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 $f(R)=R+\alpha R^2$ 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 $\varphi$ 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 $\sim 1.33M_{\odot }$, 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${}^2$.

13 pp., 6 figures, to appear in Phys. Rev. D

References in corpus (15)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Extreme neutron stars from Extended Theories of Gravity
• Causal Limit of Neutron Star Maximum Mass in $f(R)$ Gravity in View of GW190814
• I-Love-Q, Spontaneously: Slowly Rotating Neutron Stars in Scalar-Tensor Theories
• On the 1/c Expansion of f(R) Gravity
• Tracking quintessence by cosmic shear - Constraints from VIRMOS-Descart and CFHTLS and future prospects
• Scalarization of neutron stars with realistic equations of state
• The Most Massive White Dwarfs in the Solar Neighborhood
• Anisotropic quark stars in $R^2$ gravity
• Stability criterion for white dwarfs in Palatini $f(R)$ gravity
• Universal Inflationary Attractors Implications on Static Neutron Stars
• Neutron Stars in Scalar-tensor Gravity with Quartic Order Scalar Potential
• Compact Star in General $F(R)$ Gravity: Inevitable Degeneracy Problem and Non-Integer Power Correction
• White dwarf stars in modified gravity

Cited by in corpus (13)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Physical validity of anisotropic models derived from isotropic fluid dynamics in $f(R,T)$ theory: An implication of gravitational decoupling
• Decoupled Anisotropic Buchdahl's Relativistic Models in $f(\mathbb{R},\mathbb{T})$ Theory
• Metric-affine effects in crystallization processes of white dwarfs
• Gravitational Lensing in Modified Gravity: A case study for Fast Radio Bursts
• Moment of inertia and compactness of quark stars within the context of $f(R,T,L_m)$ gravity
• Revisiting compact star in $F(R)$ gravity: Roles of chameleon potential and energy conditions
• White dwarfs in regularized 4D Einstein-Gauss-Bonnet gravity
• Constraining fundamental parameters in modified gravity using Gaia-DR2 massive white dwarf observation
• Crystallized white dwarf stars in scalar-tensor gravity
• Refining fundamental constants with white dwarfs: machine learning informed constraints on fine-structure constant and proton-to-electron mass ratio
• Charged anisotropic white dwarfs in $f\left(R,T\right)$ gravity
• Maximum mass limit of strange stars in quadratic curvature-matter coupled gravity