Constraining a Possible Time Variation of the Gravitational Constant through “Gravitochemical Heating” of Neutron Stars

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 induces nonequilibrium beta processes, 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, we estimate two upper limits for this variation: (1) $|\dot{G}/G|<2\times {10}^{-10}{\mathrm{yr}}^{-1}$, if direct Urca reactions are allowed, and (2) $|\dot{G}/G|<4\times {10}^{-12}{\mathrm{yr}}^{-1}$, considering only modified Urca reactions. The latter is among the most restrictive obtained by other methods.

Figure 1

Comparison of the gravitochemical heating predictions to observations of PSR J0437-4715. The solid lines are the predicted stationary surface temperatures as functions of stellar radius, for different equations of state (A18 from 19 and BPAL from 25 ), constrained to the observationally allowed mass range for this pulsar [20]. Dashed lines correspond to the 68% and 90% confidence contours of the blackbody fit of Kargaltsev et al. [13] for the ultraviolet emission from this object. The value of $|\dot{G}/G|=2\times {10}^{-10}{\mathrm{yr}}^{-1}$ is chosen so that all stationary temperature curves lie above the observational constraints. (BPAL32 and BPAL33 allow direct Urca reactions in the observed mass range of J0437.)

Figure 2

Same as Fig. 1, but now the value of $|\dot{G}/G|=4\times {10}^{-12}{\mathrm{yr}}^{-1}$ is chosen so that only the stationary temperature curves with modified Urca reactions are above the observational constraints.