Theoretical constraints on the properties of low-mass neutron stars from the equation of state of nuclear matter in the inner crust

Abstract

By employing four typical equation of states (EOSs) of the inner crust matters, the constraint on properties of low-mass neutron stars are theoretically investigated. Based on the well known fact that there is a big gap between the neutron stars and white dwarfs in the mass-radius sequence of compact stars, here we explicitly point out the forbidden region for the central density and stellar radius to form a compact stars, that is, there is no compact star in the nature having central density in the region from about $10^{12}~kg/m^3$ to $10^{17}~kg/m^3$, and there is also no compact star having a radius in the region from about 400 km to 2000 km. It is found that for a low-mass neutron star with central densities at subnuclear densities, the stellar mass is mainly determined by the softness of the EOS at the higher density region ($ > 10^{16}~\textrm{kg.m}^{-3}$) while the stellar radius is dependent on the softness of the EOS at lower density region ($ < 10^{16}~\textrm{kg.m}^{-3}$). For a stable neutron star with stellar mass near the minimum mass, the Keplerian period is several hundred millisecond, the moment of inertia is in an order of $10^{37} kg\cdot m^{2}$, and the surface gravitational redshift is in an order of $10^{-4}$.