2023ApJ...943..163Z

Observations of optical and near-infrared counterparts of binary neutron star mergers not only enrich our knowledge about the abundance of heavy elements in the universe and help reveal the remnant object just after the merger, which is generally known, but can also effectively constrain the dense properties of the nuclear matter and the equation of state (EOS) in the interior of the merging stars. Following the relativistic mean-field description of nuclear matter, we perform a Bayesian inference of the EOS and the properties of the nuclear matter using the first multi-messenger event GW170817/AT2017gfo, together with the NICER mass-radius measurements of pulsars. The kilonova is described by a radiation-transfer model with the dynamical ejecta, and light curves connect with the EOS through the quasi-universal relations between the properties of the ejecta (the ejected mass, velocity, opacity, or electron fraction) and binary parameters (the mass ratio and reduced tidal deformability). It is found that the posterior distributions of the reduced tidal deformability from the AT2017gfo analysis display a bimodal structure, with the first peak enhanced by the GW170817 data, leading to slightly softened posterior EOSs, while the second peak cannot be achieved by a nuclear EOS with saturation properties in their empirical ranges. The inclusion of NICER data results in a stiffened EOS posterior because of the massive pulsar PSR J0740+6620. We provide the results at nuclear saturation density for the nuclear incompressibility, the symmetry energy, and its slope, as well as the nucleon effective mass, from our analysis of the observational data.