Multipole moments of bumpy black holes

General relativity predicts the existence of black holes, compact objects whose spacetimes depend on only their mass, spin, and charge in vacuum (the "no hair" theorem). As various observations probe deeper into the strong fields of black hole candidates, it is becoming possible to test this prediction. Previous work suggested that such tests can be performed by measuring whether the multipolar structure of black hole candidates has the form that general relativity demands, and introduced a family of "bumpy black hole" spacetimes to be used for making these measurements. These spacetimes have generalized multipoles, where the deviation from the Kerr metric depends on the spacetime's "bumpiness." In this paper, we show how to compute the Geroch-Hansen moments of a bumpy black hole, demonstrating that there is a clean mapping between the deviations used in the bumpy black hole formalism and the Geroch-Hansen moments. We also extend our previous results to define bumpy black holes whose {\it current} moments, analogous to magnetic moments of electrodynamics, deviate from the canonical Kerr value.Comment: 15 page

Bayesian inference for pulsar timing models

The extremely regular, periodic radio emission from millisecond pulsars makes them useful tools for studying neutron star astrophysics, general relativity, and low-frequency gravitational waves. These studies require that the observed pulse times of arrival be fit to complex timing models that describe numerous effects such as the astrometry of the source, the evolution of the pulsar's spin, the presence of a binary companion, and the propagation of the pulses through the interstellar medium. In this paper, we discuss the benefits of using Bayesian inference to obtain pulsar timing solutions. These benefits include the validation of linearized least-squares model fits when they are correct, and the proper characterization of parameter uncertainties when they are not; the incorporation of prior parameter information and of models of correlated noise; and the Bayesian comparison of alternative timing models. We describe our computational setup, which combines the timing models of Tempo2 with the nested-sampling integrator MultiNest. We compare the timing solutions generated using Bayesian inference and linearized least-squares for three pulsars: B1953+29, J2317+1439, and J1640+2224, which demonstrate a variety of the benefits that we posit.Comment: 13 pages, 4 figures, RevTeX 4.1. Revised in response to referee's suggestions; contains a broader discussion of model comparison, revised Monte Carlo runs, improved figure

Spacetime and orbits of bumpy black holes

Our universe contains a great number of extremely compact and massive objects which are generally accepted to be black holes. Precise observations of orbital motion near candidate black holes have the potential to determine if they have the spacetime structure that general relativity demands. As a means of formulating measurements to test the black hole nature of these objects, Collins and Hughes introduced "bumpy black holes": objects that are almost, but not quite, general relativity's black holes. The spacetimes of these objects have multipoles that deviate slightly from the black hole solution, reducing to black holes when the deviation is zero. In this paper, we extend this work in two ways. First, we show how to introduce bumps which are smoother and lead to better behaved orbits than those in the original presentation. Second, we show how to make bumpy Kerr black holes -- objects which reduce to the Kerr solution when the deviation goes to zero. This greatly extends the astrophysical applicability of bumpy black holes. Using Hamilton-Jacobi techniques, we show how a spacetime's bumps are imprinted on orbital frequencies, and thus can be determined by measurements which coherently track a small orbiting body's orbital phase. We find that weak-field orbits of bumpy black holes are modified exactly as expected from a Newtonian analysis of a body with a prescribed multipolar structure, reproducing well-known results from the celestial mechanics literature. The impact of bumps on strong-field orbits is especially strong, suggesting that this framework will allow observations to set robust limits on the extent to which a spacetime's multipoles deviate from the black hole expectation.Comment: 24 pages, 3 figures, accepted to Phys. Rev. D. This version corrects some typos and incorporates suggested edit

Studies of strong-field gravity : testing the black hole hypothesis and investigating spin-curvature coupling

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 151-159).Observations of gravitational systems agree well with the predictions of general relativity (GR); however, to date we have only tested gravity in the weak-field limit. In the next few years, observational advances may make it possible for us to observe motion in the strong field for the first time. This thesis is concerned with two probes of strong-field gravity: whether the spacetime of a black hole has the structure predicted by GR, and the effect of spin-curvature coupling on orbital motion in the large mass-ratio limit. The first two-thirds of this thesis develop a formalism for determining whether a candidate black hole is described by the Kerr metric, as predicted by GR for all black holes in vacuum. In the first chapter, we describe how to construct a "bumpy black hole," an object whose spacetime is almost, but not quite, the Kerr metric. We define perturbations to the mass and spin moments and relate the changes in the moments to changes in the orbital frequencies using canonical perturbation theory. In the second chapter, we extend the bumpy black hole formalism to include black holes in non-GR theories of gravity, which leads to additional functional degrees of freedom. The final chapter investigates the effects of spin-curvature coupling. For a small body with spin moving around a massive black hole, the spin of the small body couples to the background curvature, and its trajectory deviates from a geodesic. To date, there has been relatively little work that considers this effect except in the special cases of aligned spins and circular, equatorial orbits. We compute the perturbation to the trajectory and the spin precession due to spin-curvature coupling for generic orbits of Kerr and arbitrary initial spin orientations.by Sarah Jane Vigeland.Ph.D

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

Multimessenger Approaches to Supermassive Black Hole Binary Detection and Parameter Estimation II: Optimal Strategies for a Pulsar Timing Array

Pulsar timing arrays (PTAs) are Galactic-scale gravitational wave (GW) detectors consisting of precisely-timed pulsars distributed across the sky. Within the decade, PTAs are expected to detect the nanohertz GWs emitted by close-separation supermassive black hole binaries (SMBHBs), thereby opening up the low frequency end of the GW spectrum for science. Individual SMBHBs which power active galactic nuclei are also promising multi-messenger sources; they may be identified via theoretically predicted electromagnetic (EM) signatures and be followed up by PTAs for GW observations. In this work, we study the detection and parameter estimation prospects of a PTA which targets EM-selected SMBHBs. Adopting a simulated Galactic millisecond pulsar population, we envisage three different pulsar timing campaigns which observe three mock sources at different sky locations. We find that an all-sky PTA which times the best pulsars is an optimal and feasible approach to observe EM-selected SMBHBs and measure their source parameters to high precision (i.e., comparable to or better than conventional EM measurements). We discuss the implications of our findings in the context of the future PTA experiment with the planned Deep Synoptic Array-2000 and the multi-messenger studies of SMBHBs such as the well-known binary candidate OJ 287.Comment: 14 pages, 6 figures, 3 tables; ApJ accepted; data will be available with the ApJ publicatio

Reconciling optical and radio observations of the binary millisecond pulsar PSR J1640+2224

Previous optical and radio observations of the binary millisecond pulsar PSR J1640+2224 have come to inconsistent conclusions about the identity of its companion, with some observations suggesting the companion is a low-mass helium-core (He-core) white dwarf (WD), while others indicate it is most likely a high-mass carbon-oxygen (CO) WD. Binary evolution models predict PSR J1640+2224 most likely formed in a low-mass X-ray binary (LMXB) based on the pulsar's short spin period and long-period, low-eccentricity orbit, in which case its companion should be a He-core WD with mass about $0.35 - 0.39 \, M_\odot$, depending on metallicity. If it is instead a CO WD, that would suggest the system has an unusual formation history. In this paper we present the first astrometric parallax measurement for this system from observations made with the Very Long Baseline Array (VLBA), from which we determine the distance to be $1520^{+170}_{-150}\,\mathrm{pc}$. We use this distance and a reanalysis of archival optical observations originally taken in 1995 with the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope (HST) in order to measure the WD's mass. We also incorporate improvements in calibration, extinction model, and WD cooling models. We find that the existing observations are not sufficient to tightly constrain the companion mass, but we conclude the WD mass is $>0.4\,M_\odot$ with $>90\%$ confidence. The limiting factor in our analysis is the low signal-to-noise ratio of the original HST observations.Comment: 6 pages, 5 figure

Supermassive Black-hole Demographics & Environments With Pulsar Timing Arrays

Precision timing of large arrays (>50) of millisecond pulsars will detect the nanohertz gravitational-wave emission from supermassive binary black holes within the next ~3-7 years. We review the scientific opportunities of these detections, the requirements for success, and the synergies with electromagnetic instruments operating in the 2020s.Comment: Submitted to the Astro2020 Decadal Survey. One of 5 core white-papers authored by members of the NANOGrav Collaboration. 9 pages, 2 figure

Constraining alternative polarization states of gravitational waves from individual black hole binaries using pulsar timing arrays

Pulsar timing arrays are sensitive to gravitational wave perturbations produced by individual supermassive black hole binaries during their early inspiral phase. Modified gravity theories allow for the emission of gravitational dipole radiation, which is enhanced relative to the quadrupole contribution for low orbital velocities, making the early inspiral an ideal regime to test for the presence of modified gravity effects. Using a theory-agnostic description of modified gravity theories based on the parametrized post-Einsteinian framework, we explore the possibility of detecting deviations from general relativity using simulated pulsar timing array data, and provide forecasts for the constraints that can be achieved. We generalize the enterprise pulsar timing software to account for possible additional polarization states and modifications to the phase evolution, and study how accurately the parameters of simulated signals can be recovered. We find that while a pure dipole model can partially recover a pure quadrupole signal, there is little possibility for confusion when the full model with all polarization states is used. With no signal present, and using noise levels comparable to those seen in contemporary arrays, we produce forecasts for the upper limits that can be placed on the amplitudes of alternative polarization modes as a function of the sky location of the source