Thick to Thin: The Evolutionary Connection Between PG 1159 Stars and the Thin Helium-Enveloped Pulsating White Dwarf GD 358

Seismological observations with the Whole Earth Telescope (WET) allow the determination of the subsurface compositional structure of white dwarf stars. The hot DO PG 1159 has a helium surface layer with a mass of 0.001 Msun, while the cooler DB white dwarf GD 358 has a much thinner surface helium layer of 10^-6 Msun. These results imply that either there is no evolutionary relation between these two stars, or that there is an unknown mass loss mechanism. To investigate possible evolutionary links between these objects, we computed evolutionary sequences of white dwarf models including time-dependent diffusion. Our initial model is based on the PG~1159 pulsational data, and has a surface composition of 30% helium, 35% carbon, and 35% oxygen. Below this is a thin transition zone where the helium fraction falls to zero. As expected, diffusion caused a separation of the elements; a thickening surface layer of nearly pure helium overlays a deepening transition zone where the composition returns to the original surface composition. When the model reached the temperature range of GD~358 and the pulsating DB white dwarfs, this pure helium surface layer was 3x10^-6 stellar masses deep. The resulting evolved model is very similar to the model used by Bradley and Winget (1994) to match the pulsation observations of GD 358. The pulsation periods of this model also show a good fit to the WET observations. These results demonstrate the plausibility of a direct evolutionary path from PG 1159 stars to the much cooler DB white dwarfs by inclusion of time-dependent diffusion. A problem still remains in that our models have no hydrogen, and thus must retain their DB nature while their surface tempeture drops from 45,000K to 30,000K. Since there are no known DB stars in this range, we plan to address this problem in future calculations.Comment: LaTeX, 10 pages, using AAS Macros. 2 PostScript figures. Accepted for publication in The Astrophysical Journal Letters

Limits on the Halo White Dwarf Component of Baryonic Dark Matter from the {\em Hubble Deep Field}

The MACHO collaboration lensing event statistics suggest that a significant fraction of the dark galactic halo can be comprised of baryonic matter in the form of white dwarf stars with masses between 0.1 and 1.0 \Msun . Such a halo white dwarf population, in order to have escaped detection by those who observe the white dwarf luminosity function of the disk, must have formed from an old population. The observations indicate that the number of halo white dwarfs per cubic parsec per unit bolometric magnitude is less than $10^{-5}$ at $10^{-4.5}$\Lsun; the number must rise significantly at lower luminosities to provide the needed baryonic halo mass. Such white dwarfs may easily escape detection in most current and earlier surveys. Though it is limited in angular extent, the {\em Hubble Deep Field} (HDF) probes a sufficient volume of the galactic halo to provide interesting limits on the number of halo white dwarf stars, and on the fraction of the halo mass that they can make up. If the HDF field can be probed for stars down to $V=29.8$ then the MACHO result suggests that there could be up to 12 faint halo white dwarfs visible in the HDF. Finding (or not finding) these stars in turn places interesting constraints on star formation immediately following the formation of the galaxy.Comment: 10 pages, AASTEX, 1 table, no figures, accepted for publication in Ap.J. Letter

Pulsating sdB Stars: A New Approach to Probing their Interiors

Horizontal branch stars should show significant differential rotation with depth. Models that assume systematic angular momentum exchange in the convective envelope and local conservation of angular momentum in the core produce HB models that preserve a rapidly rotating core. A direct probe of core rotation is available. The nonradial pulsations of the EC14026 stars frequently show rich pulsation spectra. Thus their pulsations probe the internal rotation of these stars, and should show the effects of rapid rotation in their cores. Using models of sdB stars that include angular momentum evolution, we explore this possibility and show that some of the sdB pulsators may indeed have rapidly rotating cores.Comment: 8 pages, 3 figures; paper presented at Keele Workshop on Extreme Horizontal Branch Stars and Related Objects, June 2003 (ed. Pierre Maxsted

The internal rotation profile of the B-type star KIC10526294 from frequency inversion of its dipole gravity modes and statistical model comparison

The internal angular momentum distribution of a star is key to determine its evolution. Fortunately, the stellar internal rotation can be probed through studies of rotationally-split non-radial oscillation modes. In particular, detection of non-radial gravity modes (g modes) in massive young stars has become feasible recently thanks to the Kepler space mission. Our aim is to derive the internal rotation profile of the Kepler B8V star KIC 10526294 through asteroseismology. We interpret the observed rotational splittings of its dipole g modes using four different approaches based on the best seismic models of the star and their rotational kernels. We show that these kernels can resolve differential rotation the radiative envelope if a smooth rotational profile is assumed and the observational errors are small. Based on Kepler data, we find that the rotation rate near the core-envelope boundary is well constrained to $163\pm89$ nHz. The seismic data are consistent with rigid rotation but a profile with counter-rotation within the envelope has a statistical advantage over constant rotation. Our study should be repeated for other massive stars with a variety of stellar parameters in order to deduce the physical conditions that determine the internal rotation profile of young massive stars, with the aim to improve the input physics of their models.Comment: 52 pages, 32 figures, accepted for publication in The Astrophysical Journa

Internal rotation of subdwarf B stars: limiting cases and asteroseismological consequences

Observations of the rotation rates of horizontal branch (HB) stars show puzzling systematics. In particular, cooler HB stars often show rapid rotation (with velocities in excess of 10 km/s), while hotter HB stars typically show much smaller rotation velocities. Simple models of angular momentum evolution of stars from the main sequence through the red giant branch fail to explain these effects. In general, evolutionary models in all cases preserve a rapidly rotating core. The observed angular velocities of HB stars require that some of the angular momentum stored in the core reaches the surface. To test the idea that HB stars contain such a core, one can appeal to detailed computations of trace element abundences and rotational mixing. However, a more direct probe is available to test these limiting cases of angular momentum evolution. Some of the hottest horizontal branch stars are members of the pulsating sdB class. They frequently show rich pulsation spectra characteristic of nonradially pulsating stars. Thus their pulsations probe the internal rotation of these stars, and should show the effects of rapid rotation in their cores. Using models of sdB stars that include angular momentum evolution, we explore this possibility and show that some of the sdB pulsators may indeed have rapidly rotating cores.Comment: accepted for publication in The Astrophysical Journa