The Discovery of the Most Metal-Rich White Dwarf: Composition of a Tidally Disrupted Extrasolar Dwarf Planet

Cool white dwarf stars are usually found to have an outer atmosphere that is practically pure in hydrogen or helium. However, a small fraction have traces of heavy elements that must originate from the accretion of extrinsic material, most probably circumstellar matter. Upon examining thousands of Sloan Digital Sky Survey spectra, we discovered that the helium-atmosphere white dwarf SDSS J073842.56+183509.6 shows the most severe metal pollution ever seen in the outermost layers of such stars. We present here a quantitative analysis of this exciting star by combining high S/N follow-up spectroscopic and photometric observations with model atmospheres and evolutionary models. We determine the global structural properties of our target star, as well as the abundances of the most significant pollutants in its atmosphere, i.e., H, O, Na, Mg, Si, Ca, and Fe. The relative abundances of these elements imply that the source of the accreted material has a composition similar to that of Bulk Earth. We also report the signature of a circumstellar disk revealed through a large infrared excess in JHK photometry. Combined with our inferred estimate of the mass of the accreted material, this strongly suggests that we are witnessing the remains of a tidally disrupted extrasolar body that was as large as Ceres.Comment: 7 pages in emulateapj, 5 figures, accepted for publication in Ap

Runaway accretion of metals from compact debris disks onto white dwarfs

It was recently proposed that metal-rich white dwarfs (WDs) accrete their metals from compact debris disks found to exist around more than a dozen of them. At the same time, elemental abundances measured in atmospheres of some WDs imply vigorous metal accretion at rates up to $10^{11}$ g/s, far in excess of what can be supplied solely by Poynting-Robertson drag acting on such debris disks. To explain this observation we propose a model, in which rapid transport of metals from the disk onto the WD naturally results from interaction between this particulate disk and spatially coexisting disk of metallic gas. The latter is fed by evaporation of debris particles at the sublimation radius located at several tens of WD radii. Because of pressure support gaseous disk orbits WD slower than particulate disk. Resultant azimuthal drift between them at speed ~1 m/s causes aerodynamic drag on the disk of solids and drives inward migration of its constituent particles. Upon reaching the sublimation radius particles evaporate, enhancing the density of metallic gaseous disk and leading to positive feedback. Under favorable circumstances (low viscosity in the disk of metallic gas and efficient aerodynamic coupling between the disks) system evolves in a runaway fashion, destroying debris disk on time scale of $\sim 10^5$ yr, and giving rise to high metal accretion rates up to $10^{10}-10^{11}$ g/s, in agreement with observations.Comment: 5 pages, 2 figures, submitted to ApJ

Inner edges of compact debris disks around metal-rich white dwarfs

A number of metal-rich white dwarfs (WDs) are known to host compact, dense particle disks, which are thought to be responsible for metal pollution of these stars. In many such systems the inner radii of disks inferred from their spectra are so close to the WD that particles directly exposed to starlight must be heated above 1500 K and are expected to be unstable against sublimation. To reconcile this expectation with observations we explore particle sublimation in H-poor debris disks around WDs. We show that because of the high metal vapor pressure the characteristic sublimation temperature in these disks is 300-400 K higher than in their protoplanetary analogues, allowing particles to survive at higher temperatures. We then look at the structure of the inner edges of debris disks and show that they should generically feature superheated inner rims directly exposed to starlight with temperatures reaching 2500-3500 K. Particles migrating through the rim towards the WD (and rapidly sublimating) shield the disk behind them from strong stellar heating, making the survival of solids possible close to the WD. Our model agrees well with observations of WD+disk systems provided that disk particles are composed of Si-rich material such as olivine, and have sizes in the range ~(0.03-30) cm.Comment: 12 pages, 6 figures, submitted to Ap

Global modeling of radiatively driven accretion of metals from compact debris disks onto the white dwarfs

Recent infrared observations have revealed presence of compact (radii < R_Sun) debris disks around more than a dozen of metal-rich white dwarfs (WD), likely produced by tidal disruption of asteroids. Accretion of high-Z material from these disks may account for the metal contamination of these WDs. It was previously shown using local calculations that the Poynting-Robertson (PR) drag acting on the dense, optically thick disk naturally drives metal accretion onto the WD at the typical rate \dot M_{PR} \approx 10^8 g/s. Here we extend this local analysis by exploring global evolution of the debris disk under the action of the PR drag for a variety of assumptions about the disk properties. We find that massive disks (mass > 10^{20} g), which are optically thick to incident stellar radiation inevitably give rise to metal accretion at rates \dot M > 0.2\dot M_{PR}. The magnitude of \dot M and its time evolution are determined predominantly by the initial pattern of the radial distribution of the debris (i.e. ring-like vs. disk-like) but not by the total mass of the disk. The latter determines only the disk lifetime, which can be several Myr or longer. Evolution of an optically thick disk generically results in the development of a sharp outer edge of the disk. We also find that the low mass (< 10^{20} g), optically thin disks exhibit \dot M << \dot M_{PR} and evolve on characteristic timescale \sim 10^5-10^6 yr, independent of their total mass.Comment: 9 pages, 8 figures, submitted to Ap

Near-ultraviolet and optical effects of Debris Disks around White Dwarfs

Studies of debris disks around white dwarfs (WDs) have focused on infrared wavelengths because debris disks are much colder than the star and are believed to contribute to the spectrum only at longer wavelengths. Nevertheless, these disks are made of dust grains which absorb and scatter near-UV and optical photons from the WD, leaving a fingerprint that can be used to further constrain disk properties. Our goal is to show that it is possible to detect near-UV and optical effects of debris disks in the star + disk integrated spectrum. We make theoretical calculations and discuss the necessary observational conditions to detect the near-UV and optical effects. We show how these effects can be used to infer the disk mass, composition, optical depth, and inclination relative to the line of sight. If the IR excess is due to a disk, then near-UV and optical effects should be observed in only some systems, not all of them, while for dust shells the effects should be observed in all systems.Comment: 6 pages, 5 figure

Global Models of Runaway Accretion in White Dwarf Debris Disks

A growing sample of white dwarfs (WDs) with metal-enriched atmospheres are accompanied by excess infrared emission, indicating that they are encircled by a compact dusty disk of solid debris. Such `WD debris disks' are thought to originate from the tidal disruption of asteroids or other minor bodies, but the precise mechanism(s) responsible for transporting matter to the WD surface remains unclear, especially in those systems with the highest inferred metal accretion rates dM_Z/dt ~ 1e8-1e10 g/s. Here we present global time-dependent calculations of the coupled evolution of the gaseous and solid components of WD debris disks. Solids transported inwards (initially due to PR drag) sublimate at tens of WD radii, producing a source of gas that accretes onto the WD surface and viscously spreads outwards in radius, where it overlaps with the solid disk. If the aerodynamic coupling between the solids and gaseous disks is sufficiently strong (and/or the gas viscosity sufficiently weak), then gas builds up near the sublimation radius faster than it can viscously spread away. Since the rate of drag-induced solid accretion increases with gas density, this results in a runaway accretion process, during which the WD accretion rate reaches values orders of magnitude higher than can be achieved by PR drag alone. We explore the evolution of WD debris disks across a wide range of physical conditions and calculate the predicted distribution of observed accretion rates dM_Z/dt, finding reasonable agreement with the current sample. Although the conditions necessary for runaway accretion are at best marginally satisfied given the minimal level of aerodynamic drag between circular gaseous and solid disks, the presence of other stronger forms of solid-gas coupling---such as would result if the gaseous disk is only mildly eccentric---substantially increase the likelihood of runaway accretion.Comment: 23 pages, 20 figures, submitted to MNRA

Ideals and finiteness conditions for subsemigroups

In this paper we consider a number of finiteness conditions for semigroups related to their ideal structure, and ask whether such conditions are preserved by sub- or supersemigroups with finite Rees or Green index. Specific properties under consideration include stability, D=J and minimal conditions on ideals.Comment: 25 pages, revised according to referee's comments, to appear in Glasgow Mathematical Journa