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Search for Eccentric Binary Black Hole Mergers with Advanced LIGO and Advanced Virgo
during their First and Second Observing Runs
LIGO Scientific Collaboration, Virgo Collaboration and F. Salemi
ABSTRACT
When formed through dynamical interactions, stellar-mass binary black holes may retain eccentric
orbits (
e >
0
.
1 at 10 Hz) detectable by ground-based gravitational-wave detectors. Eccentricity can
therefore be used to differentiate dynamically-formed binaries from isolated binary black hole mergers.
Current template-based gravitational-wave searches do not use waveform models associated to eccentric
orbits, rendering the search less efficient to eccentric binary systems. Here we present results of a
search for binary black hole mergers that inspiral in eccentric orbits using data from the first and
second observing runs (O1 and O2) of Advanced LIGO and Advanced Virgo. The search uses minimal
assumptions on the morphology of the transient gravitational waveform. We show that it is sensitive to
binary mergers with a detection range that is weakly dependent on eccentricity for all bound systems.
Our search did not identify any new binary merger candidates. We interpret these results in light of
eccentric binary formation models.
Keywords:
eccentric BBH, LIGO-Virgo
1.
INTRODUCTION
In their first two observing runs, the Advanced LIGO
and Advanced Virgo detectors discovered 10 binary
black hole (BBH) mergers and a binary neutron star
merger (Abbott et al. 2018b). These detections have
already provided a wealth of information on cosmic pro-
cesses, including the rate, mass, spin and redshift dis-
tribution of BBH mergers (Abbott et al. 2016f, 2018a),
constraints on general relativity (Abbott et al. 2016e,
2019c), estimates of the Hubble constant (Abbott et al.
2017a; Soares-Santos et al. 2019; Abbott et al. 2019b),
and constraints on multi-messenger emission from the
mergers (Adri ́an-Mart ́ınez et al. 2016; Abbott et al.
2016d; Albert et al. 2017; Burns et al. 2018; Abbott
et al. 2019a, 2008).
A key question that remains unanswered is how BBHs
are formed. Viable formation channels include isolated
binary evolution (e.g. Bethe & Brown 1998; Belczyn-
ski et al. 2002, 2014, 2016; Dominik et al. 2013; Men-
nekens & Vanbeveren 2014; Spera et al. 2015; Eldridge
& Stanway 2016; Marchant et al. 2016; Mandel & de
Mink 2016; Mapelli et al. 2017; Mapelli & Giacobbo
2018; Stevenson et al. 2017; Giacobbo & Mapelli 2018;
Kruckow et al. 2018; Barrett et al. 2018) and dynamical
encounters in dense stellar environments, such as glob-
ular clusters (e.g. Portegies Zwart & McMillan 2000;
O’Leary et al. 2006; Sadowski et al. 2008; Downing et al.
2010, 2011; Rodriguez et al. 2015, 2016a,b; Rodriguez &
Loeb 2018; Askar et al. 2017; Samsing 2018; Samsing
et al. 2018; Fragione & Kocsis 2018; Zevin et al. 2019),
young star clusters (e.g. Banerjee et al. 2010; Ziosi et al.
2014; Mapelli 2016; Banerjee 2017, 2018; Di Carlo et al.
2019; Kumamoto et al. 2018) and galactic nuclei (e.g.
O’Leary et al. 2009; Antonini & Perets 2012; Antonini
& Rasio 2016; Petrovich & Antonini 2017; Stone et al.
2017b,a; Rasskazov & Kocsis 2019). Moreover, the dy-
namical process known as Kozai–Lidov (KL) resonance
(Kozai 1962; Lidov 1962) can trigger the merger of a
BBH, even if the BBH has not been formed in a dense
star cluster. In fact, if the BBH is orbited by a tertiary
body (i.e. the BBH is the inner binary of a stable hierar-
chical triple system), the KL mechanism triggers oscil-
lations of the BBH’s eccentricity, which might speed up
the merger by gravitational-wave emission. Each chan-
nel is expected to produce black hole mergers with dif-
ferent mass and spin distributions (Abbott et al. 2018a;
Mandel & O’Shaughnessy 2010; Rodriguez et al. 2016c;
Abbott et al. 2016a; Farr et al. 2017). The limited statis-
tics from the low number of systems detected through
gravitational waves and model uncertainties so far do
not allow strong constraints on the formation channels.
Orbital eccentricity is a distinguishing feature of dy-
namical formation channels. Gravitational-wave emis-
sion acts to circularize binary orbits by the time they
reach orbital frequencies to which Advanced LIGO and
Advanced Virgo are sensitive (
&
10 Hz). Eccentric or-
bits in the Advanced LIGO and Advanced Virgo band
indicate either that the binary was formed with small
arXiv:1907.09384v1 [astro-ph.HE] 22 Jul 2019
2
orbital separation and therefore did not have time to
circularize, or that some dynamical process increased
the eccentricity. For example, KL-induced mergers are
expected to be associated with high eccentricities (see,
e.g. Antonini et al. 2017). The detection of gravita-
tional waves from an eccentric binary would suggest that
binary systems can form dynamically, and could help
distinguish between different dynamical formation sce-
narios (KL oscillations in triple systems or dynamical
encounters in dense stellar clusters) (Lower et al. 2018).
In the following we define eccentricity at the time
when the gravitational-wave frequency of the binary is
at 10 Hz (Peters & Mathews 1963). Eccentricity con-
stantly evolves during the inspiral.
Template-based gravitational-wave searches used by
Advanced LIGO and Advanced Virgo currently do
not include eccentric orbital templates (Abbott et al.
2018b). Quasi-circular waveform templates are able to
detect binaries with small eccentricities (
e
.
0
.
1), but
are inefficient at extracting moderately to highly ec-
centric binaries (Brown & Zimmerman 2010). Multiple
efforts for generating the full inspiral merger ringdown
(IMR) waveforms for the binaries with eccentric orbits
are underway (Cao & Han 2017; Hinder et al. 2018;
Ireland et al. 2019; Huerta et al. 2018; Hinderer &
Babak 2017). However, the lack of a reliable and com-
plete waveform model prevents the implementation of a
matched-filtering search at this time, and led to the de-
velopment of alternative search methods (Tiwari et al.
2016; Coughlin et al. 2015; Lower et al. 2018).
Here we report the results of a search for eccentric bi-
nary black hole mergers with the coherent WaveBurst
(cWB) algorithm that does not rely on binary system
waveforms. cWB is sensitive to binaries of any eccen-
tricity, and in particular to high-mass black holes. The
search has been carried out over data from Advanced
LIGO and Advanced Virgo’s O1 and O2 observing runs,
and found no evidence of eccentric binary signals. This
paper evaluates the sensitivity of cWB to eccentric bi-
nary mergers, and infers constraints from non-detection
on the rate of eccentric mergers.
2.
DETECTORS AND ANALYSIS METHOD
2.1.
Advanced LIGO and Advanced Virgo
The Advanced LIGO detectors began their first ob-
serving run O1 on September 12, 2015, which lasted un-
til January 19, 2016 (Abbott et al. 2016b). During this
time they accumulated
T
obs
,
1
= 48 days of coincident
data during which both LIGO Hanford and LIGO Liv-
ingston detectors were operating. The second observing
run O2 started on November 30, 2016 and lasted until
August 25, 2017, resulting in
T
obs
,
2
= 118 days of coinci-
dent data (Abbott et al. 2018b). Advanced Virgo joined
the Advanced LIGO detectors on August 1, 2017. The
detectors’ sensitivity was not uniform during these runs,
and there was a marked sensitivity increase from O1 to
O2 (Abbott et al. 2018c). As adding Advanced Virgo
data was not improving the sensitivity of the search,
this analysis only uses data from the Advanced LIGO
detectors.
2.2.
Search description
The search for eccentric binary black hole mergers ue-
ses the same configuration of the cWB pipeline (Kli-
menko et al. 2008, 2016) as the binary black hole merger
search reported in Abbott et al. (2018b). An early ver-
sion of the search is described in (Tiwari et al. 2016).
cWB is designed to search for transient signals, with-
out specifying a waveform model. It identifies coherent
excess power in multi-resolution time-frequency repre-
sentations of the detectors’ strain data, for signal fre-
quencies up to 1 kHz and duration up to a few seconds.
The excess power is collected in the time-frequency plane
assuming monotonically increasing frequency for better
collection of the signal energy from binary black holes.
The search identifies events that are coherent in multi-
ple detectors and reconstructs the source sky location
and signal waveforms by using the constrained maxi-
mum likelihood method.
The cWB detection statistic
ρ
is based on the coherent
energy
E
c
obtained by cross-correlating the signal wave-
forms reconstructed in the network of detectors. It is
proportional to the coherent network signal-to-noise ra-
tio. The estimation of statistical significance of an event
is done by ranking the
ρ
of the event against the
ρ
distri-
bution for background events obtained by repeating the
analysis on time-shifted data. To exclude astrophysical
events from the background sample, the time shifts are
much larger than the expected signal delay between the
detectors. Each cWB event was assigned a False Alarm
Rate (FAR) based on the rate of background triggers
with
ρ
higher than that of the event.
To increase the robustness against non stationary
detector noise generating glitches, cWB uses signal-
independent vetoes:
the network correlation
c
c
=
E
c
/
(
E
c
+
E
n
), where
E
n
is the residual noise energy
estimated after the reconstructed signal pixels are sub-
tracted from the data. For a gravitational-wave signal
we expected
c
c
≈
1 while for glitches
c
c
1. Events
with
c
c
<
0
.
7 are rejected.
Detector characterization studies are also carried out
to ensure that candidate events are not due to instru-
mental or environmental artifacts. We have rejected the
3
times where significant instrumental artifacts make the
data unusable (Abbott et al. 2016c).
2.3.
Simulated astrophysical signals
In order to estimate the sensitivity of our search, we
simulated eccentric BBH signals, injected them into de-
tector data and searched for them using cWB. We used
a BH mass range of 5 M
−
50 M
(Abbott et al. 2018a),
and eccentricities in the
e
∈
[0
,
0
.
99] range. We assumed
that BHs have zero spin. These simulations were carried
out to quantify the search sensitivity for individual bi-
naries. Below we considered different mass distributions
to characterize our sensitivity.
At the time of the analysis only one set of templates
was available for the generation of full inspiral-merger-
ringdown eccentric binary waveforms including generic
spin configurations by East et al. (2013). It uses a pre-
scription based on the equations of motion of a geodesic
in a Kerr spacetime, coupled with the quadrupole for-
mula for the gravitational radiation. The model defines
an effective Kerr spacetime whose mass and spin param-
eters are set equal to the total mass and orbital angular
momentum of the binary. The binary is evolved based
on the behavior of a timelike geodesic in the effective
Kerr spacetime, but the mass and angular momentum
of this spacetime are changed at each time step based
on the emitted energy and angular momentum calcu-
lated in the quadrupole approximation. This approach
reproduces the correct orbital dynamics in the New-
tonian limit and general-relativistic test particle limit.
This model also incorporates strong-field features such
as pericenter precession, frame dragging, and the exis-
tence of unstable orbits and related zoom-whirl dynam-
ics (East et al. 2013). The inspiral waveforms obtained
using the above treatment are stitched to a merger
model that was developed for quasicircular mergers but
also performs well for eccentric mergers with little mod-
ification (Baker et al. 2008; Kelly et al. 2011). In Fig.
1 we show this waveform for the case of circular and
eccentric (
e
= 0
.
5) orbits.
The waveforms we used here are likely not suffi-
ciently accurate for optimal template-based detection.
Compared to gravitational waveforms obtained using
general-relativistic numerical simulations, the wave-
forms differ in overlap by up to a few percent (East
et al. 2013). However, these waveforms are sufficiently
accurate to be used to assess the efficiency of the un-
modeled search used.
3.
RESULTS
This search has detected 7 of the 10 BBH events that
were identified by template based searches (its sensitiv-
ity compared to template based searches is higher for
higher mass binaries; see Table 1 in Abbott et al. 2018b)
. We considered these events to have no eccentricity.
Our search did not detect any gravitational-wave event
beyond these. Therefore, we concluded that no eccentric
BBH merger has been detected. Below we present our
search sensitivity to interpret this non-detection.
We note that the detection by cWB and the less-
confident template-based detection of an event would
not necessarily mean that the event was an eccentric
binary (see, e.g., Abbott et al. 2018b). The eccentric-
ity of a detected event would need to be independently
measured (e.g., Lower et al. 2018).
3.1.
Sensitivity to eccentric mergers
We characterized the sensitivity of our search by cal-
culating its
range
—the distance, averaged over observa-
tion time, sky location and orientation, within which a
BBH can be detected with false alarm rate
≤
10
−
2
yr
−
1
.
For this calculation we adopted a standard cosmological
model with Hubble parameter
H
0
= 67
.
9 km s
−
1
Mpc
−
1
and Ω
M
= 0
.
3065 (Ade et al. 2016). The range de-
pends on the black hole masses, and is different for
the O1 and O2 observing runs. In particular it de-
pends on the chirp mass
M
of the binary, where
M ≡
(
m
1
m
2
)
3
/
5
(
m
1
+
m
2
)
−
1
/
5
for black hole masses
m
1
and
m
2
. We find that cWB range is independent of the ec-
centricity for the whole mass range considered (see also
Tiwari et al. 2016). Our ranges, using the eccentric
waveforms described in Section 2.3, are shown in Fig.
2. We additionally see that the sensitive range of cWB
grows faster with chirp mass than the range of template-
based searches, making cWB additionally useful for cir-
cular binaries at higher masses (see also Abbott et al.
2017b).
3.2.
Astrophysical constraints
In order to compare our results to astrophysical
source populations, we calculated the volume-time (VT)
probed by our search. VT depends on the mass distri-
bution of the BBH population. Dynamical formation
channels are expected to result in different BH mass and
mass ratio distributions than BBH mergers from field
binaries (Rodriguez et al. 2018; Kimpson et al. 2016).
We considered a BBH mass distribution such that the
mass of the more massive BH,
m
1
, follows a power-law
distribution
m
−
β
within the range [5 M
,
50M
] for dif-
ferent
β
values (see below), while the second BH’s mass,
m
2
is uniformly distributed within the range [5 M
,m
1
].
The mass distribution of BBH mergers detected by Ad-
vanced LIGO and Advanced Virgo so far is somewhat
different from this assumed distribution (Abbott et al.
2018b,a).
However, eccentric BBH merger channels
4
2.00
1.75
1.50
1.25
1.00
0.75
0.50
0.25
0.00
time [s]
0.2
0.1
0.0
0.1
0.2
amplitude [arbitrary units]
e
= 0
e
= 0.5
Figure 1.
Examples of gravitational waveforms for a 10 M
−
10 M
BBH system with eccentricities 0 (black) and 0.5 (red).
5
10
15
20
25
30
35
40
45
M
chirp
[M
]
0
200
400
600
800
1000
1200
1400
Search range [Mpc]
O2
O1
CBC (O2)
CBC (O1)
CBC O1
e
= 0
CBC O2
e
= 0
cWB O1
e
= 0
cWB O1
e
= 0.5
cWB O1
e
= 0.9
cWB O2
e
= 0
cWB O2
e
= 0.5
cWB O2
e
= 0.9
Figure 2.
Range of the cWB analysis to BBH mergers as
a function of the binary’s chirp mass, separately for the O1
and O2 observing runs, and for different orbital eccentricities
(see legend). The shaded regions represent 1
σ
uncertainties.
The dotted lines are linear fits on the ranges at chirp masses
>
30 M
for
e
= 0. For comparison, we show the sensitive
ranges for template-based searches for compact binary co-
alescence (CBC), assuming
e
= 0, for O1 and O2 (Abbott
et al. 2018c). Masses are given in source-frame.
are likely responsible for only a subset of these obser-
vations and therefore they do not fully determine the
overall spectrum. With this mass distribution model,
we find that VT(
β
)
≈{
6
.
6
,
2
.
4
,
0
.
75
}×
10
−
2
Gpc
3
yr for
β
=
{
1
,
2
,
3
}
, respectively.
The BBH merger rate density for processes that can
lead to eccentric orbits in the Advanced LIGO and Ad-
vanced Virgo band is mostly predicted to be up to a few
Gpc
−
3
yr
−
1
(Antonini & Rasio 2016; Rodriguez et al.
2016b; Silsbee & Tremaine 2017; Bartos et al. 2017;
Petrovich & Antonini 2017; Hoang et al. 2018; Hamers
et al. 2018; Yang et al. 2019; Kocsis et al. 2006), while
some more extreme models predict merger rate densi-
ties up to 100 Gpc
−
3
yr
−
1
(VanLandingham et al. 2016;
Rasskazov & Kocsis 2019). The fraction of mergers from
these processes that have high eccentricity (
e
&
0
.
1)
ranges from
∼
1% (Randall & Xianyu 2018b,a) to close
to all mergers (Petrovich & Antonini 2017; Gond ́an et al.
2018).
In order to understand the astrophysical rate density
constraints of our results, we considered a dynamical for-
mation channel that produces BBH mergers at rate den-
sity
R
dyn
, with a mass power-law index
β
(see above).
We assumed that a fraction
f
ecc
of mergers from this
channel have eccentricities
e >
0
.
1, and that this BBH
sub-population follows the mass distribution considered
here. We further assumed that all BBH mergers de-
tected by Advanced LIGO and Advanced Virgo so far
have eccentricities
e <
0
.
1. The expected number of ec-
centric mergers (
e >
0
.
1) from this model detected by
cWB during O1 and O2 is then
〈
N
cWB
,
ecc
〉
=
R
dyn
f
ecc
VT(
β
)
.
(1)
Given that no such eccentric merger was detected, the
Neyman 90% confidence-level upper limit is
R
ul
,
ecc
=
2
.
3
f
ecc
VT(
β
)
.
(2)
where
β
=
{
1
,
2
,
3
}
. We obtained
R
ul
,
ecc
=
{
30
,
90
,
300
}
f
−
1
ecc
Gpc
−
3
yr
−
1
(3)
for
β
=
{
1
,
2
,
3
}
, respectively. The quoted approxi-
mate values were rounded to the first significant digit.
We found that this result does not depend on the ec-
centricity distribution of the source population as our
search sensitivity only weakly depends on eccentricity.
Our results rule out models predicting
&
100 Gpc
−
3
yr
−
1
merger rate densities (VanLandingham et al. 2016;
5
Rasskazov & Kocsis 2019) for
β
.
2 if the majority of
mergers in the given model have eccentricities
e >
0
.
1.
4.
CONCLUSION
We searched for eccentric BBH mergers using the cWB
algorithm. We showed that the sensitivity of our method
is independent of the eccentricity at the time the binary
enters Advanced LIGO and Advanced Virgo’s frequency
band at
∼
10 Hz.
Our search only uncovered binaries that have also
been found by template-based searches that do not ap-
pear to have eccentric orbits. We interpreted this non-
detection in light of the expected merger rate density
of BBH formation channels that can produce eccentric
orbits, and the fraction of these mergers that have ec-
centricities
&
0
.
1. Our results rule out the highest end of
the rate density predictions (
&
100 Gpc
−
3
yr
−
1
) assum-
ing that the majority of the binaries from these channels
have
e >
0
.
1, and that the power-law index of the BH
mass spectrum is
.
2.
Future observing runs by Advanced LIGO, Advanced
Virgo and KAGRA (Aso et al. 2013) will provide sub-
stantially improved sensitivity to probe formation mech-
anisms resulting in eccentric binaries (Abbott et al.
2018c).
The authors gratefully acknowledge the support of the
United States National Science Foundation (NSF) for
the construction and operation of the LIGO Laboratory
and Advanced LIGO as well as the Science and Tech-
nology Facilities Council (STFC) of the United King-
dom, the Max-Planck-Society (MPS), and the State of
Niedersachsen/Germany for support of the construc-
tion of Advanced LIGO and construction and opera-
tion of the GEO600 detector. Additional support for
Advanced LIGO was provided by the Australian Re-
search Council. The authors gratefully acknowledge the
Italian Istituto Nazionale di Fisica Nucleare (INFN),
the French Centre National de la Recherche Scientifique
(CNRS) and the Foundation for Fundamental Research
on Matter supported by the Netherlands Organisation
for Scientific Research, for the construction and oper-
ation of the Virgo detector and the creation and sup-
port of the EGO consortium. The authors also grate-
fully acknowledge research support from these agencies
as well as by the Council of Scientific and Industrial Re-
search of India, the Department of Science and Technol-
ogy, India, the Science & Engineering Research Board
(SERB), India, the Ministry of Human Resource Devel-
opment, India, the Spanish Agencia Estatal de Inves-
tigaci ́on, the Vicepresid`encia i Conselleria d’Innovaci ́o,
Recerca i Turisme and the Conselleria d’Educaci ́o i Uni-
versitat del Govern de les Illes Balears, the Consel-
leria d’Educaci ́o, Investigaci ́o, Cultura i Esport de la
Generalitat Valenciana, the National Science Centre of
Poland, the Swiss National Science Foundation (SNSF),
the Russian Foundation for Basic Research, the Rus-
sian Science Foundation, the European Commission, the
European Regional Development Funds (ERDF), the
Royal Society, the Scottish Funding Council, the Scot-
tish Universities Physics Alliance, the Hungarian Scien-
tific Research Fund (OTKA), the Lyon Institute of Ori-
gins (LIO), the Paris
ˆ
Ile-de-France Region, the National
Research, Development and Innovation Office Hungary
(NKFIH), the National Research Foundation of Korea,
Industry Canada and the Province of Ontario through
the Ministry of Economic Development and Innovation,
the Natural Science and Engineering Research Council
Canada, the Canadian Institute for Advanced Research,
the Brazilian Ministry of Science, Technology, Innova-
tions, and Communications, the International Center for
Theoretical Physics South American Institute for Fun-
damental Research (ICTP-SAIFR), the Research Grants
Council of Hong Kong, the National Natural Science
Foundation of China (NSFC), the Leverhulme Trust, the
Research Corporation, the Ministry of Science and Tech-
nology (MOST), Taiwan and the Kavli Foundation. The
authors gratefully acknowledge the support of the NSF,
STFC, MPS, INFN, CNRS and the State of Niedersach-
sen/Germany for provision of computational resources.
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