Density dependent speed of sound and its consequences in neutron stars

We introduce a parametrized density-dependent speed of sound and construct an ensemble of equations of state for neutron stars which are found to closely resemble the realistic equations of state calculated using relativistic mean field theory. We show that each of these parameters display an unique feature relevant to the properties of the compact stars. The emergence of special points in the Mass-Radius plot is a significant outcome for neutron stars which is more commonly seen in case of hybrid stars. We have also shown that the curvature term in the speed of sound changes its sign for these hadronic equations of state without the matter reaching the conformal limit or undergoing any phase transition. It is related to the 1st derivative of the energy per nucleon reaching a maximum. We have also examined the detailed behavior of the trace anomaly and polytropic index for RMF models, as well as for a density-dependent parametrized speed of sound. Our analysis demonstrates that the sign of the trace anomaly at high densities is sensitive to the stiffness or softness of the EOS. Different observational constraints from mass-radius and tidal deformability can restrict the range of parameters in the proposed speed of sound model.