Recurrence Formulas for Fully Exponentially Correlated Four-Body Wavefunctions

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (>= -1) of all the interparticle distances r_ij, multiplied by an exponential containing an arbitrary linear combination of all the r_ij. These integrals are generalizations of those encountered using Hylleraas basis functions, and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill, plus some easily evaluated three-body "boundary" integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.Comment: 10 pages, no figures, accepted by Phys. Rev. A (January 2009

A Color-Magnitude Diagram for a Globular Cluster In the Giant Elliptical Galaxy NGC 5128

The Hubble Space Telescope has been used to obtain WFPC2 (V,I) photometry for a large sample of stars in the outer halo of the giant elliptical NGC 5128 (d = 4 Mpc). The globular cluster N5128-C44, at the center of the Planetary Camera field, is well enough resolved to permit the construction of a color-magnitude diagram (CMD) for it which covers the brightest two magnitudes of the giant branch. The CMD is consistent with that of a normal old, moderately low-metallicity ([Fe/H] = -1.30 globular cluster, distinctly more metal-poor than most of the field halo stars at the same projected location (which average [Fe/H] ~ -0.5). This is the most distant globular cluster in which direct color-magnitude photometry has been achieved to date, and the first one belonging to a giant E galaxy.Comment: 12 pages, LaTeX, including 5 postscript figures; submitted to Astronomical Journa

Spine-sheath layer radiative interplay in subparsec-scale jets and the TeV emission from M87

Simple one-zone homogeneous synchrotron self-Compton models have severe difficulties in explaining the TeV emission observed in the radiogalaxy M87. Also the site of the TeV emission region is uncertain: it could be the unresolved jet close to the nucleus, analogously to what proposed for blazars, or an active knot, called HST-1, tens of parsec away. We explore the possibility that the TeV emission of M87 is produced in the misaligned subpc scale jet. We base our modelling on a structured jet, with a fast spine surrounded by a slower layer. In this context the main site responsible for the emission of the TeV radiation is the layer, while the (debeamed) spine accounts for the emission from the radio to the GeV band: therefore we expect a more complex correlation with the TeV component than that expected in one-zone scenarios, in which both components are produced by the same region. Observed from small angles, the spine would dominate the emission, with an overall Spectral Energy Distribution close to those of BL Lac objects with a synchrotron peak located at low energy (LBLs).Comment: 5 pages, 2 figures. Accepted for publication in MNRAS Letter

Structural parameters for globular clusters in M31 and generalizations for the fundamental plane

The structures of globular clusters (GCs) reflect their dynamical states and past histories. High-resolution imaging allows the exploration of morphologies of clusters in other galaxies. Surface brightness profiles from new Hubble Space Telescope observations of 34 globular clusters in M31 are presented, together with fits of several different structural models to each cluster. M31 clusters appear to be adequately fit by standard King models, and do not obviously require alternate descriptions with relatively stronger halos, such as are needed to fit many GCs in other nearby galaxies. The derived structural parameters are combined with corrected versions of those measured in an earlier survey to construct a comprehensive catalog of structural and dynamical parameters for M31 GCs with a sample size similar to that for the Milky Way. Clusters in M31, the Milky Way, Magellanic Clouds, Fornax dwarf spheroidal and NGC 5128 define a very tight fundamental plane with identical slopes. The combined evidence for these widely different galaxies strongly reinforces the view that old globular clusters have near-universal structural properties regardless of host environment.Comment: AJ in press; 59 pages including 16 figure