Non-parametric inference of the neutron star equation of state from gravitational wave observations

Abstract

We develop a non-parametric method for inferring the universal neutron star (NS) equation of state (EOS) from gravitational wave (GW) observations. Many different possible realizations of the EOS are generated with a Gaussian process conditioned on a set of nuclear-theoretic models. These synthetic EOSs are causal and thermodynamically stable by construction, span a broad region of the pressure-density plane, and can be selected to satisfy astrophysical constraints on the NS mass. Associating every synthetic EOS with a pair of component masses $M_{1,2}$ and calculating the corresponding tidal deformabilities $\hat{I}{›}_{1,2}$, we perform Monte Carlo integration over the GW likelihood for $M_{1,2}$ and $\hat{I}{›}_{1,2}$ to directly infer a posterior process for the NS EOS. We first demonstrate that the method can accurately recover an injected GW signal, and subsequently use it to analyze data from GW170817, finding a canonical deformability of $\hat{I}{›}_{1.4}=160_{-113}^{+448}$ and $p(2\ddot{I}{}_{\mathrm{nuc}})=1.35_{-1.2}^{+1.8}\times 10^{34}\mathrm{dyn}/{\mathrm{cm}}^2$ for the pressure at twice the nuclear saturation density at 90$\%$ confidence, in agreement with previous studies, when assuming a loose EOS prior. With a prior more tightly constrained to resemble the theoretical EOS models, we recover $\hat{I}{›}_{1.4}=556_{-172}^{+163}$ and $p(2\ddot{I}{}_{\mathrm{nuc}})=4.73_{-2.5}^{+1.4}\times 10^{34}\mathrm{dyn}/{\mathrm{cm}}^2$. We further infer the maximum NS mass supported by the EOS to be $M_{\max }=2.09_{-0.16}^{+0.37}$ ($2.04_{-0.002}^{+0.22}$) $M_{\odot }$ with the loose (tight) prior. The Bayes factor between the two priors is $B_{\mathcal{I}}^{\mathcal{A}}\simeq 1.12$, implying that neither is strongly preferred by the data and suggesting that constraints on the EOS from GW170817 alone may be relatively prior-dominated.

27 pages, 12 figures; references added