurs in dwarf
galaxies, typically at metallicity below 10 per cent of Solar. In the next section, we will
highlight how metallicity aﬀects binary BH formation and merger rates and show which
low-metallicity stars shown in Fig. 1 mostly contribute to GW150914-like events observed
now.
3. Forming binary black hole merger progenitors
We use the BSE code (Hurley et al. (2002)) to compute the delay time distribution
of binary BH mergers with respect to the formation of the stellar progenitor. We ne-
glect BH mergers from globular clusters (Rodriguez et al. (2015)) and consider a single
set of standard assumptions on binary evolution. We have updated BSE to account for
improvement models of stellar winds (Belczynski et al. (2010)), remnant masses (Bel-
czynski et al. (2008)) and BH kicks due to supernova explosions (Dominik et al. (2013)).
Binaries undergoing common-enveloppe mass-transfer during the Hertzprung gap merge
as stars. At later stages, we set the common enveloppe eﬃciency to unity and assume
that during Roche lobe overﬂow, only half of the mass is accreted by the companion.
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42 A. Lamberts
Figure 2. Delay time distribution for massive binary black hole mergers with progenitors of
diﬀerent metallicities. Taken from Lamberts et al. (2016).
For each metallicity bin, we model 2.5 × 106 binaries with primary masses between 25
and 150 M following the Kroupa (2001) initial mass-function. The initial period dis-
tributions and mass ratios are derived from observations by Sana et al. (2012) and we
use thermal distribution for the initial eccentricity. Fig. 2 shows the BH mergers with
total mass above 40 M (per unit solar mass) for Z = 0.01, 0.1, 0.3Z according to our
models. The lowest metallicity stars produce the most massive BH, as their mass-loss is
limited and early mergers. At later times, more metal-rich stars contribute more. Stars
with metallicity above 0.3 Z produce 10 times less mergers of these high masses, owing
to the strong mass loss of the progenitor stars.
We combine our semi-analytic model for low-metallicity star-formation (Fig. 1) and
the metallicity-dependent delay-time distribution (Fig. 2) to determine where and when
the progenitor of GW150914 most likely formed. For all stars formed, at all timesteps, we
count the resulting BH mergers occurring between z = 0.1 and the present day. The con-
ditions of formation of the progenitors are shown in Fig. 3. The ﬁgure has the same axes
as Fig. 1 and the colors can be directly compared. It shows that the bimodality in low-
metallicity star formation is enhanced. Roughly half of the progenitors of GW150914-like
systems stem from Milky-Way like galaxies (M  1011M) and were formed 6 to 10 Gyrs
ago, at roughly 10 per cent of Solar metallicity. Later star formation in massive galaxies
has too high metallicity to signiﬁcantly contribute to BH merger progenitors. Recent star
formation in dwarf galaxies also signiﬁcantly contributes to BH mergers, stemming from
progenitors with metallicities below 10 per cent of Solar. Because of their low-metallicity,
galaxies below 108M overproduce BH mergers in comparison with their contribution
to the global star formation. These galaxies are faint, and unobservable at high redshift
and BH mergers may be the only way to infer some of their properties. The side panel of
the left ﬁgure shows the formation time of the progenitors of massive BH mergers, which
is mostly uniform over the past 7 Gyrs. This diﬀers from the bimodal distribution from
Belczynski et al. (2016), because of our improved model of low-metallicity star-formation.
In the next section we present preliminary results from cosmological simulations.
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Merging massive BH 43
Figure 3. Formation rate of progenitors of massive black hole mergers as a function of galaxy
mass and lookback time to formation (left) and metallicity (right). Taken from Lamberts et al.
(2016).
4. Preliminary results from high-resolution simulations
We have performed a comparable analysis based on hydrodynamical simulations of dif-
ferent galaxies. We use simulations from the Feedback In Realistic Environments project
(FIRE ,Hopkins et al. (2014)). The cosmological simulations are ran with the GIZMO
code (Hopkins (2013)) and include a multiphase model of the interstellar medium and
stellar feedback based on a complete stellar evolution model. We speciﬁcally use the
“Latte” simulation (Wetzel et al. (2016)), a cosmological simulation of a Milky-Way like
galaxy with a mass resolution of 7070 M. The left panel of ﬁg. 4 shows the normalized
star-formation rate in a Milky-Way like galaxy. The right panel only shows the stars con-
tributing to BH mergers within the detector horizon during the second observing run.
We have directly associated the delay time distributions (Fig. 2) with the star formation
in the simulation. We ﬁnd that mergers come from low-metallicity star-formation and
that eﬀectively most of the stars formed in Milky-Way-like galaxies are unable to form
merging black holes. As in Lamberts et al. (2016), we ﬁnd that the mergers come from
star formation between 6 and 10 Gyrs ago. Fig. 5 shows the total number of mergers
as a function of time in diﬀerent metallicity bins. Again, we conﬁrm the ﬁndings from
Lamberts et al. (2016), with the largest contribution coming from Z = 0.03−0.13Z. We
ﬁnd that the number of mergers increases towards redshift z = 2 (10Gyrs ago), somewhat
following the global star formation history of the galaxy. As the horizon of the detectors
increases, we thus expected an increase of the number of detections per unit volume for
contributions from massive galaxies.
5. Implications
In this talk, we presented a unique combination between a binary population synthesis
model and a complete semi-analytic cosmological model for low-metallicity star forma-
tion. We derive the contribution of diﬀerent galaxies to the present-day merger rate of
massive (> 30M) binary black holes. We ﬁnd that the progenitors of such mergers could
have formed during the peak of star formation (between 6 and 10 Gys argo) in a galaxy
that would now resemble the Milky Way or more recently (< 6 Gyrs ago) in a dwarf
galaxy. Our method solely relies on the strong metallicity dependence of binary black hole
formation (and mergers) to determine the relative contributions of diﬀerent galaxies to
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44 A. Lamberts
Figure 4. Normalized star formation rate (left) and formation rate of BBH merger
progenitors (right) from the Latte simulation.
Figure 5. Number of mergers in a Milky-Way like galaxy as a function of time for diﬀerent
metallicities of the progenitor stars. The total number of mergers is shown in the thick black
line.
present-day black hole mergers. Although absolute merger rate we predict is in agreement
with the LIGO/Virgo detection rate (LIGO/Virgo (2016)), we emphasize that it may be
revised as our understanding of massive binary evolution improves. We conﬁrm our ﬁnd-
ings using the same binary evolution model combined with a high-resolution simulation
of a Milky-way like galaxy. We ﬁnd that the merger rate in massive galaxies increases
towards redshift z = 2 and hundreds of detections are expected when LIGO and Virgo
reach their design sensitivity (about z  1). As such, these detections will provide strong
constrains on binary evolution models and star formation in high-redshift and/or faint
galaxies.
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Merging massive black holes: the right place and the right time

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