Fr.: théorie de Mestel
The first quantitative model showing that the energy of → white dwarfs is the leftover heat from the star's past nuclear fusion that leaks slowly into space. In this analytic model constructed by Mestel (1952), a white dwarf consists of two layers. The inner layer, which contains most of the mass, is assumed to be → isothermal because of efficient thermal conductivity by the → degenerate electrons. Moreover, it is supposed that the electrons do not contribute significantly to the → heat capacity. The heat capacity comes entirely from the ions, which are assumed to behave as a classical → ideal gas. The thin non-degenerate outer layer forms an insulating blanket and controls the rate at which the energy from the ion reservoir is leaked out into space. The specific rate is controlled by the radiative opacity at the boundary between these two layers, and is assumed to obey → Kramers' opacity law. The Mestel theory shows that the cooling rate of a white dwarf is proportional to its temperature (hotter white dwarfs cool faster), and gives a relationship between the luminosity (L) of the white dwarf and the cooling time: t ∝ L-5/7. More recent models take into account some or all of the following processes neglected in the Mestel theory: neutrino cooling (important for L > 10-1.5 Lsun), latent heat of crystallization release (important for L < 10-4 Lsun), nuclear energy generation via proton-proton burning (important when MH ≥ 10-4 M*), and gravitational energy release from surface layers. The Mestel theory is a very good approximation of more recent calculations. For a review of the Mestel theory see Van Horn (1971, IAU Symp. 42, 97; W. J. Luyten, Editor), Wood (1990, J. Roy. Astro. Soc. Canada 84, 150), and Kepler and Brdaley (1995, Baltic Astron. 4, 166).
Named after Leon Mestel (1927-), British astrophysicist, who put forward this theory in 1952 (MNRAS, 112, 583); → theory.