Parameter estimation of gravitational-wave signals with frequency-dependent antenna responses and higher modes

TL;DR

This paper tackles the challenge of Bayesian parameter estimation for gravitational-wave signals observed by next-generation detectors, where Earth-rotation, detector-size, and higher-order modes can induce significant biases at high SNR. It introduces frequency-dependent antenna responses and four likelihood classes (exact, multibanded, relative binning, and mode-by-mode RB) implemented within Bilby, validated against exact likelihoods using GW170817-like signals with HM at SNR ~ $1900$. The authors show substantial speed-ups while preserving accuracy, enabling feasible inference for long, HM-rich signals across detector networks, and demonstrate improved intrinsic/extrinsic parameter recovery and localization, especially when HM and Earth-rotation effects are included. The framework provides a scalable, extensible path toward robust PE for next-generation GW observations, with potential extensions to ROQ-free reduced-order models and more realistic neutron-star waveform families in future work.

Abstract

We implement frequency-dependent antenna responses and develop likelihood classes (standard likelihood, multibanded likelihood, and the relative binning (RB) likelihood) capable of handling the same within the framework of \texttt{Bilby}. We validate the approximate likelihoods by comparing them with the exact likelihood for a GW170817-like signal (signal-to-noise ratio ~ 1900) containing higher-order modes of radiation. We use the relative-binning likelihood to perform parameter estimation (PE) for a GW170817-like signal, including Earth-rotation effects, detector-size effects, and higher-order modes. We study the system in several detector networks consisting of a single 40 km Cosmic Explorer, a 20 km CE and a present-generation detector at A+ sensitivity. The PE runs with RB take around a day to complete on a typical cluster.

Figures (7)

• Figure 1: The histogram of errors in log-likelihood ratio obtained using 500 samples drawn from the relative binning posterior of GW1 and GW2 in a 40 km CE. For multibanding, we use an accuracy_factor of 1 and enabled linear interpolation. For relative binning, we set chi to 10 and epsilon to 0.1. It is worth noting that the histogram can shift left and right on the horizontal scale, which depends on the choice of approximation parameter. We only require that the errors are less than unity for unbiased PE.
• Figure 2: Inferred posteriors of intrinsic parameters of GW1 and GW2 in a 40km CE. The green posteriors use all modes for analysis, the orange posteriors ignore modes with m = 3 and the blue ones ignore m = 3 and m = 4 modes.
• Figure 3: Inferred posteriors of extrinsic parameters of GW1 and GW2 in one 40km CE. The green posteriors use all modes for analysis, the orange posterior ignores modes with m = 3, and the blue ones ignore m = 3 and m = 4 modes.
• Figure 4: Inferred posteriors of GW1 and GW2 in one 40km CE with effects due to Earth's rotation and size of the detector turned off.
• Figure 5: The antenna response for the m=2 mode as a function of frequency for GW1 and GW2 at the three detectors is analyzed. For CE and CE20, the response varies at low frequencies due to Earth's rotation and at high frequencies due to detector-size effects. In the case of A1, the signal enters the band at 20 Hz, resulting in no frequency dependence at low frequencies. Additionally, due to the detector's size, there is no effect at high frequencies. The dotted lines denote the antenna response without Earth's rotation effects.