Evolution of white dwarfs as a probe of theories of gravitation: the case of Brans–Dicke

Theories with varying gravitational constant G have long been studied. Among them, the most promising candidates as alternatives to standard general relativity are known as scalar–tensor theories. They are consistent descriptions of the observed Universe as well as the low‐energy limit of several pictures of unified interactions. Thus, increasing interest in the astrophysical, gravitational wave and pulsar evolution consequences of such theories has been sparked over the last few years. In this work we study the evolution of white dwarf stars in the framework of the simplest model of scalar–tensor theory: Brans–Dicke gravity. We assume that the star is able to see the cosmological evolution of G (obtained from relativistic equations) while adopting a Newtonian model for describing its structure. This allows us to determine how the G variation affects the energetics of the stellar interior. The white dwarfs are analysed employing a well‐tested computer code, with state‐of‐the‐art data for the equation of state, opacities, neutrinos, etc.; all these characteristics are carefully described in the text. We compute the theoretical white dwarf luminosity function and use previous observational data to compare with and extract conclusions on the feasibility of the gravitational theory analysed. We find several striking results. The cooling of white dwarfs is strongly accelerated, particularly for massive stars and low luminosities, even if the Ο parameter of Brans–Dicke theory is big enough to accord well with any other test of gravitation. This uncommon cooling process translates into several distinctive features of white dwarf evolution, among which are (a) a new profile of luminosity versus fractional mass and age, (b) different central temperature versus surface luminosity, (c) low masses of progenitors, and most importantly (d) an appreciable variation in the luminosity function. We finally analyse the possibilities of, when precise data with unique interpretation are available, converting this into a powerful new test of gravitation.