Gaussian processes for the interpolation and marginalization of waveform error in extreme-mass-ratio-inspiral parameter estimation

Abstract

A number of open problems hinder our present ability to extract scientific information from data that will be gathered by the near-future gravitational-wave mission LISA. Many of these relate to the modeling, detection and characterization of signals from binary inspirals with an extreme component-mass ratio of 10 −4 . In this paper, we draw attention to the issue of systematic error in parameter estimation due to the use of fast but approximate waveform models; this is found to be relevant for extreme-mass-ratio inspirals even in the case of waveforms with 90% overlap accuracy and moderate ( 30) signal-to-noise ratios. A scheme that uses Gaussian processes to interpolate and marginalize over waveform error is adapted and investigated as a possible precursor solution to this problem. Several new methodological results are obtained, and the viability of the technique is successfully demonstrated on a three-parameter example in the setting of the LISA Data Challenge.PACS numbers: 02.50. 04.80.Nn, 95.55.Ym, 95.75.Wx

Extreme mass-ratio inspirals around a spinning horizonless compact object

“…Finally, the upper bounds estimated here are based on the overlap calculation, and therefore neglect possible correlations among the waveform parameters, which is particularly relevant for generic orbits and relatively small signal-to-noise ratio. From the parameter-estimation point of view, it is important to develop modified kludge waveforms to include ECO effects in a practical way or, more ambitiously, to perform accurate data analyses using exact waveforms (either using the Fisher-information matrix or, ideally, a Bayesian inference), extending recent work in the context of standard waveforms [100][101][102]. and therefore lowfrequency resonances are also more narrow.…”

Rapid Generation of Fully Relativistic Extreme-Mass-Ratio-Inspiral Waveform Templates for LISA Data Analysis

“…Calculations from black-hole perturbation theory, and in particular from the ongoing gravitational self-force program [7], are on target to produce EMRI waveforms that meet the accuracy requirements of LISA science [8,9]. Such models are computationally intensive, and hence ill suited for direct use in analysis algorithms that are tailored to the EMRI problem [10][11][12][13][14]. As in the case of numericalrelativity waveforms for comparable-mass binaries, selfforce waveforms must be supplemented and approximated by template models that are (i) efficiency oriented, (ii) extensive in their description of both intrinsic and extrinsic effects, and (iii) end to end from source parameters to detector response.…”

“…Although the mode amplitudes are required only at leading order [9], they must be extended to cover the space of Kerr orbits; our fitting technique is promising for dealing with the increased dimensionality. The source-end waveform also has to be integrated with a realistic LISA response, which could be done through a frequency-domain approximation for both waveform [30] and response [11,14], or by developing accelerated versions of more accurate time-domain simulators [54,55]. Finally, the modular nature of the framework allows the incorporation of additional physics as well.…”

Detecting Subsolar-Mass Primordial Black Holes in Extreme Mass-Ratio Inspirals with LISA and Einstein Telescope

“…parameter space -they would also allow exploiting the whole technology currently under development for standard EMRIs detectable by LISA, in particular first-and second-order self-force calculations [56,83,84] and sophisticated parameter-estimation strategies [75,85,86].…”

“…Likewise, we have focused on circular equatorial orbits, but the estimated errors on the secondary mass for standard EMRIs are similar for generic orbits [74], so we expect a comparable accuracy for EMRIs with µ M . EMRI parameter estimation is a challenging and open problem [61,74,75,86], which requires developing accurate waveform models, performing expensive statistical analysis, and also taking into account that the EMRI events in LISA might overlap with glitches, data gaps [87], and with several louder simultaneous signals from supermassive BH coalescences and other sources [85,86,88]. In comparison, detecting primordial-origin EMRIs with 3G detectors should be less demanding, since the signal can be considerably shorter without compromising detectability and parameter estimation.…”