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White dwarf structure in $f(R,T,L_m)$ gravity: beyond the Chandrasekhar mass limit

Edson Otoniel, Juan M. Z. Pretel, Clésio E. Mota, César O. V. Flores, Victor B. T. Alves, Franciele M. da Silva

Abstract

In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory $f(R, T, L_m) = R + αT L_m$, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: $L_m = p$ and $L_m = -ρ$. We show that the extra $αTL_m$ term significantly alters the mass-radius relation of WDs, especially at high central densities $( ρ_c \gtrsim 10^8 - 10^9\,\rm g/cm^3)$, allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter $α$, the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that $f(R,T,L_m)$ gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter $α$ for the two choices of the Lagrangian density $L_m$.

White dwarf structure in $f(R,T,L_m)$ gravity: beyond the Chandrasekhar mass limit

Abstract

In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory , which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: and . We show that the extra term significantly alters the mass-radius relation of WDs, especially at high central densities , allowing for stable super-Chandrasekhar configurations. In particular, depending on the sign and magnitude of the parameter , the maximum mass can increase or decrease, and in some regimes, the usual critical point indicating the transition from stability to instability disappears. Our findings suggest that gravity provides a viable framework to explain the existence of massive WDs beyond the classical Chandrasekhar limit. Using Bayesian inference with WD observational data, we further constrain the coupling parameter for the two choices of the Lagrangian density .

Paper Structure

This paper contains 8 sections, 17 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. White Dwarf Matter Composition
  3. Inverse $\beta$-decay Reaction in White Dwarfs
  4. Modified TOV equations
  5. Mass-radius diagrams
  6. Theoretical predictions
  7. Bayesian constraints on $\alpha$ from WD mass-radius observations
  8. Conclusions and future perspectives

Figures (5)

  • Figure 1: $M-r_{\rm sur}$ diagram (left) and $M-\rho_c$ relation (right) for WDs in $f(R, T, L_m)= R+ \alpha TL_m$ for several values of $\alpha$. The top panel is the result of solving the modified TOV equations \ref{['TOVEq1p']} and \ref{['TOVEq2p']}, where the coupling constant $\alpha$ has been varied in the range $\alpha \in [-1.7, 1.7]\, u_1$ with $u_1 = 10^{-73}\, \rm s^4/kg^2$. The bottom panel corresponds to the choice $L_m= -\rho$ where $\alpha \in [-6.0,6.0]\, u_2$ with $u_2$ being given by $u_2= 10^{-77}\, \rm s^4/kg^2$. We have included the observational mass–radius data from some well-studied and precisely constrained WDs: Sirius B, Procyon B, 40 Eridani B and ZTF J190132.9$+$145808.7 (see Table \ref{['tabConstraints']}).
  • Figure 2: Compactness versus central density relation for the WD configurations shown in Fig. \ref{['FigMRCden']}. One observes that the two choices of Lagrangian density lead to remarkably different compactnesses.
  • Figure 3: Trace plot of the MCMC samples for the coupling parameter $\alpha$ using both choices; $L_m=p$ (top panel) and $L_m=-\rho$ (bottom panel).
  • Figure 4: Histograms showing the posterior distributions of the parameter $\alpha$ for the $L_m=p$ model on the top and the $L_m=-\rho$ model on the bottom. The dashed vertical lines represent the 0.16, 0.5, and 0.84 quantiles.
  • Figure 5: WD mass-radius relations in $f(R,T,L_m)=R+\alpha T L_m$ gravity for the values of $\alpha$ favored by the Bayesian analysis of the observational data.