61 research outputs found
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
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
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
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 , 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 . 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 with confidence. The limiting
factor in our analysis is the low signal-to-noise ratio of the original HST
observations.Comment: 6 pages, 5 figure
Noise-marginalized optimal statistic: A robust hybrid frequentist-Bayesian statistic for the stochastic gravitational-wave background in pulsar timing arrays
Observations have revealed that nearly all galaxies contain supermassive
black holes (SMBHs) at their centers. When galaxies merge, these SMBHs form
SMBH binaries (SMBHBs) that emit low-frequency gravitational waves (GWs). The
incoherent superposition of these sources produce a stochastic GW background
(GWB) that can be observed by pulsar timing arrays (PTAs). The optimal
statistic is a frequentist estimator of the amplitude of the GWB that
specifically looks for the spatial correlations between pulsars induced by the
GWB. In this paper, we introduce an improved method for computing the optimal
statistic that marginalizes over the red noise in individual pulsars. We use
simulations to demonstrate that this method more accurately determines the
strength of the GWB, and we use the noise-marginalized optimal statistic to
compare the significance of monopole, dipole, and Hellings-Downs (HD) spatial
correlations and perform sky scrambles.Comment: 8 pages, 7 figures. Published in PR
Efficient Gravitational Wave Searches with Pulsar Timing Arrays using Hamiltonian Monte Carlo
Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) by
looking for correlated deviations in pulse arrival times. Current Bayesian
searches use Markov Chain Monte Carlo (MCMC) methods, which struggle to sample
the large number of parameters needed to model the PTA and GW signals. As the
data span and number of pulsars increase, this problem will only worsen. An
alternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC),
utilizes Hamiltonian dynamics to produce sample proposals informed by
first-order gradients of the model likelihood. This in turn allows it to
converge faster to high dimensional distributions. We implement HMC as an
alternative sampling method in our search for an isotropic stochastic GW
background, and show that this method produces equivalent statistical results
to similar analyses run with standard MCMC techniques, while requiring 100-200
times fewer samples. We show that the speed of HMC sample generation scales as
where is the number of
pulsars, compared to for MCMC methods. These
factors offset the increased time required to generate a sample using HMC,
demonstrating the value of adopting HMC techniques for PTAs.Comment: 9 pages, 5 figures, submitted to Physical Review
- β¦