Constraining a possible time-variation of the gravitational constant through "gravitochemical heating" of neutron stars

Abstract

A hypothetical time-variation of the gravitational constant $G$ would cause neutron star matter to depart from beta equilibrium, due to the changing hydrostatic equilibrium. This forces non-equilibrium beta processes to occur, which release energy that is invested partly in neutrino emission and partly in heating the stellar interior. Eventually, the star arrives at a stationary state in which the temperature remains nearly constant, as the forcing through the change of $G$ is balanced by the ongoing reactions. Comparing the surface temperature of the nearest millisecond pulsar, PSR J0437-4715, inferred from ultraviolet observations, with our predicted stationary temperature, we estimate two upper limits for this variation: (1) $|\dot{G}/G|<2\times 10^{-10}$ yr${}^{-1}$, if we allow direct Urca reactions operating in the neutron star core, and (2) $|\dot{G}/G|<4\times 10^{-12}$ yr${}^{-1}$, considering only modified Urca reactions. Both results are competitive with those obtained by other methods, with (2) being among the most restrictive.

4 pages, including 2 figures. Accepted for publication in Phys. Rev. Lett. Revised version includes minor changes in the wording, and more substantial changes in the last 2 paragraphs (Discussion and Conclusions). Equations, figures, and results are unchanged

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