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 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 Ṗ = (2.3 ± 1.4) × 10 ss for the 215.2 s 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-Väisälä frequency (explicitly dependent on G) observational determination of the change of the period (more precisely the difference between observed and calculated Ṗ ) 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: | Ġ G | ≤ 4.10 × 10 yr. We also demonstrate that varying gravitational constant G does not modify cooling of white dwarfs in a significant way at least at the luminosities where white dwarfs are pulsationally unstable.