Mass-to-radius profiles of Newtonian polytropic spheres: Low-mass main-sequence stars in Palatini gravity versus dark-matter-admixed low-mass stars in general relativity

Abstract

We investigate properties of Newtonian (nonrelativistic) polytropic stars in two different scenarios: on the one hand in the Starobinsky model in Palatini formalism, and on the other hand in general relativity assuming that the star contains both ordinary and dark matter. We obtain numerical solutions to the structure equations, and we show the mass-to-radius profiles of both scenarios in the same figure for comparison. Our findings show that (a) contrary to the Palatini gravity, where the mass may be an increasing or decreasing function of the radius depending on the polytropic index, in admixed dark matter stars the mass is always a decreasing function of the radius, and (b) if the $\ensuremath{\alpha}$ parameter of the Starobinsky model is positive the two scenarios give distinct predictions, while if the $\ensuremath{\alpha}$ parameter is negative, the two scenarios exhibit similar behavior in the $n=2$ case.