Chandra Kant Mishra

We compute the leading and subleading spin effects through the second post-Newtonian order (2PN) in spherical harmonic modes of gravitational waveforms from inspiralling compact binaries in noncircular orbits with nonprecessing components. The two spin couplings, linear-in-spin (spin-orbit) and quadratic-in-spin (spin-spin) 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 (ℓ,|m|)=((2,2),(2,1),(3,3),(3,2),(3,1),(4,3),(4,1)) modes. Additionally, two m=0 modes - (2,0) and (3,0) - also contribute to the 2PN order. Closed-form expressions for these modes for compact binaries in general orbits as well as in elliptical orbits are 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 modeling for eccentric mergers including the effect of nonprecessing spins and higher modes as well as in parameter estimation analyses employing an inspiral waveform.

Advanced LIGO's recent observations of gravitational waves (GWs) from merging binary black holes have opened up a unique laboratory to test general relativity (GR) in the highly relativistic regime. One of the tests used to establish the consistency of the first LIGO event with a binary black hole merger predicted by GR was the inspiral-merger-ringdown consistency test. This involves inferring the mass and spin of the remnant black hole from the inspiral (low-frequency) part of the observed signal and checking for the consistency of the inferred parameters with the same estimated from the post-inspiral (high-frequency) part of the signal. Based on the observed rate of binary black hole mergers, we expect the advanced GW observatories to observe hundreds of binary black hole mergers every year when operating at their design sensitivities, most of them with modest signal to noise ratios (SNRs). Anticipating such observations, this paper shows how constraints from a large number of events with modest SNRs can be combined to produce strong constraints on deviations from GR. Using kludge modified GR waveforms, we demonstrate how this test could identify certain types of deviations from GR if such deviations are present in the signal waveforms. We also study the robustness of this test against reasonable variations of a variety of different analysis parameters.

We present an analytical waveform family describing gravitational waves (GWs) from the inspiral, merger, and ringdown of nonspinning black-hole binaries including the effect of several nonquadrupole modes [(=2,m=±1),(=3,m=±3),(=4,m=±4) apart from (=2,m=±2)]. We first construct spin-weighted spherical harmonics modes of hybrid waveforms by matching numerical-relativity simulations (with mass ratio 1-10) describing the late inspiral, merger, and ringdown of the binary with post-Newtonian/effective-one-body waveforms describing the early inspiral. An analytical waveform family is constructed in frequency domain by modeling the Fourier transform of the hybrid waveforms making use of analytical functions inspired by perturbative calculations. The resulting highly accurate, ready-to-use waveforms are highly faithful (unfaithfulness ≃10-4-10-2) for observation of GWs from nonspinning black-hole binaries and are extremely inexpensive to generate.

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 3G 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 3G detector was operational when these events were recorded. We also compute the detectability of higher modes by Voyager and find that only ∼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.

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=-κm3χ2, where κBH=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 composed of other exotic compact objects, as proposed in [N. V. Krishnendu, K. G. Arun, and C. K. Mishra, Phys. Rev. Lett. 119, 091101 (2017).PRLTAO0031-900710.1103/PhysRevLett.119.091101]. 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 antisymmetric 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 postinspiral 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.

We propose a novel method to test the binary black hole nature of compact binaries detectable by gravitational wave (GW) interferometers and, hence, constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a Kerr black hole are characterized by its mass and spin. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expressible solely in terms of its mass and spin. Otherwise, the quadrupole moment can depend on additional parameters (such as the equation of state of the object). The higher order spin effects in phase and amplitude of a gravitational waveform, which explicitly contains the spin-induced quadrupole moments of compact objects, hence, uniquely encode the nature of the compact binary. Thus, we argue that an independent measurement of the spin-induced quadrupole moment of the compact binaries from GW observations can provide a unique way to distinguish binary BH systems from binaries consisting of exotic compact objects.

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 (ℓ=2, |m|=2) eccentric IMR model. A simple extension to a multimode model based on this dominant mode model is also presented. Overlaps with quasicircular 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 analyzing BBHs lighter than ∼80 M⊙, 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 quasicircular models including the effect of higher modes will not be adequate in extracting source properties for signals with initial eccentricities e0≳0.1.

In a recent letter [N. V. Krishnendu et al., Phys. Rev. Lett. 119, 091101 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.091101] we explored the possibility of probing the binary black hole nature of coalescing compact binaries, by measuring their spin-induced multipole moments, observed in advanced LIGO detectors. Coefficients characterizing the spin-induced multipole moments of Kerr black holes are predicted by the "no-hair" conjecture and appear in the gravitational waveforms through quadratic and higher order spin interactions and hence can be directly measured from gravitational wave observations. By employing a nonprecessing post-Newtonian (PN) waveform model, we assess the capabilities of the third-generation gravitational wave interferometers such as Cosmic Explorer and Einstein Telescope in carrying out such measurements and use them to test the binary black hole nature of observed binaries. In this paper, we extend the investigations of [N. V. Krishnendu et al., Phys. Rev. Lett. 119, 091101 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.091101], limited to measuring the binary's spin-induced quadrupole moment using their observation in second generation detectors, by proposing to measure (a) spin-induced quadrupole effects using third generation detectors, (b) simultaneous measurements of spin-induced quadrupole and octupole effects, again in the context of the third-generation detectors. We study the accuracy of these measurements as a function of total mass, mass ratio, spin magnitudes, and spin alignments. Further, we consider two different binary black hole populations, as proxies of the population that will be observed by the third generation detectors, and obtain the resulting distribution of the spin-induced quadrupole coefficient. This helps us assess how common are those cases where this test would provide very stringent constraints on the black hole nature. These error bars provide us upper limits on the values of the coefficients that characterize the spin-induced multipoles. We find that, using third-generation detectors the symmetric combination of coefficients associated with the spin-induced quadrupole moment of each binary component may be constrained to a value ≤1.1 while a similar combination of coefficients for spin-induced octupole moment may be constrained to ≤2, where both combinations take the value of 1 for a binary black hole system. These estimates suggest that third-generation detectors can accurately constrain the first four multipole moments of the compact objects (mass, spin, quadrupole, and octupole) facilitating a thorough probe of their black hole nature.

We compute the nonlinear memory contributions to the gravitational-wave amplitudes for compact binaries in eccentric orbits at the third post-Newtonian (3PN) order in general relativity. These contributions are hereditary in nature as they are sourced by gravitational waves emitted during the binary's entire dynamical past. Combining these with already available instantaneous and tail contributions, we get the complete 3PN accurate gravitational waveform.

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 postadiabatic 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.