Isochrones and Luminosity Functions for Old White Dwarfs

Using a new grid of models of cooling white dwarfs, we calculate isochrones and luminosity functions in the Johnson-Kron/Cousins and HST filter sets for systems containing old white dwarfs. These new models incorporate a non-grey atmosphere which is necessary to properly describe the effects of molecular opacity at the cool temperatures of old white dwarfs. The various functions calculated and extensively tabulated and plotted are meant to be as utilitarian as possible for observers so all results are listed in quantities that observers will obtain. The tables and plots developed should eventually prove critical in interpreting the results of HST's Advanced Camera observations of the oldest white dwarfs in nearby globular clusters, in understanding the results of searches for old white dwarfs in the Galactic halo, and in determining ages for star clusters of all ages using white dwarfs. As a practical application we demonstrate the use of these results by deriving the white dwarf cooling age of the old Galactic cluster M67.Comment: 7 pages, 8 tables, accepted for publication in the Astrophysical Journa

Amnestically induced persistence in random walks

We study how the Hurst exponent $\alpha$ depends on the fraction $f$ of the total time $t$ remembered by non-Markovian random walkers that recall only the distant past. We find that otherwise nonpersistent random walkers switch to persistent behavior when inflicted with significant memory loss. Such memory losses induce the probability density function of the walker's position to undergo a transition from Gaussian to non-Gaussian. We interpret these findings of persistence in terms of a breakdown of self-regulation mechanisms and discuss their possible relevance to some of the burdensome behavioral and psychological symptoms of Alzheimer's disease and other dementias.Comment: 4 pages, 3 figs, subm. to Phys. Rev. Let

The Galactic Inner Halo: Searching for White Dwarfs and Measuring the Fundamental Galactic Constant, Vo/Ro

We establish an extragalactic, zero-motion frame of reference within the deepest optical image of a globular star cluster, an HST 123-orbit exposure of M4 (GO 8679, cycle 9). The line of sight beyond M4 (l,b (deg) = 351,16) intersects the inner halo (spheroid) of our Galaxy at a tangent-point distance of 7.6 kpc (for Ro = 8 kpc). We isolate these spheroid stars from the cluster based on their proper motions over the 6-year baseline between these and previous epoch HST data (GO 5461, cycle 4). Distant background galaxies are also found on the same sight line using image-morphology techniques. This fixed reference frame allows us to independently determine the fundamental Galactic constant, Vo/Ro = 25.3 +/- 2.6 km/s/kpc, thus providing a velocity of the Local Standard of Rest, v = 202.7 +/- 24.7 km/s for Ro = 8.0 +/- 0.5 kpc. Secondly, the galaxies allow a direct measurement of M4's absolute proper motion, mu_total = 22.57 +/- 0.76 mas/yr, in excellent agreement with recent studies. The clear separation of galaxies from stars in these deep data also allow us to search for inner-halo white dwarfs. We model the conventional Galactic contributions of white dwarfs along our line of sight and predict 7.9 (thin disk), 6.3 (thick disk) and 2.2 (spheroid) objects to the limiting magnitude at which we can clearly delineate stars from galaxies (V = 29). An additional 2.5 objects are expected from a 20% white dwarf dark halo consisting of 0.5 Mo objects, 70% of which are of the DA type. After considering the kinematics and morphology of the objects in our data set, we find the number of white dwarfs to be consistent with the predictions for each of the conventional populations. However, we do not find any evidence for dark halo white dwarfs.Comment: 31 pages, including 6 diagrams and 2 tables. Accepted for publication in Ap

The White Dwarf Cooling Sequence of the Globular Cluster Messier 4

We present the white dwarf sequence of the globular cluster M4, based on a 123 orbit Hubble Space Telescope exposure, with limiting magnitude V = 30, I = 28. The white dwarf luminosity function rises sharply for I >25.5, consistent with the behaviour expected for a burst population. The white dwarfs of M4 extend to approximately 2.5 magnitudes fainter than the peak of the local Galactic disk white dwarf luminosity function. This demonstrates a clear and significant age difference between the Galactic disk and the halo globular cluster M4. Using the same standard white dwarf models (Hansen 1999) to fit each luminosity function yields ages of 7.3 +/- 1.5 Gyr for the disk and 12.7 +/- 0.7 Gyr for M4 (2-sigma statistical errors).Comment: 14 pages, 4 diagrams. Accepted for publication in the Astrophysical Journal Letter

On the coupling between molecular diffusion and solvation shell exchange

The connection between diffusion and solvent exchanges between first and second solvation shells is studied by means of molecular dynamics simulations and analytic calculations, with detailed illustrations for water exchange for the Li+ and Na+ ions, and for liquid argon. First, two methods are proposed which allow, by means of simulation, to extract the quantitative speed-up in diffusion induced by the exchange events. Second, it is shown by simple kinematic considerations that the instantaneous velocity of the solute conditions to a considerable extent the character of the exchanges. Analytic formulas are derived which quantitatively estimate this effect, and which are of general applicability to molecular diffusion in any thermal fluid. Despite the simplicity of the kinematic considerations, they are shown to well describe many aspects of solvent exchange/diffusion coupling features for nontrivial systems