Revising the multipole moments of numerical spacetimes, and its consequences

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one, in order to yield a reliable representation. In this note we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass-moment), and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.Comment: article + supplemental materia

Trace Metals and Major Elements in Water-Soluble Rocks of Northwest Arkansas

Trace metals in limestone are potential water contaminants because they can enter the ground water when the limestone is dissolved by carbonic acid and other naturally occurring acids. Four local limestones, the St. Joe and Pitkin Formations (Mississippian) and the Brentwood and Kessler Members of the Bloyd Formation (Pennsylvanian) were sampled in a five county area in Northwest Arkansas. Atomic absorption analyses were made for Na, K, Mg, Ca, Zh, Cu, Ba, Fe, Co, Cr, Ni, Mn, Li and Sr on the acid soluble material of the samples. All the limestones are relatively pure CaCO3 with Pitkin the purest, 93.4%. Calcium and acid soluble material values varied only 3-5% from the average among the limestones whereas 71-108% variation occurred for Fe, Mn, K and Cr. Other elements showed intermediate variations. Only Fe and Mn are present on the average in the limestones at concentration levels which might lead to contamination of ground water to undesirably high levels. Analyses compare well with the reported average limestone except for acid insoluble elements which were not dissolved in our scheme and lithium (1.5 ppm average vs 20 in reference). Ratios of Sr/Ca and Mg/Ca were similar to reported values for limestones of comparable geologic age. Maxima in the areal variation of these ratios occurred at about the same latitude for three of the formations. The areal variation of Fe/Ca and Mn/Ca was also determined for the four limestone formations. Interelement correlations in the limestones showed: Na, Sr, Li, Fe and Zn contents increased with Mg content; Mn and Cr increased with Fe content. Indications were obtained that detrital and other materials not in the calcite structure can be determined by their relative insolubility in acetic acid compared to hydrochloric acid

Deep lithospheric dynamics beneath the Sierra Nevada during the Mesozoic and Cenozoic as inferred from xenolith petrology

Peridotite xenoliths erupted in late Miocene basalts (~8 Ma) in the central Sierra Nevada sample a lithosphere that is vertically stratified in terms of age and thermal history. The deeper portions (~45-100 km) have asthenospheric osmium isotopic compositons and possess textural and chemical evidence for cooling from >1100° to 700-820°C. The shallower portions (<60 km) have unradiogenic Os isotopic compositions, which yield Proterozoic model ages, and contain orthopyroxenes that record temperatures as low as 670°C in their cores and heating up to 900°C on their rims. These observations suggest that the deeper xenoliths represent fragments of hot asthenosphere that upwelled to intrude and/or underplate the overlying Proterozoic lithosphere represented by the shallower xenoliths. The contrasting thermal histories between the shallow and deep xenoliths suggest that hot asthenosphere and cold lithosphere were suddenly juxtaposed, a feature consistent with the aftermath of rapid lithospheric removal or sudden intrusion of asthenospheric mantle into the lithosphere rather than passive extension. On the basis of regional tectonics and various time constraints, it is possible that this lithospheric removal event was associated with the generation of the Sierra Nevada granitic batholith during Mesozoic subduction of the Farallon plate beneath North America. Pleistocene basalt-hosted xenoliths record a different chapter in the geodynamic history of the Sierras. These xenoliths are relatively fertile, come from depths shallower than 45-60 km, are characterized by asthenospheric Os isotopic compositions, record hot equilibration temperatures (1000°-1100°C), and show no evidence for cooling. The strong contrast in composition and thermal history between the Pleistocene and late Miocene suites indicate that the post-Mesozoic lithospheric mantle, as represented by the latter, was entirely replaced by the former. The hot Pleistocene peridotites may thus represent new lithospheric additions associated with a post-Miocene lithospheric removal event or extension. High elevations, low sub-Moho seismic velocities, and the presence of fast velocity anomalies at 200 km depth may be manifestations of this event. If lithospheric removal occurred in the Mesozoic and Cenozoic, the observations presented here place constraints on the styles of lithospheric removal. In the Mesozoic, the lithospheric mantle was only partially removed, whereas in the Pliocene, the entire lithospheric mantle and probably the mafic lower crust were removed

Parallel structurally-symmetric sparse matrix-vector products on multi-core processors

We consider the problem of developing an efficient multi-threaded implementation of the matrix-vector multiplication algorithm for sparse matrices with structural symmetry. Matrices are stored using the compressed sparse row-column format (CSRC), designed for profiting from the symmetric non-zero pattern observed in global finite element matrices. Unlike classical compressed storage formats, performing the sparse matrix-vector product using the CSRC requires thread-safe access to the destination vector. To avoid race conditions, we have implemented two partitioning strategies. In the first one, each thread allocates an array for storing its contributions, which are later combined in an accumulation step. We analyze how to perform this accumulation in four different ways. The second strategy employs a coloring algorithm for grouping rows that can be concurrently processed by threads. Our results indicate that, although incurring an increase in the working set size, the former approach leads to the best performance improvements for most matrices.Comment: 17 pages, 17 figures, reviewed related work section, fixed typo

Spectral and Rotational Changes in the Isolated Neutron Star RX J0720.4-3125

RX J0720.4-3125 is an isolated neutron star that, uniquely in its class, has shown changes in its thermal X-ray spectrum. We use new spectra taken with Chandra's Low Energy Transmission Grating Spectrometer, as well as archival observations, to try to understand the timescale and nature of these changes. We construct lightcurves, which show both small, slow variations on a timescale of years, and a larger event that occurred more quickly, within half a year. From timing, we find evidence for a `glitch' coincident with this larger event, with a fractional increase in spin frequency of 5x10^{-8}. We compare the `before' and `after' spectra with those from RX J1308.6+2127, an isolated neutron star with similar temperature and magnetic field strength, but with a much stronger absorption feature in its spectrum. We find that the `after' spectrum can be represented remarkably well by the superposition of the `before' spectrum, scaled by two thirds, and the spectrum of RX J1308.6+2127, thus suggesting that the event affected approximately one third of the surface. We speculate the event reflects a change in surface composition caused by, e.g., an accretion episode.Comment: 4 pages, 2 figures, 2 tables, emulateapj format. ApJL, accepte

What Sets the Radial Locations of Warm Debris Disks?

The architectures of debris disks encode the history of planet formation in these systems. Studies of debris disks via their spectral energy distributions (SEDs) have found infrared excesses arising from cold dust, warm dust, or a combination of the two. The cold outer belts of many systems have been imaged, facilitating their study in great detail. Far less is known about the warm components, including the origin of the dust. The regularity of the disk temperatures indicates an underlying structure that may be linked to the water snow line. If the dust is generated from collisions in an exo-asteroid belt, the dust will likely trace the location of the water snow line in the primordial protoplanetary disk where planetesimal growth was enhanced. If instead the warm dust arises from the inward transport from a reservoir of icy material farther out in the system, the dust location is expected to be set by the current snow line. We analyze the SEDs of a large sample of debris disks with warm components. We find that warm components in single-component systems (those without detectable cold components) follow the primordial snow line rather than the current snow line, so they likely arise from exo-asteroid belts. While the locations of many warm components in two-component systems are also consistent with the primordial snow line, there is more diversity among these systems, suggesting additional effects play a role

A Comprehensive Dust Model Applied to the Resolved Beta Pictoris Debris Disk from Optical to Radio Wavelengths

We investigate whether varying the dust composition (described by the optical constants) can solve a persistent problem in debris disk modeling--the inability to fit the thermal emission without over-predicting the scattered light. We model five images of the beta Pictoris disk: two in scattered light from HST/STIS at 0.58 microns and HST/WFC3 at 1.16 microns, and three in thermal emission from Spitzer/MIPS at 24 microns, Herschel/PACS at 70 microns, and ALMA at 870 microns. The WFC3 and MIPS data are published here for the first time. We focus our modeling on the outer part of this disk, consisting of a parent body ring and a halo of small grains. First, we confirm that a model using astronomical silicates cannot simultaneously fit the thermal and scattered light data. Next, we use a simple, generic function for the optical constants to show that varying the dust composition can improve the fit substantially. Finally, we model the dust as a mixture of the most plausible debris constituents: astronomical silicates, water ice, organic refractory material, and vacuum. We achieve a good fit to all datasets with grains composed predominantly of silicates and organics, while ice and vacuum are, at most, present in small amounts. This composition is similar to one derived from previous work on the HR 4796A disk. Our model also fits the thermal SED, scattered light colors, and high-resolution mid-IR data from T-ReCS for this disk. Additionally, we show that sub-blowout grains are a necessary component of the halo.Comment: 23 pages, 20 figures, accepted to Ap