Maximal masses of white dwarfs for polytropes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>R</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math> 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 $f(R)=R+\ensuremath{\alpha}{R}^{2}$ gravity, and calculate the parameters of the stellar configurations with polytropic equation of state of the form $p=K{\ensuremath{\rho}}^{1+1/n}$ for various values of the parameter $n$. In order to simplify our analysis we use the equivalent Einstein frame form of ${R}^{2}$-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 $\ensuremath{\phi}$ leaving only the potential term for it. Our analysis indicates that for the nonrelativistic case with $n=3/2$, discrepancies between the ${R}^{2}$-gravity and general relativity can appear only when the parameter $\ensuremath{\alpha}$ of the ${R}^{2}$ term, takes values close to maximal limit derived from the binary pulsar data namely ${\ensuremath{\alpha}}_{\mathrm{max}}=5\ifmmode\times\else\texttimes\fi{}{10}^{15}\text{ }\text{ }{\mathrm{cm}}^{2}$. Thus, the study of low-mass white dwarfs can hardly give restrictions on the parameter $\ensuremath{\alpha}$. For relativistic polytropes with $n=3$ we found that Chandrasekhar limit can in principle change for smaller $\ensuremath{\alpha}$ values. The main conclusion from our calculations is the existence of white dwarfs with large masses $\ensuremath{\sim}1.33{M}_{\ensuremath{\bigodot}}$, which can impose stricter limits on the parameter $\ensuremath{\alpha}$ for the ${R}^{2}$ gravity model. Specifically, our estimations on the parameter $\ensuremath{\alpha}$ of the ${R}^{2}$ model is $\ensuremath{\alpha}\ensuremath{\sim}{10}^{13}\text{ }\text{ }{\mathrm{cm}}^{2}$.

Topics & Concepts