White dwarfs in minimal dilatonic gravity

Abstract

We study static, spherically symmetric white dwarfs in minimal dilatonic gravity (MDG) -- a Brans-Dicke theory with fixed coupling ${\alpha }^2=1/3$ and free Compton length ${\lambda }_{\Phi }$. Solving the full relativistic structure equations we find that MDG white dwarfs are strictly sub-Chandrasekhar for every ${\lambda }_{\Phi }$: the maximum mass falls from $1.425M_{\odot }$ in GR to $1.27M_{\odot }$ at $200$ km and $1.09M_{\odot }$ at $500$ km. The ratio by which MDG reduces the maximum mass is robust against the equation of state. Including rigid rotation near mass shedding, consistency with the most massive observed white dwarfs restricts ${\lambda }_{\Phi }\lesssim 300$ km. An independent gravitational-redshift bound gives ${\lambda }_{\Phi }\lesssim 720$ km. Because the dilaton mass is density-independent the same coupling produces a percent-level altitude dependence of the Kepler-inferred $G{M}_{\oplus }$, constraining it from the Solar-System side. To tackle the problem, we introduce a free-boundary collocation method with a linearized-exterior Robin condition that eliminates the exponential stiffness of shooting methods and gives access to the screened regime in double precision.

14 pages, 6 figures, 5 tables