Asteroseismology, Cosmochronology, Planetology, and Stellar Evolution at the Bottom of the HR Diagram

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This proposal is about a research program aimed, in part, at further exploiting the unique properties of white dwarf stars. As the final products of stellar evolution for the vast majority of stars, white dwarfs bear the signature of past events of fundamental importance in stellar life: mass loss, phases of convective mixing, loss and redistribution of angular momentum, thermonuclear burning. They are also ideal cosmic laboratories for testing our theories of matter under extreme conditions of pressure and temperature. White dwarfs may also be used as cosmochronometers and distance indicators for the different components of the Galaxy (disk, halo, open and globular clusters). Recently, planetary debris have been identified at the surface of several white dwarfs, which has led to the excitingpossibility of determining in a unique and novel way the *bulk* composition of these ancient planets.To decipher the information contained in white dwarfs, which, in many ways, behave as "fossils" of stellar evolution, researchers in thefield dispose of powerful tools based on model atmosphere theory, stellar evolution theory, and stellar pulsation theory. In the lattercase, Nature has chosen to cooperate with us since no less than 6 distinct types of pulsating white dwarfs -- each corresponding to adifferent evolutionary phase -- are now known, including the recent discoveries of two new types in 2012 and 2013. Asteroseismology can be used to determine, among other things, the internal chemical layering of white dwarfs (core composition and envelope chemicalstratification), which is an essential input in cooling calculations. Hence, white dwarf asteroseismology may be used to "calibrate", so to speak, the internal chemical structure, a step necessary for exploiting fully the cosmochronological potential of these stars.This proposal is also concerned with another category of evolved and compact stars, the hot subdwarfs, whose origin is still being debated. They constitute a sort of "gray zone" in the grand scheme of stellar evolution and, as such, their very existence represents a challenge for those interested in stellar evolution theory. It is known that hot subdwarfs are former red giant stars and that their destiny is to become low-mass white dwarfs, but the details of their formation process are still uncertain. A number of competing formation scenarios have been proposed, some involving binary evolution (common envelope evolution, Roche lobe overflow, mergers), others single star evolution (with peculiar mass loss rates in the red giant phase). It has been proposed recently that planets orbiting around "isolated" hot subdwarfs (i.e., not part of binary systems) may provide the necessary "kick" needed to expel extra mass in the red giant phase. And planets have been detected around hot subdwarfs.One of the long-term goals of this proposal is to discriminate between the various formation scenarios that have been proposed for hot subdwarfs. This can best be done by deriving the empirical mass distribution of these stars, which bears the signature of the actual formation process. Unfortunately, reliable mass estimates for these stars coming from the standard methods are far and few. For instance, spectroscopic masses are notoriously uncertain for hot subdwarfs. However, the powerful method of asteroseismology can again come to the rescue as Nature has provided us with no less than 4 different types of pulsating hot subdwarfs (first type discovered in 1997, and the newest one in 2011). In fact, the pulsating hot subdwarfs have turned out to be the best asteroseismological tesbeds that currently exist, and masses, along with many other properties, can be determined both accurately and precisely for these stars.