arXiv subjects

Antoine Klein

Publications and source records attributed to Antoine Klein.

At least 55 records · Page 3Linked to original sources

arXiv2017

Analytic gravitational waveforms for generic precessing compact binaries

Binary systems of two compact objects circularize and spiral toward each other via the emission of gravitational waves. The coupling of the spins of each object with the orbital angular momentum causes the orbital plane to precess, which leads to modulation of the gravitational wave signal. Until now, generating frequency-domain waveforms for fully precessing systems for use in gravitational wave data analysis meant numerically integrating the equations of motion, then Fourier transforming the result, which is very computationally intensive for systems that complete hundreds or thousands of cycles in the sensitive band of a detector. Previously, analytic solutions were only available for certain special cases or for simplified models. Here we describe the construction of closed-form, frequency-domain waveforms for fully-precessing, quasi-circular binary inspirals.

gr-qc↗

arXiv2016

eLISA eccentricity measurements as tracers of binary black hole formation

Up to hundreds of black hole binaries individually resolvable by eLISA will coalesce in the Advanced LIGO/Virgo band within ten years, allowing for multi-band gravitational wave observations. Binaries formed via dynamical interactions in dense star clusters are expected to have eccentricities $e_0\sim 10^{-3}$-$10^{-1}$ at the frequencies $f_0=10^{-2}$ Hz where eLISA is most sensitive, while binaries formed in the field should have negligible eccentricity in both frequency bands. We estimate that eLISA should always be able to detect a nonzero $e_0$ whenever $e_0\gtrsim 10^{-2}$; if $e_0\sim 10^{-3}$, eLISA should detect nonzero eccentricity for a fraction $\sim 90\%$ ($\sim 25\%$) of binaries when the observation time is $T_{\rm obs}=5$ ($2$) years, respectively. Therefore eLISA observations of BH binaries have the potential to distinguish between field and cluster formation scenarios.

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arXiv2016

Constraining stellar binary black hole formation scenarios with eLISA eccentricity measurements

A space-based interferometer such as eLISA could observe few to few thousands progenitors of black hole binaries (BHBs) similar to those recently detected by Advanced LIGO. Gravitational radiation circularizes the orbit during inspiral, but some BHBs retain a measurable eccentricity at the low frequencies where eLISA is most sensitive. The eccentricity of a BHB carries precious information about its formation channel: BHBs formed in the field, in globular clusters, or close to a massive black hole (MBH) have distinct eccentricity distributions in the eLISA band. We generate mock eLISA observations, folding in measurement errors, and using Bayesian model selection we study whether eLISA measurements can identify the BHB formation channel. We find that a handful of observations would suffice to tell whether BHBs were formed in the gravitational field of a MBH. Conversely, several tens of observations are needed to tell apart field formation from globular cluster formation. A five-year eLISA mission with the longest possible armlength is desirable to shed light on BHB formation scenarios.

astro-ph.HE↗

arXiv2016

Science with the space-based interferometer eLISA. I: Supermassive black hole binaries

We compare the science capabilities of different eLISA mission designs, including four-link (two-arm) and six-link (three-arm) configurations with different arm lengths, low-frequency noise sensitivities and mission durations. For each of these configurations we consider a few representative massive black hole formation scenarios. These scenarios are chosen to explore two physical mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and (ii) the delays between the merger of two galaxies and the merger of the black holes hosted by those galaxies. We assess the eLISA parameter estimation accuracy using a Fisher matrix analysis with spin-precessing, inspiral-only waveforms. We quantify the information present in the merger and ringdown by rescaling the inspiral-only Fisher matrix estimates using the signal-to-noise ratio from non-precessing inspiral-merger-ringdown phenomenological waveforms, and from a reduced set of precessing numerical relativity/post-Newtonian hybrid waveforms. We find that all of the eLISA configurations considered in our study should detect some massive black hole binaries. However, configurations with six links and better low-frequency noise will provide much more information on the origin of black holes at high redshifts and on their accretion history, and they may allow the identification of electromagnetic counterparts to massive black hole mergers.

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arXiv2015

Testing General Relativity with Present and Future Astrophysical Observations

One century after its formulation, Einstein's general relativity has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that general relativity should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of general relativity. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einstein's theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

gr-qc↗

arXiv2015

Probing the Internal Composition of Neutron Stars with Gravitational Waves

Gravitational waves from neutron star binary inspirals contain information about the equation of state of supranuclear matter. In the absence of definitive experimental evidence that determines the correct equation of state, a number of diverse models that give the pressure in a neutron star as function of its density have been proposed. These models differ not only in the approximations and techniques they use to solve the many-body Schrödinger equation, but also in the neutron star composition they assume. We study whether gravitational wave observations of neutron star binaries in quasicircular inspirals will allow us to distinguish between equations of state of differing internal composition, thereby providing important information about the properties of extremely high density matter. We carry out a Bayesian model selection analysis, and find that second generation gravitational wave detectors can heavily constrain equations of state that contain only quark matter, but hybrid stars containing both normal and quark matter are harder to distinguish from normal matter stars. A gravitational wave detection with a signal-to-noise ratio of 30 and masses around $1.4M_{\odot}$ could either detect or rule out strange quark stars with a 20 to 1 confidence. The presence of kaon condensates or hyperons in neutron star inner cores cannot be easily confirmed. For example, for the equations of state studied in this paper, even a gravitational wave signal with a signal-to-noise ratio as high as 60 would not allow us to claim a detection of kaon condensates or hyperons with confidence greater than 5 to 1. On the other hand, if kaon condensates and hyperons do not form in neutron stars, a gravitational wave signal with similar signal-to-noise ratio would be able to constrain their existence with an 11 to 1 confidence for high-mass systems.

gr-qc↗

arXiv2015

Precessional instability in binary black holes with aligned spins

Binary black holes on quasicircular orbits with spins aligned with their orbital angular momentum have been testbeds for analytic and numerical relativity for decades, not least because symmetry ensures that such configurations are equilibrium solutions to the spin-precession equations. In this work, we show that these solutions can be unstable when the spin of the higher-mass black hole is aligned with the orbital angular momentum and the spin of the lower-mass black hole is anti-aligned. Spins in these configurations are unstable to precession to large misalignment when the binary separation $r$ is between the values $r_{\rm ud\pm}= (\sqrt{χ_1} \pm \sqrt{q χ_2})^4 (1-q)^{-2} M$, where $M$ is the total mass, $q \equiv m_2/m_1$ is the mass ratio, and $χ_1$ ($χ_2$) is the dimensionless spin of the more (less) massive black hole. This instability exists for a wide range of spin magnitudes and mass ratios and can occur in the strong-field regime near merger. We describe the origin and nature of the instability using recently developed analytical techniques to characterize fully generic spin precession. This instability provides a channel to circumvent astrophysical spin alignment at large binary separations, allowing significant spin precession prior to merger affecting both gravitational-wave and electromagnetic signatures of stellar-mass and supermassive binary black holes.

gr-qc↗

arXiv2014

Spin-Precession: Breaking the Black Hole--Neutron Star Degeneracy

Mergers of compact stellar remnant are prime targets for the LIGO/Virgo gravitational wave detectors. One hopes that the gravitational wave signals from these merger events can be used to study the mass and spin distribution of stellar remnants, and provide information about black hole horizons and the material properties of neutron stars. However, it has been suggested that degeneracies in the way that the star's mass and spin are imprinted in the waveforms may make it impossible to distinguish between black holes and neutron stars. Here we show that the precession of the orbital plane due to spin-orbit coupling breaks the mass-spin degeneracy, and allows us to distinguish between standard neutron stars and alternative possibilities, such as black holes or exotic neutron stars with large masses and spins.

gr-qc↗

arXiv2014

Fast Frequency-domain Waveforms for Spin-Precessing Binary Inspirals

The detection and characterization of gravitational wave signals from compact binary coalescence events relies on accurate waveform templates in the frequency domain. The stationary phase approximation (SPA) can be used to compute closed-form frequency-domain waveforms for non-precessing, quasi-circular binary inspirals. However, until now, no fast frequency-domain waveforms have existed for generic, spin-precessing quasi-circular compact binary inspirals. Templates for these systems have had to be computed via a discrete Fourier transform of finely sampled time-domain waveforms, which is far more computationally expensive than those constructed directly in the frequency-domain, especially for those systems that are dominated by the inspiral part. There are two obstacles to deriving frequency-domain waveforms for precessing systems: (i) the spin-precession equations do not admit closed-form solutions for generic systems; (ii) the SPA fails catastrophically. Presently there is no general solution to the first problem, so we must resort to numerical integration of the spin precession equations. This is not a significant obstacle, as numerical integration on the slow precession timescale adds very little to the computational cost of generating the waveforms. Our main result is to solve the second problem, by providing an alternative to the SPA that we call the method of Shifted Uniform Asymptotics, or SUA, that cures the divergences in the SPA. The construction of frequency-domain templates using the SUA can be orders of magnitude more efficient than the time-domain ones obtained through a discrete Fourier transform. Moreover, this method is very faithful to the discrete Fourier transform, with mismatches on the order of $10^{-5}$.

gr-qc↗

arXiv2014

Projected Constraints on Scalarization with Gravitational Waves from Neutron Star Binaries

Certain scalar-tensor theories have the property of endowing stars with scalar hair, sourced either by the star's own compactness (spontaneous scalarization) or, for binary systems, by the companion's scalar hair (induced scalarization) or by the orbital binding energy (dynamical scalarization). Scalarized stars in binaries present different conservative dynamics than in General Relativity, and can also excite a scalar mode in the metric perturbation that carries away dipolar radiation. As a result, the binary orbit shrinks faster than predicted in General Relativity, modifying the rate of decay of the orbital period. In spite of this, scalar-tensor theories can pass existing binary pulsar tests, because observed pulsars may not be compact enough or sufficiently orbitally bound to activate scalarization. Gravitational waves emitted during the last stages of compact binary inspirals are thus ideal probes of scalarization effects. For the standard projected sensitivity of advanced LIGO, we here show that, if neutron stars are sufficiently compact to enter the detector's sensitivity band already scalarized, then gravitational waves could place constraints at least comparable to binary pulsars. If the stars dynamically scalarize while inspiraling in band, then constraints are still possible provided the scalarization occurs sufficiently early in the inspiral, roughly below an orbital frequency of 50Hz. In performing these studies, we derive an easy-to-calculate data analysis measure, an integrated phase difference between a General Relativistic and a modified signal, that maps directly to the Bayes factor so as to determine whether a modified gravity effect is detectable. Finally, we find that custom-made templates are equally effective as model-independent, parameterized post-Einsteinian waveforms at detecting such modified gravity effects at realistic signal-to-noise ratios.

gr-qc↗

arXiv2014

Mixing of spherical and spheroidal modes in perturbed Kerr black holes

The angular dependence of the gravitational radiation emitted in compact binary mergers and gravitational collapse is usually separated using spin-weighted spherical harmonics ${}_sY_{\ell m}$ of spin weight $s$, that reduce to the ordinary spherical harmonics $Y_{\ell m}$ when $s=0$. Teukolsky first showed that the perturbations of the Kerr black hole that may be produced as a result of these events are separable in terms of a different set of angular functions: the spin-weighted spheroidal harmonics ${}_sS_{\ell m n}$, where $n$ denotes the "overtone index" of the corresponding Kerr quasinormal mode frequency $ω_{\ell m n}$. In this paper we compute the complex-valued scalar products of the ${}_sS_{\ell m n}$'s with the ${}_sY_{\ell m}$'s ("spherical-spheroidal mixing coefficients") and with themselves ("spheroidal-spheroidal mixing coefficients") as functions of the dimensionless Kerr parameter $j$. Tables of these coefficients and analytical fits of their dependence on $j$ are available online for use in gravitational-wave source modeling and in other applications of black-hole perturbation theory.

gr-qc↗

arXiv2014

Detection and Parameter Estimation of Gravitational Waves from Compact Binary Inspirals with Analytical Double-Precessing Templates

We study the performance of various analytical frequency-domain templates for detection and parameter estimation of gravitational waves from spin-precessing, quasi-circular, compact binary inspirals. We begin by assessing the extent to which non-spinning, spin-aligned, and the new (analytical, frequency-domain, small-spin) double-precessing frequency-domain templates can be used to detect signals from such systems. For effective, dimensionless spin values above $0.2$, the use of non-spinning or spin-aligned templates for detection purposes will result in a loss of up to $30%$ of all events, while in the case of the double-precessing model, this never exceeds $6%$. Moreover, even for signals from systems with small spins, non-spinning and spin-aligned templates introduce large biases in the extracted masses and spins. The use of a model that encodes spin-induced precession effects, such as the double-precessing model, improves the mass and spin extraction by up to an order of magnitude. The additional information encoded in the spin-orbit interaction is invaluable if one wishes to extract the maximum amount of information from gravitational wave signals.

gr-qc↗

arXiv2013

Gravitational Waveforms for Precessing, Quasicircular Compact Binaries with Multiple Scale Analysis: Small Spin Expansion

We obtain analytical gravitational waveforms in the frequency-domain for precessing, quasi-circular compact binaries with small spins, applicable, for example, to binary neutron star inspirals. We begin by calculating an analytic solution to the precession equations, obtained by expanding in the dimensionless spin parameters and using multiple-scale analysis to separate timescales. We proceed by analytically computing the Fourier transform of time-domain waveform through the stationary phase approximation. We show that the latter is valid for systems with small spins. Finally, we show that these waveforms have a high overlap with numerical waveforms obtained through direct integration of the precession equations and discrete Fourier transformations. The resulting, analytic waveform family is ideal for detection and parameter estimation of gravitational waves emitted by inspiraling binary neutron stars with ground-based detectors.

gr-qc↗

arXiv2013

Gravitational Waveforms for Precessing, Quasi-circular Binaries via Multiple Scale Analysis and Uniform Asymptotics: The Near Spin Alignment Case

We calculate analytical gravitational waveforms in the time- and frequency-domain for precessing quasi-circular binaries with spins of arbitrary magnitude, but nearly aligned with the orbital angular momentum. We first derive an analytical solution to the precession equations by expanding in the misalignment angle and using multiple scale analysis to separate timescales. We then use uniform asymptotic expansions to analytically Fourier transform the time-domain waveform, thus extending the stationary-phase approximation, which fails when precession is present. The resulting frequency-domain waveform family has a high overlap with numerical waveforms obtained by direct integration of the post-Newtonian equations of motion and discrete Fourier transformations. Such a waveform family lays the foundations for the accurate inclusion of spin precession effects in analytical gravitational waveforms, and thus, it can aid in the detection and parameter estimation of gravitational wave signals from the inspiral phase of precessing binary systems.

gr-qc↗

arXiv2012

Power spectrum of gravitational waves from unbound compact binaries

Unbound interacting compact binaries emit gravitational radiation in a wide frequency range. Since short burst-like signals are expected in future detectors, such as LISA or advanced LIGO, it is interesting to study their energy spectrum and the position of the frequency peak. Here we derive them for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation, following the work of Capozziello et al. In particular, we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. Within numerical approximation our formula is in agreement with the two known limiting cases: for the eccentricity ε = 1, the parabolic case, whose spectrum was computed by Berry and Gair, and the large ε limit with the formula given by Turner.

gr-qc↗

arXiv2012

Low-frequency gravitational-wave science with eLISA/NGO

We review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultracompact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISA's high signal-to-noise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.

gr-qc↗

arXiv2012

Testing General Relativity with LISA including Spin Precession and Higher Harmonics in the Waveform

We compute the accuracy at which a LISA-like space-based gravitational wave detector will be able to observe deviations from General Relativity in the low frequency approximation. To do so, we introduce six correction parameters that account for modified gravity in the second post-Newtonian gravitational wave phase for inspiralling supermassive black hole binaries with spin precession on quasi-circular orbits. Our implementation can be regarded as a subset of the ppE formalism developed by Yunes and Pretorius, being able to investigate also next-to-leading order effects. In order to find error distributions for the alternative theory parameters, we use the Fisher information formalism and carry out Monte Carlo simulations for 17 different binary black hole mass configurations in the range 10^5 Msun < M < 10^8 Msun with 10^3 randomly distributed points in the parameter space each, comparing the full (FWF) and restricted (RWF) version of the gravitational waveform. We find that the binaries can roughly be separated into two groups: one with low (< ~10^7 Msun) and one with high total masses (> ~10^7 Msun). The RWF errors on the alternative theory parameters are two orders of magnitude higher than the FWF errors for high-mass binaries while almost comparable for low-mass binaries. Due to dilution of the available information, the accuracy of the binary parameters is reduced by factors of a few, except for the luminosity distance which is affected more seriously in the high-mass regime. As an application and to compare our research with previous work, we compute an optimal lower bound on the graviton Compton wavelength which is increased by a factor of ~1.6 when using the FWF.

gr-qc↗

arXiv2012

Gravitational wave energy spectrum of hyperbolic encounters

The emission of gravitational waves is studied for a system of massive objects interacting on hyperbolic orbits within the quadrupole approximation following the work of Capozziello et al. Here we focus on the derivation of an analytic formula for the energy spectrum of the emitted waves. We checked numerically that our formula is in agreement with the two limiting cases for which results were already available: for the eccentricity ε = 1, the parabolic case whose spectrum was computed by Berry and Gair, and the large ε limit with the formula given by Turner.

gr-qc↗