Maximal masses of white dwarfs for polytropes in R2 gravity and theoretical constraints

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 + alpha R2 gravity, and calculate the parameters of the stellar configurations with polytropic equation of state of the form p = K rho 1+1/n for various values of the parameter n. In order to simplify our analysis we use the equivalent Einstein frame form of R2-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 phi leaving only the potential term for it. Our analysis indicates that for the nonrelativistic case with n = 3/2, discrepancies between the R2-gravity and general relativity can appear only when the parameter alpha of the R2 term, takes values close to maximal limit derived from the binary pulsar data namely alpha max = 5 x 1015 cm2. Thus, the study of low-mass white dwarfs can hardly give restrictions on the parameter alpha. For relativistic polytropes with n = 3 we found that Chandrasekhar limit can in principle change for smaller alpha values. The main conclusion from our calculations is the existence of white dwarfs with large masses ''1.33M circle dot, which can impose stricter limits on the parameter alpha for the R2 gravity model. Specifically, our estimations on the parameter alpha of the R2 model is alpha '' 1013 cm2.