The Galactic population of close white dwarf binaries is expected to provide the largest number of gravitational wave sources for low frequency detectors such as the Laser Interferometer Space Antenna (LISA). Current data analysis techniques have dem
onstrated the capability of resolving on the order of $10^4$ white dwarf binaries from a 2 year observation. Resolved binaries are either at high frequencies or large amplitudes. Such systems are more likely to be high-mass binaries, a subset of which will be progenitors of SNe Ia in the double degenerate scenario. We report on results of a study of the properties of resolved binaries using a population synthesis model of the Galactic white dwarf binaries and a LISA data analysis algorithm using Mock LISA Data Challenge tools.
Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of sources. We show
that the comparison of instantaneous time-frequency and time- amplitude maps provided by the Hilbert-Huang Transform (HHT) can be used effectively for relative signal timing of common signals, to discriminate between the case of identical coincident signals and random noise coincidences, and to provide a classification of signals based on their time-frequency trajectories. The comparison is done with a chi-square goodness-of-fit method which includes contributions from both the instantaneous amplitude and frequency components of the HHT to match two signals in the time domain. This approach naturally allows the analysis of waveforms with strong frequency modulation.
We study the effect of short term variations of the evolution of AM CVn systems on their gravitational wave emissions and in particular LISA observations. We model the systems according to their equilibrium mass-transfer evolution as driven by gravit
ational wave emission and tidal interaction, and determine their reaction to a sudden perturbation of the system. This is inspired by the suggestion to explain the orbital period evolution of the ultra-compact binary systems V407 Vul and RX-J0806+1527 by non-equilibrium mass transfer. The characteristics of the emitted gravitational wave signal are deduced from a Taylor expansion of a Newtonian quadrupolar emission model, and the changes in signal structure as visible to the LISA mission are determined. We show that short term variations can significantly change the higher order terms in the expansion, and thus lead to spurious (non) detection of frequency derivatives. This may hamper the estimation of the parameters of the system, in particular their masses and distances. However, we find that overall detection is still secured as signals still can be described by general templates. We conclude that a better modelling of the effects of short term variations is needed to prepare the community for astrophysical evaluations of real gravitational wave data of AM CVn systems.
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 backg
round 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.
The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency resolution
but also renders it susceptible to degradation from noise. We show that complementing the HHT with techniques such as zero-phase filtering, kernel density estimation and Fourier analysis allows it to be used effectively to detect and characterize signals with low signal to noise ratio.
The Ninja data analysis challenge allowed the study of the sensitivity of data analysis pipelines to binary black hole numerical relativity waveforms in simulated Gaussian noise at the design level of the LIGO observatory and the VIRGO observatory. W
e analyzed NINJA data with a pipeline based on the Hilbert Huang Transform, utilizing a detection stage and a characterization stage: detection is performed by triggering on excess instantaneous power, characterization is performed by displaying the kernel density enhanced (KD) time-frequency trace of the signal. Using the simulated data based on the two LIGO detectors, we were able to detect 77 signals out of 126 above SNR 5 in coincidence, with 43 missed events characterized by signal to noise ratio SNR less than 10. Characterization of the detected signals revealed the merger part of the waveform in high time and frequency resolution, free from time-frequency uncertainty. We estimated the timelag of the signals between the detectors based on the optimal overlap of the individual KD time-frequency maps, yielding estimates accurate within a fraction of a millisecond for half of the events. A coherent addition of the data sets according to the estimated timelag eventually was used in a characterization of the event.
In this paper we describe a Bayesian inference framework for analysis of data obtained by LISA. We set up a model for binary inspiral signals as defined for the Mock LISA Data Challenge 1.2 (MLDC), and implemented a Markov chain Monte Carlo (MCMC) al
gorithm to facilitate exploration and integration of the posterior distribution over the 9-dimensional parameter space. Here we present intermediate results showing how, using this method, information about the 9 parameters can be extracted from the data.
We report on the analysis of selected single source data sets from the first round of the Mock LISA Data Challenges (MLDC) for white dwarf binaries. We implemented an end-to-end pipeline consisting of a grid-based coherent pre-processing unit for sig
nal detection, and an automatic Markov Chain Monte Carlo post-processing unit for signal evaluation. We demonstrate that signal detection with our coherent approach is secure and accurate, and is increased in accuracy and supplemented with additional information on the signal parameters by our Markov Chain Monte Carlo approach. We also demonstrate that the Markov Chain Monte Carlo routine is additionally able to determine accurately the noise level in the frequency window of interest.
We demonstrate the use of automatic Bayesian inference for the analysis of LISA data sets. In particular we describe a new automatic Reversible Jump Markov Chain Monte Carlo method to evaluate the posterior probability density functions of the a prio
ri unknown number of parameters that describe the gravitational wave signals present in the data. We apply the algorithm to a simulated LISA data set containing overlapping signals from white dwarf binary systems (DWD) and to a separate data set containing a signal from an extreme mass ratio inspiral (EMRI). We demonstrate that the approach works well in both cases and can be regarded as a viable approach to tackle LISA data analysis challenges.
