A Bayesian approach to the study of white dwarf binaries in LISA data: The application of a reversible jump Markov chain Monte Carlo method

The Laser Interferometer Space Antenna (LISA) defines new demands on data analysis efforts in its all-sky gravitational wave survey, recording simultaneously thousands of galactic compact object binary foreground sources and tens to hundreds of background sources like binary black hole mergers and extreme mass ratio inspirals. We approach this problem with an adaptive and fully automatic Reversible Jump Markov Chain Monte Carlo sampler, able to sample from the joint posterior density function (as established by Bayes theorem) for a given mixture of signals "out of the box'', handling the total number of signals as an additional unknown parameter beside the unknown parameters of each individual source and the noise floor. We show in examples from the LISA Mock Data Challenge implementing the full response of LISA in its TDI description that this sampler is able to extract monochromatic Double White Dwarf signals out of colored instrumental noise and additional foreground and background noise successfully in a global fitting approach. We introduce 2 examples with fixed number of signals (MCMC sampling), and 1 example with unknown number of signals (RJ-MCMC), the latter further promoting the idea behind an experimental adaptation of the model indicator proposal densities in the main sampling stage. We note that the experienced runtimes and degeneracies in parameter extraction limit the shown examples to the extraction of a low but realistic number of signals.Comment: 18 pages, 9 figures, 3 tables, accepted for publication in PRD, revised versio

Optimizing gravitational-wave searches for a population of coalescing binaries: Intrinsic parameters

We revisit the problem of searching for gravitational waves from inspiralling compact binaries in Gaussian coloured noise. For binaries with quasicircular orbits and non-precessing component spins, considering dominant mode emission only, if the intrinsic parameters of the binary are known then the optimal statistic for a single detector is the well-known two-phase matched filter. However, the matched filter signal-to-noise ratio is /not/ in general an optimal statistic for an astrophysical population of signals, since their distribution over the intrinsic parameters will almost certainly not mirror that of noise events, which is determined by the (Fisher) information metric. Instead, the optimal statistic for a given astrophysical distribution will be the Bayes factor, which we approximate using the output of a standard template matched filter search. We then quantify the possible improvement in number of signals detected for various populations of non-spinning binaries: for a distribution of signals uniformly distributed in volume and with component masses distributed uniformly over the range $1\leq m_{1,2}/M_\odot\leq 24$, $(m_1+m_2) /M_\odot\leq 25$ at fixed expected SNR, we find $\gtrsim 20\%$ more signals at a false alarm threshold of $10^{-6}\,$Hz in a single detector. The method may easily be generalized to binaries with non-precessing spins.Comment: Version accepted by Phys. Rev.

How would GW150914 look with future GW detector networks?

The first detected gravitational wave signal, GW150914, was produced by the coalescence of a stellar-mass binary black hole. Along with the subsequent detection of GW151226, GW170104 and the candidate event LVT151012, this gives us evidence for a population of black hole binaries with component masses in the tens of solar masses. As detector sensitivity improves, this type of source is expected to make a large contribution to the overall number of detections, but has received little attention compared to binary neutron star systems in studies of projected network performance. We simulate the observation of a system like GW150914 with different proposed network configurations, and study the precision of parameter estimates, particularly source location, orientation and masses. We find that the improvements to low frequency sensitivity that are expected with continued commissioning will improve the precision of chirp mass estimates by an order of magnitude, whereas the improvements in sky location and orientation are driven by the expanded network configuration. This demonstrates that both sensitivity and number of detectors will be important factors in the scientific potential of second generation detector networks.Comment: 18 pages, 5 figures, 2 table

Markov chain Monte Carlo searches for Galactic binaries in Mock LISA Data Challenge 1B data sets

We are developing a Bayesian approach based on Markov chain Monte Carlo techniques to search for and extract information about white dwarf binary systems with the Laser Interferometer Space Antenna (LISA). Here we present results obtained by applying an initial implementation of this method to some of the data sets released in Round 1B of the Mock LISA Data Challenges. For Challenges 1B.1.1a and 1b the signals were recovered with parameters lying within the 95.5% posterior probability interval and the correlation between the true and recovered waveform is in excess of 99%. Results were not submitted for Challenge 1B.1.1c due to some convergence problems of the algorithms, despite this, the signal was detected in a search over a 2 mHz band.Comment: 11 pages, 5 figures, 12th GWDAW (Gravitational Wave Data Analysis Workshop). Accepted for publication in CQ

Accelerating gravitational wave parameter estimation with multi-band template interpolation

Parameter estimation on gravitational wave signals from compact binary coalescence (CBC) requires the evaluation of computationally intensive waveform models, typically the bottleneck in the analysis. This cost will increase further as low frequency sensitivity in later second and third generation detectors motivates the use of longer waveforms. We describe a method for accelerating parameter estimation by exploiting the chirping behaviour of the signals to sample the waveform sparsely for portions where the full frequency resolution is not required. We demonstrate that the method can reproduce the original results with a waveform mismatch of $\leq 5\times 10^{-7}$, but with a waveform generation cost up to $\sim 50$ times lower for computationally costly frequency-domain waveforms starting from below 8 Hz

Measuring intermediate mass black hole binaries with advanced gravitational wave detectors

We perform a systematic study to explore the accuracy with which the parameters of intermediate-mass black-hole binary systems can be measured from their gravitational wave (GW) signatures using second-generation GW detectors. We make use of the most recent reduced-order models containing inspiral, merger and ringdown signals of aligned-spin effective-one-body waveforms (SEOBNR) to significantly speed up the calculations. We explore the phenomenology of the measurement accuracies for binaries with total masses between 50 and 500 $M_\odot$ and mass ratios between 0.1 and 1. We find that (i) at total masses below ~200 $M_\odot$, where the signal-to-noise-ratio is dominated by the inspiral portion of the signal, the chirp mass parameter can be accurately measured; (ii) at higher masses, the information content is dominated by the ringdown, and total mass is measured more accurately; (iii) the mass of the lower-mass companion is poorly estimated, especially at high total mass and more extreme mass ratios; (iv) spin cannot be accurately measured for our injection set with non-spinning components. Most importantly, we find that for binaries with non-spinning components at all values of the mass ratio in the considered range and at network signal-to-noise ratio of 15, analyzed with spin-aligned templates, the presence of an intermediate-mass black hole with mass >100 $M_\odot$ can be confirmed with 95% confidence in any binary that includes a component with a mass of 130 $M_\odot$ or greater.Comment: 6 pages, 8 figures; published versio