Maximal Masses of White Dwarfs for Polytropes in $R^2$ Gravity and Theoretical Constraints

Abstract

We examine the Chandrasekhar limit for white dwarfs in f (R) gravity, with a simple polytropic equation of state describing stellar matter. We use the most popular f (R) gravity model, namely the f (R) = R + αR 2 gravity, and calculate the parameters of the stellar configurations with polytropic equation of state of the form p = Kρ 1+1/n for various values of the parameter n. In order to simplify our analysis we use the equivalent Einstein frame form of R 2 -gravity which is basically a scalar-tensor theory with well-known potential for the scalar field. In this description one can use simple approximations for the scalar field φ leaving only the potential term for it. Our analysis indicates that for the non-relativistic case with n = 3/2, discrepancies between the R 2 -gravity and General Relativity can appear only when the parameter α of the R 2 term, takes values close to maximal limit derived from the binary pulsar data namely αmax = 5 × 10 15 cm 2 . Thus, the study of low-mass white dwarfs can hardly give restrictions on the parameter α. For relativistic polytropes with n = 3 we found that Chandrasekhar limit can in principle change for smaller α values. The main conclusion from our calculations is the existence of white dwarfs with large masses ∼ 1.33M , which can impose more strict limits on the parameter α for the R 2 gravity model. Specifically, our estimations on the parameter α of the R 2 model is α ∼ 10 13 cm 2 .

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