Source Galerkin Calculations in Scalar Field Theory

In this paper, we extend previous work on scalar $\phi^4$ theory using the Source Galerkin method. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using polynomial expansions for the generating functional $Z$, we calculate propagators and mass-gaps for a number of systems. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. The use of polynomial expansions illustrates in a clear and simple way the ideas of the Source Galerkin method. But at the same time, this choice has serious limitations. Even after exploiting symmetries, the size of calculations become prohibitive except for small systems. The calculations in this paper were made on a workstation of modest power using a fourth order polynomial expansion for lattices of size $8^2$,$4^3$,$2^4$ in $2D$, $3D$, and $4D$. In addition, we present an alternative to the Galerkin procedure that results in sparse matrices to invert.Comment: 31 pages, latex, figures separat

New Numerical Method for Fermion Field Theory

A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using Grassmann polynomial expansions for the generating functional $Z$, we calculate propagators for systems of interacting fermions. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. Because it is not based on a statistical technique, it does not have many of the difficulties often encountered when simulating fermions. Since no determinant is ever calculated, solutions to problems with dynamical fermions are handled more easily. This approach is very flexible, and can be taylored to specific problems based on convenience and computational constraints. We present simple examples to illustrate the method; more general schemes are desirable for more complicated systems.Comment: 24 pages, latex, figures separat

The Demography of Massive Dark Objects in Galaxy Centres

We construct dynamical models for a sample of 36 nearby galaxies with Hubble Space Telescope photometry and ground-based kinematics. The models assume that each galaxy is axisymmetric, with a two-integral distribution function, arbitrary inclination angle, a position-independent stellar mass-to-light ratio Upsilon, and a central massive dark object (MDO) of arbitrary mass M_bh. They provide acceptable fits to 32 of the galaxies for some value of M_bh and Upsilon; the four galaxies that cannot be fit have kinematically decoupled cores. The mass-to-light ratios inferred for the 32 well-fit galaxies are consistent with the fundamental plane correlation Upsilon \propto L^0.2, where L is galaxy luminosity. In all but six galaxies the models require at the 95% confidence level an MDO of mass M_bh ~ 0.006 M_bulge = 0.006 Upsilon L. Five of the six galaxies consistent with M_bh=0 are also consistent with this correlation. The other (NGC 7332) has a much stronger upper limit on M_bh. We consider various parameterizations for the probability distribution describing the correlation of the masses of these MDOs with other galaxy properties. One of the best models can be summarized thus: a fraction f ~0.97 of galaxies have MDOs, whose masses are well described by a Gaussian distribution in log (M_bh/M_bulge) of mean -2.27 and width ~0.07.Comment: 28 pages including 13 figures and 4 tables. Submitted to A

When Is a Bulge Not a Bulge? Inner Disks Masquerading as Bulges in NGC 2787 and NGC 3945

We present a detailed morphological, photometric, and kinematic analysis of two barred S0 galaxies with large, luminous inner disks inside their bars. We show that these structures, in addition to being geometrically disk-like, have exponential profiles (scale lengths $\sim$ 300--500 pc) distinct from the central, non-exponential bulges. We also find them to be kinematically disk-like. The inner disk in NGC 2787 has a luminosity roughly twice that of the bulge; but in NGC 3945, the inner disk is almost ten times more luminous than the bulge, which itself is extremely small (half-light radius $\approx$ 100 pc, in a galaxy with an outer ring of radius $\approx$ 14 kpc) and only $\sim$ 5% of the total luminosity -- a bulge/total ratio much more typical of an Sc galaxy. We estimate that at least 20% of (barred) S0 galaxies may have similar structures, which means that their bulge/disk ratios may be significantly overestimated. These inner disks dominate the central light of their galaxies; they are at least an order of magnitude larger than typical ``nuclear disks'' found in ellipticals and early-type spirals. Consequently, they must affect the dynamics of the bars in which they reside.Comment: LaTeX, 37 pages, 14 EPS figures. To appear in The Astrophysical Journal (November 10, 2003 issue). Version with full-resolution figures available at http://www.iac.es/galeria/erwin/research

Evidence for the Direct Detection of the Thermal Spectrum of the Non-Transiting Hot Gas Giant HD 88133 b

We target the thermal emission spectrum of the non-transiting gas giant HD 88133 b with high-resolution near-infrared spectroscopy, by treating the planet and its host star as a spectroscopic binary. For sufficiently deep summed flux observations of the star and planet across multiple epochs, it is possible to resolve the signal of the hot gas giant's atmosphere compared to the brighter stellar spectrum, at a level consistent with the aggregate shot noise of the full data set. To do this, we first perform a principal component analysis to remove the contribution of the Earth's atmosphere to the observed spectra. Then, we use a cross-correlation analysis to tease out the spectra of the host star and HD 88133 b to determine its orbit and identify key sources of atmospheric opacity. In total, six epochs of Keck NIRSPEC L band observations and three epochs of Keck NIRSPEC K band observations of the HD 88133 system were obtained. Based on an analysis of the maximum likelihood curves calculated from the multi-epoch cross correlation of the full data set with two atmospheric models, we report the direct detection of the emission spectrum of the non-transiting exoplanet HD 88133 b and measure a radial projection of the Keplerian orbital velocity of 40 $\pm$ 15 km/s, a true mass of 1.02$^{+0.61}_{-0.28}M_J$, a nearly face-on orbital inclination of 15${^{+6}_{-5}}^{\circ}$, and an atmosphere opacity structure at high dispersion dominated by water vapor. This, combined with eleven years of radial velocity measurements of the system, provides the most up-to-date ephemeris for HD 88133.Comment: 9 pages, 6 figures; accepted for publication in Ap

Superheating fields of superconductors: Asymptotic analysis and numerical results

The superheated Meissner state in type-I superconductors is studied both analytically and numerically within the framework of Ginzburg-Landau theory. Using the method of matched asymptotic expansions we have developed a systematic expansion for the solutions of the Ginzburg-Landau equations in the limit of small $\kappa$, and have determined the maximum superheating field $H_{\rm sh}$ for the existence of the metastable, superheated Meissner state as an expansion in powers of $\kappa^{1/2}$. Our numerical solutions of these equations agree quite well with the asymptotic solutions for $\kappa<0.5$. The same asymptotic methods are also used to study the stability of the solutions, as well as a modified version of the Ginzburg-Landau equations which incorporates nonlocal electrodynamics. Finally, we compare our numerical results for the superheating field for large-$\kappa$ against recent asymptotic results for large-$\kappa$, and again find a close agreement. Our results demonstrate the efficacy of the method of matched asymptotic expansions for dealing with problems in inhomogeneous superconductivity involving boundary layers.Comment: 14 pages, 8 uuencoded figures, Revtex 3.

Pseudobulges in the Disk Galaxies NGC 7690 and NGC 4593

We present Ks-band surface photometry of NGC 7690 (Hubble type Sab) and NGC 4593 (SBb). We find that, in both galaxies, a major part of the "bulge" is as flat as the disk and has approximately the same color as the inner disk. In other words, the "bulges" of these galaxies have disk-like properties. We conclude that these are examples of "pseudobulges" -- that is, products of secular dynamical evolution. Nonaxisymmetries such as bars and oval disks transport disk gas toward the center. There, star formation builds dense stellar components that look like -- and often are mistaken for -- merger-built bulges but that were constructed slowly out of disk material. These pseudobulges can most easily be recognized when, as in the present galaxies, they retain disk-like properties. NGC 7690 and NGC 4593 therefore contribute to the growing evidence that secular processes help to shape galaxies. NGC 4593 contains a nuclear ring of dust that is morphologically similar to nuclear rings of star formation that are seen in many barred and oval galaxies. The nuclear dust ring is connected to nearly radial dust lanes in the galaxy's bar. Such dust lanes are a signature of gas inflow. We suggest that gas is currently accumulating in the dust ring and hypothesize that the gas ring will starburst in the future. The observations of NGC 4593 therefore suggest that major starburst events that contribute to pseudobulge growth can be episodic.Comment: 10 pages, 3 Postscript figures; requires emulateapj.cls, apjfonts.sty, and psfig.sty; accepted for publication in ApJ; for a version with full resolution figures, see http://chandra.as.utexas.edu/~kormendy/n7690.pd

The ACS Virgo Cluster Survey. VII. Resolving the Connection Between Globular Clusters and Ultra-Compact Dwarf Galaxies

We investigate the connection between globular clusters and ultra-compact dwarf galaxies (UCDs) by examining the properties of several compact objects associated with M87, all of which were previously classified as globular clusters. Combining imaging from the Hubble Space Telescope with ground-based Keck spectroscopy, we find two objects to have half-light radii, velocity dispersions and mass-to-light ratios that are consistent with the predictions of population synthesis models for old, metal-rich, luminous globular clusters. Three other objects are much larger, with half-light radii of approximately 20pc, and have V-band mass-to-light ratios in the range 6-9. These objects, which we consider to be UCDs, resemble the nuclei of nucleated dwarf elliptical galaxies in Virgo, having similar mass-to-light ratios, luminosities and colors. These UCDs are found to obey the extrapolated scaling relations of galaxies more closely than those of Galactic globular clusters. There appears to be a transition between the two types of stellar systems at a mass of about two million solar masses. If the UCDs are gravitationally bound, then we suggest that the presence of dark matter is the fundamental property distinguishing globular clusters from UCDs. More than half of the UCD candidates uncovered in the ACS Virgo Cluster Survey are associated with a single galaxy -- M87 -- which suggests that proximity to the Virgo center may be of critical importance for the formation of these objects. These results show that distinguishing bonafide UCDs from bright globular clusters requires a careful analysis of their detailed structural and dynamical properties, particularly their mass-to-light ratios. (ABRIDGED)Comment: 56 pages, with 17 postscript figures. Accepted for publication in ApJ. Also available at: http://www.physics.rutgers.edu/~pcote/acs/publications.htm