Bayesian constraints on quadratic $f(Q)$ gravity from the ADM mass of white dwarfs

Abstract

We calculate static equilibrium sequences for white dwarfs (WDs) in quadratic symmetric teleparallel gravity, f(Q)=Q+alpha Q^2, and perform a Bayesian comparison between the negative-coupling sector, general relativity (GR), and the positive-coupling sector using mass-radius measurements. Regular interior solutions are obtained by imposing the affine field equation and selecting the analytic branch C=r exp(B/2), and are matched to asymptotically flat exterior spacetimes to determine the ADM mass. The matter sector is described by a cold carbon-12 equation of state including relativistic electron degeneracy, nuclear rest energy, and Coulomb lattice corrections. Central density is marginalized at fixed alpha with a log-uniform prior. The sequences span 10^14 <= |alpha|/cm^2 <= 10^21. Positive couplings shift the compact branch toward larger radii and lower masses, whereas negative couplings produce high-mass extensions, including an admissible equilibrium configuration with M_ADM=14.34 solar masses. Using Sirius B, QS Vir, V471 Tau B, ZTF J1901+1458, and LHS 4033, we obtain conditional posterior medians alpha_-= -1.12x10^16 cm^2 and alpha_+=1.85x10^17 cm^2. With equal prior weights, the posterior probabilities for the negative, GR, and positive sectors are 0.228, 0.378, and 0.395, respectively, with ln(B_+/GR)=0.043. Current data therefore provide conditional constraints on the coupling but no direct evidence for modified gravity, emphasizing that the ADM mass prescription and admissible stellar domain must be consistently defined when using WD observations to constrain the theory.