The Science Case for LIGO-India
M. Saleem
1,7
, Javed Rana
9
, V. Gayathri
5,6
, Aditya Vijaykumar
2
,
Srashti Goyal
2
, Surabhi Sachdev
9
, Jishnu Suresh
11
, S.
Sudhagar
4
, Arunava Mukherjee
8
, Gurudatt Gaur
12
, Bangalore
Sathyaprakash
9
, Archana Pai
5
, Rana X Adhikari
2,3
, P. Ajith
2
,
Sukanta Bose
4,10
1
Chennai Mathematical Institute, Siruseri 603103, Tamilnadu, India
2
International Centre for Theoretical Sciences, Tata Institute of Fundamental
Research, Bangalore 560089, India
3
LIGO Laboratory, California Institute of Technology, USA
4
Inter-University Centre for Astronomy and Astrophysics (IUCAA), Post Bag 4,
Ganeshkhind, Pune 411 007, India
5
Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400
076, India
6
Department of Physics, University of Florida, PO Box 118440, Gainesville, FL
32611-8440, USA
7
School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455,
USA
8
Saha Institute of Nuclear Physics, HBNI, 1/AF Bidhannagar, Kolkata-700064, India
9
Institute for Gravitation and the Cosmos, The Pennsylvania State University,
University Park, PA 16802, USA
10
Department of Physics and Astronomy, Washington State University, 1245 Webster,
Pullman, WA 99164-2814, USA
11
Institute for Cosmic Ray Research (ICRR), The University of Tokyo, Kashiwa City,
Chiba 277-8582, Japan
12
Institute of Advanced Research, Gandhinagar 382 426, Gujarat, India
E-mail:
sukanta@iucaa.in
4 January 2022
Abstract.
The global network of gravitational-wave detectors has completed three
observing runs with
∼
50 detections of merging compact binaries.
A third LIGO
detector, with comparable astrophysical reach, is to be built in India (LIGO-Aundha)
and expected to be operational during the latter part of this decade. Such additions to
the network increase the number of baselines and the network SNR of GW events. These
enhancements help improve the sky-localization of those events. Multiple detectors
simultaneously in operation will also increase the baseline duty factor, thereby, leading
to an improvement in the detection rates and, hence, the completeness of surveys. In
this paper, we quantify the improvements due to the expansion of the LIGO Global
Network (LGN) in the precision with which source properties will be measured. We also
present examples of how this expansion will give a boost to tests of fundamental physics.
arXiv:2105.01716v2 [gr-qc] 31 Dec 2021
CONTENTS
2
Contents
1 Introduction
3
1.1 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.2 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2 CBC Detection rates
5
2.1 Detection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
2.2 Improvement in the effective duty-factor of a network . . . . . . . . . . . .
6
2.3 Detection rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
3 Parameter estimation
8
3.1 Improvement in errors for binary black hole events . . . . . . . . . . . . . .
9
3.1.1 Sky-localization: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.1.2 Luminosity distance and inclination angle: . . . . . . . . . . . . . . . 10
3.1.3 Source masses: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Improved measurements of matter effects: source classification and BNS
properties: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4 Sky localization and early warning
14
4.1 Early warning of binary neutron star mergers . . . . . . . . . . . . . . . . . 17
5 Tests of GR
20
5.1 Improved constraints on deviations from GR . . . . . . . . . . . . . . . . . . 20
5.2 Constraints on the nature of GW polarisations . . . . . . . . . . . . . . . . . 21
6 Conclusions and summary
22
CONTENTS
3
1. Introduction
The global network of gravitational-wave (GW) detectors (comprising the two LIGO
interferometers [1] and the Virgo interferometer [2]) has completed three observing
runs with
∼
50 detections of merging compact binaries [3]. A fourth detector in Japan [4]
is now being commissioned and is expected to join the global network in 2022. A
third LIGO detector with comparable astrophysical reach is being built in India [5]
and is expected to be operational during the latter part of this decade.
Several
detectors operating in different parts of the globe provide multiple long baselines and
an increased network SNR. These characteristics help improve the sky-localization of
GW events, among other things [6]. Multiple detectors operating simultaneously will
also improve the duty factor of the network leading to improvements in the detection
rates.
In this paper we quantify the improvements arising due to the addition of a LIGO
detector in India to the LIGO Global Network (LGN). The global GW detector network
will include, additionally, Virgo and KAGRA, further enhancing the improvements
described herein. In this work, we choose to focus on the LGN to understand the
improvement in the network during times when Virgo and KAGRA are not taking
data. We quantitatively describe how this leads to better astrophysical insights about
the source properties and how that improves our ability to probe fundamental physics
and cosmological models. We find that the addition of a new detector in India brings
substantial benefits to the scientific capabilities of the LGN.
1.1. Detectors
The LGN will consist of 3 interferometers in the upgraded configuration of Advanced
LIGO (so-called A+) [7], with the third detector in Aundha, in the Hingoli district,
in the eastern part of the state of Maharashtra, India. It is expected that the two
LIGO detectors in the U.S. will be upgraded into this configuration in
∼
2026 and that
the detector in Aundha will come online soon after. Following the existing naming
convention
‡
the detector in India will be referred to as LIGO–Aundha (A). The LIGO
Global Network with and without LIGO-Aundha will be denoted as AHL and HL,
respectively. Our studies below compare their performances, mainly related to the
compact binary coalescence searches. Networks involving additional detectors will
likely see further improvement in performances than what is found here. Moreover,
the involvement of other detectors may reduce the impact of the improvements that the
addition of LIGO-Aundha alone would bring. The broader study is, however, beyond
the scope of this work.
‡
where the detectors are named after the nearby town; LIGO–Hanford (H) and LIGO–Livingston (L)
CONTENTS
4
10
1
10
2
10
3
Frequency [Hz]
10
−
24
10
−
23
10
−
22
10
−
21
Strain [1/
√
Hz]
O1
O2
O3
O3 Virgo
Adv LIGO Design
Adv LIGO+
Figure 1: Strain noise spectral density of the LIGO Interferometers during the
observing runs O1-O3. Also shown are the Virgo O3 noise, the Advanced LIGO
design sensitivity, and the A+ sensitivity for the LIGO detectors Aundha, Hanford,
and Livingston (labeled as “Adv LIGO+").
1.2. Simulations
The compact binary coalescences (CBCs) observed in the GW window range in total
mass from 3 – 150
M
Ø
. While most of the binary systems harbor primary objects with
masses
<
45
M
Ø
, a few systems have the primary heavier than 45
M
Ø
. The recently
released gravitational-wave transient catalog (GWTC-2) considers several population
mass distribution models to obtain the merger rates [3, 8]. For the simulations in
this study, we use one of those mass models with the model parameters taken from
the observed binary black-hole mergers [8]. In this model, the primary mass follows
a power-law distribution with some spectral index up to a certain maximum mass
and a uniform Gaussian component with a finite width to account for high masses,
together with a smoothing function at low masses to avoid a hard cut-off. The mass
ratio follows a smoothed power-law distribution. We choose the median values of the
hyper-parameters of these distributions inferred in [8] for simulations.
Astrophysical models suggest that binary black holes with isotropically distributed
component spins can form in dense environments, such as globular clusters and galactic
centers. At the same time, we expect black-hole spins to get aligned with the orbital
angular momentum in isolated binaries [9, 10]. The black hole spin distribution uses a
CONTENTS
5
model that is a mixture of both these possibilities [8]. We use this model for drawing
the spins of both the compact objects in a binary for our simulations. Besides, the
binary sources are oriented uniformly and distributed uniformly over the sky and
placed uniformly in co-moving volume up to a red-shift of 1.5 using the Planck 2015
cosmology [11].
The binary black hole (BBH) simulations described above are used in various
studies below on quantifying the improvement in the performance of the network
arising from its expansion to include LIGO-Aundha. These include a discussion of
BBH detection rates in Section 2 and quantifying the improvement in the estimation of
binary parameters in Section 3. In Section 4, we discuss the possibility of sending early
warning alerts to electromagnetic and particle observatories before the epoch of binary
coalescence. We make projections in Section 5 on how a detected BBH population can
be used to place observational bounds on deviations from General Relativity (GR).
2. CBC Detection rates
Coalescing compact binaries involving neutron stars and black holes are, so far, the only
GW sources detected in past GW observing runs [12, 3]. The inclusion of LIGO-Aundha
in the LGN will boost the rate at which we detect such binaries. This enhancement
will arise owing to improved sky-coverage, distance reach, and baseline duty factor,
which is the effective observation period of a detector network. In this section, we
quantitatively assess the improvement in the CBC detection rate (
R
det
) for AHL
vis à
vis
the HL network.
We focus here on the stellar-mass BBHs, which are the main contributor to
the menagerie of signals observed by LIGO-Virgo so far.
Our analysis can be
straightforwardly extended to classes of CBC sources that involve neutron stars.
For an astrophysical population of BBHs with a comoving constant merger-rate
density
r
merg
in units of Gpc
−
3
yr
−
1
, the detection rate (per year) is given by
R
det
=
r
merg
×〈
V T
〉
, where
〈
V T
〉
is the population-marginalized detection volume averaged
over the period of observation for any given detector network (for more details, see
[3, 13] and the references therein). The assumption that
r
merg
is non-evolving w.r.t.
redshift is a simplified assumption and hence could affect the rates we reported in this
paper, however it has negligible impact on the rates comparison between two networks
which is the goal of this study. The factor
〈
V T
〉
crucially depends on the number of
detectors, their sensitivity as well as the search methodologies and their ability to treat
the non-Gaussian noisy transients in the multi-detector data.
CONTENTS
6
2.1. Detection criteria
We simulate the noise in any detector as Gaussian, with a vanishing mean, and
uncorrelated with the noise in any other detector.
§
Then the network coherent
SNR-squared is the sum of the SNR-squared of signals in the individual detectors
[18, 19]. Below we discuss two alternative criteria for assessing whether a signal can
be considered as detected by a network (similar considerations are made in [20]):
(i)
Coherent network SNR criterion
: For an
N
-detector network, this criterion
is
√
∑
N
k
=
1
ρ
2
k
≥
ρ
net
thresh
, where
ρ
k
is the SNR at the
k
th
detector. Here we set the
threshold of
ρ
net
thresh
to a value that keeps the false-alarm probability associated
with it low enough to make a confident detection case.
(ii)
Multi-detector coincidence criterion
:
√
∑
N
k
=
1
ρ
2
k
≥
ρ
net
thresh
and
ρ
k
>
4 for at least
two of the
N
detectors.
For the LGN studied here we set
ρ
net
thresh
=
12, which is conservative in the sense
that there have been detections with two or three detectors with network SNR below
12. We present search performance metrics for both criteria below.
Arguably, the simplest way to identify interesting detection candidates is to apply
the first criterion. Its biggest advantage is that it allows for picking up sources that are
loud enough in one detector but weak in the others, e.g., if located in their blind-spots.
This can happen since no two detectors have the same orientation. Nevertheless, this
criterion has a few limitations: For instance, a loud noise-transient in a single detector
(
e.g,
non-Gaussian glitches) can give rise to a trigger that satisfies this network criterion
and, therefore, gets misclassified as a detection candidate. On the other hand, if one
requires that at least two detectors record a high enough SNR, such as what the second
criterion above employs, then the false-alarm rate reduces significantly (such as by
mitigating the effects of non-Gaussian glitches), albeit by sacrificing some degree of sky
coverage (figure 1).
2.2. Improvement in the effective duty-factor of a network
Duty factor of a detector (network) is defined as the fraction of clock time for which the
detector (network) acquires science quality data. Assuming that each detector in the
network has a duty factor of
d
f
, one can analytically compute the effective duty factor
d
f
eff
for each multi-detector network. For the multi-detector coincidence criterion,
d
f
eff
is the fraction of the observation period during which at least two of the detectors
§
This is a simplification since real detector noise contains non-Gaussian transients, which contribute
to the background rate. Still modeling detector noise as Gaussian is useful. As has been demonstrated
in multiple LIGO-Virgo CBC and detector characterization papers [14, 15, 16, 17], glitch classification
and mitigation techniques have achieved some degree of success in cleaning the background to make
it largely Gaussian-like. Simulation studies, like ours, are not the first ones, and are useful also for
providing targets and benchmarks for those data quality/cleaning efforts. It is for these reasons Gaussian
studies remain relevant.
CONTENTS
7
50
60
70
80
90
100
Single detector duty factor (%)
30
40
50
60
70
80
90
100
Network duty factor (%)
HL (criterion-(i))
AHL (criterion-(i))
HL (criterion-(ii))
AHL (criterion-(ii))
400
500
600
700
800
900
R
det
per year
0.0000
0.0025
0.0050
0.0075
0.0100
0.0125
0.0150
0.0175
0.0200
Probability density
HL (criterion-(i))
AHL (criterion-(i))
HL (criterion-(ii))
AHL (criterion-(ii))
Figure 2: [Left] Network duty factors of the HL and AHL networks as functions of the
single-detector duty factor. [Right] The distribution of the detection rates of stellar-
mass binary black-hole detection rates for the same two networks using the GWTC-2
population models.
are simultaneously collecting science-quality data while for the network SNR criterion,
it is the fraction of observing period when at least one of the detectors is observing in
science mode. For an
N
-detector network, the effective duty factor is
d
f
eff
=
N
∑
k
=
N
min
N
C
k
d
k
f
(1
−
d
f
)
N
−
k
,
(1)
where the summation runs from
k
=
N
min
to
k
=
N
with
N
min
being the minimum
number of detectors required by the coincidence criterion. Specifically, we have
N
min
=
1 for criterion-(i) and
N
min
=
2 for criterion-(ii). The combinatorics symbol
N
C
k
denotes
the number of possible unique
k
-detector combinations one can form in a network of
N
detectors. Figure 2 shows how the effective duty factor improves with the addition
of LIGO-Aundha. Assuming 90% single-detector duty-factor, the AHL duty-factor gets
boosted by a factor of
∼
1
.
2 compared to the HL network if one follows criterion-(ii),
while the improvement is only one per-cent under criterion-(i); see, e.g., Figure 2.
‖
2.3. Detection rates
We perform extensive simulations to estimate the detection rates of merging compact
binaries for the HL and AHL configurations. The published detections of binary black
hole mergers provide an up to date median BBH merger rate density of
r
merg
=
23 Gpc
−
3
yr
−
1
[8]. With this rate density and a uniform source distribution in the comoving
volume, we populate
∼
8684 sources up to a redshift of 1.5.
¶
We perform 8000
‖
Here it is assumed that the unlocked time-stretches are randomly and uniformly distributed over the
full observation period, which excludes any stretches of time scheduled for concurrent downtime for all
detectors.
¶
It is a somewhat arbitrary choice that we truncate the population at a maximum redshift of 1.5.
However, this is motivated by the fact that at higher redshifts, the actual comoving rate density could
significantly be different from the merger rate density at
z
=
0 (the one we assumed in this study)
CONTENTS
8
Network
Criterion (i)
Criterion (ii)
HL
550
.
0
+
30.0
−
29.0
502
.
0
+
29.0
−
27.0
AHL
775
.
0
+
35.0
−
35.0
754
.
0
+
35.0
−
33.0
Table 1: Detection rates (in yr
−
1
) of stellar-mass binary black holes in HL and AHL
networks, assuming A+ sensitivity and a duty factor of 90% for every detector.
batches of simulations, with each batch containing 8684 sources with the mass and
spin distributions following the ones detailed in Section 1.2. We further distribute the
sources uniformly over the sky with the binary orientation distributed uniformly. For
all the sources, we apply the detection criteria (i) and (ii) and obtain the detection rates
(
R
det
). The right panel of Figure 2 provides the distribution of the estimated
R
det
.
Table 1 provides the detection rate estimates of BBH for HL and AHL network
configurations assuming 90% single-detector duty factor.
Compared to HL, the
detection rate in AHL increases by 41% and 50% for criteria (i) and (ii), respectively.
Besides the duty factor, the sky coverage of the two networks determines their detection
rates. Since the coincidence criterion-(ii) exhibits a preference for shortlisting highly
significant events, one can expect that with LIGO-Aundha one will see a perceptible
increase in such events under that criterion.
3. Parameter estimation
With the expansion of the LIGO global network and the consequent enhancement in the
signal-to-noise ratios of the CBC detections and mitigation of parameter degeneracies,
one would anticipate improvements in the astrophysical parameter estimation. In
this section, we employ CBC signal simulations to obtain quantitative support for this
expectation.
For a BBH system in a circular orbit, the gravitational-wave signal is characterized
by component masses (
m
1
,
m
2
), component spins (
~
S
1
,
~
S
2
), the luminosity distance (
D
L
),
orbital inclination angle (
ι
), polarisation angle (
ψ
), sky-position angles (
α
,
δ
) and the
coalescence time and phase (
t
c
,
φ
c
). For a binary neutron star (BNS) system, we
require at least two additional parameters in the form of component tidal deformability
parameters (
Λ
1
,
Λ
2
).
The CBC signal’s multi-dimensional parameter space harbors correlations and
degeneracies among different parameter pairs, contributing to the uncertainties in the
measurements of the individual parameters. For several of these parameters, the error-
bar scales inversely with the signal-to-noise ratio (for loud signals) [21]. While this
holds particularly well for the intrinsic binary parameters, such as component masses
and spins, the aforementioned degeneracies among some pairs, e.g., (i) the sky-location
angles
α
and
δ
and (ii)
d
L
and
ι
, can not often be removed despite high SNR. The
due to the star formation rate as well as the distribution of delay time between the formation and the
coalescence of the binary.
CONTENTS
9
expansion of LGN with LIGO-Aundha, in addition to increasing the SNR, will enhance
parameter estimation accuracy by providing an independent observation of the source
that can significantly reduce the degeneracies among some of the parameters.
In Sec. 3.1 we focus on general parameter estimation for select BBH events, and in
Sec. 3.2 we present the primary results of masses and tidal effects in BNS systems.
3.1. Improvement in errors for binary black hole events
For this study, we simulated binary black hole signals modeled after two of the observed
binary black holes, namely, (i) the loudest BBH, GW150914 [22] and (ii) the most
massive BBH, GW190521 [23]. In fact, GW150914 is the first binary black hole merger
observed by two LIGO detectors and the loudest event so far, with a coherent SNR of
24. The observed component masses were 36
M
Ø
and 29
M
Ø
with a remnant BH of
62
M
Ø
, and the event was located at a luminosity distance of 450 Mpc. It was localized
in a huge sky-patch, spanning 590 sq. degs.
GW190521 is the most massive and among the farthest (5 Gpc) binary black hole
mergers observed so far. Its component masses are 85
M
Ø
and 66
M
Ø
. The remnant was
estimated to have a mass of 142
M
Ø
. This is the first intermediate-mass BH candidate
observed in the gravitational-wave window.
For our two simulations, the injected values of the key parameters are listed in
Table 2 where we choose the masses and spins to be identical to those inferred for
GW150914 and GW190521. From our 8000 batches of BBH simulations described in
Sec. 2, it was found that the population-averaged ratio of SNR at AHL to the SNR at
HL lies in the range of 1.3 – 1.4. We choose the injected sky positions in such a way
that the SNR at AHL is
∼
1
.
4 times the SNR at the HL so that it resembles the average
behaviour of SNR improvement.
The run-of-the-mill Bayesian parameter estimation approach assumes stationary
Gaussian detector noise and a reliable, faithful Einstein’s GR signal model for the GW
signal from the compact binary merger. An up to date suite of models for complete CBC
waveforms constructed by combining various approaches include phenomenological
models, such as IMRPhenom models [24], the effective one-body EOBNR waveforms
that use inputs from numerical relativity [25, 26, 27], and the NRSurrogates waveforms
derived from numerical relativity simulations [28, 29, 30]. In our analysis, we use
the
IMRPhenomPv2
[31, 32, 33, 34, 35] waveform model for both injections as well as
recovery. We use the
Bilby
[36] software package, with its in-built sampler
dynesty
,
to perform the parameter estimation. We perform this analysis with
zero-noise
signal
injections
+
and the likelihood computed using the A+ PSD.
We tabulate the results in terms of improvement in the 90% credible intervals
on various astrophysical parameters in Table 2 and present pictorially in Fig. 3 the
posterior probability contours (at 90%, and 68% credible levels). In that figure, the left
and right panels depict the results for the GW150914- and GW190521-like injections,
+
A zero-noise signal injection refers to data that has only a simulated GW signal and no added noise.
CONTENTS
10
respectively.
Parameter
GW150914-like
GW190521-like
Injected
Improvement
Injected
Improvement
Chirpmass (
M
Ø
)
28.1
33%
64.6
39%
Total mass (
M
Ø
)
65.0
33%
149.6
40%
D
L
in Gpc
2.5
35%
5.3
36%
ι
in deg.
45
27%
45
70%
Sky localization in deg
2
.
92%
96%
Table 2: Parameter estimation improvement in 90% credible intervals in expanding
the network from HL to AHL: We use BBH signals modelled after GW150914 and
GW190521 and estimate the improvement in sky-localization, luminosity distance,
binary inclination, masses and spins. The imporvemnt for a parameter
X
is defined
as ((
∆
X
AHL
−
∆
X
HL
)/
∆
X
HL
)
×
100 where
∆
X
is the 90% credible error bar.
3.1.1.
Sky-localization:
The detector pair comprising LIGO-Aundha and LIGO-
Livingston provides the longest baseline amongst all pairs of existing / in-construction
detectors. This improves the precision with which sources can be localized in the
sky. For the GW150914-like injection, the 90% credible 2-D localization area is
∼
114
deg
2
which improves to
∼
9 deg
2
with AHL. This amounts to 92% reduction in the
localization uncertainty. For GW190521-like injection, we find a
∼
96% reduction, with
the respective localization area for HL and AHL configurations being
∼
971 deg
2
and
∼
35 deg
2
. More discussion on the sky-localization can be found in Sec. 4 and the reader
may also refer to earlier studies on localization, e.g., Refs. [37, 38] and the references
therein.
3.1.2. Luminosity distance and inclination angle:
The three-detector configuration
plays a crucial role in breaking the degeneracy between the luminosity distance
D
L
and the inclination angle
ι
. For the GW150914-like system, the errors in
D
L
and the inclination shrink by 35% and 27%, respectively, for AHL relative to HL.
Similarly, for the GW190521-like injection the error reduction in the same parameters
is 36% and 70%, respectively. The improved distance estimates also benefit from
the reduced 2D sky-localization of the source by the AHL network since, aided by
an improved network SNR, it helps break the degeneracy between distance and sky
position. This will have direct implications in the measurements of cosmological
parameters [39, 40, 41, 42, 43, 44]. We also find significant improvement in the
inclination angle measurement of the binary (
ι
) which is partly due to the resolution
of the distance-inclination degeneracy. Though this analysis has been performed on
binary black hole mergers, similar improvements are expected in the inclination angles
of binary neutron stars and neutron star-black hole mergers as well [45] which are
CONTENTS
11
favourite candidates to have associated EM counterparts. Accurate knowledge of the
inclination angle is key in doing multimessenger astronomy, for making predictions on
the possible EM counterparts and in understanding the physical process that drives
the EM counterparts [46, 47, 48]. Further, improved precision in the binary inclination
helps to probe the gravitational-wave polarisation of the signal. This improvement
directly impacts probing alternative theories of gravity with gravitational wave signals.
In Sec. 5.2 we discuss how polarisation measurements benefit from the expansion of
LGN.
3.1.3. Source masses:
Source-frame masses are defined as the detector-frame masses
divided by a factor (1
+
z
), where
z
is the source redshift, which in turn can reveal the
source luminosity distance given a cosmological model. Therefore, the measurement
of source-frame masses benefits from both the improved SNR and the improved
luminosity distance measurement. For the GW150914-like injection, the errors in
both the source-frame chirpmass and total mass improve by
∼
33%. Similarly, for the
GW190521-like injection, these improvements are 39% and 40%, respectively. See Fig. 3
for the
m
1
−
m
2
contour plots for both the events. Accurate knowledge of the intrinsic
source parameters helps in the population synthesis studies of compact binary mergers
and obtain constraints on the merger rate density [8].
3.2. Improved measurements of matter effects: source classification and BNS
properties:
Binary neutron stars are characterized by the masses (
m
1
,
m
2
) and the tidal
deformability parameters (
Λ
1
,
Λ
2
) [49] of their components. The presence of matter
is predominantly captured by the effective tidal deformability parameter (
̃
Λ
) which is
defined by a suitable combination of
m
1
,
m
2
,
Λ
1
and
Λ
2
[50]. Black holes in general
relativity are predicted to have zero tidal deformability, i.e.,
Λ
1
=
Λ
2
=
0. For a BBH
system, this leads to
̃
Λ
=
0 irrespective of their component masses and spins. Moreover,
precise estimation of the tidal deformability parameters can constrain the theoretically
proposed equations of state of neutron stars and, thus, shed light on the nature of their
internal composition [51, 52, 53].
Here we illustrate how the addition of the LIGO-Aundha detector can potentially
impact our ability to constrain the effective tidal deformability parameter (
̃
Λ
) as well
as discriminate it from the
̃
Λ
=
0 case corresponding to BBHs. We do so by employing a
fully Bayesian statistical framework [54].
We analyze a set of simulated BNS events with source properties consistent with
the first BNS event, GW170817 [51, 54]. Although the chirp-mass (
M
c
) was very well
determined to be 1.188
M
Ø
, the component masses have broader uncertainties due
to the less precisely measured mass-ratio parameter (e.g., the symmetric mass-ratio,
η
). Moreover, although GW170817 could successfully rule out the stiffest equations
of state, it still has sufficiently broader uncertainty in estimated tidal deformability
CONTENTS
12
30
35
40
45
50
m
src
1
(
M
)
20.0
22.5
25.0
27.5
30.0
32.5
35.0
37.5
m
src
2
(
M
)
HL
AHL
60
70
80
90
100
110
120
130
m
src
1
(
M
)
30
40
50
60
70
80
90
m
src
2
(
M
)
HL
AHL
2000
2500
3000
3500
D
L
(
Mpc
)
0.2
0.4
0.6
0.8
1.0
1.2
1.4
jn
HL
AHL
3000
4000
5000
6000
7000
8000
9000
D
L
(
Mpc
)
0.0
0.5
1.0
1.5
2.0
2.5
jn
HL
AHL
0.45
0.50
0.55
0.60
0.65
0.70
Ra
0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Dec
HL
AHL
0.2
0.4
0.6
0.8
1.0
1.2
Ra
0.4
0.2
0.0
0.2
0.4
0.6
0.8
Dec
HL
AHL
Figure 3: Posterior distributions of certain parameters for GW150914-like (left) and
GW190521-like (right) simulated signals in the HL and AHL networks: Top, middle
and bottom panels correspond to the parameters
m
sr c
1
−
m
sr c
2
,
D
L
−
ι
and
R A
−
D ec
,
respectively. The true values are shown by a black star. The 95% and 65% confidence
intervals are shown by solid and dash-dotted lines, respectively.
parameters, thereby, leaving a wide variety of neutron star EOSs viable.
We perform a systematic injection study of Bayesian parameter estimation for a set
of simulated signals from BNS events covering the extreme corners of the parameter
space, comprising component masses and tidal deformability parameters that are
CONTENTS
13
Source parameters
Measurement accuracies
Improvements in %
m
1
,
m
2
Λ
1
,
Λ
2
[
̃
Λ
]
D
L
Network
∆
M
c
∆
η
∆
̃
Λ
∆
M
c
∆
η
∆
̃
Λ
(
M
Ø
)
(Mpc)
(
M
Ø
)
(in %)
(in %)
(in %)
1.35,1.35
400,400 [400]
40
LH
9.7e-5
6.8e-3
131.9
23.7
14.7
24.5
AHL
7.4e-5
5.8e-3
99.6
1.35,1.35
857,857 [857]
40
LH
9.8e-5
6.8e-3
156.9
15.3
14.7
26.6
AHL
8.3e-5
5.8e-3
115.2
1.60,1.17
120,980 [551.5]
40
LH
1.3e-4
9.6e-3
147.9
15.4
13.5
25.5
AHL
1.1e-4
8.3e-3
110.9
1.35,1.35
400,400 [400]
100
LH
1.6e-4
7.6e-3
269.0
18.8
16.3
19.1
AHL
1.3e-4
5.6e-3
217.7
1.35,1.35
857,857 [857]
100
LH
1.7e-4
7.5e-3
418.7
17.6
10.6
47.8
AHL
1.4e-4
6.7e-3
218.6
1.60,1.17
120,980 [551.5]
100
LH
1.9e-4
1.0e-2
384.2
15.8
10.0
44.1
AHL
1.6e-4
9.0e-3
215.0
1.35,1.35
400,400 [400]
250
LH
4.7e-4
8.5e-3
1141.5
25.5
10.6
40.8
AHL
3.5e-4
7.6e-3
675.4
1.35,1.35
857,857 [857]
250
LH
3.5e-4
6.9e-3
1298.6
20.0
17.4
54.7
AHL
2.8e-4
5.7e-3
588.5
1.60,1.17
120,980 [551.5]
250
LH
3.2e-4
1.0e-2
2264.7
9.4
10.0
69.9
AHL
2.9e-4
9.0e-3
638.51
Table 3: This table summarizes comparisons of key properties of binary neutron star
mergers events with high and relatively low-SNR events. Each of the BNS events is
simulated with two neutron star EOSs, one softer (SLy4) and one stiffer (BHB
Λ
φ
).
The uncertainties in mass parameters, namely in chirp-mass (
∆
M
c
) and symmetric
mass-ratio (
∆
η
) as well as uncertainties in the effective tidal deformability parameter
(
∆
̃
Λ
) of the BNS systems are quoted with 90% credible level (see subsection 3.2). The
percentage improvements are quntified following the expresion in Table 2 caption.
consistent with GW170817. Initially, we consider all the sources to be located at a
luminosity distance (
D
L
) of 40 Mpc (similar to the GW170817 event). We consider one
equal-mass BNS (
m
1
=
m
2
=
1
.
35
M
Ø
) and one unequal-mass BNS (
m
1
=
1
.
60
M
Ø
,
m
2
=
1
.
17
M
Ø
), with soft EOS, namely SLy4 [55], consistent with the GW170817 observation.
For the equal-mass case, we also consider the possibility that the neutron stars have a
stiff EOS, namely, BHB
Λ
φ
[56].
Given the current estimation of BNS merger event rates (see Sec. 2), it is
improbable that such an event will be observed at a distance
D
L
.
40 Mpc in the
near future. We, therefore, perform additional simulations with the entire set of
events (a) at
D
L
=
100 Mpc as well as (b) at
D
L
=
250 Mpc. In our simulations, we
use IMRP
HENOM
DNRT
IDAL
waveform model [57] for the coalescing BNS systems
with slow (
|
s
1
|
,
|
s
2
|≤
0
.
05), in-plane component spinning configurations for simplicity
since astronomical distributions demonstrate that more rapidly spinning BNS systems
CONTENTS
14
are rare as well as this configuration captures the key aspects reasonably well. We
summarize the measurements of mass and tidal deformability parameters with 90%
Bayesian uncertainty intervals in table 3.2.
This study demonstrates that for the very high SNR events (with comparable
single detector SNRs
∼
110
−
130 in each of the H, L, and A detectors) the improvement
of precision in
M
c
is in the range of 15
−
25% and in
η
is of about 10
−
17% for the
AHL-network of detectors as compared to the HL-network. The improvement in
̃
Λ
estimation in favor of the AHL-network relative to two US-based detectors is also
nominal – at about 25%. As the source distance increases resulting in a decrease in
SNR, the improvement in precision for
D
L
and
η
does not change much for comparable
SNRs in the three detectors. However, we find that for low SNR events the precision in
̃
Λ
improves significantly. For the set of BNS observation at
D
L
=
100 Mpc, we find that
improvements can be in the range of 20% to 45%. For the more distant sources, e.g., at
D
L
=
250 the improvements are generally more than 40%, and can be as high as 70%
in favor of AHL relative to the HL-network. Moreover, for such distant sources, the
lack of precision in
̃
Λ
can render it difficult to rule out the BBH-case corresponding
to
̃
Λ
=
0, particularly for the soft (SLy4-like) EOS. (As a comparison to the range
of
̃
Λ
parameter for different theoretically motivated neutron star EOS models please
refer to [58].) Thus, for the events with relatively weak signals – which will be at
farther distances and, hence, in relatively abundant numbers – the source classification
(i.e., BBH
vs
BNS/NSBH) will get significantly enhanced. This will be important for
generating alerts for the subsequent follow-up with astronomical observations across
the electromagnetic spectrum.
4. Sky localization and early warning
One of the main advantages of expanding the HL network to include LIGO-Aundha
is that it substantially improves the localization of CBCs in the sky [6, 37]. BNSs
and a fraction of NSBHs have long been expected to produce prompt counterparts and
afterglows in all electromagnetic (EM) bands. For BNS mergers in particular, it has
been hypothesized that the post-merger central engine can launch short gamma-ray
bursts (sGRBs) [59, 60], kilonovae [61, 62], and radio waves and X-rays before and after
merger [63, 64, 65, 66].
These emissions carry information about both the progenitors – e.g., the equation
of state of neutron stars – and the circum-merger environment. The prompt, and often,
transient emission on the one hand and the late-time afterglow on the other hand
complement each other in conveying that information, as was demonstrated amply by
the multi-messenger observations of the binary neutron star event, GW170817 [67].
The joint observation of GWs followed by the sGRB, GRB 170817A, and the kilonova
AT 2017gfo, [67] confirmed the several-decade-old hypothesis that compact object
mergers were progenitors of these exotic transients. However, GW170817 is so far
the only gravitational-wave event to be observed in other channels. Improvements in
CONTENTS
15
GW detectors and expansion of the GW network is therefore required to realize more
multi-messenger observations and expand our knowledge about the physical processes
that occur in these systems.
The chances of telescopes spotting that EM emission improve if the localization
area in the sky associated with the GW signal is small. This is particularly true for
tracking down optical counterparts since the fields of view (FOV), or beam sizes, of these
telescopes are small (sub-arcminutes) compared to the the typical GW sky-localization
area. The small localization with the rapid search strategies [68, 69, 70] can enhance
the probability of finding the optical counterpart of the GW source. For prompt and
transient emission, a narrow sky-area implies a small number of telescope slews and
a quicker locking on to the target before it fades [71]. The search for kilonovae and
prolonged afterglows is aided by narrow sky-areas since they are scannable quickly by
telescopes and make multiple observations of the same telescope fields of view in those
areas more feasible. This, in turn, improves the probablity for spotting their onset.
In the case of larger localizations, the early observations are likely to be missed. In
some cases (e.g., GW190425 [72]), large localizations can prohibit identification of the
EM counterpart entirely. Also, radio follow-up affords complementary observations for
day-time and dust-obscured events, where the hunt in optical is difficult. In that case, a
small volume in 3D localization is important for the galaxy targeted radio observation
to get arcsecond localization [73].
Moreover, if the sky-localization is sharper, then spectroscopy becomes possible,
which can provide not only clues on the progenitor composition but also the redshift
of the event. Spectroscopy requires longer exposure times. A narrow sky error region
implies a smaller number of fields of view to search in for finding the counterpart.
This allows for a quicker homing in on potential counterparts and, therefore, extended
exposures thereafter.
The first discovery of the optical-counterpart of the event
GW170817 was after
∼
11 hours of the GW trigger. Detection of the EM-counterparts
must be much quicker if their prompt emissions are the desired target.
To demonstrate the benefit of including LIGO-Aundha in the GW network, we
simulate a population of binary neutron stars and compare the distribution of GW
localization in the two detector networks: HL and AHL. We generate a population
of 9,308,544 simulated BNS signals using the
TaylorF2
[74, 75, 76, 77] waveform
model. Both source-frame component masses are drawn from a Gaussian distribution
between 1
.
0
M
Ø
<
m
1
,
m
2
<
2
.
0
M
Ø
with mean mass of 1
.
33
M
Ø
and standard deviation
of 0
.
09
M
Ø
, modeled after observations of galactic BNSs [78] (note, however [72]).
The component spins are aligned or anti-aligned with respect to the orbital angular
momentum with the dimensionless spin amplitude on the neutron stars restricted
to 0
.
05, motivated by the low spins of BNSs expected to merge within a Hubble
time [79, 80]. The signals are distributed uniformly in sky, orientation, and comoving
volume up to a redshift of
z
=
0
.
4. We simulate the GW signal and calculate the expected
SNR in Gaussian noise considering the three LIGO detectors at A+ sensitivity for each
BNS. We mimic the results from a matched-filter GW search pipeline (current low-
CONTENTS
16
latency matched-filter searches running on LIGO-Virgo data include
GstLAL
[81, 82],
PyCBCLive
[83],
MBTAOnline
[84],
SPIIR
[85]) by considering the signals that pass
a network SNR threshold of 12.0 to be ‘detected’.
We then calculate the sky-
localization posteriors for the detected candidates using a rapid Bayesian localization
tool,
BAYESTAR
[86]. We use the most recent BNS local merger rate from [72] of
320
+
410
−
240
Gpc
−
3
yr
−
1
to estimate the number of events detected per year in the detector
network.
In Figure 4, we show the distributions (left: cumulative, right: density) of the sky
localizations (90% credible interval) of the BNSs that pass the fiducial SNR threshold
of 12 for the two detector networks: HL in purple and AHL in blue. The shaded regions
show the uncertainty in the number of detections due to the uncertainty in the current
local BNS merger rate of 320 Gpc
−
3
yr
−
1
[72]. The improvement due to the addition of
LIGO-Aundha to the network is clearly visible in this figure; the AHL network detects
about twice (17 – 175) as many signals as the HL (8 – 84) network. Further the peak of
distribution for HL is around 800 deg
2
, about twice that for the AHL network.
Figure 5 shows the shape and the areal projection of several localizations on the
sky. The HL (AHL) localizations are shown in purple (blue) contours. Most of the
HL localizations are long arcs that extend over both hemispheres. When we include
LIGO-Aundha, the degeneracy breaks and the localizations typically shrink to one
of the hemispheres. In this plot, a few blue contours have no corresponding purple
contours. These are the events detected by AHL but not by HL. The orientations of
the HL localizations are concentric. On the other hand AHL localizations are randomly
oriented. This is because a single baseline offers a single time delay for any event,
which in turn is consistent with source sky-positions that all lie on a single circle in
the sky. Of course, detector antenna functions help localize the source position further
in those circles, thereby, reducing the localization area to arcs. The addition of a third
detector provides additional time delays that aid in reducing the error patches further,
as evident in the blue error contours.
The study in Figure 6 compares gravitational-wave sky-localization by HL and
AHL for similar sources in different parts of the sky. For this purpose, we divide the
entire sky into equal-area pixels in HEALPix
∗
format of NSIDE 16 [87]. We inject one
BNS source in each of the 3072 pixels and calculate the localization area of the source
using
BAYESTAR
for HL and AHL. All the injected sources are of
m
1
,
m
2
=
1
.
4
M
Ø
at a
distance of 100 Mpc and have an orbital inclination of 5 deg. In Figure 6, the colorbar
represents the area of the 90% credible region of the localization in deg
2
. In other
words, the pixel value is the 90% probable area of the localization of the source injected
in that pixel. For the HL network, the smallest localization area is
∼
45 deg
2
, and the
largest one is
∼
1732 deg
2
. On the other hand, the smallest and the largest localization
areas for AHL are
∼
1 deg
2
and
∼
21 deg
2
. Compared to HL, the AHL sky areas are
∗
A HEALPix map parameterized by the variable NSIDE is a representation of the full-sky filled with
N
pix
=
12
×
N S I DE
2
equal-area pixels. The value corresponding to a pixel is the probability of finding
the GW source in that pixel in the sky.
CONTENTS
17
10
1
10
2
10
3
10
4
90% credible area (deg
2
)
0
25
50
75
100
125
150
175
Number of events per year
HL
AHL
10
1
10
2
10
3
10
4
90% credible area (deg
2
)
10
−
4
10
−
3
10
−
2
10
−
1
10
0
10
1
Density of events
HL
AHL
Figure 4: Distributions (left: cumulative, right: density) of the sky localizations (90%
credible interval) of the BNSs that pass the fiducial SNR threshold of 12 for the two
detector networks: HL (purple) and AHL (blue). Using the latest median BNS merger
rate from [72] of 320 Gpc
−
3
yr
−
1
, we find that the HL (AHL) network is expected to
detect
∼
33 (69) events per year. The shaded regions represent the uncertainty in the
BNS merger rate estimate.
not smaller by a constant factor. How much the area shrinks depends on the true
position of the source. The results in Figure 5 and Figure 6 are consistent and are two
different representations of sky-localization analysis using the same aforementioned
code. Furthermore, in Figure 6 we observe that the AHL network localizes all the 3072
events with 90% credible area within 20 sq.deg. On the other hand, the HL localizes
793 events within 100 deg
2
and 239 events within 50 deg
2
.
4.1. Early warning of binary neutron star mergers
August 17, 2017 saw the beginning of a new era in multi-messenger astronomy. The
joint detection of GWs by the LIGO and Virgo interferometers and the sGRB by the
Fermi-GBM and INTEGRAL satellite from the BNS coalescence, GW170817 [51, 67]
confirmed the long-standing hypothesis that compact object mergers were progenitors
of short GRBs. Apart from the gamma-ray burst, which was observed
∼
2 s after
the merger event, the first manual follow-up observations took place
∼
8 hours after
the epoch of merger [67]. This delay was caused by the delay in sending out GW
information: the GW alert was sent out
∼
40 minutes [88], and the sky localization
∼
4
.
5 hours [89] after the signal arrived on earth. By the time EM telescopes participating
in the follow-up program received the alerts the source was below the horizon for them.
For a fraction of BNS events it will be possible to issue alerts up to
δ
t
∼
60 s
before the epoch of merger [90, 91, 92].
Pre-merger or
early warning
detections
will facilitate electromagnetic observations of the prompt emission, which encodes
the initial conditions of the outflow and the state of the merger remnant. Early