Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

The Extended Shapes of Galactic Satellites

We are exploring the extended stellar distributions of Galactic satellite galaxies and globular clusters. For seven objects studied thus far, the observed profile departs from a King function at large r, revealing a ``break population'' of stars. In our sample, the relative density of the ``break'' correlates to the inferred M/L of these objects. We discuss opposing hypotheses for this trend: (1) Higher M/L objects harbor more extended dark matter halos that support secondary, bound, stellar ``halos''. (2) The extended populations around dwarf spheroidals (and some clusters) consist of unbound, extratidal debris from their parent objects, which are undergoing various degrees of tidal disruption. In this scenario, higher M/L ratios reflect higher degrees of virial non-equilibrium in the parent objects, thus invalidating a precept underlying the use of core radial velocities to obtain masses.Comment: 8 pages, including 2 figures Yale Cosmology Workshop: The Shapes of Galaxies and Their Halo

Re-entrant Layer-by-Layer Etching of GaAs(001)

We report the first observation of re-entrant layer-by-layer etching based on {\it in situ\/} reflection high-energy electron-diffraction measurements. With AsBr$_3$ used to etch GaAs(001), sustained specular-beam intensity oscillations are seen at high substrate temperatures, a decaying intensity with no oscillations at intermediate temperatures, but oscillations reappearing at still lower temperatures. Simulations of an atomistic model for the etching kinetics reproduce the temperature ranges of these three regimes and support an interpretation of the origin of this phenomenon as the site-selectivity of the etching process combined with activation barriers to interlayer adatom migration.Comment: 11 pages, REVTeX 3.0. Physical Review Letters, in press

The Three-Dimensional Circumstellar Environment of SN 1987A

We present the detailed construction and analysis of the most complete map to date of the circumstellar environment around SN 1987A, using ground and space-based imaging from the past 16 years. PSF-matched difference-imaging analyses of data from 1988 through 1997 reveal material between 1 and 28 ly from the SN. Careful analyses allows the reconstruction of the probable circumstellar environment, revealing a richly-structured bipolar nebula. An outer, double-lobed ``Peanut,'' which is believed to be the contact discontinuity between red supergiant and main sequence winds, is a prolate shell extending 28 ly along the poles and 11 ly near the equator. Napoleon's Hat, previously believed to be an independent structure, is the waist of this Peanut, which is pinched to a radius of 6 ly. Interior to this is a cylindrical hourglass, 1 ly in radius and 4 ly long, which connects to the Peanut by a thick equatorial disk. The nebulae are inclined 41\degr south and 8\degr east of the line of sight, slightly elliptical in cross section, and marginally offset west of the SN. From the hourglass to the large, bipolar lobes, echo fluxes suggest that the gas density drops from 1--3 cm^{-3} to >0.03 cm^{-3}, while the maximum dust-grain size increases from ~0.2 micron to 2 micron, and the Si:C dust ratio decreases. The nebulae have a total mass of ~1.7 Msun. The geometry of the three rings is studied, suggesting the northern and southern rings are located 1.3 and 1.0 ly from the SN, while the equatorial ring is elliptical (b/a < 0.98), and spatially offset in the same direction as the hourglass.Comment: Accepted for publication in the ApJ Supplements. 38 pages in apjemulate format, with 52 figure

Absolute Proper Motions to B~22.5: V. Detection of Sagittarius Dwarf Spheroidal Debris in the Direction of the Galactic Anticenter

We have detected a population of predominantly blue (B-V <= 1.1) stars in the direction l = 167 deg., b = -35 deg. (Kapteyn Selected Area 71) that cannot be accounted for by standard starcount models. Down to V ~ 20, the colors and magnitudes of these stars are similar to those of the southern overdensity detected by the Sloan Digital Sky Survey, and identified as stripped material from the Sagittarius dwarf spheroidal galaxy. We present absolute proper motions for the stars in SA 71, and we find that the excess blue stars represent a distinct, kinematically cooler component than the Galactic field, and in reasonable agreement with predictions of Sgr disruption models. The density of the excess SA 71 stars at V ~ 18.8 and B-V <=1.1 is within a factor of two of the density of the SDSS-south Sgr stripped material, and of that predicted by the Helmi and White disruption model. Three additional anticenter fields (SA 29, 45 and 118) show very good agreement with standard starcount models.Comment: 13 pages, 3 figures, submitted to ApJL, accepted for Ap

A New View of the Circumstellar Environment of SN 1987A

We summarize the analysis of a uniform set of both previously-known and newly-discovered scattered-light echoes, detected within 30" of SN 1987A in ten years of optical imaging, and with which we have constructed the most complete three-dimensional model of the progenitor's circumstellar environment. Surrounding the SN is a richly-structured bipolar nebula. An outer, double-lobed ``peanut,'' which we believe is the contact discontinuity between the red supergiant and main sequence winds, is a prolate shell extending 28 ly along the poles and 11 ly near the equator. Napoleon's Hat, previously believed to be an independent structure, is the waist of this peanut, which is pinched to a radius of 6 ly. Interior, the innermost circumstellar material lies along a cylindrical hourglass, 1 ly in radius and 4 ly long, which connects to the peanut by a thick equatorial disk. The nebulae are inclined 41o south and 8o east of the line of sight, slightly elliptical in cross section, and marginally offset west of the SN. The 3-D geometry of the three circumstellar rings is studied, suggesting the equatorial ring is elliptical (b/a<0.98), and spatially offset in the same direction as the hourglass. Dust-scattering models suggest that between the hourglass and bipolar lobes: the gas density drops from 1--3 cm^{-3} to >0.03 cm^{-3}; the maximum dust-grain size increases from ~0.2 micron to 2 micron; and the Si:C dust ratio decreases. The nebulae have a total mass of ~1.7 Msun, yielding a red-supergiant mass loss around 5*10^{-6} Msun yr^{-1}.Comment: Accepted for publication in ApJ 2/14/05. 16 pages in emualteapj forma