Parameter estimation with gravitational waves

Abstract

The new era of gravitational wave astronomy truly began on September 14, 2015 with the detection of GW150914, the sensational first direct observation of gravitational waves from the inspiral and merger of two black holes by the two Advanced LIGO detectors. In the subsequent first three observing runs of the LIGO/Virgo network, gravitational waves from ∼ 50 compact binary mergers have been announced, with more results to come. The events have mostly been produced by binary black holes, but two binary neutron star mergers have so far been observed, as well as the mergers of two neutron star -black hole systems. Furthermore, gravitational waves emitted by core-collapse supernovae, pulsars and the stochastic gravitational wave background are within the LIGO/Virgo/KAGRA sensitivity band and are likely to be observed in future observation runs. Beyond signal detection, a major challenge has been the development of statistical and computational methodology for estimating the physical waveform parameters and quantifying their uncertainties in order to accurately characterise the emitting system. These methods depend on the sources of the gravitational waves and the gravitational waveform model that is used. This article reviews the main waveform models and parameter estimation methods used to extract physical parameters from gravitational wave signals detected to date by LIGO and Virgo and from those expected to be observed in the future, which will include KAGRA, and how these methods interface with various aspects of LIGO/Virgo/KAGRA science. Also presented are the statistical methods used by LIGO and Virgo to estimate detector noise, test general relativity, and draw conclusions about the rates of compact binary mergers in the universe. Furthermore, a summary of major publicly available gravitational wave parameter estimation software packages is given. BinaryBlack Hole Population Results from GWTC-2 42 B. Binary Neutron Stars 43 C. Neutron Star -Black Hole Binaries 43 IX. Other Signal Searches for LIGO and Virgo 44 A. Stochastic Gravitational Wave Background 44 B. Continuous Wave Signals 47 C.

Formulation of an extended null channel formalism for a triangular gravitational wave interferometer configuration in the case of non-identical and correlated noise

“…A first method is to simultaneously model noise and signals using for instance a joint Bayesian parameter estimation framework [20,21]. This paper is investigating a different approach relying on the sky location independent null channel which can be constructed for triangular configurations of interferometers ET and LISA.…”

“…After the proof of concept of the A, E and T channels for the ET in earlier sections, one should develop a Bayesian framework to enable parameter estimation of the noise PSDs as well as correlated noise PSDs, that is S I n and S IJ n or in the more general scenario S X n , S Y n , S Z n , S XY n , S XZ n and S Y Z n [20,21]. Here one should consider multiple scenarios such as identical noise sources, unique noise sources for each X, Y and Z interferometer, absence/presence of correlated noise.…”

“…A first method to tackle the challenge of noise PSD estimation is to use joint Bayesian parameter estimation to model the noise PSD and signals simultaneously [20,21]. However this method does not address the problem of correlated noise and more work is needed, to demonstrate how this method should work in the presence of many signals, as well as non-identical and correlated noise.…”

Accelerating gravitational-wave parameterized tests of General Relativity using a multiband decomposition of likelihood

“…where d i denotes the data taken from the i-th detector, θ the set of model parameters consisting of one of the non-GR parameters and GR parameters, π(θ) the prior distribution function determined from our belief or prior knowledge on θ, and L(d|θ) the likelihood function. For the likelihood, the Gaussian-noise likelihood function is typically used [44,45],…”

Parameter Estimation of Gravitational Waves with a Quantum Metropolis Algorithm

“…Historically, the computational advances have been very large. Over the last 20 years, different types of algorithms have been proposed (see Refs [2,3]), but those based on the formalism of Bayesian inference have stood out from the rest, making Bayesian parameter estimation the language of gravitational-wave astronomy. Among these algorithms the most important are the Metropolis-Hastings algorithms based on Monte Carlo Markov chains [4].…”