A new white dwarf constraint on the rate of change of the gravitational constant

Abstract

In this paper we derive a bound on the rate of change of the gravitational constant G coming from the pulsating white dwarf G117-B15A. This star is a ZZ Ceti pulsator extensively studied with astroseismological techniques for last three decades. The most recent determination of {\dot P} = (2.3 \pm 1.4) * 10^{-15} s/s^{-1} for the 215.2s fundamental mode agrees very well with predictions of the best fit theoretical model. The rate of change of the oscillation period can be explained by two effects: the cooling (dominant factor) and change of gravitational binding energy (residual gravitational contraction). Since the white dwarfs are pulsating in g-modes whose frequencies are related to the Brunt-Vaisala frequency (explicitly dependent on G) observational determination of the change of the period (more precisely the difference between observed and calculated \dot P) can be used to set the upper bound on the rate of change of G. In the light of the current data concerning G117-B15A we derive the following bound: |{\frac {\dot G}{G}}| \leq 4.10 \times 10^{-10} yr^{-1}. Our result is model independent in the sense that it does not need to invoke a concrete physical theory (such like Brans-Dicke theory)underlying the temporal variability of G. We also demonstrate that varying gravitational constant G does not modify cooling of white dwarfs in a significant way. This result implies that some earlier claims present in the literature that varying G can be reflected in the WD luminosity function are not correct.