Models of binary neutron star remnants with tabulated equations of state

The emergence of novel differential rotation laws that can reproduce the rotational profile of binary neutron star merger remnants has opened the way for the construction of equilibrium models with properties that resemble those of remnants in numerical simulations. We construct models of merger remnants, using a recently introduced 4-parameter differential rotation law and three tabulated, zero-temperature equations of state. The models have angular momenta that are determined by empirical relations, constructed through numerical simulations. After a systematic exploration of the parameter space of merger remnant equilibrium sequences, which includes the determination of turning points along constant angular momentum sequences, we find that a particular rotation law can reproduce the threshold mass to prompt collapse to a black hole with a relative difference of only $\sim 1\%$ with respect to numerical simulations, in all cases considered. Furthermore, our results indicate a possible correlation between the compactness of equilibrium models of remnants at the threshold mass and the compactness of maximum-mass nonrotating models. Another key prediction of binary neutron star merger simulations is a relatively slowly rotating inner region, where the angular velocity $\Omega$ (as measured by an observer at infinity) is mostly due to the frame dragging angular velocity $\omega$. In our investigation of the parameter space of the adopted differential rotation law, we naturally find quasi-spherical (Type A) remnant models with this property. Our investigation clarifies the impact of the differential rotation law and of the equation of state on key properties of binary neutron star remnants and lays the groundwork for including thermal effects in future studies.