The evolution of white dwarfs with a varying gravitational constant

Abstract

Context. Within the theoretical framework of some modern unification theories the constants of nature are functions of cosmological time. White dwarfs offer the possibility of testing a possible variation of G and, thus, to place constraints on these theories. Aims. We present full white dwarf evolutionary calculations for a scenario where G decreases with time. Methods. White dwarf evolution is computed in a self-consistent way, including the most up-to-date physical inputs, non-gray model atmospheres and a detailed core chemical composition that results from the calculation of the full evolution of progenitor stars. Results. We find that the mechanical structure and the energy balance of white dwarfs are strongly modified by a varying G. In particular, for a rate of change of G higher thanĠ/G = −1 × 10 −12 yr −1 , the evolution of cool white dwarfs is markedly affected. The impact of a varying G is more pronounced for more massive white dwarfs. Conclusions. In view of the recent results reporting that a very accurate white dwarf cooling age can be derived for the old and metal-rich open cluster NGC 6791, our study suggests that this cluster could be a potential target to constrain or detect a hypothetical secular variation of G.

The white dwarf luminosity function

“…This result was challenged by , who obtained a much tighter bound using the same method, but their analysis was subsequently shown to be flawed. This issue was finally settled by detailed evolutionary calculations (Althaus et al, 2011;García-Berro et al, 2011a), which corroborated the preliminary analytical calculations of Garcia-Berro et al (1995). We mention here that a tighter bound was obtained by García-Berro et al (2011b)…”

An upper limit to the secular variation of the gravitational constant from white dwarf stars

“…In this study we adopt the most recent and reliable white dwarf cooling tracks available so far [21]. These cooling sequences incorporate the most up-to-date description of the stellar plasma and incorporate self-consistently the effects of a secularly varying G. In particular these cooling sequences consider 22 Ne diffusion and its associated energy release [20,27,31].…”

White dwarf constraints on a secularly varying gravitational constant

“…For the specific case of white dwarfs this effect is particularly noticeable 13,14 , as the mechanical structure of these compact stars is supported by the pressure of degenerate electrons, which is sensitive to the value of G. Hence, any variation of G changes the hydrostratic equilibrium balance, and releases energy, that must be radiated away. Thus, since the evolution of white dwarfs is driven by the release of gravothermal energy their cooling rate is severely affected.…”

“…In this expression G 0 is the present value of the gravitational constant, and τ 0 MS stands for the progenitor lifetime computed using G 0 . For the white dwarf cooling times we adopted the most recent and reliable white dwarf evolutionary sequences available so far 14 , which incorporate the most up-to-date physical inputs and were computed taking into account the effects of a secularly varying G self-consistently. Specifically, these cooling sequences consider 22 Ne diffusion and its associated energy release 16,18,19 , as well as the effects of carbon-oxygen phase separation upon crystallization 20,21 , and together with the main sequence lifetimes given by Eq.…”