Abstract
We analyze here whether polytropic equations of state can be a good approximation for neutron stars. Dividing the matter in the star interior in different regions that can be well-reproduced by different polytropics and imposing the continuity of the pressure among the regions, we obtain the corresponding neutron star mass–radius diagram. A comparison with the results obtained with the polytropic approximation and the exact relativistic mean-field equation of state (EoS) is shown for two compositions of the hadronic matter. We conclude that with more than one polytropic EoS, it is possible to obtain a good fit to neutron stars only if the pressure is written as a power-law in the energy density (or mass density) and not in the baryonic density (the usual polytropic). We also found a correlation between the sound velocity at the star center and its mass. The sound velocity at the interface between the polytropic regions shows a small discontinuity that is greater for the hadronic matter including hyperons.
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