Neutron and quark stars: constraining the parameters for simple EoS using the GW170817

Abstract: It is well known that the equation of state (EoS) of compact objects like neutron and quark stars is not determined despite there are several sophisticated models to describe it. From the electromagnetic observations, summarized in \cite{Lattimer01}, and the recent observation of gravitational waves from binary neutron star inspiral GW170817 \cite{Abbott2017_etal} and GW190425 \cite{Abbott2019}, it is possible to make an estimation of the range of masses and so constraint the mass of the neutron and quark stars, determining not only the best approximation for the EoS, but which kind of stars we would be observing. In this paper we explore several configurations of neutron stars assuming a simple polytropic equation of state, using a single layer model without crust. In particular, when the EoS depends on the mass rest density, $p=K \rho_{0}^{\Gamma}$, and when it depends on the energy density $p=K \rho^{\Gamma}$, considerable differences in the mass-radius relationships are found. On the other hand, we also explore quark stars models using the MIT bag EoS for different values of the vacuum energy density $B$.