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

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 Bilby . We validate the approximate likelihoods by comparing them with the exact likelihood for a GW170817-like signal (luminosity distance scaled such that signal-to-noise ratio ∼1000) containing higher-order modes of radiation. We use the RB likelihood to perform parameter estimation (PE) for a GW170817-like signal, including Earth-rotation effects, detector-size effects, and higher-order modes. To the best of our knowledge, we are the first to perform proof-of-concept Bayesian PE, including all the above-mentioned effects. 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. We find that higher-order modes significantly improve sky localization in scenarios where only a single next-generation detector is operating. This advantage diminishes when a second detector is added to the network; however, in such cases, we observe improved recovery of the polarization angle. While ignoring higher-order modes leads to a reduction in precision, it does not introduce bias in parameter recovery. In contrast, neglecting the effects of Earth’s rotation and the finite size of long-arm detectors can result in biased parameter estimates.