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

TL;DR

This paper investigates how $R^2$ gravity affects the maximum mass of white dwarfs, finding potential deviations from general relativity that could constrain the gravity model's parameters.

Contribution

It provides the first detailed analysis of white dwarf masses in $f(R)=R+ ext{const} imes R^2$ gravity using the Einstein frame scalar-tensor formulation.

Findings

Discrepancies with GR appear only near the maximal $ ext{alpha}$ limit from pulsar data.

Relativistic white dwarfs can have masses up to ~1.33 solar masses in $R^2$ gravity.

Estimated $ ext{alpha}$ parameter constrained to about $10^{13}$ cm$^2$.

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 $f(R)=R+\alpha R^2$ 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 $R^2$-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 $\phi$ 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 $\alpha$ of the $R^2$ term, takes values close to maximal limit derived from the binary pulsar data namely $\alpha_{max}=5\times 10^{15}$ cm$^2$. 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 $\sim 1.33 M_{\odot}$, which can impose more strict limits on the parameter $\alpha$ for the $R^2$ gravity model. Specifically, our estimations on the parameter $\alpha$ of the $R^2$ model is $\alpha \sim 10^{13}$ cm$^2$.