Systematic and statistical errors in a Bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors

Abstract

Advanced ground-based gravitational-wave detectors are capable of measuring tidal influences in binary neutron-star systems. In this work, we report on the statistical uncertainties in measuring tidal deformability with a full Bayesian parameter estimation implementation. We show how simultaneous measurements of chirp mass and tidal deformability can be used to constrain the neutron-star equation of state. We also study the effects of waveform modeling bias and individual instances of detector noise on these measurements. We notably find that systematic error between post-Newtonian waveform families can significantly bias the estimation of tidal parameters, thus motivating the continued development of waveform models that are more reliable at high frequencies. DOI: 10.1103/PhysRevD.89.103012 PACS numbers: 95.85.Sz, 26.60.Kp I. BACKGROUND AND MOTIVATIONAdvanced interferometric gravitational-wave (GW) detectors currently under construction are expected to begin operating in the next few years. Advanced LIGO [1] is expected to achieve its design sensitivity c. 2019 [2], at which time the detection rate of binary neutron-star (BNS) events in a single detector is expected to be ∼40 yr −1 , though this value is quite uncertain and ranges from 0.4 − 400 yr −1 [3]. When a compact binary coalescence (CBC) signal is detected [4,5], the corresponding interferometer data stream segment is sent through a parameter estimation pipeline to determine the source parameters of the system. Some of these source parameters include the binary component masses and spins, the sky location, distance, and orientation of the system. Bayesian inference is used to explore the probability distribution of the CBC's source parameters by comparing model waveform templates, whose form depends on these source parameters, to the data stream segment containing the GW. For this work, we use LALINFERENCE_MCMC, which is included in the LALINFERENCE LSC Algorithm Library [6], as our parameter estimation pipeline. It is a Markov Chain Monte Carlo (MCMC) sampler designed to efficiently explore the full waveform parameter space in order to make reliable and meaningful statements about CBC source parameters [7][8][9]. This paper's focus is on measuring the effect of tidal influence on BNS GW signals with advanced detectors. Neutron stars (NSs) in merging CBC systems will be tidally deformed by the gravitational gradient of their companion across their finite diameter. This effect is insignificant at large separations but becomes increasingly significant as the NSs near each other [10]. The internal structure of a NS, which is characterized by its equation of state (EOS), determines how much each star will deform. The amount that a NS deforms will affect the orbital decay rate, which is encoded in the observed gravitational waveform. Therefore, if a gravitational signal from a BNS system is detected, then such a detection could provide insight into the NS EOS [10][11][12][13].In order to make meaningful statements regarding the recoverability of tidal param...

Quasiequilibrium sequences of binary neutron stars undergoing dynamical scalarization

“…[37] and from GR computations shown in this paper (and also a direct integration of the TaylorT4-PN approximant with tidal effects [62]), we find that in general relativity tidal effects produce a difference of only a few GW cycles (i.e., ∼1-3 GW cycles depending on the EOS) between 130 and 1200 Hz with respect to the point-particle case. Those small differences in GW cycles induced by tidal effects at high frequency can be measured by advanced detectors in one single event only if the SNR is roughly 30-35 [63,64]. Note that depending on the EOS those differences can be smaller than or comparable to what we have found in dynamical scalarization (see Table II).…”

Comprehensive comparison of numerical relativity and effective-one-body results to inform improvements in waveform models for binary neutron star systems

“…for large κ T 2 , the EOB models tend to underestimate tidal effects irrespective of the mass ratio. To quantify the impact of these differences on measurements with advanced GW detectors requires parameter estimation studies that are the subject of ongoing work, see also [86][87][88]. Nevertheless, understanding and improving waveform models in the regime close to merger will be essential for future GW detectors.…”

Quasiuniversal Properties of Neutron Star Mergers

“…Furthermore, the simple LSO analysis gives reasonable estimates of merger relations for any EOS, mass ratio and (aligned) spins! Outlook.-Modeling GWs from neutron star mergers is a challenging open problem (see e.g., [32] for very recent work) that can be tackled interfacing accurate nonlinear simulations with the EOB analytical framework. While pursuing this approach we have identified κ T as fundamental "coupling constants" of the binary tidal interactions, together with κ T -universal relations and their physical origin.…”