Spectral Decomposition of the Tent Map with Varying Height

The generalized spectral decomposition of the Frobenius-Perron operator of the tent map with varying height is determined at the band-splitting points. The decomposition includes both decay onto the attracting set and the approach to the asymptotically periodic state on the attractor. Explicit compact expressions for the polynomial eigenstates are obtained using algebraic techniques.Comment: 39 pages, 7 figures, in LATeX with embedded PS figure

White Dwarfs in NGC 6791: Avoiding the Helium Flash

We propose that the anomalously bright white dwarf luminosity function observed in NGC 6791 (Bedin et al 2005) is the consequence of the formation of 0.5 Msun white dwarfs with Helium cores instead of Carbon cores. This may happen if mass loss during the ascent of the Red Giant Branch is strong enough to prevent a star from reaching the Helium flash. Such a model can explain the slower white dwarf cooling (relative to standard models) and fits naturally with scenarios advanced to explain Extreme Horizontal Branch stars, a population of which are also found in this cluster.Comment: 4 pages, 4 postscript figures, submitted to Ap

The Temperature and Cooling Age of the White-Dwarf Companion to the Millisecond Pulsar PSR B1855+09

We report on Keck and {\em Hubble Space Telescope} observations of the binary millisecond pulsar PSR B1855+09. We detect its white-dwarf companion and measure \mv=25.90\pm0.12 and \mi=24.19\pm0.11 (Vega system). From the reddening-corrected color, (\mv-\mi)_0=1.06\pm0.21, we infer a temperature \Teff=4800\pm800 K. The white-dwarf mass is known accurately from measurements of the Shapiro delay of the pulsar signal, \Mcomp=0.258^{+0.028}_{-0.016} \Msun. Hence, given a cooling model, one can use the measured temperature to determine the cooling age. The main uncertainty in the cooling models for such low-mass white dwarfs is the amount of residual nuclear burning, which is set by the thickness of the hydrogen layer surrounding the helium core. From the properties of similar systems, it has been inferred that helium white dwarfs form with thick hydrogen layers, with mass \simgt3\times10^{-3} \Msun, which leads to significant additional heating. This is consistent with expectations from simple evolutionary models of the preceding binary evolution. For PSR B1855+09, though, such models lead to a cooling age of $\sim10$Gyr, which is twice the spin-down age of the pulsar. It could be that the spin-down age were incorrect, which would call the standard vacuum dipole braking model into question. For two other pulsar companions, however, ages well over 10 Gyr are inferred, indicating that the problem may lie with the cooling models. There is no age discrepancy for models in which the white dwarfs are formed with thinner hydrogen layers (\simlt3\times10^{-4} \Msun).Comment: 7 pages, 1 figure, aas4pp2.sty. Accepted for publication in ApJ

Optical Identification of Close White Dwarf Binaries in the LISA Era

The Laser Interferometer Space Antenna (LISA) is expected to detect close white dwarf binaries (CWDBs) through their gravitational radiation. Around 3000 binaries will be spectrally resolved at frequencies > 3 mHz, and their positions on the sky will be determined to an accuracy ranging from a few tens of arcminutes to a degree or more. Due to the small binary separation, the optical light curves of >~ 30% of these CWDBs are expected to show eclipses, giving a unique signature for identification in follow-up studies of the LISA error boxes. While the precise optical location improves binary parameter determination with LISA data, the optical light curve captures additional physics of the binary, including the individual sizes of the stars in terms of the orbital separation. To optically identify a substantial fraction of CWDBs and thus localize them very accurately, a rapid monitoring campaign is required, capable of imaging a square degree or more in a reasonable time, at intervals of 10--100 seconds, to magnitudes between 20 and 25. While the detectable fraction can be up to many tens of percent of the total resolved LISA CWDBs, the exact fraction is uncertain due to unknowns related to the white dwarf spatial distribution, and potentially interesting physics, such as induced tidal heating of the WDs due to their small orbital separation.Comment: 4 pages, 2 figure

White Dwarf Donors in Ultracompact Binaries: The Stellar Structure of Finite Entropy Objects

We discuss the mass-radius (M-R) relations for low-mass (M<0.1 Msun) white dwarfs (WDs) of arbitrary degeneracy and evolved (He, C, O) composition. We do so with both a simple analytical model and models calculated by integration of hydrostatic balance using a modern equation of state valid for fully ionized plasmas. The M-R plane is divided into three regions where either Coulomb physics, degenerate electrons or a classical gas dominate the WD structure. For a given M and central temperature, T_c, the M-R relation has two branches differentiated by the model's entropy content. We present the M-R relations for a sequence of constant entropy WDs of arbitrary degeneracy parameterized by M and T_c for pure He, C, and O. We discuss the applications of these models to the recently discovered accreting millisecond pulsars. We show the relationship between the orbital inclination for these binaries and the donor's composition and T_c. In particular we find from orbital inclination constraints that the probability XTE J1807-294 can accommodate a He donor is approximately 15% while for XTE J0929-304, it is approximately 35%. We argue that if the donors in ultracompact systems evolve adiabatically, there should be 60-160 more systems at orbital periods of 40 min than at orbital periods of 10 min, depending on the donor's composition.Comment: emulateapj style, 11 pages, 12 figures. Accepted to the Astrophysical Journal. Tables with interpolation routines of the M-R relations are available at http://www.physics.ucsb.edu/~cjdeloye/research.htm

The Clusters AgeS Experiment (CASE). I. V209 omega Cen - An Eclipsing Post-Common Envelope Binary in the Globular Cluster omega Cen

We use photometric and spectroscopic observations of the detached eclipsing binary V209 omega Cen to derive the masses, radii, and luminosities of the component stars. The system exhibits total eclipses and, based on the measured systemic velocity and the derived distance, is a member of the globular cluster omega Cen. We obtain 0.945 +/- 0.043 Msun, 0.983 +/- 0.015 Rsun and 6.68 +/- 0.88 Lsun for the cooler, but larger and more luminous primary component. The secondary component has 0.144 +/- 0.008 Msun, 0.425 +/- 0.008 Rsun and 2.26 +/- 0.28 Lsun. The effective temperatures are estimated at 9370 K for the primary and at 10866 K for the secondary. On the color-magnitude diagram of the cluster, the primary component occupies a position between the tip of the blue straggler region and the extended horizontal branch while the secondary component is located close to the red border of the area occupied by hot subdwarfs. However, its radius is too large and its effective temperature is too low for it to be an sdB star. We propose a scenario leading to the formation of a system with such unusual properties with the primary component ``re-born'' from a former white dwarf which accreted a new envelope through mass transfer from its companion. The secondary star has lost most of its envelope while starting its ascent onto the sub-giant branch. It failed to ignite helium in its core and is currently powered by a hydrogen burning shell.Comment: 24 pages, 9 figures, AJ, in pres