arXiv subjects

Scott A. Hughes

Publications and source records attributed to Scott A. Hughes.

At least 37 records · Page 2Linked to original sources

arXiv2023

Extreme mass-ratio inspiral of a spinning body into a Kerr black hole I: Evolution along generic trajectories

The study of spinning bodies moving in curved spacetime has relevance to binary black hole systems with large mass ratios, as well as being of formal interest. At zeroth order in a binary's mass ratio, the smaller body moves on a geodesic of the larger body's spacetime. Post-geodesic corrections describing forces driving the small body's worldline away from geodesics must be incorporated to model the system accurately. An important post-geodesic effect is the gravitational self-force, which describes the small body's interaction with its own spacetime curvature. This effect includes the backreaction due to gravitational-wave emission that leads to the inspiral of the small body into the black hole. When a spinning body orbits a black hole, its spin couples to spacetime curvature. This introduces another post-geodesic correction known as the spin-curvature force. An osculating geodesic integrator that includes both the backreaction due to gravitational waves and spin-curvature forces can be used to generate a spinning-body inspiral. In this paper, we use an osculating geodesic integrator to combine the leading backreaction of gravitational waves with the spin-curvature force. Our analysis only includes the leading orbit-averaged dissipative backreaction, and examines the spin-curvature force to leading order in the small body's spin. This is sufficient to build generic inspirals of spinning bodies, and serves as a foundation for further work examining how to include secondary spin in large-mass-ratio waveform models.

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arXiv2023

Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations

Understanding the orbits of spinning bodies in curved spacetime is important for modeling binary black hole systems with small mass ratios. At zeroth order in mass ratio, the smaller body moves on a geodesic. Post-geodesic effects are needed to model the system accurately. One very important post-geodesic effect is the gravitational self-force, which describes the small body's interaction with its own contribution to a binary's spacetime. Another post-geodesic effect, the spin-curvature force, is due to the smaller body's spin coupling to spacetime curvature. In this paper, we combine the leading orbit-averaged backreaction of point-particle gravitational-wave emission with the spin-curvature force to construct the worldline and gravitational waveform for a spinning body spiraling into a Kerr black hole. We use an osculating geodesic integrator, which treats the worldline as evolution through a sequence of geodesic orbits, as well as near-identity transformations, which eliminate dependence on orbital phases, allowing for fast computation of inspirals. The resulting inspirals and waveforms include all critical dynamical effects which govern such systems (orbit and precession frequencies, inspiral, strong-field gravitational-wave amplitudes), and as such form an effective first model for the inspiral of spinning bodies into Kerr black holes. We emphasize that our present calculation is not self consistent, since we neglect effects which enter at the same order as effects we include. However, our analysis demonstrates that the impact of spin-curvature forces can be incorporated into EMRI waveform tools with relative ease. The calculation is sufficiently modular that it should not be difficult to include neglected post-geodesic effects as efficient tools for computing them become available. (Abridged)

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arXiv2023

Asymptotic gravitational-wave fluxes from a spinning test body on generic orbits around a Kerr black hole

This work provides gravitational wave energy and angular momentum asymptotic fluxes from a spinning body moving on generic orbits in a Kerr spacetime up to linear in spin approximation. To achieve this, we have developed a new frequency domain Teukolsky equation solver that calculates asymptotic amplitudes from generic orbits of spinning bodies with their spin aligned with the total orbital angular momentum. However, the energy and angular momentum fluxes from these orbits in the linear in spin approximation are appropriate for adiabatic models of extreme mass ratio inspirals even for spins non-aligned to the orbital angular momentum. To check the newly obtained fluxes, they were compared with already known frequency domain results for equatorial orbits and with results from a time domain Teukolsky equation solver called Teukode for off-equatorial orbits. The spinning body framework of our work is based on the Mathisson-Papapetrou-Dixon equations under the Tulczyjew-Dixon spin supplementary condition.

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arXiv2022

Measuring quasi-normal mode amplitudes with misaligned binary black hole ringdowns

In recent work, we examined how different modes in the ringdown phase of a binary coalescence are excited as a function of the final plunge geometry. At least in the large mass ratio limit, we found a clean mapping between angles describing the plunge and the amplitude of different quasi-normal modes (QNMs) which constitute the ringdown. In this study, we use that mapping to construct a waveform model expressed as a sum of QNMs where the mode amplitudes and phases are determined by the source plunge parameters. We first generate a large number of calibration waveforms and interpolate between fits of each mode amplitude and phase up to $\ell \leq 8$ and $\ell - |m| \leq 4$. The density of our calibration data allows us to resolve important features such as phase transition discontinuities at large misalignments. Using our ringdown waveform model, we then perform Bayesian parameter estimation with added white Gaussian noise to demonstrate that, in principle, the mode amplitudes can be measured and used to constrain the plunge geometry. We find that inferences are substantially improved by incorporating prior information constraining mode excitation, which motivates work to understand and characterize how the QNM excitation depends on the coalescence geometry. These results are part of a broader effort to map the mode excitation from arbitrary masses and spins, which will be useful for characterizing ringdown waves in upcoming gravitational-wave measurements.

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arXiv2022

Surrogate model for gravitational wave signals from non-spinning, comparable- to large-mass-ratio black hole binaries built on black hole perturbation theory waveforms calibrated to numerical relativity

We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, \texttt{BHPTNRSur1dq1e4}, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. \texttt{BHPTNRSur1dq1e4} extends an earlier waveform model, \texttt{EMRISur1dq1e4}, by using an updated transition-to-plunge model, covering longer durations up to 30,500 $m_1$ (where $m_1$ is the mass of the primary black hole), includes several more spherical harmonic modes up to $\ell=10$, and calibrates subdominant modes to numerical relativity (NR) data. In the comparable mass-ratio regime, including mass ratios as low as $2.5$, the gravitational waveforms generated through ppBHPT agree surprisingly well with those from NR after this simple calibration step. We also compare our model to recent SXS and RIT NR simulations at mass ratios ranging from $15$ to $32$, and find the dominant quadrupolar modes agree to better than $\approx 10^{-3}$. We expect our model to be useful to study intermediate-mass-ratio binary systems in current and future gravitational-wave detectors.

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arXiv2022

Precisely computing bound orbits of spinning bodies around black holes I: General framework and results for nearly equatorial orbits

Very large mass ratio binary black hole systems are of interest both as a clean limit of the two-body problem in general relativity, as well as for their importance as sources of low-frequency gravitational waves. At lowest order, the smaller body moves along a geodesic of the larger black hole's spacetime. Post-geodesic effects include the gravitational self force, which incorporates the backreaction of gravitational-wave emission, and the spin-curvature force, which arises from coupling of the small body's spin to the black hole's spacetime curvature. In this paper, we describe a method for precisely computing bound orbits of spinning bodies about black holes. Our analysis builds off of pioneering work by Witzany which demonstrated how to describe the motion of a spinning body to linear order in the small body's spin. Exploiting the fact that in the large mass-ratio limit spinning-body orbits are close to geodesics and using closed-form results due to van de Meent describing precession of the small body's spin along black hole orbits, we develop a frequency-domain formulation of the motion which can be solved very precisely. We examine a range of orbits with this formulation, focusing in this paper on orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is $\mathcal{O}(S)$ out of the equatorial plane), but for which the small body's spin is arbitrarily oriented. We discuss generic orbits with general small-body spin orientation in a companion paper. We characterize the behavior of these orbits and show how the small body's spin shifts the frequencies $Ω_r$ and $Ω_ϕ$ which affect orbital motion. These frequency shifts change accumulated phases which are direct gravitational-wave observables, illustrating the importance of precisely characterizing these quantities for gravitational-wave observations. (Abridged)

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arXiv2022

Precisely computing bound orbits of spinning bodies around black holes II: Generic orbits

In this paper, we continue our study of the motion of spinning test bodies orbiting Kerr black holes. Non-spinning test bodies follow geodesics of the spacetime in which they move. A test body's spin couples to the curvature of that spacetime, introducing a "spin-curvature force" which pushes the body's worldline away from a geodesic trajectory. The spin-curvature force is an important example of a post-geodesic effect which must be modeled carefully in order to accurately characterize the motion of bodies orbiting black holes. One motivation for this work is to understand how to include such effects in models of gravitational waves produced from the inspiral of stellar mass bodies into massive black holes. In this paper's predecessor, we describe a technique for computing bound orbits of spinning bodies around black holes with a frequency-domain description which can be solved very precisely. In that paper, we present an overview of our methods, as well as present results for orbits which are eccentric and nearly equatorial (i.e., the orbit's motion is no more than $\mathcal{O}(S)$ out of the equatorial plane). In this paper, we apply this formulation to the fully generic case -- orbits which are inclined and eccentric, with the small body's spin arbitrarily oriented. We compute the trajectories which such orbits follow, and compute how the small body's spin affects important quantities such as the observable orbital frequencies $Ω_r$, $Ω_θ$ and $Ω_ϕ$.

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arXiv2021

FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis

We present the FastEMRIWaveforms (FEW) package, a collection of tools to build and analyze extreme mass ratio inspiral (EMRI) waveforms. Here, we expand on the Physical Review Letter that introduced the first fast and accurate fully-relativistic EMRI waveform template model. We discuss the construction of the overall framework; constituent modules; and the general methods used to accelerate EMRI waveforms. Because the fully relativistic FEW model waveforms are for now limited to eccentric orbits in the Schwarzschild spacetime, we also introduce an improved Augmented Analytic Kludge (AAK) model that describes generic Kerr inspirals. Both waveform models can be accelerated using graphics processing unit (GPU) hardware. With the GPU-accelerated waveforms in hand, a variety of studies are performed including an analysis of EMRI mode content, template mismatch, and fully Bayesian Markov Chain Monte Carlo-based EMRI parameter estimation. We find relativistic EMRI waveform templates can be generated with fewer harmonic modes ($\sim10-100$) without biasing signal extraction. However, we show for the first time that extraction of a relativistic injection with semi-relativistic amplitudes can lead to strong bias and anomalous structure in the posterior distribution for certain regions of parameter space.

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arXiv2021

Divergences in gravitational-wave emission and absorption from extreme mass ratio binaries

A powerful technique to calculate gravitational radiation from binary systems involves a perturbative expansion: if the masses of the two bodies are very different, the "small" body is treated as a point particle of mass $m_p$ moving in the gravitational field generated by the large mass $M$, and one keeps only linear terms in the small mass ratio $m_p/M$. This technique usually yields finite answers, which are often in good agreement with fully nonlinear numerical relativity results, even when extrapolated to nearly comparable mass ratios. Here we study two situations in which the point-particle approximation yields a divergent result: the instantaneous flux emitted by a small body as it orbits the light ring of a black hole, and the total energy absorbed by the horizon when a small body plunges into a black hole. By integrating the Teukolsky (or Zerilli/Regge-Wheeler) equations in the frequency and time domains we show that both of these quantities diverge. We find that these divergences are an artifact of the point-particle idealization, and are able to interpret and regularize this behavior by introducing a finite size for the point particle. These divergences do not play a role in black-hole imaging, e.g. by the Event Horizon Telescope.

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arXiv2020

Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis

The future space mission LISA will observe a wealth of gravitational-wave sources at millihertz frequencies. Of these, the extreme-mass-ratio inspirals of compact objects into massive black holes are the only sources that combine the challenges of strong-field complexity with that of long-lived signals. Such signals are found and characterized by comparing them against a large number of accurate waveform templates during data analysis, but the rapid generation of such templates is hindered by computing the $\sim10^3$-$10^5$ harmonic modes in a fully relativistic waveform. We use order-reduction and deep-learning techniques to derive a global fit for these modes, and implement it in a complete waveform framework with hardware acceleration. Our high-fidelity waveforms can be generated in under $1\,\mathrm{s}$, and achieve a mismatch of $\lesssim 5\times 10^{-4}$ against reference waveforms that take $\gtrsim 10^4$ times longer. This marks the first time that analysis-length waveforms with full harmonic content can be produced on timescales useful for direct implementation in LISA analysis algorithms.

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arXiv2020

Prospects for Fundamental Physics with LISA

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics.

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arXiv2020

Tidal heating as a discriminator for horizons in extreme mass ratio inspirals

The defining feature of a classical black hole is being a perfect absorber. Any evidence showing otherwise would indicate a departure from the standard black-hole picture. Energy and angular momentum absorption by the horizon of a black hole is responsible for tidal heating in a binary. This effect is particularly important in the latest stages of an extreme mass ratio inspiral around a spinning supermassive object, one of the main targets of the future LISA mission. We study how this effect can be used to probe the nature of supermassive objects in a model independent way. We compute the orbital dephasing and the gravitational-wave signal emitted by a point particle in circular, equatorial motion around a spinning supermassive object to the leading order in the mass ratio. Absence of absorption by the central object can affect the gravitational-wave signal dramatically, especially at high spin. This effect will make it possible to put an unparalleled upper bound on the reflectivity of exotic compact objects, at the level of ${\cal O}(0.01)\%$. This stringent bound would exclude the possibility of observing echoes in the ringdown of a supermassive binary merger.

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arXiv2019

Exciting black hole modes via misaligned coalescences: I. Inspiral, transition, and plunge trajectories using a generalized Ori-Thorne procedure

The last gravitational waves emitted in the coalescence of two black holes are quasi-normal ringing modes of the merged remnant. In general relativity, the mass and the spin of the remnant black hole uniquely determine the frequency and damping time of each radiated mode. The amplitudes of these modes are determined by the mass ratio of the system and the geometry of the coalescence. This paper is part I of an analysis that aims to compute the "excitation factors" associated with misaligned binary black hole coalescence. To simplify the analysis, we consider a large mass ratio system consisting of a non-spinning body of mass $μ$ that inspirals on a quasi-circular trajectory into a Kerr black hole of mass $M$ and spin parameter $a$, with $μ/M \ll 1$. Our goal is to understand how different modes are excited as a function of the black hole spin $a$ and an angle $I$ which characterizes the misalignment of the orbit with the black hole's spin axis. Though the large mass ratio limit does not describe the binaries that are being observed by gravitational-wave detectors today, this limit makes it possible to quickly and easily explore the binary parameter space, and to develop insight into how the system's late ringing waves depend on the binary's geometry. In this first analysis, we develop the worldline which the small body follows as it inspirals and then plunges into the large black hole. Our analysis generalizes earlier work by Ori and Thorne to describe how a non-equatorial circular inspiral transitions into a plunging trajectory that falls into the black hole. The worldlines which we develop here are used in part II as input to a time-domain black hole perturbation solver. This solver computes the gravitational waves generated by such inspirals and plunges, making it possible to characterize the modes which the coalescence excites.

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arXiv2019

Exciting black hole modes via misaligned coalescences: II. The mode content of late-time coalescence waveforms

Using inspiral and plunge trajectories we construct with a generalized Ori-Thorne algorithm, we use a time-domain black hole perturbation theory code to compute the corresponding gravitational waves. The last cycles of these waveforms are a superposition of Kerr quasinormal modes. In this paper, we examine how the modes' excitations vary as a function of source parameters, such as the larger black hole's spin and the geometry of the smaller body's inspiral and plunge. We find that the mixture of quasinormal modes that characterize the final gravitational waves from a coalescence is entirely determined by the spin $a$ of the larger black hole, an angle $I$ which characterizes the misalignment of the orbital plane from the black hole's spin axis, a second angle $θ_{\rm fin}$ which describes the location at which the small body crosses the black hole's event horizon, and the direction sgn$(\dotθ_{\rm fin})$ of the body's final motion. If these large-mass-ratio results hold at less extreme mass ratios, then measuring multiple ringdown modes of binary black hole coalescence gravitational waves may provide important information about the source's binary properties, such as the misalignment of the orbit's angular momentum with black hole spin. This may be particularly useful for large mass binaries, for which the early inspiral waves are out of the detectors' most sensitive band.

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arXiv2019

Learning about black hole binaries from their ringdown spectra

The coalescence of two black holes generates gravitational waves that carry detailed information about the properties of those black holes and their binary configuration. The final coalescence cycles are in the form of a {\it ringdown}: a superposition of quasi-normal modes of the merged remnant black hole. Each mode has an oscillation frequency and decay time that in general relativity is determined by the remnant's mass and spin. Measuring the frequency and decay time of multiple modes makes it possible to measure the remnant's mass and spin, and to test the waves against the predictions of gravity theories. In this {\it Letter}, we show that the relative amplitudes of these modes encodes information about a binary's {\it geometry}. Focusing on the large mass-ratio limit, which provides a simple-to-use tool for effectively exploring parameter space, we demonstrate how a binary's geometry is encoded in the relative amplitudes of these modes, and how to parameterize the modes in this limit. Although more work is needed to assess how well this carries over to less extreme mass ratios, our results indicate that measuring multiple ringdown modes from coalescence may aid in measuring important source properties, such as the misalignment of its members' spins and orbit.

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arXiv2019

Tidal resonance in extreme mass-ratio inspirals

We describe a new class of resonances for extreme mass-ratio inspirals (EMRIs): tidal resonances, induced by the tidal field of nearby stars or stellar-mass black holes. A tidal resonance can be viewed as a general relativistic extension of the Kozai-Lidov resonances in Newtonian systems, and is distinct from the transient resonance already known for EMRI systems. Tidal resonances will generically occur for EMRIs. By probing their influence on the phase of an EMRI waveform, we can learn about the tidal environmental of the EMRI system, albeit at the cost of a more complicated waveform model. Observations by LISA of EMRI systems therefore have the potential to provide information about the distribution of stellar-mass objects near their host galactic-center black holes.

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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

Bound orbits of a slowly evolving black hole

Bound orbits of black holes are very well understood. Given a Kerr black hole of mass $M$ and spin $S = aM^2$, it is simple to characterize its orbits as functions of the orbit's geometry. How do the orbits change if the black hole is itself evolving? How do the orbits change if the orbiting body evolves? In this paper, we consider a process that changes a black hole's mass and spin, acting such that the spacetime is described by the Kerr solution at any moment, or that changes the orbiting body's mass. Provided this change happens slowly, the orbit's actions ($J_r, J_θ, J_ϕ$) are {\it adiabatic invariants}, and thus are constant during this process. By enforcing adiabatic invariance of the actions, we deduce how an orbit evolves due to changes in the black hole's mass and spin and in the orbiting body's mass. We demonstrate the impact of these results with several examples: how an orbit responds if accretion changes a black hole's mass and spin; how it responds if the orbiting body's mass changes due to accretion; and how the inspiral of a small body into a black hole is affected by change to the hole's mass and spin due to the gravitational radiation absorbed by the event horizon. In all cases, the effect is very small, but can be an order of magnitude or more larger than what was found in previous work which did not take into account how the orbit responds due to these effects.

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