Table of contents

We develop, implement and test a set of algorithms for estimating N-point correlation functions from pixelized sky maps. These algorithms are slow, in the sense that they do not break the (N) barrier, and yet, they are fast enough for efficient analysis of data sets up to several hundred thousand pixels. The typical application of these methods is Monte Carlo analysis using several thousand realizations, and therefore we organize our programs so that the initialization cost is paid only once. The effective cost is then reduced to a few additions per pixel multiplet (pair, triplet, etc.). Further, the algorithms waste no CPU time on computing undesired geometric configurations, and, finally, the computations are naturally divided into independent parts, allowing for trivial (i.e., optimal) parallelization.

In this paper, we describe the performance and accuracy of the P²M² tree code. The P²M² tree code is a high-accuracy tree code based on the pseudoparticle multipole method (P²M²). P²M² is a method to express multipole expansion using a small number of pseudoparticles. The potential field of physical particles is approximated by the field generated by the pseudoparticles. The primary advantage of the P²M² tree code is that it can use Gravity Pipe (GRAPE) special-purpose computers efficiently for high-accuracy calculations. Although the tree code has been implemented on GRAPE, it could not handle terms of the multipole expansion higher than dipole, since GRAPE can calculate forces from point mass particles only. Thus, the calculation cost grows quickly when high accuracy is required. In the P²M² tree code, the multipole expansion is expressed by particles, and thus we can evaluate high-order terms on GRAPE. We implemented the P²M² tree code on both MDGRAPE-2 and a conventional workstation and measured the performance. The results show that MDGRAPE-2 accelerates the calculation by a factor between 20 (for low accuracy) and 200 (for high accuracy). Even on general-purpose programmable computers, the P²M² tree code offers the advantage that the mathematical formulae, and therefore the actual program, are much simpler than that of the direct implementation of multipole expansion, although the calculation cost becomes somewhat higher.

We present 2.5-30 μm spectra from the Short-Wavelength Spectrometer of the Infrared Space Observatory for a total of 23 sources. The sources include embedded young stellar objects spanning a wide range of mass and luminosity, together with field stars sampling quiescent dark clouds and the diffuse interstellar medium. Expanding on results of previous studies, we use these spectra to investigate ice composition as a function of environment. The spectra reveal an extremely rich set of absorption features attributed to simple molecules in the ices. We discuss the observed properties of these absorption features and review their assignments. Among the species securely identified are H₂O, CO, CO₂, CH₃OH, and CH₄. Likely identified species include OCS, H₂CO, and HCOOH. There is also evidence for NH₃ and OCN^- ice features, but these identifications are more controversial.

     Features that continue to defy identification include the 3.3-3.7 μm "ice band wing" and the bulk of the 6.8 μm feature. In addition, we find evidence for excess absorption at 6.0 μm that cannot be attributed to H₂O ice. We examine the degree of intercorrelation of the 6.8 μm, 4.62 μm ("XCN") and 6.0 μm (excess) features. Our results are consistent with the interpretation of the 6.8 and 4.62 μm features as due to NH and OCN^- ions, respectively, though alternative explanations cannot currently be ruled out. We find that the optical depth correlations are dependent on the profile of the 6.8 μm feature but not on the mass of the YSO nor the ice temperature along the line of sight. We discuss the implications for our current understanding of ice processing. We briefly discuss the composition, origin, and evolution of interstellar ices.

Multizone models of Type I X-ray bursts are presented that use an adaptive nuclear reaction network of unprecedented size, up to 1300 isotopes, for energy generation and include the most recent measurements and estimates of critical nuclear physics. Convection and radiation transport are included in calculations that carefully follow the changing composition in the accreted layer, both during the bursts themselves and in their ashes. Sequences of bursts, up to 15 in one case, are followed for two choices of accretion rate and metallicity, up to the point at which a limit cycle equilibrium is established. For = 1.75 × 10^-9M_⊙ yr^-1 (and = 3.5 × 10^-10M_⊙ yr^-1, for low metallicity), combined hydrogen-helium flashes occur. These bursts have light curves with slow rise times (seconds) and long tails. The rise times, shapes, and tails of these light curves are sensitive to the efficiency of nuclear burning at various waiting points along the rp-process path, and these sensitivities are explored. Each displays "compositional inertia" in that its properties are sensitive to the fact that accretion occurs onto the ashes of previous bursts that contain leftover hydrogen, helium, and CNO nuclei. This acts to reduce the sensitivity of burst properties to metallicity. Only the first anomalous burst in one model produces nuclei as heavy as A = 100. For the present choice of nuclear physics and accretion rates, other bursts and models make chiefly nuclei with A ≈ 64. The amount of carbon remaining after hydrogen-helium bursts is typically ≲1% by mass and decreases further as the ashes are periodically heated by subsequent bursts. For = 3.5 × 10^-10M_⊙ yr^-1 and solar metallicity, bursts are ignited in a hydrogen-free helium layer. At the base of this layer, up to 90% of the helium has already burned to carbon prior to the unstable ignition of the helium shell. These helium-ignited bursts have (1) briefer, brighter light curves with shorter tails, (2) very rapid rise times (<0.1 s), and (3) ashes lighter than the iron group.

We have produced a catalog of 378 Galactic O stars with accurate spectral classifications that is complete for V < 8 but includes many fainter stars. The catalog provides cross-identifications with other sources; coordinates (obtained in most cases from Tycho-2 data); astrometric distances for 24 of the nearest stars; optical (Tycho-2, Johnson, and Strömgren) and NIR photometry; group membership, runaway character, and multiplicity information; and a Web-based version with links to on-line services.

While working on an adaptive mesh refinement (AMR) scheme for divergence-free magnetohydrodynamics (MHD), Balsara discovered a unique strategy for the reconstruction of divergence-free vector fields. Balsara also showed that for one-dimensional variations in flow and field quantities the reconstruction reduces exactly to the total variation diminishing (TVD) reconstruction. In a previous paper by Balsara the innovations were put to use in studying AMR-MHD. While the other consequences of the invention especially as they pertain to numerical scheme design were mentioned, they were not explored in any detail. In this paper we begin such an exploration. We study the problem of divergence-free numerical MHD and show that the work done so far still has four key unresolved issues. We resolve those issues in this paper. It is shown that the magnetic field can be updated in divergence-free fashion with a formulation that is better than the one in Balsara & Spicer. The problem of reconstructing MHD flow variables with spatially second-order accuracy is also studied. Some ideas from weighted essentially non-oscillatory (WENO) reconstruction, as they apply to numerical MHD, are developed. Genuinely multidimensional reconstruction strategies for numerical MHD are also explored. The other goal of this paper is to show that the same well-designed second-order-accurate schemes can be formulated for more complex geometries such as cylindrical and spherical geometry. Being able to do divergence-free reconstruction in those geometries also resolves the problem of doing AMR in those geometries; the appendices contain detailed formulae for the same. The resulting MHD scheme has been implemented in Balsara's RIEMANN framework for parallel, self-adaptive computational astrophysics. The present work also shows that divergence-free reconstruction and the divergence-free time update can be done for numerical MHD on unstructured meshes. As a result, we establish important analogies between MHD on structured meshes and MHD on unstructured meshes because such analogies can guide the design of MHD schemes and AMR-MHD techniques on unstructured meshes. The present paper also lays out the roadmap for designing MHD schemes for structured and unstructured meshes that have better than second-order accuracy in space and time. All the schemes designed here are shown to be second-order-accurate. We also show that the accuracy does not depend on the quality of the Riemann solver. We have compared the numerical dissipation of the unsplit MHD schemes presented here with the dimensionally split MHD schemes that have been used in the past and found the former to be superior. The dissipation does depend on the Riemann solver, but the dependence becomes weaker as the quality of the interpolation is improved. Several stringent test problems are presented to show that the methods work, including problems involving high-velocity flows in low-plasma-β magnetospheric environments. Similar advances can be made in other fields, such as electromagnetics, radiation MHD, and incompressible flow, that rely on a Stokes-law type of update strategy.