Asteroseismological bound onĠ/Gfrom pulsating white dwarfs

We study the secular variation of the period of nonradial pulsations of white dwarfs when a temporal dependence of the gravitational constant G is assumed. We consider models that reproduce accurately the main characteristics of the best studied DA (hydrogen-rich atmosphere) white dwarf G117-B15A. For this object it has been possible to measure the secular variation of the main observed period of 215.2 s $(\mathrm{Ṗ}=2.3\mathrm{}\pm 1.4\times {10}^{-15}{\mathrm{s}}^{-1})$ with unprecedented accuracy. Comparing our models with observations we obtain that for $Ġ<0\mathrm{}$ the allowed values are in the range $-2.5\times {10}^{-10}{\mathrm{yr}}^{-1}\lesssim Ġ/G\lesssim 0,$ whereas, for $Ġ>0,$ the allowed values are $0\lesssim Ġ/G\lesssim 4.0\times {10}^{-11}{\mathrm{yr}}^{-1}$ at the $2\sigma$ confidence level, which are comparable to other bounds established by independent methods. We also show that in order to improve this bound significantly an improvement in the precision of the observed change in $\mathrm{Ṗ}$ which is too large to be reached in the foreseeable future is required.