Nonparametric inference of the neutron star equation of state from gravitational wave observations

We develop a nonparametric 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 ${\mathrm{\ensuremath{\Lambda}}}_{1,2}$, we perform Monte Carlo integration over the GW likelihood for ${M}_{1,2}$ and ${\mathrm{\ensuremath{\Lambda}}}_{1,2}$ to directly infer a posterior process for the NS EOS. We first demonstrate that the method can accurately recover the properties of an injected GW signal, and subsequently use it to analyze data from GW170817, finding a canonical deformability of ${\mathrm{\ensuremath{\Lambda}}}_{1.4}=16{0}_{\ensuremath{-}113}^{+448}$ and $p(2{\ensuremath{\rho}}_{\mathrm{nuc}})=1.3{5}_{\ensuremath{-}1.2}^{+1.8}\ifmmode\times\else\texttimes\fi{}{10}^{34}\text{ }\text{ }\mathrm{dyn}/{\mathrm{cm}}^{2}$ 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 ${\mathrm{\ensuremath{\Lambda}}}_{1.4}=55{6}_{\ensuremath{-}172}^{+163}$ and $p(2{\ensuremath{\rho}}_{\mathrm{nuc}})=4.7{3}_{\ensuremath{-}2.5}^{+1.4}\ifmmode\times\else\texttimes\fi{}{10}^{34}\text{ }\text{ }\mathrm{dyn}/{\mathrm{cm}}^{2}$. We further infer the maximum NS mass supported by the EOS to be ${M}_{\mathrm{max}}=2.0{9}_{\ensuremath{-}0.16}^{+0.37}$ ($2.0{4}_{\ensuremath{-}0.002}^{+0.22}$) ${M}_{\ensuremath{\bigodot}}$ with the loose (tight) prior. The Bayes factor between the two priors is ${B}_{\mathcal{I}}^{\mathcal{A}}\ensuremath{\simeq}1.12$, suggesting that neither is strongly preferred by the data and that constraints on the EOS from GW170817 alone may be sensitive to the choice of prior.