Direct Inference of Nuclear Equation-of-State Parameters from Gravitational-Wave Observations

Abstract

The observation of neutron star mergers with gravitational waves (GWs) has provided a new method to constrain the dense-matter equation of state (EOS) and to better understand its nuclear physics. However, inferring nuclear microphysics from GW observations necessitates the sampling of EOS model parameters that serve as input for each EOS used during the GW data analysis. The sampling of the EOS parameters requires solving the Tolman-Oppenheimer-Volkoff (TOV) equations a large number of times -- a process that slows down each likelihood evaluation in the analysis on the order of a few seconds. Here, we employ emulators for the TOV equations built using multilayer perceptron neural networks to enable direct inference of nuclear EOS parameters from GW strain data. Our emulators allow us to rapidly solve the TOV equations, taking in EOS parameters and outputting the associated tidal deformability of a neutron star in only a few tens of milliseconds. We implement these emulators in \texttt{PyCBC} to directly infer the EOS parameters using the event GW170817, providing posteriors on these parameters informed solely by GWs. We benchmark these runs against analyses performed using the full TOV solver and find that the emulators achieve speed ups of nearly \emph{two orders of magnitude}, with negligible differences in the recovered posteriors. Additionally, we constrain the slope and curvature of the symmetry energy at the 90\% upper credible interval to be $L_{\rm sym}\lesssim106$ MeV and $K_{\rm sym}\lesssim26$ MeV.

Figures (6)

• Figure 1: Comparison of convergence for different numbers of live sampling points between the 5-parameter emulator (circle) and the full TOV solver (star). For each setting, the error bars correspond to the 68% credible interval. Left: Combined tidal deformability $\tilde{\Lambda}$ vs. number of live points. Right: Mass ratio $q$ vs. number of live points. In both cases, we see that the sampling converges for 8000 live points.
• Figure 2: Corner plot of the EOS parameters for the 5-parameter model. We state the central values with their 90% credible levels. The values of the $c_s^2$ are in units of the speed of light squared ($c^2$), while the other EOS parameters are given in units of MeV. We also show the 1D histograms of the prior distribution (red) and posterior from the emulators (black).
• Figure 3: Same as \ref{['fig:NEP_corner']} but for the 10-parameter model and showing the two lowest-density sound speeds.
• Figure 4: Continuation of \ref{['fig:10par_1']}, showing the remaining sound-speed parameters of the model.
• Figure 5: Corner plot of various NS observables using the posteriors for the 5-parameter EOS model. We state the central values with 90% credible intervals and show the 1D marginalized histograms for the prior (red) and the posterior (black). The maximum NS mass $M_{\rm TOV}$ is given in units of $M_{\odot}$ and R$_{1.4}$ in units of km.