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

In this paper we derive a bound on the rate of change of the gravitational constant G based on observations of the pulsating white dwarf G117-B15A. This star is a ZZ Ceti pulsator which has been extensively studied with astroseismological techniques for the last three decades. The most recent determination of (P)over dot =(2.3+/-1.4) x 10(-15) s s(-1) for the 215.2-s fundamental mode agrees very well with predictions of the best-fitting 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, the frequencies of which are related to the Brunt-Vaisala frequency (explicitly dependent on G), observational determination of the change of the period (more precisely the difference between the observed and calculated (P)over dot) can be used to set an upper bound on the rate of change of G. In light of the current data concerning G117-B15A we derive the following bound: \(G)over dot/G\ less than or equal to4.10x10(-10) yr(-1). We also demonstrate that a varying gravitational constant G does not modify the cooling of white dwarfs in a significant way, at least at the luminosities where white dwarfs are pulsationally unstable.