Classification of String-like Solutions in Dilaton Gravity

The static string-like solutions of the Abelian Higgs model coupled to dilaton gravity are analyzed and compared to the non-dilatonic case. Except for a special coupling between the Higgs Lagrangian and the dilaton, the solutions are flux tubes that generate a non-asymptotically flat geometry. Any point in parameter space corresponds to two branches of solutions with two different asymptotic behaviors. Unlike the non-dilatonic case, where one branch is always asymptotically conic, in the present case the asymptotic behavior changes continuously along each branch.Comment: 15 pages, 6 figures. To be published in Phys. Rev.

Second virial coefficient in one dimension, as a function of asymptotic quantities

A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be obtained from a phase shift formalism, if one includes the contribution of oscillating terms. The result is important in work to follow, for the third virial coefficient, for which a similar formalism is being developed. We examine a number of fine points in the quantum mechanical formalisms.Comment: 7 pages, no figures, submitted to Molecular Physic

Structure and Mass of a Young Globular Cluster in NGC 6946

Using the Wide Field Planetary Camera 2 on board the Hubble Space Telescope, we have imaged a luminous young star cluster in the nearby spiral galaxy NGC 6946. The cluster has an absolute visual magnitude M(V)=-13.2, comparable to the brightest young `super-star clusters' in the Antennae merger galaxy. UBV colors indicate an age of about 15 Myr. The cluster has a compact core (core radius = 1.3 pc), surrounded by an extended envelope. We estimate that the effective radius (Reff) = 13 pc, but this number is uncertain because the outer parts of the cluster profile gradually merge with the general field. Combined with population synthesis models, the luminosity and age of the cluster imply a mass of 8.2x10^5 Msun for a Salpeter IMF extending down to 0.1 Msun, or 5.5x10^5 Msun if the IMF is log-normal below 0.4 Msun. Depending on model assumptions, the central density of the cluster is between 5300 Msun pc^-3 and 17000 Msun pc^-3, comparable to other high-density star forming regions. We also estimate a dynamical mass for the cluster, using high-dispersion spectra from the HIRES spectrograph on the Keck I telescope. The velocity dispersion is 10.0 +/- 2.7 km/s, implying a total cluster mass within 65 pc of (1.7 +/- 0.9) x 10^6 Msun. Comparing the dynamical mass with the mass estimates based on the photometry and population synthesis models, the mass-to-light ratio is at least as high as for a Salpeter IMF extending down to 0.1 Msun, although a turn-over in the IMF at 0.4 Msun is still possible within the errors. The cluster will presumably remain bound, evolving into a globular cluster-like object.Comment: 33 pages, including 10 figures and 3 tables. Accepted for publication in the Astrophysical Journa

Using mixed data in the inverse scattering problem

Consider the fixed-$\ell$ inverse scattering problem. We show that the zeros of the regular solution of the Schr\"odinger equation, $r_{n}(E)$, which are monotonic functions of the energy, determine a unique potential when the domain of the energy is such that the $r_{n}(E)$ range from zero to infinity. This suggests that the use of the mixed data of phase-shifts $\{\delta(\ell_0,k), k \geq k_0 \} \cup \{\delta(\ell,k_0), \ell \geq \ell_0 \}$, for which the zeros of the regular solution are monotonic in both domains, and range from zero to infinity, offers the possibility of determining the potential in a unique way.Comment: 9 pages, 2 figures. Talk given at the Conference of Inverse Quantum Scattering Theory, Hungary, August 200

Young Super Star Clusters in the Starburst of M82: The Catalogue

Recent results from Hubble Space Telescope (HST) have resolved starbursts as collections of compact young stellar clusters. Here we present a photometric catalogue of the young stellar clusters in the nuclear starburst of M82, observed with the HST WFPC2 in Halpha (F656N) and in four optical broad-band filters. We identify 197 young super stellar clusters. The compactness and high density of the sources led us to develop specific techniques to measure their sizes. Strong extinction lanes divide the starburst into five different zones and we provide a catalogue of young super star clusters for each of these. In the catalogue we include relative coordinates, radii, fluxes, luminosities, masses, equivalent widths, extinctions, and other parameters. Extinction values have been derived from the broad-band images. The radii range between 3 and 9 pc, with a mean value of 5.7 +/- 1.4pc, and a stellar mass between 10e4 and 10e6 Mo. The inferred masses and mean separation, comparable to the size of super star clusters, together with their high volume density, provides strong evidence for the key ingredients postulated by Tenorio et al. (2003) as required for the development of a supergalactic wind.Comment: 45 pages, 5 figures, 12 tables. Accepted for publication in ApJ. Added Erratu

Quantum Coherent String States in AdS_3 and SL(2,R) WZWN Model

In this paper we make the connection between semi-classical string quantization and exact conformal field theory quantization of strings in 2+1 Anti de Sitter spacetime. More precisely, considering the WZWN model corresponding to SL(2,R) and its covering group, we construct quantum {\it coherent} string states, which generalize the ordinary coherent states of quantum mechanics, and show that in the classical limit they correspond to oscillating circular strings. After quantization, the spectrum is found to consist of two parts: A continuous spectrum of low mass states (partly tachyonic) fulfilling the standard spin-level condition necessary for unitarity |j|< k/2, and a discrete spectrum of high mass states with asymptotic behaviour m^2\alpha'\propto N^2 (N positive integer). The quantization condition for the high mass states arises from the condition of finite positive norm of the coherent string states, and the result agrees with our previous results obtained using semi-classical quantization. In the k\to\infty limit, all the usual properties of coherent or {\it quasi-classical} states are recovered. It should be stressed that we consider the circular strings only for simplicity and clarity, and that our construction can easily be used for other string configurations too. We also compare our results with those obtained in the recent preprint hep-th/0001053 by Maldacena and Ooguri.Comment: Misprints corrected. Final version to appear in Phys. Rev.

S-matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy