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Abstract Gravitational-wave observations of binary neutron-star (BNS) mergers have the potential to revolutionize our understanding of the nuclear equation of state (EOS) and the fundamental interactions that determine its properties. However, Bayesian parameter estimation frameworks do not typically sample over microscopic nuclear-physics parameters that determine the EOS. One of the major hurdles in doing so is the computational cost involved in solving the neutron-star structure equations, known as the Tolman–Oppenheimer–Volkoff (TOV) equations. In this paper, we explore approaches to emulating solutions for the TOV equations: multilayer perceptrons (MLPs), Gaussian processes, and a data-driven variant of the reduced basis method (RBM). We implement these emulators for three different parameterizations of the nuclear EOS, each with a different degree of complexity represented by the number of model parameters. We find that our MLP-based emulators are generally more accurate than the other two algorithms, whereas the RBM results in the largest speedup with respect to the full high-fidelity TOV solver. We employ these emulators for a simple parameter inference using a potentially loud BNS observation and show that the posteriors predicted by our emulators are in excellent agreement with those obtained from the full TOV solver. 

Abstract A major aim of gravitational wave astronomy is to test observationally the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black hole spectroscopy. For the gravitational wave merger event GW190521, we have previously claimed the detection of two ringdown modes emitted by the remnant black hole. In this paper we provide further evidence for the detection of multiple ringdown modes from this event. We analyse the recovery of simulated gravitational wave signals designed to replicate the ringdown properties of GW190521. We quantify how often our detection statistic reports strong evidence for a sub-dominant $(\ell ,m,n)=(3,3,0)$ringdown mode, even when no such mode is present in the simulated signal. We find this only occurs with a probability ∼0.02, which is consistent with a Bayes factor of $56\pm 1$(1σuncertainty) found for GW190521. We also quantify our agnostic analysis of GW190521, in which no relationship is assumed between ringdown modes, and find that only 1 in 250 simulated signals without a $(3,3,0)$mode yields a result as significant as GW190521. Conversely, we verify that when simulated signals do have an observable $(3,3,0)$mode they consistently yield a strong evidence and significant agnostic results. We also find that constraints on deviations from the $(3,3,0)$mode on GW190521-like signals with a $(3,3,0)$mode are consistent with what was obtained from our previous analysis of GW190521. Our results support our previous conclusion that the gravitational wave signal from GW190521 contains an observable sub-dominant $(\ell ,m,n)=(3,3,0)$mode.