4,831 research outputs found
Bayesian inference on compact binary inspiral gravitational radiation signals in interferometric data
Presented is a description of a Markov chain Monte Carlo (MCMC) parameter
estimation routine for use with interferometric gravitational radiational data
in searches for binary neutron star inspiral signals. Five parameters
associated with the inspiral can be estimated, and summary statistics are
produced. Advanced MCMC methods were implemented, including importance
resampling and prior distributions based on detection probability, in order to
increase the efficiency of the code. An example is presented from an
application using realistic, albeit fictitious, data.Comment: submitted to Classical and Quantum Gravity. 14 pages, 5 figure
Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals
A global network of laser interferometric gravitational wave detectors is
projected to be in operation by around the turn of the century. Here, the noisy
output of a single instrument is examined. A gravitational wave is assumed to
have been detected in the data and we deal with the subsequent problem of
parameter estimation. Specifically, we investigate theoretical lower bounds on
the minimum mean-square errors associated with measuring the parameters of the
inspiral waveform generated by an orbiting system of neutron stars/black holes.
Three theoretical lower bounds on parameter estimation accuracy are considered:
the Cramer-Rao bound (CRB); the Weiss-Weinstein bound (WWB); and the Ziv-Zakai
bound (ZZB). We obtain the WWB and ZZB for the Newtonian-form of the coalescing
binary waveform, and compare them with published CRB and numerical Monte-Carlo
results. At large SNR, we find that the theoretical bounds are all identical
and are attained by the Monte-Carlo results. As SNR gradually drops below 10,
the WWB and ZZB are both found to provide increasingly tighter lower bounds
than the CRB. However, at these levels of moderate SNR, there is a significant
departure between all the bounds and the numerical Monte-Carlo results.Comment: 17 pages (LaTeX), 4 figures. Submitted to Physical Review
Introduction to dynamical horizons in numerical relativity
This paper presents a quasi-local method of studying the physics of dynamical
black holes in numerical simulations. This is done within the dynamical horizon
framework, which extends the earlier work on isolated horizons to
time-dependent situations. In particular: (i) We locate various kinds of
marginal surfaces and study their time evolution. An important ingredient is
the calculation of the signature of the horizon, which can be either spacelike,
timelike, or null. (ii) We generalize the calculation of the black hole mass
and angular momentum, which were previously defined for axisymmetric isolated
horizons to dynamical situations. (iii) We calculate the source multipole
moments of the black hole which can be used to verify that the black hole
settles down to a Kerr solution. (iv) We also study the fluxes of energy
crossing the horizon, which describes how a black hole grows as it accretes
matter and/or radiation.
We describe our numerical implementation of these concepts and apply them to
three specific test cases, namely, the axisymmetric head-on collision of two
black holes, the axisymmetric collapse of a neutron star, and a
non-axisymmetric black hole collision with non-zero initial orbital angular
momentum.Comment: 20 pages, 16 figures, revtex4. Several smaller changes, some didactic
content shortene
Gravitational Wave Experiments and Early Universe Cosmology
Gravitational-wave experiments with interferometers and with resonant masses
can search for stochastic backgrounds of gravitational waves of cosmological
origin. We review both experimental and theoretical aspects of the search for
these backgrounds. We give a pedagogical derivation of the various relations
that characterize the response of a detector to a stochastic background. We
discuss the sensitivities of the large interferometers under constructions
(LIGO, VIRGO, GEO600, TAMA300, AIGO) or planned (Avdanced LIGO, LISA) and of
the presently operating resonant bars, and we give the sensitivities for
various two-detectors correlations. We examine the existing limits on the
energy density in gravitational waves from nucleosynthesis, COBE and pulsars,
and their effects on theoretical predictions. We discuss general theoretical
principles for order-of-magnitude estimates of cosmological production
mechanisms, and then we turn to specific theoretical predictions from
inflation, string cosmology, phase transitions, cosmic strings and other
mechanisms. We finally compare with the stochastic backgrounds of astrophysical
origin.Comment: 99 pages, Latex, 17 figures. To appear in Physics Report. v4:
conceptual changes in sect. 7.
Rapid model comparison of equations of state from gravitational wave observation of binary neutron star coalescences
The discovery of the coalescence of binary neutron star GW170817 was a watershed moment in the field of gravitational wave astronomy. Among the rich variety of information that we were able to uncover from this discovery was the first non-electromagnetic measurement of the neutron star radius, and the cold nuclear equation of state. It also led to a large equation of state model-selection study from gravitational-wave data. In those studies Bayesian nested sampling runs were conducted for each candidate equation of state model to compute their evidence in the gravitational-wave data. Such studies, though invaluable, are computationally expensive and require repeated, redundant, computation for any new models. We present a novel technique to conduct model-selection of equation of state in an extremely rapid fashion (~minutes) on any arbitrary model. We test this technique against the results of a nested-sampling model-selection technique published earlier by the LIGO/Virgo collaboration, and show that the results are in good agreement with a median fractional error in Bayes factor of about 10%, where we assume that the true Bayes factor is calculated in the aforementioned nested sampling runs. We found that the highest fractional error occurs for equation of state models that have very little support in the posterior distribution, thus resulting in large statistical uncertainty. We then used this method to combine multiple binary neutron star mergers to compute a joint-Bayes factor between equation of state models. This is achieved by stacking the evidence of the individual events and computing the Bayes factor from these stacked evidences for each pairs of equation of state
Discontinuous Galerkin methods for general-relativistic hydrodynamics: formulation and application to spherically symmetric spacetimes
We have developed the formalism necessary to employ the
discontinuous-Galerkin approach in general-relativistic hydrodynamics. The
formalism is firstly presented in a general 4-dimensional setting and then
specialized to the case of spherical symmetry within a 3+1 splitting of
spacetime. As a direct application, we have constructed a one-dimensional code,
EDGES, which has been used to asses the viability of these methods via a series
of tests involving highly relativistic flows in strong gravity. Our results
show that discontinuous Galerkin methods are able not only to handle strong
relativistic shock waves but, at the same time, to attain very high orders of
accuracy and exponential convergence rates in smooth regions of the flow. Given
these promising prospects and their affinity with a pseudospectral solution of
the Einstein equations, discontinuous Galerkin methods could represent a new
paradigm for the accurate numerical modelling in relativistic astrophysics.Comment: 24 pages, 19 figures. Small changes; matches version to appear in PR
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