arXiv subjects

Badri Krishnan

Publications and source records attributed to Badri Krishnan.

At least 37 records · Page 2Linked to original sources

arXiv2022

Tidal deformation of dynamical horizons in binary black hole mergers

An important physical phenomenon that manifests itself during the inspiral of two orbiting compact objects is the tidal deformation of each under the gravitational influence of its companion. In the case of binary neutron star mergers, this tidal deformation and the associated Love numbers have been used to probe properties of dense matter and the nuclear equation of state. Non-spinning black holes on the other hand have a vanishing (field) tidal Love number in General Relativity. This pertains to the deformation of the asymptotic gravitational field. In certain cases, especially in the late stages of the inspiral phase when the black holes get close to each other, the source multipole moments might be more relevant in probing their properties and the No-Hair conjecture; contrastingly, these Love numbers do not vanish. In this paper, we track the source multipole moments in simulations of several binary black hole mergers and calculate these Love numbers. We present evidence that, at least for modest mass ratios, the behavior of the source multipole moments is universal.

gr-qc↗

arXiv2022

Quasinormal modes and their overtones at the common horizon in a binary black hole merger

It is expected that all astrophysical black holes in equilibrium are well described by the Kerr solution. Moreover, any black hole far away from equilibrium, such as one initially formed in a compact binary merger or by the collapse of a massive star, will eventually reach a final equilibrium Kerr state. At sufficiently late times in this process of reaching equilibrium, we expect that the black hole is modeled as a perturbation around the final state. The emitted gravitational waves will then be damped sinusoids with frequencies and damping times given by the quasinormal mode spectrum of the final Kerr black hole. An observational test of this scenario, often referred to as black hole spectroscopy, is one of the major goals of gravitational wave astronomy. It was recently suggested that the quasinormal mode description including the higher overtones might hold even right after the remnant black hole is first formed. At these times, the black hole is expected to be highly dynamical and nonlinear effects are likely to be important. In this paper we investigate this remarkable scenario in terms of the horizon dynamics. Working with high accuracy simulations of a simple configuration, namely the head-on collision of two nonspinning black holes with unequal masses, we study the dynamics of the final common horizon in terms of its shear and its multipole moments. We show that they are indeed well described by a superposition of ringdown modes as long as a sufficiently large number of higher overtones are included. This description holds even for the highly dynamical final black hole shortly after its formation. We discuss the implications and caveats of this result for black hole spectroscopy and for our understanding of the approach to equilibrium.

gr-qc↗

arXiv2021

Testing gravitational waveform models using angular momentum

The anticipated enhancements in detector sensitivity and the corresponding increase in the number of gravitational wave detections will make it possible to estimate parameters of compact binaries with greater accuracy assuming general relativity(GR), and also to carry out sharper tests of GR itself. Crucial to these procedures are accurate gravitational waveform models. The systematic errors of the models must stay below statistical errors to prevent biases in parameter estimation and to carry out meaningful tests of GR. Comparisons of the models against numerical relativity (NR) waveforms provide an excellent measure of systematic errors. A complementary approach is to use balance laws provided by Einstein's equations to measure faithfulness of a candidate waveform against exact GR. Each balance law focuses on a physical observable and measures the accuracy of the candidate waveform vis a vis that observable. Therefore, this analysis can provide new physical insights into sources of errors. In this paper we focus on the angular momentum balance law, using post-Newtonian theory to calculate the initial angular momentum, surrogate fits to obtain the remnant spin and waveforms from models to calculate the flux. The consistency check provided by the angular momentum balance law brings out the marked improvement in the passage from \texttt{IMRPhenomPv2} to \texttt{IMRPhenomXPHM} and from \texttt{SEOBNRv3} to \texttt{SEOBNRv4PHM} and shows that the most recent versions agree quite well with exact GR. For precessing systems, on the other hand, we find that there is room for further improvement, especially for the Phenom models.

gr-qc↗

arXiv2021

Model systematics in time domain tests of binary black hole evolution

We perform several consistency tests between different phases of binary black hole dynamics; the inspiral, the merger, and the ringdown on the gravitational wave events GW150914 and GW170814. These tests are performed explicitly in the time domain, without any spectral leakage between the different phases. We compute posterior distributions on the mass and spin of the initial black holes and the final black hole. We also compute the initial areas of the two individual black holes and the final area from the parameters describing the remnant black hole. This facilitates a test of Hawking's black hole area theorem. We use different waveform models to quantify systematic waveform uncertainties for the area increase law with the two events. We find that these errors may lead to overstating the confidence with which the area theorem is confirmed. For example, we find $>99\%$ agreement with the area theorem for GW150914 if a damped sinusoid consisting of a single-mode is used at merger to estimate the final area. This is because this model overestimates the final mass. Including an overtone of the dominant mode decreases the confidence to $\sim94\%$; using a full merger-ringdown model further decreases the confidence to $\sim 85-90\%$. We find that comparing the measured change in the area to the expected change in area yields a more robust test, as it also captures over estimates in the change of area. We find good agreement with GR when applying this test to GW150914 and GW170814.

gr-qc↗

arXiv2021

Testing GR with the Gravitational Wave Inspiral Signal GW170817

Observations of gravitational waves from compact binary mergers have enabled unique tests of general relativity in the dynamical and non-linear regimes. One of the most important such tests are constraints on the post-Newtonian (PN) corrections to the phase of the gravitational wave signal. The values of these PN coefficients can be calculated within standard general relativity, and these values are different in many alternate theories of gravity. It is clearly of great interest to constrain these deviations based on gravitational wave observations. In the majority of such tests which have been carried out, and which yield by far the most stringent constraints, it is common to vary these PN coefficients individually. While this might in principle be useful for detecting certain deviations from standard general relativity, it is a serious limitation. For example, we would expect alternate theories of gravity to generically have additional parameters. The corrections to the PN coefficients would be expected to depend on these additional non-GR parameters whence, we expect that the various PN coefficients to be highly correlated. We present an alternate analysis here using data from the binary neutron star coalescence GW170817. Our analysis uses an appropriate linear combination of non-GR parameters that represent absolute deviations from the corresponding post-Newtonian inspiral coefficients in the TaylorF2 approximant phase. These combinations represent uncorrelated non-GR parameters which correspond to principal directions of their covariance matrix in the parameter subspace. Our results illustrate good agreement with GR. In particular, the integral non-GR phase is $Ψ_{\mbox{non-GR}} = (0.447\pm253)\times10^{-1}$ and the deviation from GR percentile is $p^{\mbox{Dev-GR}}_{n}=25.85\%$.

gr-qc↗

arXiv2020

Search for Continuous Gravitational Waves from Scorpius X-1 in LIGO O2 Data

We present the results of a search in LIGO O2 public data for continuous gravitational waves from the neutron star in the low-mass X-ray binary Scorpius X-1. We search for signals with $\approx$ constant frequency in the range 40-180 Hz. Thanks to the efficiency of our search pipeline we can use a long coherence time and achieve unprecedented sensitivity, significantly improving on existing results. This is the first search that has been able to probe gravitational wave amplitudes that could balance the accretion torque at the neutron star radius. Our search excludes emission at this level between 67.5 Hz and 131.5 Hz, for an inclination angle $44^\circ \pm 6^\circ$ derived from radio observations (Fomalont et al. 2001), and assuming that the spin axis is perpendicular to the orbital plane. If the torque arm is $\approx $ 26 km -- a conservative estimate of the \alfven\ radius -- our results are more constraining than the indirect limit across the band. This allows us to exclude certain mass-radius combinations and to place upper limits on the strength of the star's magnetic field. We also correct a mistake that appears in the literature in the equation that gives the gravitational wave amplitude at the torque balance (Abbott et al. 2017b, 2019a) and we re-interpret the associated latest LIGO/Virgo results in light of this.

astro-ph.HE↗

arXiv2020

Inferring the gravitational wave memory for binary coalescence events

Full, non-linear general relativity predicts a memory effect for gravitational waves. For compact binary coalescence, the total gravitational memory serves as an inferred observable, conceptually on the same footing as the mass and the spin of the final black hole. Given candidate waveforms for any LIGO event, then, one can calculate the posterior probability distribution functions for the total gravitational memory, and use them to compare and contrast the waveforms. In this paper we present these posterior distributions for the binary black hole merger events reported in the first Gravitational Wave Transient Catalog (GWTC-1), using the Phenomenological and Effective-One-Body waveforms. On the whole, the two sets of posterior distributions agree with each other quite well though we find larger discrepancies for the $\ell=2, m=1$ mode of the memory. This signals a possible source of systematic errors that was not captured by the posterior distributions of other inferred observables. Thus, the posterior distributions of various angular modes of total memory can serve as diagnostic tools to further improve the waveforms. Analyses such as this would be valuable especially for future events as the sensitivity of ground based detectors improves, and for LISA which could measure the total gravitational memory directly.

gr-qc↗

arXiv2020

Horizons in a binary black hole merger I: Geometry and area increase

Recent advances in numerical relativity have revealed how marginally trapped surfaces behave when black holes merge. It is now known that interesting topological features emerge during the merger, and marginally trapped surfaces can have self-intersections. This paper presents the most detailed study yet of the physical and geometric aspects of this scenario. For the case of a head-on collision of non-spinning black holes, we study in detail the world tube formed by the evolution of marginally trapped surfaces. In the first of this two-part study, we focus on geometrical properties of the dynamical horizons, i.e. the world tube traced out by the time evolution of marginally outer trapped surfaces. We show that even the simple case of a head-on collision of non-spinning black holes contains a rich variety of geometric and topological properties and is generally more complex than considered previously in the literature. The dynamical horizons are shown to have mixed signature and are not future marginally trapped everywhere. We analyze the area increase of the marginal surfaces along a sequence which connects the two initially disjoint horizons with the final common horizon. While the area does increase overall along this sequence, it is not monotonic. We find short durations of anomalous area change which, given the connection of area with entropy, might have interesting physical consequences. We investigate the possible reasons for this effect and show that it is consistent with existing proofs of the area increase law.

gr-qc↗

arXiv2020

Horizons in a binary black hole merger II: Fluxes, multipole moments and stability

We study in detail the dynamics and stability of marginally trapped surfaces during a binary black hole merger. This is the second in a two-part study. The first part studied the basic geometric aspects of the world tubes traced out by the marginal surfaces and the status of the area increase law. Here we continue and study the dynamics of the horizons during the merger, again for the head-on collision of two non-spinning black holes. In particular we follow the spectrum of the stability operator during the course of the merger for all the horizons present in the problem and implement systematic spectrum statistics for its analysis. We also study more physical aspects of the merger, namely the fluxes of energy which cross the horizon and cause the area to change. We construct a natural coordinate system on the horizon and decompose the various fields appearing in the flux, primarily the shear of the outgoing null normal, in spin weighted spherical harmonics. For each of the modes we extract the decay rates as the final black hole approaches equilibrium. The late part of the decay is consistent with the expected quasi-normal mode frequencies, while the early part displays a much steeper fall-off. Similarly, we calculate the decay of the horizon multipole moments, again finding two different regimes. Finally, seeking an explanation for this behavior, motivated by the membrane paradigm interpretation, we attempt to identify the different dynamical timescales of the area increase. This leads to the definition of a ``slowness parameter'' for predicting the onset of transition from a faster to a slower decay.

gr-qc↗

arXiv2020

Stringent constraints on neutron-star radii from multimessenger observations and nuclear theory

The properties of neutron stars are determined by the nature of the matter that they contain. These properties can be constrained by measurements of the star's size. We obtain stringent constraints on neutron-star radii by combining multimessenger observations of the binary neutron-star merger GW170817 with nuclear theory that best accounts for density-dependent uncertainties in the equation of state. We construct equations of state constrained by chiral effective field theory and marginalize over these using the gravitational-wave observations. Combining this with the electromagnetic observations of the merger remnant that imply the presence of a short-lived hyper-massive neutron star, we find that the radius of a $1.4\,\rm{M}_\odot$ neutron star is $R_{1.4\,\mathrm{M}_\odot} = 11.0^{+0.9}_{-0.6}~{\rm km}$ (90% credible interval). Using this constraint, we show that neutron stars are unlikely to be disrupted in neutron-star black-hole mergers; subsequently, such events will not produce observable electromagnetic emission.

astro-ph.HE↗

arXiv2020

News from horizons in binary black hole mergers

In a binary black hole merger, it is known that the inspiral portion of the waveform corresponds to two distinct horizons orbiting each other, and the merger and ringdown signals correspond to the final horizon being formed and settling down to equilibrium. However, we still lack a detailed understanding of the relation between the horizon geometry in these three regimes and the observed waveform. Here we show that the well known inspiral chirp waveform has a clear counterpart on black hole horizons, namely, the shear of the outgoing null rays at the horizon. We demonstrate that the shear behaves very much like a compact binary coalescence waveform with increasing frequency and amplitude. Furthermore, the parameters of the system estimated from the horizon agree with those estimated from the waveform. This implies that even though black hole horizons are causally disconnected from us, assuming general relativity to be true, we can potentially infer some of their detailed properties from gravitational wave observations.

gr-qc↗

arXiv2019

The next decade of black hole spectroscopy

Gravitational wave observations of the ringdown of the remnant black hole in a binary black hole coalescence provide a unique opportunity of confronting the black hole no-hair theorem in general relativity with observational data. The most robust tests are possible if multiple ringdown modes can be observed. In this paper, using state-of-the-art Bayesian inference methods and the most up-to-date knowledge of binary black hole population parameters and ringdown mode amplitudes, we evaluate the prospects for black hole spectroscopy with current and future ground based gravitational wave detectors over the next 10 years. For different population models, we estimate the likely number of events for which the subdominant mode can be detected and distinguished from the dominant mode. We show that black hole spectroscopy could significantly test general relativity for events seen by the proposed LIGO Voyager detectors.

gr-qc↗

arXiv2019

Detectability of the subdominant mode in a binary black hole ringdown

The ringdown is the late part of the post-merger signature emitted during the coalescence of two black holes and comprises of a superposition of quasi-normal-modes. Within general relativity, because of the no-hair theorems, the frequencies and damping times of these modes are entirely determined by the mass and angular momentum of the final Kerr black hole. A detection of multiple ringdown modes would potentially allow us to test the no-hair theorem from observational data. The parameters which determine whether sub-dominant ringdown modes can be detected are primarily the overall signal-to-noise ratio present in the ringdown signal, and on the amplitude of the subdominant mode with respect to the dominant mode. In this paper, we use Bayesian inference to determine the detectability of a subdominant mode in a set of simulated analytical ringdown signals. Focusing on the design sensitivity of the Advanced LIGO detectors, we systematically vary the signal-to-noise ratio of the ringdown signal, and the mode amplitude ratio in order to determine what kind of signals are promising for performing black hole spectroscopy.

gr-qc↗

arXiv2019

The interior of a binary black hole merger

We find strong numerical evidence for a new phenomenon in a binary black hole spacetime, namely the merger of marginally outer trapped surfaces (MOTSs). By simulating the head-on collision of two non-spinning unequal mass black holes, we observe that the MOTS associated with the final black hole merges with the two initially disjoint surfaces corresponding to the two initial black holes. This yields a connected sequence of MOTSs interpolating between the initial and final state all the way through the non-linear binary black hole merger process. In addition, we show the existence of a MOTS with self-intersections formed immediately after the merger. This scenario now allows us to track physical quantities (such as mass, angular momentum, higher multipoles, and fluxes) across the merger, which can be potentially compared with the gravitational wave signal in the wave-zone, and with observations by gravitational wave detectors. This also suggests a possibility of proving the Penrose inequality mathematically for generic astrophysical binary back hole configurations.

gr-qc↗

arXiv2019

Self-intersecting marginally outer trapped surfaces

We have shown previously that a merger of marginally outer trapped surfaces (MOTSs) occurs in a binary black hole merger and that there is a continuous sequence of MOTSs which connects the initial two black holes to the final one. In this paper, we confirm this scenario numerically and we detail further improvements in the numerical methods for locating MOTSs. With these improvements, we confirm the merger scenario and demonstrate the existence of self-intersecting MOTSs formed in the immediate aftermath of the merger. These results will allow us to track physical quantities across the non-linear merger process and to potentially infer properties of the merger from gravitational wave observations.

gr-qc↗

arXiv2019

1-OGC: The first open gravitational-wave catalog of binary mergers from analysis of public Advanced LIGO data

We present the first Open Gravitational-wave Catalog (1-OGC), obtained by using the public data from Advanced LIGO's first observing run to search for compact-object binary mergers. Our analysis is based on new methods that improve the separation between signals and noise in matched-filter searches for gravitational waves from the merger of compact objects. The three most significant signals in our catalog correspond to the binary black hole mergers GW150914, GW151226, and LVT151012. We assume a common population of binary black holes for these three signals by defining a region of parameter space that is consistent with these events. Under this assumption, we find that LVT151012 has a 97.6\% probability of being astrophysical in origin. No other significant binary black hole candidates are found, nor did we observe any significant binary neutron star or neutron star--black hole candidates. We make available our complete catalog of events, including the sub-threshold population of candidates.

gr-qc↗

arXiv2018

The existence and stability of marginally trapped surfaces

Marginally outer trapped surfaces (MOTSs, or marginal surfaces in short) are routinely used in numerical simulations of black hole spacetimes. They are an invaluable tool for locating and characterizing black holes quasi-locally in real time while the simulation is ongoing. It is often believed that a MOTS can behave unpredictably under time evolution; an existing MOTS can disappear, and a new one can appear without any apparent reason. In this paper we show that in fact the behavior of a MOTS is perfectly predictable and its behavior is dictated by a single real parameter, the \emph{stability parameter}, which can be monitored during the course of a numerical simulation. We demonstrate the utility of the stability parameter to fully understand the variety of marginal surfaces that can be present in binary black hole initial data. We also develop a new horizon finder capable of locating very highly distorted marginal surfaces and we show that even in these cases, the stability parameter perfectly predicts the existence and stability of marginal surfaces.

gr-qc↗

arXiv2018

Observational tests of the black hole area increase law

The black hole area theorem implies that when two black holes merge, the area of the final black hole should be greater than the sum of the areas of the two original black holes. We examine how this prediction can be tested with gravitational-wave observations of binary black holes. By separately fitting the early inspiral and final ringdown stages, we calculate the posterior distributions for the masses and spins of the two initial and the final black holes. This yields posterior distributions for the change in the area and thus a statistical test of the validity of the area increase law. We illustrate this method with a GW150914-like binary black hole waveform calculated using numerical relativity, and detector sensitivities representative of both the first observing run and the design configuration of Advanced LIGO. We obtain a $\sim74.6\%$ probability that the simulated signal is consistent with the area theorem with current sensitivity, improving to $\sim99.9\%$ when Advanced LIGO reaches design sensitivity. An important ingredient in our test is a method of estimating when the post-merger signal is well-fit by a damped sinusoid ringdown waveform.

gr-qc↗