Resonantly enhanced and diminished strong-field gravitational-wave fluxes

The inspiral of a stellar mass ($1 - 100\,M_\odot$) compact body into a massive ($10^5 - 10^7\,M_\odot$) black hole has been a focus of much effort, both for the promise of such systems as astrophysical sources of gravitational waves, and because they are a clean limit of the general relativistic two-body problem. Our understanding of this problem has advanced significantly in recent years, with much progress in modeling the "self force" arising from the small body's interaction with its own spacetime deformation. Recent work has shown that this self interaction is especially interesting when the frequencies associated with the orbit's $\theta$ and $r$ motions are in an integer ratio: $\Omega_\theta/\Omega_r = \beta_\theta/\beta_r$, with $\beta_\theta$ and $\beta_r$ both integers. In this paper, we show that key aspects of the self interaction for such "resonant" orbits can be understood with a relatively simple Teukolsky-equation-based calculation of gravitational-wave fluxes. We show that fluxes from resonant orbits depend on the relative phase of radial and angular motions. The purpose of this paper is to illustrate in simple terms how this phase dependence arises using tools that are good for strong-field orbits, and to present a first study of how strongly the fluxes vary as a function of this phase and other orbital parameters. Future work will use the full dissipative self force to examine resonant and near resonant strong-field effects in greater depth, which will be needed to characterize how a binary evolves through orbital resonances.Comment: 25 pages, 6 figures, 4 tables. Accepted to Phys Rev D; accepted version posted here, including referee feedback and other useful comment

Gyroscopes orbiting black holes: A frequency-domain approach to precession and spin-curvature coupling for spinning bodies on generic Kerr orbits

A small body orbiting a black hole follows a trajectory that, at leading order, is a geodesic of the black hole spacetime. Much effort has gone into computing "self-force" corrections to this motion, arising from the small body's own contributions to the system's spacetime. Another correction to the motion arises from coupling of the small body's spin to the black hole's spacetime curvature. Spin-curvature coupling drives a precession of the small body, and introduces a "force" (relative to the geodesic) which shifts the small body's worldline. These effects scale with the small body's spin at leading order. In this paper, we show that the equations which govern spin-curvature coupling can be analyzed with a frequency-domain decomposition, at least to leading order in the small body's spin. We show how to compute the frequency of precession along generic orbits, and how to describe the small body's precession and motion in the frequency domain. We illustrate this approach with a number of examples. This approach is likely to be useful for understanding spin coupling effects in the extreme mass ratio limit, and may provide insight into modeling spin effects in the strong field for nonextreme mass ratios.National Science Foundation (U.S.) (Grant PHY-1403261

Effects of resonances and spin-curvature coupling in extreme mass ratio inspirals

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2016.Cataloged from PDF version of thesis.Includes bibliographical references.Since Einstein proposed the theory of general relativity (GR) as a theory of gravity, it has passed all experimental checks and tests. Until recently, all of these tests have been done in the weak gravity limit. The first test of strong-field GR came just a few months ago, when the LIGO collaboration directly detected gravitational waves for the first time. Using gravitational waves as a tool to test the validity of GR requires us to know the waveforms that GR predicts from various sources. The ultimate goal of the research described in this thesis is to compute the waveform generated by a stellar mass Kerr black hole as it inspirals into a much more massive black hole (SMBH). To compute this waveform, we must first compute the inspiral trajectory of the stellar mass black hole. The trajectory of the smaller black hole differs from the geodesic structure taught in GR textbooks due to the influence of this body's mass and spin. In this thesis, I examine these two effects separately. Later work will need to consider the two effects simultaneously, but the separate impact of these effects provides insight which helps us to understand how to model these sources. The small body's mass perturbs the spacetime and pushes its trajectory away from textbook geodesic motion. I show how to compute the dissipative part of this "self force," whose average impact is equivalent to the loss of energy and angular momentum due to gravitational wave emission. I study in particular how the self force's averaged behavior changes near orbital resonances, quantifying the impact that such resonances will have on the small body's inspiral. The small body's spin couples to spacetime curvature. This coupling leads to a force which also pushes the small body's trajectory away from the geodesic. This force is comparable in magnitude to the self force associated with the small body's mass, indicating that future work will need to assess the impact of these effects together in a self consistent way in order to make accurate inspiral waveforms.by Uchupol Ruangsri.Ph. D

Census of transient orbital resonances encountered during binary inspiral

Transient orbital resonances have recently been identified as potentially important to the inspiral of small bodies into large black holes. These resonances occur as the inspiral evolves through moments in which two fundamental orbital frequencies, Ω[subscript θ] and Ω[subscript r], are in a small integer ratio to one another. Previous work has demonstrated that a binary’s parameters are “kicked” each time the inspiral passes through a resonance, changing the orbit’s characteristics relative to a model that neglects resonant effects. In this paper, we use exact Kerr geodesics coupled to an accurate but approximate model of inspiral to survey orbital parameter space and estimate how commonly one encounters long-lived orbital resonances. We find that the most important resonances last for a few hundred orbital cycles at mass ratio 10[superscript −6], and that resonances are almost certain to occur during the time that a large-mass-ratio binary would be a target of gravitational wave observations. Resonances appear to be ubiquitous in large-mass-ratio inspiral, and to last long enough that they are likely to affect binary evolution in observationally important ways.National Science Foundation (U.S.) (Grant PHY-1068720)John Simon Guggenheim Memorial Foundatio