6,147 research outputs found
Using spin to understand the formation of LIGO's black holes
With the detection of four candidate binary black hole (BBH) mergers by the
Advanced LIGO detectors thus far, it is becoming possible to constrain the
properties of the BBH merger population in order to better understand the
formation of these systems. Black hole (BH) spin orientations are one of the
cleanest discriminators of formation history, with BHs in dynamically formed
binaries in dense stellar environments expected to have spins distributed
isotropically, in contrast to isolated populations where stellar evolution is
expected to induce BH spins preferentially aligned with the orbital angular
momentum. In this work we propose a simple, model-agnostic approach to
characterizing the spin properties of LIGO's BBH population. Using measurements
of the effective spin of the binaries, which is LIGO's best constrained spin
parameter, we introduce a simple parameter to quantify the fraction of the
population that is isotropically distributed, regardless of the spin magnitude
distribution of the population. Once the orientation characteristics of the
population have been determined, we show how measurements of effective spin can
be used to directly constrain the underlying BH spin magnitude distribution.
Although we find that the majority of the current effective spin measurements
are too small to be informative, with LIGO's four BBH candidates we find a
slight preference for an underlying population with aligned spins over one with
isotropic spins (with an odds ratio of 1.1). We argue that it will be possible
to distinguish symmetric and anti-symmetric populations at high confidence with
tens of additional detections, although mixed populations may take
significantly more detections to disentangle. We also derive preliminary spin
magnitude distributions for LIGO's black holes, under the assumption of aligned
or isotropic populations
A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves
Ground-based gravitational wave detectors are sensitive to a narrow range of
frequencies, effectively taking a snapshot of merging compact-object binary
dynamics just before merger. We demonstrate that by adopting analysis
parameters that naturally characterize this 'picture', the physical parameters
of the system can be extracted more efficiently from the gravitational wave
data, and interpreted more easily. We assess the performance of MCMC parameter
estimation in this physically intuitive coordinate system, defined by (a) a
frame anchored on the binary's spins and orbital angular momentum and (b) a
time at which the detectors are most sensitive to the binary's gravitational
wave emission. Using anticipated noise curves for the advanced-generation LIGO
and Virgo gravitational wave detectors, we find that this careful choice of
reference frame and reference time significantly improves parameter estimation
efficiency for BNS, NS-BH, and BBH signals.Comment: 11 pages, 5 figures, submitted to Phys. Rev.
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Estimating Residual Faults from Code Coverage
Many reliability prediction techniques require an estimate for the number of residual faults. In this paper, a new theory is developed for using test coverage to estimate the number of residual faults. This theory is applied to a specific example with known faults and the results agree well with the theory. The theory is used to justify the use of linear extrapolation to estimate residual faults. It is also shown that it is important to establish the amount of unreachable code in order to make a realistic residual fault estimate
An Efficient Interpolation Technique for Jump Proposals in Reversible-Jump Markov Chain Monte Carlo Calculations
Selection among alternative theoretical models given an observed data set is
an important challenge in many areas of physics and astronomy. Reversible-jump
Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for
performing Bayesian model selection, but it suffers from a fundamental
difficulty: it requires jumps between model parameter spaces, but cannot
efficiently explore both parameter spaces at once. Thus, a naive jump between
parameter spaces is unlikely to be accepted in the MCMC algorithm and
convergence is correspondingly slow. Here we demonstrate an interpolation
technique that uses samples from single-model MCMCs to propose inter-model
jumps from an approximation to the single-model posterior of the target
parameter space. The interpolation technique, based on a kD-tree data
structure, is adaptive and efficient in modest dimensionality. We show that our
technique leads to improved convergence over naive jumps in an RJMCMC, and
compare it to other proposals in the literature to improve the convergence of
RJMCMCs. We also demonstrate the use of the same interpolation technique as a
way to construct efficient "global" proposal distributions for single-model
MCMCs without prior knowledge of the structure of the posterior distribution,
and discuss improvements that permit the method to be used in
higher-dimensional spaces efficiently.Comment: Minor revision to match published versio
Basic Parameter Estimation of Binary Neutron Star Systems by the Advanced LIGO/Virgo Network
Within the next five years, it is expected that the Advanced LIGO/Virgo
network will have reached a sensitivity sufficient to enable the routine
detection of gravitational waves. Beyond the initial detection, the scientific
promise of these instruments relies on the effectiveness of our physical
parameter estimation capabilities. The majority of this effort has been towards
the detection and characterization of gravitational waves from compact binary
coalescence, e.g. the coalescence of binary neutron stars. While several
previous studies have investigated the accuracy of parameter estimation with
advanced detectors, the majority have relied on approximation techniques such
as the Fisher Matrix. Here we report the statistical uncertainties that will be
achievable for optimal detection candidates (SNR = 20) using the full parameter
estimation machinery developed by the LIGO/Virgo Collaboration via Markov-Chain
Monte Carlo methods. We find the recovery of the individual masses to be
fractionally within 9% (15%) at the 68% (95%) credible intervals for equal-mass
systems, and within 1.9% (3.7%) for unequal-mass systems. We also find that the
Advanced LIGO/Virgo network will constrain the locations of binary neutron star
mergers to a median uncertainty of 5.1 deg^2 (13.5 deg^2) on the sky. This
region is improved to 2.3 deg^2 (6 deg^2) with the addition of the proposed
LIGO India detector to the network. We also report the average uncertainties on
the luminosity distances and orbital inclinations of ideal detection candidates
that can be achieved by different network configurations.Comment: Second version: 15 pages, 9 figures, accepted in Ap
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