arXiv subjects

Chandra Kant Mishra

Publications and source records attributed to Chandra Kant Mishra.

At least 19 recordsLinked to original sources

arXiv2026

Chase Orbits, not Time: A Scalable Paradigm for Long-Duration Eccentric Gravitational-Wave Surrogates

Orbital eccentricity is a key tracer of the astrophysical origins of compact binaries. Yet it remains absent from routine LIGO-Virgo-KAGRA analyses, in part because of the prohibitive computational cost of generating eccentric template waveforms. The complicated morphology of these waveforms due to the eccentric orbital timescale variations makes it difficult to construct their accurate and efficient surrogate models, especially for waveforms long enough to comprehensively cover the sensitivity bands of current ground-based gravitational-wave detectors. We present a novel and scalable surrogate building technique which makes surrogate modeling of long-duration eccentric binary black hole waveforms both feasible and highly efficient. The technique aims to simplify the harmonic content of intermediate eccentric waveform data-pieces by modeling them in terms of an angular orbital element called the mean anomaly, instead of time. We show that this parameterization yields much more compressed surrogates than the standard time-based parameterizations. We also significantly simplify variations in waveform data-pieces across the parameter space by expressing them in terms of the instantaneous orbital eccentricity and mean anomaly to ease their parametric fitting. Building on these developments, we construct InspiralESIGMASur: a $2.77 \times 10^6M$ (850-1250 orbits) long non-spinning surrogate for the inspiral-only eccentric waveform model InspiralESIGMA [K. Paul et al., Phys. Rev. D 111, 084074 (2025)]. The methods presented in this work make it feasible to build long-duration eccentric surrogates for current as well as future third-generation gravitational-wave detectors.

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arXiv2026

Spin-induced Quadrupole Moment (SIQM) Test for Eccentric Compact Binaries

Spin-induced deformations of individual components of a binary can be quantified using the gravitational wave signal the binary emits. Such deformations are characterised by a parameter, $ κ$, which takes a value of 1 for a black hole and thus its measurement can be used to test the no-hair conjecture. However, in practice, only a symmetric combination of this parameter for a binary ($ κ_s $) can be measured, thus instead enabling a test for the no-hair conjecture in the context of a binary black hole system; see for instance, Krishnendu et al., Phys. Rev. Lett. 119, 091101 (2017), arXiv:1701.06318. While previous studies have focused on circular binaries, we extend this test to eccentric systems in a Fisher matrix based analysis. We find that the error in the measurement of the parameter $ κ_s $ reduces from a value of about 18% (for the circular case) to close to 8% (4%) for a $ 10 M_{\odot} $ system with dimensionless component spins $ >0.8 $ and with a reference initial eccentricity ($ e_0 $) of 0.2 (0.4) evaluated at 5 Hz for a third generation detector, Cosmic Explorer (CE). Compared to the estimates obtained by using Advanced LIGO design sensitivity, eccentricity and the overall improved sensitivity of CE detectors together seem to improve these estimates almost by an order of magnitude.

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arXiv2026

Biased parameter inference of eccentric, spin-precessing binary black holes

While the majority of gravitational wave (GW) events observed by the LIGO and Virgo detectors are consistent with mergers of binary black holes (BBHs) on quasi-circular orbits, some events are also consistent with non-zero orbital eccentricity, indicating that the binaries could have formed via dynamical interactions. Moreover, there may be GW events which show support for spin-precession, eccentricity, or both. In this work, we study the interplay of spins and eccentricity on the parameter estimation of GW signals from BBH mergers. We inject eccentric signals with no spins, aligned spins, and precessing spins using hybrids, TEOBResumS-DALI, and new Numerical Relativity (NR) simulations, respectively, and study the biases in the posteriors of source parameters when these signals are recovered with a quasi-circular precessing-spin waveform model, as opposed to an aligned-spin eccentric waveform model. We find significant biases in the source parameters, such as chirp mass and spin-precession ($χ_p$), when signals from highly-eccentric BBHs are recovered with a quasi-circular waveform model. Moreover, we find that for signals with both eccentricity and spin-precession effects, Bayes factor calculations confirm that an eccentric, aligned-spin model is preferred over a quasi-circular precessing-spin model. Our study highlights the complex nature of GW signals from eccentric, precessing-spin binaries and the need for readily usable inspiral-merger-ringdown eccentric, spin-precessing waveform models for unbiased parameter estimation.

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arXiv2026

Testing the Kerr hypothesis beyond the quadrupole with GW241011

All multipole moments of a Kerr black hole are uniquely determined by its mass and spin. Gravitational wave observations can test this prediction by measuring spin-induced multipole moments imprinted on the inspiral phase of compact binary mergers. In this Letter, we show that the recently reported compact binary coalescence GW241011 enables a simultaneous test of deviations in the spin-induced quadrupole and octupole moments of the binary components from their black hole values. We find no evidence for deviations from the Kerr prediction and place the first constraints on spin-induced octupole moments of the compact binary. This approach complements tests of the Kerr nature of compact binary merger remnants based on quasinormal mode measurements in the ringdown phase.

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arXiv2026

5PN eccentric waveforms for intermediate-mass-ratio-inspirals (IMRIs) from post-Newtonian and black hole perturbation theory

Detection of gravitational waves from compact binaries involving at least one intermediate mass black hole, and component mass ratios in the range $0.1$-$10^{-4}$, are among the primary sources for future space detectors with target strain sensitivities in the deci-Hertz (dHz) band. Tuned to the waveform requirements for analyzing such sources, a hybrid model is obtained by combining waveforms from the post-Newtonian (PN) and black hole perturbation (BHP) theory. Components of the binary are assumed to be nonspinning and on eccentric orbits. This hybrid model is 3PN accurate in terms of results from PN theory and 5PN in results from BHP theory. In terms of eccentricity, corrections through the order $\mathcal{O}(e^{10})$ are included. Further, using number of gravitational wave cycles estimates for a few representative binaries observable in the dHz band, we demonstrate the significance of the mass ratio information from the PN approach, of contributions from the BHP theory at high PN orders, and also of higher order eccentricity corrections. In particular, we find an almost 10-fold increase in number of gravitational wave cycles for a fixed mass ratio of 0.1 and $e_0\sim0.3$ (evaluated at $0.01$Hz) when contributions beyond the leading order in eccentricity are accounted for. We also confirm the requirement to go beyond 5PN order in the circular part of the waveform from BHP theory.

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arXiv2025

An Accurate Modeling of Nano-hertz Gravitational Wave Signal from Eccentric Supermassive Binary Black Holes: An Essential Step Toward a Robust Discovery

The stochastic gravitational wave background (SGWB) in the nanohertz (nHz) regime, detectable by pulsar timing arrays (PTAs), provides a promising probe of the cosmic population of supermassive black hole binaries (SMBHBs). These binaries are expected to retain significant eccentricity throughout their evolution. We present a new technique to model the nHz SGWB by incorporating eccentricity into a multi-scale adaptive simulation framework. Using the time-domain eccentric waveform model ESIGMAHM, we generate realistic GW signals from astrophysical populations of SMBHBs. Unlike circular binaries, eccentric systems emit across multiple frequencies, introducing spectral correlations between frequency bins. These correlations provide a novel observational signature of the eccentricity distribution of the SMBHB population. In this work, we adopt simplified power-law models for the eccentricity distribution. While this does not capture the full complexity of galactic environments, it effectively highlights the key features of GW emission from eccentric binaries and their imprint on the SGWB. Our approach advances nHz GW signal modeling by incorporating eccentricity at small scales, enabling more realistic predictions and offering a new avenue for probing SMBHB astrophysics with future PTA observations.

astro-ph.CO↗

arXiv2025

Inferring additional physics through unmodelled signal reconstructions

Parameter estimation of gravitational wave data is often computationally expensive, requiring simplifying assumptions such as circularisation of binary orbits. Although, if included, the sub-dominant effects like orbital eccentricity may provide crucial insights into the formation channels of compact binary mergers. To address these challenges, we present a pipeline strategy leveraging minimally modelled waveform reconstruction to identify the presence of eccentricity in real time. Using injected signals, we demonstrate that ignoring eccentricity ($e_{\rm 20Hz} \gtrsim 0.1$) leads to significant biases in parameter recovery, including chirp mass estimates falling outside the 90% credible interval. Waveform reconstruction shows inconsistencies increase with eccentricity, and this behaviour is consistent for different mass ratios. Our method enables low-latency inferences of binary properties supporting targeted follow-up analyses and can be applied to identify any physical effect of measurable strength.

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arXiv2025

Spin effects in the phasing formula of eccentric compact binary inspirals up to the third post-Newtonian order

Compact binary sources that emit gravitational waves (GW) are expected to be both spinning and on eccentric orbits. No closed-form expression for the phasing of GWs are available to date that contain information from both spin and eccentricity. The introduction of eccentricity can slow waveform generation, often requiring slower numerical methods governing its evolution. However, closed-form expressions for the waveform phase can be obtained when eccentricity is treated as a small parameter, enabling quick waveform generation. In this paper, closed-form expressions for the GW phasing in the form of Taylor approximants up to the eighth power in initial eccentricity $(e_0)$ are obtained while also including aligned spins up to the third post-Newtonian order. The phasing is obtained in both time and frequency domains. The fully analytical approximant (TaylorT2) is also resummed for usage in scenarios where initial eccentricities are as high as 0.5. The frequency domain approximant (TaylorF2) based on Stationary Phase approximation is compared with an existing model (TaylorF2Ecc) to assess the importance of the newly computed eccentric/spinning terms. The findings indicate that for eccentricities $\gtrsim 0.15$ (defined at 10 Hz) and small spins $(\sim 0.2)$, the mismatches can be higher than 1%. This leads to an overall loss in signal-to-noise ratio and lower detection efficiency of GWs coming from eccentric spinning compact binary inspirals if the combined effects of eccentricity and aligned spins are neglected in the waveforms.

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arXiv2025

Improved inspiral-merger-ringdown model for BBHs on elliptical orbits

Gravitational waveforms capturing binary evolution through the early-inspiral phase play a critical role in extracting orbital features that nearly disappear during the late-inspiral and subsequent merger phase due to radiation reaction forces; for instance, the effect of orbital eccentricity. Phenomenological approaches that model compact binary mergers rely heavily on combining inputs from both analytical and numerical approaches to reduce the computational cost of generating templates for data analysis purposes. In a recent work, Chattaraj et al., Phys. Rev. D 106, 124008 (2022) constructed a dominant ($\ell=2$, $|m|=2$) mode model for nonspinning binary black holes (BBHs) on elliptical orbits. The model was constructed in time domain and is fully analytical. The current work is an attempt to improve this model by making a few important changes in our approach. The most significant of those involves identifying initial values of orbital parameters with which the inspiral part of the model is evolved. While the ingredients remain the same as in the previous work, the resulting (new) model, when compared against a set of target waveforms constructed here, produces match values better than 96.5% for systems heavier than $80M_\odot$, while with the old model this limit on the total mass is $115M_\odot$. The updated model is validated against an independent eccentric waveform family (TEOBResumS-Dali) for an initial eccentricity ($e_0$), mass ratio ($q$) and mean anomaly ($l_0$) in the range $0\lesssim e_0\lesssim0.3$, $1\lesssim q\lesssim3$ and $-π\leq l_0\leqπ$, respectively. Further, an alternate model including the effect of higher order modes is also provided. Finally, while our model assumes nonspinning components, we show that it could also be used for systems with component spin vectors (anti-) aligned w.r.t. the orbital angular momentum and small spin magnitudes.

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arXiv2025

ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes

We present a time-domain inspiral-merger-ringdowm (IMR) waveform model ESIGMAHM constructed within a framework we named ESIGMA for coalescing binaries of spinning black holes on moderately eccentric orbits (Huerta et al. (2018) [Phys. Rev. D 97, 024031]). We now include the effect of black hole spins on the dynamics of eccentric binaries, as well as model sub-dominant waveform harmonics emitted by them. The inspiral evolution is described by a consistent combination of latest results from post-Newtonian theory, self-force, and black hole perturbation theory. We assume that these moderately eccentric binaries radiate away most of their orbital eccentricity before merger, and seamlessly connect the eccentric inspiral with a numerical relativity based surrogate waveform model for mergers of spinning binaries on quasi-circular orbits. We validate ESIGMAHM against eccentric Numerical Relativity simulations, and also against contemporary effective-one-body and phenomenological models in the quasi-circular limit. We find that ESIGMAHM achieves match values greater than $99\%$ for quasi-circular spin-aligned binaries with mass ratios up to $8$, and above $97\%$ for non-spinning and spinning eccentric systems with small or positively aligned spins. Using IMRESIGMA, we quantify the impact of orbital eccentricity on GW signals, showing that next-generation detectors can detect eccentric sources up to $10\%$ louder than quasi-circular ones. We also show that current templated LIGO-Virgo searches will lose more than $10\%$ of optimal SNR for about $20\%$ of all eccentric sources by using only quasi-circular waveform templates. The same will result in a $25\%$ loss in detection rate for eccentric sources with mass ratios $m_1/m_2\geq 4$. Our results highlight the need for including eccentricity and higher-order modes in GW source models and searches for asymmetric eccentric BBH signals.

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arXiv2024

Parametrized tests of general relativity using eccentric compact binaries

Astrophysical population simulations predict that a subset of dynamically formed binary black holes (BBHs) may possess eccentricity $\gtrsim 0.1$ at a gravitational wave (GW) frequency of $10 \,\text{Hz}$. Presently, the LIGO-Virgo-KAGRA (LVK) Collaboration tests general relativity (GR) assuming that the binary eccentricity has decayed well before it enters the detector's frequency band. Previous works have shown that binary eccentricity can bias GR tests if unaccounted for. Here we develop two methods to extend parametrized tests of GR to eccentric binaries. The first method extends the standard null parametrized test for quasicircular binaries by adding fractional deviations at each post-Newtonian (PN) order in the eccentric part of the GW phasing (assuming the small-eccentricity limit). Simultaneous measurement of the circular and eccentric deviation parameters ($δ\hatφ, δ\hatφ^e$) allows us to constrain deviations from GR for eccentric binaries. While strong constraints on the deviation parameters are not achievable with LIGO's projected sensitivity, the multibanding of LISA and CE observations can constrain these deviations to $|δ\hatφ_2| \lesssim 3 \times 10^{-3}$ and $|δ\hatφ^e_2|\lesssim 2\times 10^{-2}$. The second method looks for GR deviations in the rate of periastron advance ($Δα$). The parameter $Δα$ ($Δα^{\rm GR} \to 0$) can be constrained with LIGO to $|Δα|\lesssim 4 \times 10^{-2}$ (with $1 σ$ confidence). Multiband sources observed by LISA and CE provide an improved constraint of $|Δα|\lesssim 3\times 10^{-5}$. The space-based detector DECIGO provides the best constraint on $Δα$ with $|Δα|\lesssim 8 \times 10^{-6}$.

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arXiv2024

Blind spots and biases: the dangers of ignoring eccentricity in gravitational-wave signals from binary black holes

Most gravitational wave (GW) events observed by the LIGO and Virgo detectors are consistent with mergers of binary black holes (BBHs) on quasi-circular orbits. However, some events are also consistent with non-zero orbital eccentricity, which can indicate that the binary formed via dynamical interactions. Active GW search pipelines using quasi-circular waveform templates are inefficient for detecting eccentric mergers. Also, analysing eccentric GW signals with waveform models neglecting eccentricity can lead to biases in the recovered parameters. We explore the detectability and characterisation of eccentric signals when searches and analyses rely on quasi-circular waveform models. We find that for a reference eccentric population, the fraction of events having fitting factor (FF) $< 0.95$ can be up to $\approx 2.2\%$ compared to $\approx 0.4\%$ for the baseline population. This leads to the loss in signal recovery fraction for up to $6\%$ for parameter space with non-negligible eccentricity ($e_{10} > 0.01$) and high mass ratio ($q > 3$). We perform parameter estimation (PE) for non-spinning and aligned-spin eccentric GW injections from BBHs with a total mass $M=35 M_\odot$, based on numerical relativity simulations and an EOB based inspiral-merger-ringdown model (TEOBResumS). We recover these injections using both quasi-circular and eccentric waveform models. For cases with $e_{20} \sim 0.1$, quasi-circular models fail to estimate chirp mass within the 90% credible interval accurately. Further, for these low-mass injections, spin-induced precession does not mimic eccentricity. For injections of $e_{20}\sim 0.1$, PE conducted with an inspiral-only eccentric waveform model correctly characterises the injected signal to within 90% confidence, and recovers the injected eccentricities, suggesting that such models are sufficient for characterisation of low-mass eccentric BBH. (abridged)

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arXiv2024

Effect of double spin-precession and higher harmonics on spin-induced quadrupole moment measurements

We investigate the prospect of performing a null test of binary black hole (BBH) nature using spin-induced quadrupole moment (SIQM) measurements. This is achieved by constraining a deviation parameter ($δκ$) related to the parameter ($κ$) that quantifies the degree of deformation due to the spin of individual binary components on leading (quadrupolar) spin-induced moment. Throughout the paper, we refer to $κ$ as the SIQM parameter and $δκ$ as the SIQM-deviation parameter. The test presented here extends the earlier SIQM-based null tests for BBH nature by employing waveform models that account for double spin-precession and higher modes. We find that waveform with double spin-precession gives better constraints for $δκ$, compared to waveform with single spin-precession. We also revisit earlier constraints on the SIQM-deviation parameter for selected GW events observed through the first three observing runs (O1-O3) of LIGO-Virgo detectors. Additionally, the effects of higher-order modes on the test are also explored for a variety of mass-ratio and spin combinations by injecting simulated signals in zero-noise. Our analyses indicate that binaries with mass-ratio greater than 3 and significant spin precession may require waveforms that account for spin-precession and higher modes to perform the parameter estimation reliably.

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arXiv2023

Spin effects in Spherical Harmonic Modes of Gravitational Waves from Eccentric Compact Binary Inspirals

We compute the leading and sub-leading spin effects through the second post-Newtonian order (2PN) in spherical harmonic modes of gravitational waveforms from inspiralling compact binaries in non-circular orbits with non-precessing components. The two spin couplings, linear-in-spin (spin-orbit; SO) and quadratic-in-spin (spin-spin; SS), that appear in 2PN waveforms are computed with desired accuracy and explicit expressions for relevant modes are derived. The modes that have spin corrections through 2PN include $(\ell, |m|)$=$((2,2),\,(2,1),\,(3,3),\,(3,2),\,(3,1),\,(4,3),\,(4,1))$ modes. Closed form expressions for these modes for compact binaries in general orbits as well as in elliptical orbits are being provided. While the general orbit results can be used to study signals from binaries in orbits of arbitrary shape and nature, elliptical orbit results are applicable to systems with arbitrary eccentricities. We also express the elliptical orbit results as leading eccentric corrections to the circular results. Our prescription represents, the first, fully analytical treatment that combines spins, eccentricity and higher modes together and completes computation of spin effects through 2PN order. These should find immediate applications in inspiral-merger-ringdown modelling for eccentric mergers including the effect of non-precessing spins and higher modes as well as in parameter estimation analyses employing inspiral waveform.

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arXiv2022

High accuracy post-Newtonian and numerical relativity comparisons involving higher modes for eccentric binary black holes and a dominant mode eccentric inspiral-merger-ringdown model

Spherical harmonic modes of gravitational waveforms for inspiraling compact binaries in eccentric orbits from post-Newtonian (PN) theory accurate to third post-Newtonian order, and those extracted from numerical relativity (NR) simulations for binary black holes (BBHs) are compared. We combine results from the two approaches (PN and NR) to construct time-domain hybrid waveforms that describe the complete evolution of BBH mergers through inspiral-merger-ringdown (IMR) stages. These hybrids are then used in constructing a fully analytical dominant mode ($\ell$=2, $|m|$=2) eccentric IMR model. A simple extension to a multi-mode model based on this dominant mode model is also presented. Overlaps with quasi-circular IMR waveform models including the effect of higher modes, maximized over a time- and phase-shift, hint at the importance (mismatches $>1\%$) of including eccentricity in gravitational waveforms when analysing BBHs lighter than $\sim 80 M_{\odot}$, irrespective of the binary's eccentricity (as it enters the LIGO bands), or mass-ratio. Combined impact of eccentricity and higher modes seems to become more apparent through smaller overlaps with increasing inclination angles and mass ratios. Additionally, we show that the state-of-the-art quasi-circular models including the effect of higher modes will not be adequate in extracting source properties for signals with initial eccentricities $e_0$ $\gtrsim0.1$.

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arXiv2021

Detectability of gravitational higher order modes in the third-generation era

Detection of higher order modes of gravitational waves in third-generation (3G) ground-based detectors such as Cosmic Explorer and Einstein Telescope is explored. Using the astrophysical population of binary black holes based on events reported in the second gravitational wave catalog by Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo (GWTC-2), in conjunction with the Madau-Dickinson model for redshift evolution of the binary black hole mergers, we assess the detectability of these higher order modes using a network consisting of three third-generation detectors. We find that the two subleading modes [(3,3) and (4,4)] can be detected in approximately 30% of the population with a network signal-to-noise ratio of 3 or more, and for nearly 10% of the sources, the five leading modes will be detectable. Besides, a study concerning the effect of binary's mass ratio and its orbital inclination with the observer's line-of-sight in detecting various modes is presented. For a few selected events of the LIGO-Virgo catalog, we identify the modes that would have been detected if a third-generation detector was operational when these events were recorded. We also compute the detectability of higher modes by Voyager and find that only $\sim$ 6 and 2% of the detectable population will have an associated detection of (3,3) and (4,4) modes, respectively. Observing these higher order modes in the 3G era would have a huge impact on the science possible with these detectors ranging from astrophysics and cosmology to testing strong-field gravity.

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arXiv2019

Constraints on the binary black hole nature of GW151226 and GW170608 from the measurement of spin-induced quadrupole moments

According to the "no-hair" conjecture, a Kerr black hole (BH) is completely described by its mass and spin. In particular, the spin-induced quadrupole moment of a Kerr BH with mass $m$ and dimensionless spin $χ$ can be written as $Q=-κ\,m^3χ^2$, where $κ_{\rm BH}=1$. Thus by measuring the spin-induced quadrupole parameter $κ$, we can test the binary black hole nature of compact binaries and distinguish them from binaries comprised of other exotic compact objects, as proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we present a Bayesian framework to carry out this test where we measure the symmetric combination of individual spin-induced quadrupole moment parameters fixing the anti-symmetric combination to be zero. The analysis is restricted to the inspiral part of the signal as the spin-induced deformations are not modeled in the post-inspiral regime. We perform detailed simulations to investigate the applicability of this method for compact binaries of different masses and spins and also explore various degeneracies in the parameter space which can affect this test. We then apply this method to the gravitational wave events, GW151226 and GW170608 detected during the first and second observing runs of Advanced LIGO and Advanced Virgo detectors. We find the two events to be consistent with binary black hole mergers in general relativity. By combining information from several more of such events in future, this method can be used to set constraints on the black hole nature of the population of compact binaries that are detected by the Advanced LIGO and Advanced Virgo detectors.

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arXiv2019

Gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian order: Tail contributions and post-adiabatic corrections

We compute the tail contributions to the gravitational-wave mode amplitudes for compact binaries in eccentric orbits at the third post-Newtonian order of general relativity. We combine them with the already available instantaneous pieces and include the post-adiabatic corrections required to fully account for the effects of radiation-reaction forces on the motion. We compare the resulting waveform in the small eccentricity limit to the circular one, finding perfect agreement.

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