Constraint on Phase Transition with the Multi-messenger Data of Neutron Stars.

The equation of state (EoS) of the neutron star (NS) matter remains an enigma. In this work we perform the Bayesian parameter inference with the gravitational wave data (GW170817) and mass-radius observations of some NSs (PSR J0030+0451, PSR J0437-4715, and 4U 1702-429) using the phenomenologically constructed EoS models to search potential first-order phase transition. Our phenomenological EoS models take the advantages of current widely used parameterizing methods, which are flexible to resemble various theoretical EoS models. We find that current observation data are still not informative enough to support/rule out phase transition, due to the comparable evidences for models with and without phase transition. But the bulk properties of canonical $1.4M_\odot$ NS and the pressure at around $2\rho_{\rm sat}$ are well constrained by the data, where $\rho_{\rm sat}$ is the nuclear saturation density. Moreover, strong phase transition at low densities is disfavored, and the $1\sigma$ lower bound of transition density is constrained to $1.84\rho_{\rm sat}$.