Searcharxiv⌕ Search

arXiv subjects

Sanjeev Dhurandhar

Publications and source records attributed to Sanjeev Dhurandhar.

At least 19 recordsLinked to original sources
arXiv2026

A $χ^2$ statistic for the identification of strongly lensed gravitational waves from compact binary coalescences

Gravitational waves (GWs) emanated by stellar mass compact binary coalescences (CBCs), and lensed by galaxy- or cluster-scale lenses, will produce two or more copies of the GW signal. These will have identical phase evolution but differing amplitudes. Such lensing signatures are expected to be detected by the end of the LIGO-Virgo-Kagra's (LVK's) fifth observing run (O5). In this work, we propose a novel $χ_{\mathrm{lens}}^2$ statistic to segregate pairs of detected GW events as either lensed or unlensed, using templates typically used in GW searches. The statistic is an application of the generalized $χ^2$ discriminator described in \citet{dhurandhar2017}, tailored to probe the similarity (or lack thereof) between the phase evolutions of two CBC signals. We assess the performance of $χ_{\mathrm{lens}}^2$ on a realistic astrophysical dataset of lensed and unlensed CBCs detectable in O4, assuming a single LIGO-like detector at design sensitivity. We find that we can correctly identify lensed events with efficiencies comparable to existing Bayesian and machine learning methods. Evaluating $χ_{\mathrm{lens}}^2$ is orders of magnitude faster than Bayesian methods. Moreover, the statistics of $χ_{\mathrm{lens}}^2$, in stationary Gaussian noise, are fully understood, in contrast to machine learning methods. $χ_{\mathrm{lens}}^2$ can, therefore, be used to rapidly and accurately weed out the vast majority of unlensed candidate pairs and identify lensed pairs.

gr-qc↗
arXiv2026

The Physics presented in the Film Interstellar and its Astrophysical Applications

The film Interstellar is grounded in real physics calculations. A key requirement in the film is that of a planet orbiting a supermassive black hole such that one hour on the planet corresponds to seven years on Earth. Such extreme time dilation is possible only if the planet orbits the black hole very close to its horizon. For a non-rotating (Schwarzschild) black hole, the innermost stable circular orbit (ISCO) lies at three times the Schwarzschild radius; a bound orbit between the ISCO and the event horizon is not possible. Surprisingly, general relativity allows such orbits to exist if the black hole is spinning rapidly. In this work, we present computations that are non-trivial and interesting in themselves, but more importantly, they may have useful astrophysical implications.

gr-qc↗
arXiv2026

Detection of Gravitational Wave modes in third generation detectors

We investigate the detectability of Gravitational Wave (GW) modes (emitted by black-holes and neutron stars) by third generation, ground-based gravitational wave detectors planned to be operational in the next decade. Our analysis focuses on the Cosmic Explorer and Einstein Telescope projects, which are expected to have arm lengths of tens of kilometers and to experience the amplification of a gravitational wave signal at their Full-Spectral Range (FSR) frequencies. We find that both projects will also observe with good Signal-to-Noise ratio (SNR) the elusive {\it w-modes}, which are expected to be emitted at these frequencies by spinning neutron stars.

gr-qc↗
arXiv2026

Improved Binary Black Hole Search Discriminator from the Singular Value Decomposition of Non-Gaussian Noise Transients

The sensitivity of current gravitational wave (GW) detectors to transient GW signals is severely affected by a variety of non-Gaussian and non-stationary noise transients, such as the blip, tomte, koi fish, and low-frequency blip 'glitches'. These glitches share some time-frequency resemblance with GW signals from binary black holes. In earlier works [Joshi et al., Phys. Rev. D 103, 044035 (2021); Choudhary et al., Phys. Rev. D 110, 044051 (2024)], the authors presented a method for constructing a $χ^2$-distributed optimized statistic, based on the unified formalism of $χ^2$ discriminators [Dhurandhar et al., Phys. Rev. D 96, 103018 (2017)], to distinguish the blip glitches from the compact binary coalescence (CBC) signals. Unlike past works, the new $χ^2$ discriminator is constructed from the most significant singular vectors obtained from the singular value decomposition of different classes of glitches in real detector data. We find that the chi-square developed in this work performs as efficiently as in Choudhary et al. [Phys. Rev. D 110, 044051 (2024)], which used sine-Gaussian basis vectors. This result supports past empirical findings that these glitches are reasonably well-modeled by sine-Gaussians. It also introduces a method for constructing signal- and glitch-based $χ^2$ discriminators by directly using real data containing the glitches and, thus, holds promise for extensions to glitches that are captured less well by sine-Gaussians or other analytical functions.

gr-qc↗
arXiv2025

A White Paper on The Multi-Messenger Science Landscape in India

The multi-messenger science using different observational windows to the Universe such as Gravitational Waves (GWs), Electromagnetic Waves (EMs), Cosmic Rays (CRs), and Neutrinos offer an opportunity to study from the scale of a neutron star to cosmological scales over a large cosmic time. At the smallest scales, we can explore the structure of the neutron star and the different energetics involved in the transition of a pre-merger neutron star to a post-merger neutron star. This will open up a window to study the properties of matter in extreme conditions and a guaranteed discovery space. On the other hand, at the largest cosmological scales, multi-messenger observations allow us to study the long-standing problems in physical cosmology related to the Hubble constant, dark matter, and dark energy by mapping the expansion history of the Universe using GW sources. Moreover, the multi-messenger studies of astrophysical systems such as white dwarfs, neutron stars, and black holes of different masses, all the way up to a high redshift Universe, will bring insightful understanding into the physical processes associated with them that are inaccessible otherwise. This white paper discusses the key cases in the domain of multi-messenger astronomy and the role of observatories in India which can explore uncharted territories and open discovery spaces in different branches of physics ranging from nuclear physics to astrophysics.

astro-ph.HE↗
arXiv2025

A Novel Search Technique for Low-Frequency Periodic Gravitational Waves

We quantify the advantages of a recently proposed data processing technique to search for continuous gravitational wave (GW) signals from isolated rotating asymmetric neutron stars in data measured by ground-based GW interferometers. This technique relies on the symmetry of the motion around the Sun of an Earth-bound gravitational wave interferometer. By multiplying the measured data time series with a half-year time-shifted copy of it, we obtain two advantages: (i) the main Doppler phase modulation of a monochromatic gravitational wave signal is exactly removed, and (ii) the signal in the product data are located at twice the GW signal frequency. The first significantly reduces the size of the signal's parameter space over which a search is to be performed. The second is advantageous at low frequencies; we find that, with currently available computer processing speeds, this technique is capable of achieving sensitivity that is comparable to or even better than coherent and other possibly non-coherent methods. Further, since our proposed method is implemented over a year-long data segment, it requires processing time comparable to the data acquisition time of currently available computers.

gr-qc↗
arXiv2025

Unified $χ^2$ discriminators for gravitational wave searches from compact coalescing binaries

Gravitational wave (GW) signals of astrophysical origin are typically weak. This is because gravity is a weak force, the weakest among the four forces we know of. In order to detect GW signals, one must make differential measurements of effective lengths less than a thousandth of the size of a proton. In spite of the detectors achieving extraordinary sensitivity, the detector noise typically overwhelms the signal, so that GW signals are deeply buried in the data. The challenge to the data analyst is of extracting the GW signal from the noise, that is, first deciding whether a signal is present or not then if present, measuring its parameters. However, in the search for coalescing compact binary (CBC) signals, short-duration non-Gaussian noise transients (glitches) in the detector data significantly affect the search sensitivity. $χ^2$ discriminators are therefore employed to mitigate their effect. We show that the underlying mathematical structure of any $χ^2$ is a vector bundle over the signal manifold $\mathcal{P}$, that is, the manifold traced out by the signal waveforms in the Hilbert space of data segments $\mathcal{D}$. The $χ^2$ is then defined as the square of the $L_2$ norm of the data vector projected onto a finite-dimensional subspace $\mathcal{S}$ (fibre) of $\mathcal{D}$ chosen orthogonal to the triggered template waveform. Any such fibre leads to a $χ^2$ discriminator and the full vector bundle comprising the subspaces $\mathcal{S}$ and the base manifold $\mathcal{P}$ contitute the discriminator. We show that this structure paves the way for constructing effective discriminators against different morphologies of glitches. Here we specifically demonstrate our method on blip glitches, which can be modelled as sine-Gausians, which then generates an optimal $χ^2$ statistic for blip glitches.

gr-qc↗
arXiv2024

Improved binary black hole searches through better discrimination against noise transients

Short-duration noise transients in LIGO and Virgo detectors significantly affect the search sensitivity of compact binary coalescence (CBC) signals, especially in the high mass region. In a previous work by the authors \cite{Joshi_2021}, a $χ^2$ statistic was proposed to distinguish them, when modeled as sine-Gaussians, from non-spinning CBCs. The present work is an extension where we demonstrate the better noise-discrimination of an improved $χ^2$ statistic -- called the optimized sine-Gaussian $χ^2$ -- in real LIGO data. The extension includes accounting for the initial phase of the noise transients and use of a well-informed choice of sine-Gaussian basis vectors selected to discern how CBC signals and some of the most worrisome noise-transients project differently on them~\cite{sunil_2022}. To demonstrate this improvement, we use data with blip glitches from the third observational run (O3) of LIGO-Hanford and LIGO-Livingston detectors. Blips are a type of short-duration non-Gaussian noise disturbance known to adversely affect high-mass CBC searches. For CBCs, spin-aligned binary black hole signals were simulated using the \textsc{IMRPhenomPv2} waveform and injected into real LIGO data from the same run. We show that in comparison to the sine-Gaussian $χ^2$, the optimized sine-Gaussian $χ^2$ improves the overall true positive rate by around 6\% in a lower-mass bin ($m_1,m_2 \in [20,40]M_{\odot}$) and by more than 3\% in a higher-mass bin ($m_1,m_2 \in [60,80]M_{\odot}$). On the other hand, we see a larger improvement -- of more than 20\% -- in both mass bins in comparison to the traditional $χ^2$.

gr-qc↗
arXiv2023

Obtaining Statistical Significance of Gravitational Wave Signals in Hierarchical Search

Gravitational Wave (GW) astronomy has experienced remarkable growth in recent years, driven by advancements in ground-based detectors. While detecting compact binary coalescences (CBCs) has become routine, searching for more complex ones, such as mergers involving eccentric and precessing binaries and sub-solar mass binaries, has presented persistent challenges. These challenges arise from using the standard matched filtering algorithm, whose computational cost increases with the dimensionality and size of the template bank. This urges the pressing need for faster search pipelines to efficiently identify GW signals, leading to the emergence of the hierarchical search strategy. This method looks for potential candidate events using a sparse template bank in the first stage, followed by dense templates around potential events in the second stage. Although the hierarchical search speeds up the standard PyCBC analysis by more than a factor of 20, as demonstrated in a previous work~\cite{kanchan_hierarchical}, assigning statistical significance to detected signals was done in a heuristic way. In this article, we present a robust approach for background estimation in a two-stage hierarchical search. Our method models background triggers from time-shifted triggers in a two-detector network, extrapolating to higher statistic values. Through an extensive injection campaign for a population of simulated signals on real data, we test the effectiveness of our background estimation approach. The results show our method achieves a sensitive volume-time product comparable to the standard two-detector PyCBC search. This equivalence holds for an inverse false alarm rate of 10 years and chirp mass $1.4-10~\text{M}_\odot$, substantially reducing computational cost with a remarkable speed-up of nearly 13 times compared to PyCBC analysis.

astro-ph.IM↗
arXiv2023

Higher-order Time-Delay Interferometry

Time-Delay Interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. In a previous publication we derived TDI combinations that exactly cancel the laser phase fluctuations up to first order in the inter-spacecraft velocities. This was done by interfering two digitally-synthesized optical beams propagating a number of times clock- and counter-clock-wise around the array. Here we extend that approach by showing that the number of loops made by each beam before interfering corresponds to a specific higher-order TDI space. In it the cancellation of laser noise terms that depend on the acceleration and higher-order time derivatives of the inter-spacecraft light-travel-times is achieved exactly. Similarly to what we proved for the second-generation TDI space, elements of a specific higher-order TDI space can be obtained by first ``lifting'' the basis ($\a, \b, \g, X$) of the $1^{\rm st}$-generation TDI space to the higher-order space of interest and then taking linear combinations of them with coefficients that are polynomials of the six delays operators. Higher-Order TDI might be required by future interplanetary gravitational wave missions whose inter-spacecraft distances vary appreciably with time, in particular, relative velocities are much larger than those of currently planned arrays.

gr-qc↗
arXiv2023

The International Pulsar Timing Array checklist for the detection of nanohertz gravitational waves

Pulsar timing arrays (PTAs) provide a way to detect gravitational waves at nanohertz frequencies. In this band, the most likely signals are stochastic, with a power spectrum that rises steeply at lower frequencies. Indeed, the observation of a common red noise process in pulsar-timing data suggests that the first credible detection of nanohertz-frequency gravitational waves could take place within the next few years. The detection process is complicated by the nature of the signals and the noise: the first observational claims will be statistical inferences drawn at the threshold of detectability. To demonstrate that gravitational waves are creating some of the noise in the pulsar-timing data sets, observations must exhibit the Hellings and Downs curve -- the angular correlation function associated with gravitational waves -- as well as demonstrating that there are no other reasonable explanations. To ensure that detection claims are credible, the International Pulsar Timing Array (IPTA) has a formal process to vet results prior to publication. This includes internal sharing of data and processing pipelines between different PTAs, enabling independent cross-checks and validation of results. To oversee and validate any detection claim, the IPTA has also created an eight-member Detection Committee (DC) which includes four independent external members. IPTA members will only publish their results after a formal review process has concluded. This document is the initial DC checklist, describing some of the conditions that should be fulfilled by a credible detection. At the present time none of the PTAs have a detection claim; therefore this document serves as a road map for the future.

astro-ph.IM↗
arXiv2022

Second-Generation Time-Delay Interferometry

Time-Delay Interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the heterodyne Doppler measurements made by unequal-arm space-based gravitational wave interferometers. The space of all TDI combinations was first derived under the simplifying assumption of a stationary array, for which the three time-delay operators commute. In this model, any element of the TDI space can be written as a linear combination of four TDI variables, the generators of the "first-generation" TDI space. To adequately suppress the laser phase fluctuations in a realistic array configuration, the rotation of the array and the time-dependence of the six inter-spacecraft light-travel-times have to be accounted for. In the case of the Laser Interferometer Space Antenna (LISA), a joint ESA-NASA mission characterized by slowly time varying arm-lengths, it has been possible to identify data combinations that, to first order in the inter-spacecraft velocities, either exactly cancel or suppress the laser phase fluctuations below the level identified by the noise sources intrinsic to the heterodyne measurements (the so called "secondary" noises). Here we reanalyze the problem of exactly canceling the residual laser noise terms linear in the inter-spacecraft velocities. We find that the procedure for obtaining elements of the $2^{\rm nd}$-generation TDI space can be generalized in an iterative way. This allows us to "lift-up" the generators of the $1^{\rm st}$-generation TDI space and construct elements of the higher order TDI space.

gr-qc↗
arXiv2022

Hierarchical search for compact binary coalescences in the Advanced LIGO's first two observing runs

Detection of many compact binary coalescences (CBCs) is one of the primary goals of the present and future ground-based gravitational-wave (GW) detectors. While increasing the detectors' sensitivities will be crucial in achieving this, efficient data analysis strategies can play a vital role. With given computational power in hand, efficient data analysis techniques can expand the size and dimensionality of the parameter space to search for a variety of GW sources. Matched filtering based analyses that depend on modeled signals to produce adequate signal-to-noise ratios for signal detection may miss them if the parameter space is too restrained. Specifically, the CBC search is currently limited to non-precessing binaries only, where the spins of the components are either aligned or anti-aligned to the orbital angular momentum. A hierarchical search for CBCs is thus well motivated. The first stage of this search is performed by matched filtering coarsely sampled data with a coarse template bank to look for candidate events. These candidates are then followed up for a finer search around the vicinity of an event's parameter space. Performing such a search leads to enormous savings in computational cost. Here we report the first successful implementation of the hierarchical search as a PyCBC-based production pipeline to perform a complete analysis of LIGO observing runs. With this, we analyze Advanced LIGO's first and second observing run data. We recover all the events detected by the PyCBC (flat) search in the first GW catalog, GWTC-1, published by the LIGO-Virgo collaboration, with nearly the same significance using a scaled background. In the analysis, we get an impressive factor of 20 reduction in computation compared to the flat search. With a standard injection study, we show that the sensitivity of the hierarchical search remains comparable to the flat search within the error bars.

gr-qc↗
arXiv2021

The Varied Avatars of Time-delay Interferometry

Time-Delay Interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. By taking finite linear combinations of properly time-shifted Doppler measurements, laser phase fluctuations are removed at any time t and gravitational wave signals can be studied at a requisite level of sensitivity. In the past, other approaches to this problem have been proposed. Recently, matrix based approaches have been put forward; two such approaches are by Vallisneri et al. and Tinto, Dhurandhar and Joshi. In this paper we establish a close relationship between these approaches. In fact we show that the matrices involved in defining the operators in the two approaches exhibit an isomorphism and therefore in both approaches one is dealing with matrix representations of the time-delay operators.

gr-qc↗
arXiv2021

Matrix Representation of Time-Delay Interferometry

Time-Delay Interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. By taking finite linear combinations of properly time-shifted Doppler measurements, laser phase fluctuations are removed at any time $t$ and gravitational wave signals can be studied at a requisite level of precision. In this article we show the delay operators used in TDI can be represented as matrices acting on arrays associated with the laser noises and Doppler measurements. The matrix formulation is nothing but the group theoretic representation (ring homomorphism) of the earlier approach involving time-delay operators and so in principle is the same. It is shown that the homomorphism is valid generally and we cover all situations of interest. To understand the potential advantages the matrix representation brings, care must be taken by the data analyst to account for the light travel times when linearly relating the one-way Doppler measurements to the laser noises. This is especially important in view of the future gravitational wave projects envisaged. We show that the matrix formulation of TDI results in the cancellation of the laser noises at an arbitrary time $t$ by only linearly combining a finite number of samples of the one-way Doppler data measured at and around time $t$.

gr-qc↗
arXiv2021

Reply to the Bayle {\it et al.} gr-qc document dated June 7, 2021}

We address the two issues raised by Bayle, Vallisneri, Babak, and Petiteau (in their gr-qc document arXiv:2106.03976) about our matrix formulation of Time-Delay Interferometry (TDI) (arXiv:2105.02054) \cite{TDJ21}. In so doing we explain and quantify our concerns about the results derived by Vallisneri, Bayle, Babak and Petiteau \cite{Vallisneri2020} by applying their data processing technique (named TDI-$\infty$) to the two heterodyne measurements made by a two-arm space-based GW interferometer. First we show that the solutions identified by the TDI-$\infty$ algorithm derived by Vallisneri, Bayle, Babak and Petiteau \cite{Vallisneri2020} {\underbar {do}} depend on the boundary-conditions selected for the two-way Doppler data. We prove this by adopting the (non-physical) boundary conditions used by Vallisneri {\it et al.} and deriving the corresponding analytic expression for a laser-noise-canceling combination. We show it to be characterized by a number of Doppler measurement terms that grows with the observation time and works for any time-dependent time delays. We then prove that, for a constant-arm-length interferometer whose two-way light times are equal to twice and three-times the sampling time, the solutions identified by TDI-$\infty$ are linear combinations of the TDI variable $X$. In the second part of this document we address the concern expressed by Bayle {\it et al.} regarding our matrix formulation of TDI when the two-way light-times are constant but not equal to integer multiples of the sampling time. We mathematically prove the homomorphism between the delay operators and their matrix representation \cite{TDJ21} holds in general. By sequentially applying two order-$m$ Fractional-Delay (FD) Lagrange filters of delays $l_1$, $l_2$ we find its result to be equal to applying an order-$m$ FD Lagrange filter of delay $l_1 + l_2$.

gr-qc↗
arXiv2020

An optimal $χ^2$ discriminator against modelled noise-transients in interferometric data in searches for binary black-hole mergers

A vitally important requirement for detecting gravitational wave (GW) signals from compact coalescing binaries (CBC) with high significance is the reduction of the false-alarm rate of the matched-filter statistic. The data from GW detectors contain transient noise artifacts, or glitches, which adversely affect the performance of search algorithms by producing false alarms. Glitches with large amplitudes can produce triggers in the SNR time-series in spite of their small overlap with the templates. This contributes to false alarms. Historically, the traditional $χ^2$ test has proved quite useful in distinguishing triggers arising from CBC signals and those caused by glitches. In a recent paper, a large class of unified $χ^2$ discriminators was formulated, along with a procedure to construct an optimal $χ^2$ discriminator, especially, when the glitches can be modeled. A large variety of glitches that often occur in GW detector data can be modeled as sine-Gaussians, with quality factor and central frequency, ($Q,f_0$), as parameters. We use Singular Value Decomposition to identify the most significant degrees of freedom in order to reduce the computational cost of our $χ^2$. Finally, we construct a $χ^2$ statistic that optimally discriminates between sine-Gaussian glitches and CBC signals. We also use Receiver-Operating-Characteristics to quantify the improvement in search sensitivity when it employs the optimal $χ^2$ compared to the traditional $χ^2$. The improvement in detection probability is by a few to several percentage points, near a false-alarm probability of a few times $10^{-3}$, and holds for binary black holes (BBHs) with component masses from several to a hundred solar masses. Moreover, the glitches that are best discriminated against are those that are like sine-Gaussians with $Q\in [25,50]$ and $f_0\in [40,80]$Hz.

gr-qc↗
arXiv2018

Hierarchical search strategy for the efficient detection of gravitational waves from non-precessing coalescing compact binaries with aligned-spins

In the first two years of Gravitational Wave (GW) Astronomy, half a dozen compact binary coalescences (CBCs) have been detected. As the sensitivities and bandwidths of the detectors improve and new detectors join the network, many more sources are expected to be detected. The goal will not only be to find as many sources as possible in the data but to understand the dynamics of the sources much more precisely. Standard searches are currently restricted to a smaller parameter space which assumes aligned spins. Construction of a larger and denser parameter space, and optimising the resultant increase in false alarms, pose a serious computational challenge. We present here a two-stage hierarchical strategy to search for CBCs in data from a network of detectors and demonstrate the computational advantage in real life scenario by introducing it in the standard {\tt PyCBC} pipeline with the usual restricted parameter space. With this strategy, in simulated data containing stationary Gaussian noise, we obtain a computational gain of $\sim 20$ over the flat search. In real data, we expect the computational gain up to a factor of few. This saving in the computational effort will, in turn, allow us to search for precessing binaries. Freeing up computation time for the regular analyses will provide more options to search for sources of different kinds and to fulfil the never-ending urge for extracting more science out of the data with limited resources.

astro-ph.IM↗