arXiv subjects

Nicholas Loutrel

Publications and source records attributed to Nicholas Loutrel.

27 records · Page 2Linked to original sources

arXiv2021

Numerical computation of second order vacuum perturbations of Kerr black holes

Motivated by the desire to understand the leading order nonlinear gravitational wave interactions around arbitrarily rapidly rotating Kerr black holes, we describe a numerical code designed to compute second order vacuum perturbations on such spacetimes. A general discussion of the formalism we use is presented in (arXiv:2008.11770); here we show how we numerically implement that formalism with a particular choice of coordinates and tetrad conditions, and give example results for black holes with dimensionless spin parameters $a=0.7$ and $a=0.998$. We first solve the Teukolsky equation for the linearly perturbed Weyl scalar $Ψ_4^{(1)}$, followed by direct reconstruction of the spacetime metric from $Ψ_4^{(1)}$, and then solve for the dynamics of the second order perturbed Weyl scalar $Ψ_4^{(2)}$. This code is a first step toward a more general purpose second order code, and we outline how our basic approach could be further developed to address current questions of interest, including extending the analysis of ringdown in black hole mergers to before the linear regime, exploring gravitational wave "turbulence" around near-extremal Kerr black holes, and studying the physics of extreme mass ratio inspiral.

gr-qc↗

arXiv2020

Analytic Waveforms for Eccentric Gravitational Wave Bursts

We here present the first analytic effective fly-by (EFB) waveforms designed to accurately capture the burst of gravitational radiation from the closest approach of highly eccentric compact binaries. The waveforms are constructed by performing a re-summation procedure on the well-known Fourier series representation of the two-body problem at leading post-Newtonian order. This procedure results in two models: one in the time-domain, and one in the Fourier domain, which makes use of the stationary phase approximation. We discuss the computational efficiency of these models, and find that the time-domain model is roughly twice as fast as a numerical quadrupole waveform. We compare the time-domain model to both numerical, leading post-Newtonian order, quadrupole waveforms and numerical relativity fly-by waveforms using the match statistic. While the match is typically $>0.97$ when compared to the quadrupole waveforms, it is much lower when comparing to the numerical relativity fly-by waveforms, due to neglecting relativistic effects within the model. We further show how to use these individual waveforms to detect a repeated burst source.

gr-qc↗

arXiv2019

Hereditary Effects in Eccentric Compact Binary Inspirals to Third Post-Newtonian Order

While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than $10^{-3}$ relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than $10^{-8}$ at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary's orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision.

gr-qc↗

arXiv2019

Nature Abhors a Circle

The loss of orbital energy and angular momentum to gravitational waves produced in a binary inspiral forces the orbital eccentricity to adiabatically evolve and oscillate. For comparable-mass binaries, the osculating eccentricity is thought to decrease monotonically in the inspiral. Contrary to this, we here show that, once the osculating eccentricity is small enough, radiation reaction forces it to grow secularly before the binary reaches the last stable orbit. We explore this behavior, its physical interpretation and consequences, and its potential impact on future gravitational wave observations.

gr-qc↗

arXiv2019

The Eccentric Behavior of Inspiraling Compact Binaries

Eccentricity of binary systems is not a gauge invariant quantity, but has an important impact on the observed gravitational wave signal of such systems, generating power in all possible harmonics of the orbital period. We here clarify the possible discrepancies between different eccentricity parameters used to describe the orbital dynamics of binary systems across different approximations, specifically the post-Newtonian approximation, the self-force approximation, and numerical relativity. To this end, we highlight disparities between the typically used orbit averaged method of evolving binary systems under radiation reaction, and more direct techniques of solving the two-body problem in post-Newtonian theory. We show, both numerically and analytically, that the orbit averaged method breaks down in the late inspiral, failing to capture a strong secular growth in the Keplerian eccentricity parameter and producing a orbital de-phasing relative to direct integration of the two-body equations of motion. We show that the secular growth and de-phasing affect the observed gravitational wave signal, which could bias how accurately we may recover parameters for systems with signal-to-noise ratios $\gtrsim 100$. We further develop a frequency domain post-adiabatic waveform model to capture these effects, and study the precision to which we may estimate parameters with this model through a Fisher information matrix analysis.

gr-qc↗

arXiv2018

Spin-Precessing Black Hole Binaries in Dynamical Chern-Simons Gravity

Gravitational waves from spin-precessing binaries exhibit amplitude oscillations that provide an invaluable method to extract the spins of the inspiraling compact objects. The spin-spin and spin-orbit interactions that cause this effect are sensitive to the fundamental nature of gravity, which will allow us to constrain modified theories of gravity using gravitational wave observations of precessing binaries. We here consider precessing black hole binaries in dynamical Chern-Simons gravity, an effective theory of gravity that enhances parity violating interactions. We model the black holes as modified point particles using effective field theory, and derive the spin-precession equations for a binary system by working within the post-Newtonian formalism. We find that the spin-spin and quadrupole-monopole interactions of General Relativity are modified due to an interaction between the scalar dipoles of the two black holes and the modified black hole quadrupole as a result of the violation of the no hair theorems. These modifications enter the precession equations at leading post-Newtonian order. We further show that these precession equations admit seven constants of motion when neglecting radiation reaction, with only the mass-weighted effective spin being modified from General Relativity. We discuss how these may be used to reduce the precession equations to quadrature and the possibility of constructing analytic Fourier domain waveforms for generic spin-precessing binaries in dCS gravity.

gr-qc↗

arXiv2018

A Fourier Domain Waveform for Non-Spinning Binaries with Arbitrary Eccentricity

Although the gravitational waves observed by advanced LIGO and Virgo are consistent with compact binaries in a quasi-circular inspiral prior to coalescence, eccentric inspirals are also expected to occur in Nature. Due to their complexity, we currently lack ready-to-use, analytic waveforms in the Fourier domain valid for sufficiently high eccentricity, and such models are crucial to coherently extract weak signals from the noise. We here take the first steps to derive and properly validate an analytic waveform model in the Fourier domain that is valid for inspirals of arbitrary orbital eccentricity. As a proof-of-concept, we build this model to leading post-Newtonian order by combining the stationary phase approximation, a truncated sum of harmonics, and an analytic representation of hypergeometric functions. Through comparisons with numerical post-Newtonian waveforms, we determine how many harmonics are required for a faithful (matches above 99%) representation of the signal up to orbital eccentricities as large as 0.9. As a first byproduct of this analysis, we present a novel technique to maximize the match of eccentric signals over time of coalescence and phase at coalescence. As a second byproduct, we determine which of the different approximations we employ leads to the largest loss in match, which could be used to systematically improve the model because of our analytic control. The future extension of this model to higher post-Newtonian order will allow for an accurate and fast phenomenological hybrid that can account for arbitrary eccentricity inspirals and mergers.

gr-qc↗

arXiv2018

Scalar Tops and Perturbed Quadrupoles: Probing Fundamental Physics with Spin-Precessing Binaries

Parity violation in the gravitational interaction has an important impact on fundamental observables and the evolution of the universe. We here investigate for the first time our ability to probe the parity violating nature of the gravitational interaction using gravitational waves from spin-precessing binaries. Focusing on dynamical Chern-Simons gravity, we derive the spin-precession equations, calculate the gravitational waves emitted by spin-precessing, quasi-circular black hole binaries and estimate the level to which the theory could be constrained with future gravitational wave observations.

gr-qc↗

arXiv2017

A Parametrized post-Einsteinian Framework for Gravitational Wave Bursts

The population of stellar-mass, compact object binaries that merge with non-negligible eccentricity may be large enough to motivate searches with ground-based gravitational wave detectors. Such events could be exceptional laboratories to test General Relativity in the dynamical, strong-field regime, as a larger fraction of the energy is emitted at high-velocities, compared to quasi-circular inspirals. A serious obstacle here, however, is the challenge of computing theoretical waveforms for eccentric systems with the requisite accuracy for use in a matched-filter search. The corresponding waveforms are more a sequence of concentrated bursts of energy emitted near periapse than a continuous waveform. Based on this, an alternative approach, stacking excess power over the set of time-frequency tiles coincident with the bursts, was recently suggested as a more practical (though sub-optimal) detection strategy. The leading-order "observable" that would be inferred from such a detection would be a sequence of discrete numbers characterizing the position and size of each time-frequency tile. In General Relativity, this (possibly large) sequence of numbers is uniquely determined by the small set of parameters describing the binary at formation. In this work, following the spirit of the parameterized post-Einsteinian framework developed for quasi-circular inspiral, we propose a simple, parameterized deformation of the baseline general relativistic burst algorithm for eccentric inspiral events that would allow for model-independent tests of Einstein's theory in this high-velocity, strong-field regime.

gr-qc↗