Evolution of Helium White Dwarfs of Low and Intermediate Masses

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Abstract
We present detailed calculations of the evolution of low-mass, helium white dwarf models with masses from M = 0.1 to M = 0.5 M☉ at intervals of 0.05 M☉ and with a metallicity of Z = 10-3. For this purpose, we have taken fully into account finite-temperature effects by means of a detailed and updated stellar evolutionary code, in which the convective energy transport is described according to the new model for turbulent convection developed by Canuto & Mazzitelli. Furthermore, our code considers the most recent opacity data computed by the Livermore Group (OPAL data), and also the new equation of state for helium plasmas developed by Saumon, Chabrier, & Van Horn. Neutrino emission is fully taken into account as well. For models with M ≤ 0.3 M☉ we started our calculations from fully convective models located at the helium-Hayashi line for each configuration, far away from the white dwarf regime. By contrast, the evolutionary sequences corresponding to 0.35, 0.4, 0.45, and 0.5 M☉ were started from initial models resembling white dwarf structures. This was necessary in order to avoid the onset of helium burning. A consequence of this constraint is the existence of a "forbidden region" in the HR diagram above log (L/L☉) = -0.25 and hotter than log Teff = 4.45, where helium white dwarfs can exist only for brief intervals. All the models were evolved to log (L/L☉) = -5. The evolutionary tracks in the HR diagram have been carefully analyzed, and we found that the convective efficiency affects the tracks noticeably only in the high-luminosity (pre-white dwarf) regime. We also examined the evolution of central conditions, neutrino luminosity, radii, surface gravity, and ages. Central densities, radii, and surface gravities asymptotically approach the zero temperature Hamada-Salpeter results, as expected. Neutrino losses are important for the more massive helium white dwarf configurations and should be taken into account in detailed evolutionary studies of these objects. Finally, the structure of the outer convective zone was analyzed in both the framework of the mixing length theory (for different convective efficiencies) and the Canuto & Mazzitelli theory. We found that the profile of the outer convective zone given by the Canuto & Mazzitelli model is very different from that given by any version of the mixing length theory. This behavior is critical for pulsational instability; however, stellar parameters such as radius and surface gravity are not significantly affected in the white dwarf domain. These models should be especially suitable for the interpretation of the data about the recently discovered low-mass white dwarfs in systems containing another white dwarf or a millisecond pulsar.