The neutron star inner crust: an empirical essay

Abstract: In this work we study how the small contribution of the inner crust to the total equation of state (EoS) of a neutron star affects its mass-radius relation, focusing on the canonical mass of 1.4$M_\odot$. We build empirical EoS of the kind - $p = K\epsilon^{\gamma} + b$ - in the range of 0.003 fm$^{-3}~<~n~<~$0.08 fm$^{-3}$ and also calculate the speed of sound in this region. We see that different behaviours of the speed of sound can affect the radius of the canonical star by more than 1.1 km. This result can help us understand extreme results as GW170817, where some studies indicate that the radius of the canonical star cannot exceed 11.9 km.