Dirichlet L-series with real and complex characters and their application to solving double sums

A description of the properties of \L with complex characters is given. By using these, together with the more familiar \L with real characters, it is shown how certain two dimensional lattice sums, which previously could not be put into closed form, may now be expressed in this way.Comment: 21 pages, 1 tabl

Orbital migration and the frequency of giant planet formation

We present a statistical study of the post-formation migration of giant planets in a range of initial disk conditions. For given initial conditions we model the evolution of giant planet orbits under the influence of disk, stellar, and mass loss torques. We determine the mass and semi-major axis distribution of surviving planets after disk dissipation, for various disk masses, lifetimes, viscosities, and initial planet masses. The majority of planets migrate too fast and are destroyed via mass transfer onto the central star. Most surviving planets have relatively large orbital semi-major axes of several AU or larger. We conclude that the extrasolar planets observed to date, particularly those with small semi-major axes, represent only a small fraction (~25% to 33%) of a larger cohort of giant planets around solar-type stars, and many undetected giant planets must exist at large (>1-2 AU) distances from their parent stars. As sensitivity and completion of the observed sample increases with time, this distant majority population of giant planets should be revealed. We find that the current distribution of extrasolar giant planet masses implies that high mass (more than 1-2 Jupiter masses) giant planet formation must be relatively rare. Finally, our simulations imply that the efficiency of giant planet formation must be high: at least 10% and perhaps as many as 80% of solar-type stars possess giant planets during their pre-main sequence phase. These predictions, including those for pre-main sequence stars, are testable with the next generation of ground- and space-based planet detection techniquesComment: 25 pages, 5 figures. Double-space, single-column format to show long equations. Accepted for publication in A&

The Smallest Mass Ratio Young Star Spectroscopic Binaries

Using high resolution near-infrared spectroscopy with the Keck telescope, we have detected the radial velocity signatures of the cool secondary components in four optically identified pre-main-sequence, single-lined spectroscopic binaries. All are weak-lined T Tauri stars with well-defined center of mass velocities. The mass ratio for one young binary, NTTS 160905-1859, is M2/M1 = 0.18+/-0.01, the smallest yet measured dynamically for a pre-main-sequence spectroscopic binary. These new results demonstrate the power of infrared spectroscopy for the dynamical identification of cool secondaries. Visible light spectroscopy, to date, has not revealed any pre-main-sequence secondary stars with masses <0.5 M_sun, while two of the young systems reported here are in that range. We compare our targets with a compilation of the published young double-lined spectroscopic binaries and discuss our unique contribution to this sample.Comment: Accepted for publication in the April, 2002, ApJ; 6 figure

Vacuum energy for the supersymmetric twisted D-brane in constant electromagnetic field

We calculate vacuum energy for twisted SUSY D-brane on toroidal background with constant magnetic or constant electric field. Its behaviour for toroidal D-brane (p=2) in constant electric field shows the presence of stable minimum for twisted versions of the theory. That indicates such a background maybe reasonable groundstate.Comment: LaTeX, 10 page

Dynamical Casimir Effect and Quantum Cosmology

We apply the background field method and the effective action formalism to describe the four-dimensional dynamical Casimir effect. Our picture corresponds to the consideration of quantum cosmology for an expanding FRW universe (the boundary conditions act as a moving mirror) filled by a quantum massless GUT which is conformally invariant. We consider cases in which the static Casimir energy is repulsive and attractive. Inserting the simplest possible inertial term, we find, in the adiabatic (and semiclassical) approximation, the dynamical evolution of the scale factor and the dynamical Casimir stress analytically and numerically (for SU(2) super Yang-Mills theory). Alternative kinetic energy terms are explored in the Appendix.Comment: 14 pages, REVTeX 4, 6 eps figure

Modelling the dynamical evolution of the Bootes dwarf spheroidal galaxy

We investigate a wide range of possible evolutionary histories for the recently discovered Bootes dwarf spheroidal galaxy, a Milky Way satellite. By means of N-body simulations we follow the evolution of possible progenitor galaxies of Bootes for a variety of orbits in the gravitational potential of the Milky Way. The progenitors considered cover the range from dark-matter-free star clusters to massive, dark-matter dominated outcomes of cosmological simulations. For each type of progenitor and orbit we compare the observable properties of the remnant after 10 Gyr with those of Bootes observed today. Our study suggests that the progenitor of Bootes must have been, and remains now, dark matter dominated. In general our models are unable to reproduce the observed high velocity dispersion in Bootes without dark matter. Our models do not support time-dependent tidal effects as a mechanism able to inflate significantly the internal velocity dispersion. As none of our initially spherical models is able to reproduce the elongation of Bootes, our results suggest that the progenitor of Bootes may have had some intrinsic flattening. Although the focus of the present paper is the Bootes dwarf spheroidal, these models may be of general relevance to understanding the structure, stability and dark matter content of all dwarf spheroidal galaxies.Comment: 10 pages, 7 figures, accepted by MNRA