Note on neutron star equation of state in the light of GW170817

From the very first multimessenger event of GW170817, clean robust constraints can be obtained for the tidal deformabilities of the two stars involved in the merger, which provides us unique opportunity to study the equation of states (EOSs) of dense stellar matter. In this contribution, we employ a model from the quark level, describing consistently a nucleon and many-body nucleonic system from a quark potential. We check that our sets of EOSs are consistent with available experimental and observational constraints at both sub-nuclear saturation densities and higher densities. The agreements with ab-initio calculations are also good. Especially, we tune the density dependence of the symmetry energy (characterized by its slope at nuclear saturation $L$) and study its influence on the tidal deformability. The so-called $QMF18$ EOS is named after the case of $L=40~\rm MeV$, and it gives $M_{\rm TOV} =2.08~M_\odot$ and $R= 11.77~\rm km$, $\Lambda=331$ for a $1.4\,M_\odot$ star. The tidal signals are demonstrated to be insensitive to the uncertain crust-core matching, despite the good correlation between the symmetry energy slope and the radius of the star.