A hypothetical time-variation of the gravitational constant $G$ would make neutron stars expand or contract, so the matter in their interiors would depart from beta equilibrium. This induces non-equilibrium weak reactions, which release energy that is invested partly in neutrino emission and partly in internal heating. 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. Using the surface temperature of the nearest millisecond pulsar (PSR J0437$-$4715) inferred from ultraviolet observations and results from theoretical modelling of the thermal evolution, we estimate two upper limits for this variation: (1) $|\dot G/G| < 2 \times 10^{ -10}\mathrm{ yr}^{ -1},$ if the fast, "direct Urca" reactions are allowed, and (2) $|\dot G/G|<4\times 10^{ -12}\mathrm{ yr}^{ -1},$ considering only the slower, "modified Urca" reactions. The latter is among the most restrictive upper limits obtained by other methods.
Categories: astro-ph.HE