arXiv subjects

Niels Warburton

Publications and source records attributed to Niels Warburton.

At least 55 records · Page 3Linked to original sources

arXiv2019

Second-order self-force calculation of the gravitational binding energy in compact binaries

Self-force theory is the leading method of modeling extreme-mass-ratio inspirals (EMRIs), key sources for the gravitational-wave detector LISA. It is well known that for an accurate EMRI model, second-order self-force effects are critical, but calculations of these effects have been beset by obstacles. In this letter we present the first implementation of a complete scheme for second-order self-force computations, specialized to the case of quasicircular orbits about a Schwarzschild black hole. As a demonstration, we calculate the gravitational binding energy of these binaries.

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arXiv2019

Unveiling the Gravitational Universe at μ-Hz Frequencies

We propose a space-based interferometer surveying the gravitational wave (GW) sky in the milli-Hz to $μ$-Hz frequency range. By the 2040s', the $μ$-Hz frequency band, bracketed in between the Laser Interferometer Space Antenna (LISA) and pulsar timing arrays, will constitute the largest gap in the coverage of the astrophysically relevant GW spectrum. Yet many outstanding questions related to astrophysics and cosmology are best answered by GW observations in this band. We show that a $μ$-Hz GW detector will be a truly overarching observatory for the scientific community at large, greatly extending the potential of LISA. Conceived to detect massive black hole binaries from their early inspiral with high signal-to-noise ratio, and low-frequency stellar binaries in the Galaxy, this instrument will be a cornerstone for multimessenger astronomy from the solar neighbourhood to the high-redshift Universe.

astro-ph.IM↗

arXiv2019

Probing the Nature of Black Holes: Deep in the mHz Gravitational-Wave Sky

Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo's telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein's gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature.

astro-ph.HE↗

arXiv2019

Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. III: the spinning test-body terms

We present new calculations of the energy flux of a spinning test-body on circular orbits around a Schwarzschild black hole at linear order in the particle spin. We compute the multipolar fluxes up to $\ell=m=6$ using two independent numerical solvers of theTeukolsky equation, one in the time domain and the other in the frequency domain. After linearization in the spin of the particle, we obtain an excellent agreement ($\sim 10^{-5}$) between the two numerical results.The calculation of the multipolar fluxes is also performed analytically (up to $\ell=7$) using the post-Newtonian (PN) expansion of the Teukolsky equation solution; each mode is obtained at 5.5PN order beyond the corresponding leading-order contribution. From the analytical fluxes we obtain the PN-expanded analytical waveform amplitudes. These quantities are then resummed using new procedures either based on the factorization of the orbital contribution (and resumming it independently from the spin-dependent factor) or on the factorization of the tail contribution solely for odd-parity multipoles. We compare these prescriptions and the resummation procedure proposed in Pan et al. [Phys. Rev. D 83 (2011) 064003] to the numerical data. We find that the new procedures significantly improve over the existing one that, notably, is inconsistent with the numerical data for $\ell+m=\text{odd}$ multipoles already at low orbital frequencies. Our study suggests that the approach to waveform resummation used in current effective-one-body-based waveform models should be modified to improve its robustness and accuracy all over the binary parameter space.

gr-qc↗

arXiv2019

Gravitational waves from bodies orbiting the Galactic Center black hole and their detectability by LISA

We present the first fully relativistic study of gravitational radiation from bodies in circular equatorial orbits around the massive black hole at the Galactic Center, Sgr A* and we assess the detectability of various kinds of objects by the gravitational wave detector LISA. Our computations are based on the theory of perturbations of the Kerr spacetime and take into account the Roche limit induced by tidal forces in the Kerr metric. The signal-to-noise ratio in the LISA detector, as well as the time spent in LISA band, are evaluated. We have implemented all the computational tools in an open-source SageMath package, within the Black Hole Perturbation Toolkit framework. We find that white dwarfs, neutrons stars, stellar black holes, primordial black holes of mass larger than $10^{-4} M_\odot$, main-sequence stars of mass lower than $\sim 2.5\, M_\odot$ and brown dwarfs orbiting Sgr A* are all detectable in one year of LISA data with a signal-to-noise ratio above 10 during at least $10^5$ years in the slow inspiral towards either the innermost stable circular orbit (compact objects) or the Roche limit (main-sequence stars and brown dwarfs). The longest times in-band, of the order of $10^6$ years, are achieved for primordial black holes of mass $\sim 10^{-3} M_\odot$ down to $10^{-5} M_\odot$, depending on the spin of Sgr A*, as well as for brown dwarfs, just followed by white dwarfs and low mass main-sequence stars. The long time in-band of these objects makes Sgr A* a valuable target for LISA. We also consider bodies on close circular orbits around the massive black hole in the nucleus of the nearby galaxy M32 and find that, among them, compact objects and brown dwarfs stay for $10^3$ to $10^4$ years in LISA band with a 1-year signal-to-noise ratio above 10.

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arXiv2019

High-order asymptotics for the Spin-Weighted Spheroidal Equation at large real frequency

The spin-weighted spheroidal eigenvalues and eigenfunctions arise in the separation by variables of spin-field perturbations of Kerr black holes. We derive a large, real-frequency asymptotic expansion of the spin-weighted spheroidal eigenvalues and eigenfunctions to high order. This expansion corrects and extends existing results in the literature and we validate it via a numerical calculation.

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arXiv2018

Fast Self-forced Inspirals

We present a new, fast method for computing the inspiral trajectory and gravitational waves from extreme mass-ratio inspirals that can incorporate all known (and future) self-force results. Using near-identity (averaging) transformations we formulate equations of motion that do not explicitly depend upon the orbital phases of the inspiral, making them fast to evaluate, and whose solutions track the evolving constants of motion, orbital phases and waveform phase of a full self-force inspiral to $O(η)$, where $η$ is the (small) mass ratio. As a concrete example, we implement these equations for inspirals of non-spinning (Schwarzschild) binaries. Our code computes inspiral trajectories in milliseconds which is a speed up of 2-5 orders of magnitude (depending on the mass-ratio) over previous self-force inspiral models which take minutes to hours to evaluate. Computing two-year duration waveforms using our new model we find a mismatch better than $\sim 10^{-4}$ with respect to waveforms computed using the (slower) full self-force models. The speed of our new approach is comparable with kludge models but has the added benefit of easily incorporating self-force results which will, once known, allow the waveform phase to be tracked to sub-radian accuracy over an inspiral.

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arXiv2018

Accelerated motion and the self-force in Schwarzschild spacetime

We provide expansions of the Detweiler-Whiting singular field for motion along arbitrary, planar accelerated trajectories in Schwarzschild spacetime. We transcribe these results into mode-sum regularization parameters, computing previously unknown terms that increase the convergence rate of the mode-sum. We test our results by computing the self-force along a variety of accelerated trajectories. For non-uniformly accelerated circular orbits we present results from a new 1+1D discontinuous Galerkin time-domain code which employs an effective-source. We also present results for uniformly accelerated circular orbits and accelerated bound eccentric orbits computed within a frequency-domain treatment. Our regularization results will be useful for computing self-consistent self-force inspirals where the particle's worldline is accelerated with respect to the background spacetime.

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arXiv2017

Evolution of small-mass-ratio binaries with a spinning secondary

We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (non-rotating) black hole. We extend our previous model for a non-spinning binary [Phys. Rev. D 93, 064024] to include the Mathisson-Papapetrou-Dixon spin-curvature force. For spin-aligned binaries we calculate the dephasing of the inspiral and associated waveforms relative to models that do not include spin-curvature effects. We find this dephasing can be either positive or negative depending on the initial separation of the binary. For binaries in which the spin and orbital angular momentum are not parallel, the orbital plane precesses and we use a more general osculating element prescription to compute inspirals.

gr-qc↗

arXiv2016

Inspiral into Gargantua

We model the inspiral of a compact object into a more massive black hole rotating very near the theoretical maximum. We find that once the body enters the near-horizon regime the gravitational radiation is characterized by a constant frequency, equal to (twice) the horizon frequency, with an exponentially damped profile. This contrasts with the usual "chirping" behavior and, if detected, would constitute a "smoking gun" for a near-extremal black hole in nature.

gr-qc↗

arXiv2016

Highly eccentric inspirals into a black hole

We model the inspiral of a compact stellar-mass object into a massive nonrotating black hole including all dissipative and conservative first-order-in-the-mass-ratio effects on the orbital motion. The techniques we develop allow inspirals with initial eccentricities as high as $e\sim0.8$ and initial separations as large as $p\sim 50$ to be evolved through many thousands of orbits up to the onset of the plunge into the black hole. The inspiral is computed using an osculating elements scheme driven by a hybridized self-force model, which combines Lorenz-gauge self-force results with highly accurate flux data from a Regge-Wheeler-Zerilli code. The high accuracy of our hybrid self-force model allows the orbital phase of the inspirals to be tracked to within $\sim0.1$ radians or better. The difference between self-force models and inspirals computed in the radiative approximation is quantified.

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arXiv2015

Particle on the Innermost Stable Circular Orbit of a Rapidly Spinning Black Hole

We compute the radiation emitted by a particle on the innermost stable circular orbit of a rapidly spinning black hole both (a) analytically, working to leading order in the deviation from extremality and (b) numerically, with a new high-precision Teukolsky code. We find excellent agreement between the two methods. We confirm previous estimates of the overall scaling of the power radiated, but show that there are also small oscillations all the way to extremality. Furthermore, we reveal an intricate mode-by-mode structure in the flux to infinity, with only certain modes having the dominant scaling. The scaling of each mode is controlled by its conformal weight, a quantity that arises naturally in the representation theory of the enhanced near-horizon symmetry group. We find relationships to previous work on particles orbiting in precisely extreme Kerr, including detailed agreement of quantities computed here with conformal field theory calculations performed in the context of the Kerr/CFT correspondence.

gr-qc↗

arXiv2015

Self force on a scalar charge in Kerr spacetime: circular equatorial orbits

We present a calculation of the scalar field self-force (SSF) acting on a scalar-charge particle in a strong-field orbit around a Kerr black hole. Our calculation specializes to circular and equatorial geodesic orbits. The analysis is an implementation of the standard mode-sum regularization scheme: We first calculate the multipole modes of the scalar-field perturbation using numerical integration in the frequency domain, and then apply a certain regularization procedure to each of the modes. The dissipative piece of the SSF is found to be consistent with the flux of energy and angular momentum carried by the scalar waves through the event horizon and out to infinity. The conservative (radial) component of the SSF is found to be attractive (inward pointing) for $r_0>r_{\rm c}(a)$ and repulsive (outward pointing) for $r_0<r_{\rm c}(a)$, where $a$ is the Kerr spin parameter, $r_0$ is the Boyer-Lindquist orbital radius, and $r_{\rm c}$ is a critical $a$-dependent radius at which the conservative SSF vanishes. When the motion is retrograde the conservative SSF is repulsive for all $r_0$ (as in the Schwarzschild case). The dominant conservative effect of the SSF in Schwarzschild spacetime is known to be of 3rd post-Newtonian (PN) order (with a logarithmic running). Our numerical results suggest that the leading-order PN correction due to the black hole's spin arises from spin-orbit coupling at 3PN, which dominates the overall SSF effect at large $r_0$. In PN language, the change-of-sign of the radial SSF is attributed to an interplay between the spin-orbit term ($\propto -ar_0^{-4.5}$) and the "Schwarzschild" term ($\propto r_0^{-5}\log r_0$).

gr-qc↗

arXiv2015

Octupolar invariants for compact binaries on quasi-circular orbits

We extend the gravitational self-force methodology to identify and compute new $O(μ)$ tidal invariants for a compact body of mass $μ$ on a quasi-circular orbit about a black hole of mass $M \gg μ$. In the octupolar sector we find seven new degrees of freedom, made up of 3+3 conservative/dissipative `electric' invariants and 3+1 `magnetic' invariants, satisfying 1+1 and 1+0 trace conditions. After formulating for equatorial circular orbits on Kerr spacetime, we calculate explicitly for Schwarzschild spacetime. We employ both Lorenz gauge and Regge-Wheeler gauge numerical codes, and the functional series method of Mano, Suzuki and Takasugi. We present (i) highly-accurate numerical data and (ii) high-order analytical post-Newtonian expansions. We demonstrate consistency between numerical and analytic results, and prior work. We explore the application of these invariants in effective one-body models, and binary black hole initial-data formulations, and conclude with a discussion of future work.

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arXiv2015

Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits

The gravitational self-force (GSF) and post-Newtonian (PN) schemes are complementary approximation methods for modelling the dynamics of compact binary systems. Comparison of their results in an overlapping domain of validity provides a crucial test for both methods, and can be used to enhance their accuracy, e.g. via the determination of previously unknown PN parameters. Here, for the first time, we extend such comparisons to noncircular orbits---specifically, to a system of two nonspinning objects in a bound (eccentric) orbit. To enable the comparison we use a certain orbital-averaged quantity $\langle U \rangle$ that generalizes Detweiler's redshift invariant. The functional relationship $\langle U \rangle(Ω_r,Ω_ϕ)$, where $Ω_r$ and $Ω_ϕ$ are the frequencies of the radial and azimuthal motions, is an invariant characteristic of the conservative dynamics. We compute $\langle U \rangle(Ω_r,Ω_ϕ)$ numerically through linear order in the mass ratio $q$, using a GSF code which is based on a frequency-domain treatment of the linearized Einstein equations in the Lorenz gauge. We also derive $\langle U \rangle(Ω_r,Ω_ϕ)$ analytically through 3PN order, for an arbitrary $q$, using the known near-zone 3PN metric and the generalized quasi-Keplerian representation of the motion. We demonstrate that the $\mathcal{O}(q)$ piece of the analytical PN prediction is perfectly consistent with the numerical GSF results, and we use the latter to estimate yet unknown pieces of the 4PN expression at $\mathcal{O}(q)$.

gr-qc↗

arXiv2015

Self force on a scalar charge in Kerr spacetime: eccentric equatorial orbits

We present a numerical code for calculating the self force on a scalar charge moving in a bound (eccentric) geodesic in the equatorial plane of a Kerr black hole. We work in the frequency domain and make use of the method of extended homogeneous solutions [Phys.\ Rev.\ D {\bf 78}, 084021 (2008)], in conjunction with mode-sum regularization. Our work is part of a program to develop a computational architecture for fast and efficient self-force calculations, alternative to time-domain methods. We find that our frequency-domain method outperforms existing time-domain schemes for small eccentricities, and, remarkably, remains competitive up to eccentricities as high as $\sim 0.7$. As an application of our code we (i) compute the conservative scalar-field self-force correction to the innermost stable circular equatorial orbit, as a function of the Kerr spin parameter; and (ii) calculate the variation in the rest mass of the scalar particle along the orbit, caused by the component of the self force tangent to the four-velocity.

gr-qc↗

arXiv2015

Self force on a scalar charge in Kerr spacetime: inclined circular orbits

Accurately modeling astrophysical extreme-mass-ratio-insprials requires calculating the gravitational self-force for orbits in Kerr spacetime. The necessary calculation techniques are typically very complex and, consequently, toy scalar-field models are often developed in order to establish a particular calculational approach. To that end, I present a calculation of the scalar-field self-force for a particle moving on a (fixed) inclined circular geodesic of a background Kerr black hole. I make the calculation in the frequency-domain and demonstrate how to apply the mode-sum regularization procedure to all four components of the self-force. I present results for a number of strong-field orbits which can be used as benchmarks for emerging self-force calculation techniques in Kerr spacetime.

gr-qc↗

arXiv2015

Tidal invariants for compact binaries on quasi-circular orbits

We extend the gravitational self-force approach to encompass `self-interaction' tidal effects for a compact body of mass $μ$ on a quasi-circular orbit around a black hole of mass $M \gg μ$. Specifically, we define and calculate at $O(μ)$ (conservative) shifts in the eigenvalues of the electric- and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of a geodesic in a regular perturbed vacuum spacetime admitting a helical Killing vector and a reflection symmetry. Next, we specialize to focus on circular orbits in the equatorial plane of Kerr spacetime at $O(μ)$. We present accurate numerical results for the Schwarzschild case for orbital radii up to the light-ring, calculated via independent implementations in Lorenz and Regge-Wheeler gauges. We show that our results are consistent with leading-order post-Newtonian expansions, and demonstrate the existence of additional structure in the strong-field regime. We anticipate that our strong-field results will inform (e.g.) effective one-body models for the gravitational two-body problem that are invaluable in the ongoing search for gravitational waves.

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