EMRI Data Analysis with a Phenomenological Waveform

Abstract

Extreme mass ratio inspirals (EMRIs) (capture and inspiral of a compact stellar mass object into a Massive Black Hole (MBH)) are among the most interesting objects for the gravitational wave astronomy. It is a very challenging task to detect those sources with the accurate estimation parameters of binaries primarily due to a large number of the secondary maxima on the likelihood surface. Search algorithms based on the matched filtering require computation of the gravitational waveform hundreds of thousands of times, which is currently not feasible with the most accurate (faithful) models of EMRIs. Here we propose to use a phenomenological template family which covers a large range of EMRIs parameter space. We use these phenomenological templates to detect the signal in the simulated data and then, assuming a particular EMRI model, estimate the physical parameters of the binary. We have separated the detection problem, which is done in a model-independent way, from the parameter estimation. For the latter one, we need to adopt the model for inspiral in order to map phenomenological parameters onto the physical parameter characterizing EMRIs. * yan.wang@aei.mpg.de † Shang.Yu@aei.mpg.de ‡ Stanislav.Babak@aei.mpg.de arXiv:1207.4956v1 [gr-qc]

Extreme Mass Ratio Inspirals: Perspectives for Their Detection

“…Usually the likelihood (or log-likelihood) can be maximised over some parameters of the signal analytically, whereas maximisation over other parameters requires a numerical search. The analytically maximised likelihood is quite often referred as the F -statistic [67,64,63]. Based on the equations (40), (41) we can introduce a cumulative likelihood (or cumulative F -statistic) in the time and/or in the frequency domain by varying the upper limit of integration.…”

“…The large dimensionality of the parameter space of possible signals makes a grid-type search completely infeasible, so instead we will rely on (pseudo)-stochastic search methods, primarily based on Markov chain Monte-Carlo (MCMC) techniques. Various implementations of MCMC for searches for EMRIs signals are described in [63,4,64], but the basic idea is to construct a chain which moves predominantly in the direction of increasing likelihood. The complication is that the EMRI likelihood hyper-surface has numerous local maxima some of which could be as much as 70 − 80% of the global maximum and these local maxima are widely separated in the parameter space.…”

“…Usually the likelihood (or log-likelihood) can be maximised over some parameters of the signal analytically, whereas maximisation over other parameters requires a numerical search. The analytically maximised likelihood is quite often referred as the F -statistic [67,64,63].…”

“…In this subsection we summarise the method described in [64]. The main idea of this approach was to detect GW signals from EMRIs in a model independent way using a minimal set of assumptions about the signal: (1) the orbital motion can be described by six slowly (on the radiation reaction time scale) changing quantities; and (2) the signal is represented by a set of harmonics of those (three) orbital frequencies with slowly changing amplitude.…”

“…Here we describe the simulations performed in [64]. Three month long data sets were simulated containing an EMRI signal (SN R = 50) using the numerical kludge as a model.…”