Pulsating objects are important to physicists because an analysis of them gives information about the interior structure of the object; this is the principle underlying the study of seismic disturbances to determine the Earth's interior structure. Astronomers have discovered that the Sun and other classes of stars undergo many types of "nonradial pulsations", and the analysis of these observations is now responsible for the most rapidly developing disciplines of solar physics. Many white dwarf stars, which are the most common product of stellar evolution, undergo many types of nonradial oscillations as well. The large number of pulsation modes in these stars, together with their simple "degenerate" state (which allows a model to be formulated with very few physical variables), has moved the study of seismology of white dwarfs to the forefront of variable star research. The Principal Investigator (PI) has used a previous, five-year Presidential Young Investigator award to help underwrite simultaneous observing of white dwarfs of unusual interest by a group of astronomers located around the globe. By pooling their observations they are able to circumvent the severe data-gaps imposed by the Earth's day/night rotation cycle and conduct observations for several days -- in the best case over nearly 10 continuous days. The PI and his collaborators have used such extraordinarily long data strings to detect and identify over 100 independent pulsation modes in the white dwarf PG+1159-035. The identification of these pulsations has permitted astronomers to estimate the mass of this star to within 0.4% (the most accurate determination of a stellar mass other than the Sun's), to estimate the star's rotation rate including the tilt of the star's rotational axis in the sky, and to infer the presence of at least three regions of the star with different chemical compositions. The NSF award will support a continuation of international observing campaigns on other white dwarfs of special interest. The study will emphasis emphasis in particular the details of their chemical structure as well as the effect of rotation of the excitation of the NRP modes. Eventually, these studies may also permit the measurement of the change of some white dwarfs' sizes with time. This would allow in turn an accurate estimate of the cooling rate of these stars as they evolve to "cold embers". Such cooling rates will permit an estimate of the ages of these stars. Since these stars are among the oldest stars in the disk of our Milky Way Galaxy, these ages will provide strong constraints on the age of our Galaxy and hence of the Universe.
