Is the energy density of the ground state of the sine-Gordon model unbounded from below for beta^2 > 8 pi ?

We discuss Coleman's theorem concerning the energy density of the ground state of the sine-Gordon model proved in Phys. Rev. D 11, 2088 (1975). According to this theorem the energy density of the ground state of the sine-Gordon model should be unbounded from below for coupling constants beta^2 > 8 pi. The consequence of this theorem would be the non-existence of the quantum ground state of the sine-Gordon model for beta^2 > 8 pi. We show that the energy density of the ground state in the sine-Gordon model is bounded from below even for beta^2 > 8 pi. This result is discussed in relation to Coleman's theorem (Comm. Math. Phys. 31, 259 (1973)), particle mass spectra and soliton-soliton scattering in the sine-Gordon model.Comment: 22 pages, Latex, no figures, revised according to the version accepted for publication in Journal of Physics

The Changing AGN Population

We investigate how the fraction of broad-line sources in the AGN population changes with X-ray luminosity and redshift. We first construct the rest-frame hard-energy (2-8 keV) X-ray luminosity function (HXLF) at z=0.1-1 using Chandra Lockman Hole-Northwest wide-area data, Chandra Deep Field-North 2 Ms data, other Chandra deep field data, and the ASCA Large Sky Survey data. We find that broad-line AGNs dominate above 3e43 ergs/s and have a mean luminosity of 1.3e44 ergs/s. Type II AGNs can only become an important component of the X-ray population at Seyfert-like X-ray luminosities. We then construct z=0.1-0.5 and z=0.5-1 HXLFs and compare them with both the local HXLF measured from HEAO-1 A2 survey data and the z=1.5-3 HXLF measured from soft-energy (0.5-2 keV) Chandra and ROSAT data. We find that the number density of >1e44 ergs/s sources (quasars) steadily declines with decreasing redshift, while the number density of 1e43-1e44 ergs/s sources peaks at z=0.5-1. Strikingly, however, the number density of broad-line AGNs remains roughly constant with redshift while their average luminosities decline at the lower redshifts, showing another example of cosmic downsizing.Comment: Accepted by The Astrophysical Journal Letters, 5 page

M32+/-1

WFPC-2 images are used to study the central structure of M31, M32, and M33. The dimmer peak, P2, of the M31 double nucleus is centered on the bulge to 0.1", implying that it is the dynamical center of M31. P2 contains a compact source discovered by King et al. (1995) at 1700 A. This source is resolved, with r_{1/2} approx0.2 pc. It dominates the nucleus at 3000 A, and is consistent with late B-early A stars. This probable cluster may consist of young stars and be an older version of the cluster of hot stars at the center of the Milky Way, or it may consist of heavier stars built up from collisions in a possible cold disk of stars orbiting P2. In M32, the central cusp rises into the HST limit with gamma approx0.5, and the central density rho_0>10^7M_sol pc^-3. The V-I and U-V color profiles are flat, and there is no sign of an inner disk, dust, or any other structure. This total lack of features seems at variance with a nominal stellar collision time of 2 X 10^10 yr, which implies that a significant fraction of the light in the central pixel should come from blue stragglers. InM33, the nucleus has an extremely steep gamma=1.49 power-law profile for 0.05"<r<0.2" that becomes shallower as the HST resolution limit is approached. The profile for r<0.04" has either a gamma approx 0.8 cusp or a small core with r_c ~<0.13 pc. The central density is rho_0 > 2 10^6M_sol pc^-3, and the implied relaxation time is only ~3 X 10^6 yr, indicating that the nucleus is highly relaxed. The accompanying short collision time of 7 X 10^9 yr predicts a central blue straggler component quantitatively consistent with the strong V-I and B-R color gradients seen with HST and from the ground.Comment: 44 pages, 22 figures (7 as separate JPEG images), submitted to The Astronomical Journal. Full postscript image available at http://www.noao.edu/noao/staff/lauer/lauer_paper

Computing top intersections in the tautological ring of MgM_g

We derive effective recursion formulae of top intersections in the tautological ring $R^*(M_g)$ of the moduli space of curves of genus $g\geq 2$. As an application, we prove a convolution-type tautological relation in $R^{g-2}(M_g)$.Comment: 18 page

The Finite Field Kakeya Problem

A Besicovitch set in AG(n,q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, and substantially improve the known bounds for n greater than 4.Comment: 13 page

Relativistic Calculations of Coalescing Binary Neutron Stars

We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and quasi-circular orbits of equilibrium solutions. By adding in a radiation reaction treatment, we compute the full evolution of a coalescing binary neutron star system. We find that the amount of mass ejected from the system, much less than a percent, is greatly reduced by the inclusion of relativistic gravitation. The gravity wave energy spectrum shows a clear divergence away from the Newtonian point-mass form, consistent with the form derived from relativistic quasi-equilibrium fluid sequences.Comment: 7 pages, proceedings of the ICGC 2004 meeting, to appear in Praman

Supermassive Black Holes and the Evolution of Galaxies

Black holes, an extreme consequence of the mathematics of General Relativity, have long been suspected of being the prime movers of quasars, which emit more energy than any other objects in the Universe. Recent evidence indicates that supermassive black holes, which are probably quasar remnants, reside at the centers of most galaxies. As our knowledge of the demographics of these relics of a violent earlier Universe improve, we see tantalizing clues that they participated intimately in the formation of galaxies and have strongly influenced their present-day structure.Comment: 20 pages, - This is a near-duplicate of the paper in Nature 395, A14, 1998 (Oct 1

Relativistic neutron star merger simulations with non-zero temperature equations of state I. Variation of binary parameters and equation of state

An extended set of binary neutron star (NS) merger simulations is performed with an approximative conformally flat treatment of general relativity to systematically investigate the influence of the nuclear equation of state (EoS), the neutron star masses, and the NS spin states prior to merging. We employ the two non-zero temperature EoSs of Shen et al. (1998a,b) and Lattimer & Swesty (1991). In addition, we use the cold EoS of Akmal et al. (1998) with a simple ideal-gas-like extension according to Shibata & Taniguchi (2006), and an ideal-gas EoS with parameters fitted to the supernuclear part of the Shen-EoS. We estimate the mass sitting in a dilute high-angular momentum ``torus'' around the future black hole (BH). The dynamics and outcome of the models is found to depend strongly on the EoS and on the binary parameters. Larger torus masses are found for asymmetric systems (up to ~0.3 M_sun for a mass ratio of 0.55), for large initial NSs, and for a NS spin state which corresponds to a larger total angular momentum. We find that the postmerger remnant collapses either immediately or after a short time when employing the soft EoS of Lattimer& Swesty, whereas no sign of post-merging collapse is found within tens of dynamical timescales for all other EoSs used. The typical temperatures in the torus are found to be about 3-10 MeV depending on the strength of the shear motion at the collision interface between the NSs and thus depending on the initial NS spins. About 10^{-3}-10^{-2} M_sun of NS matter become gravitationally unbound during or right after the merging process. This matter consists of a hot/high-entropy component from the collision interface and (only in case of asymmetric systems) of a cool/low-entropy component from the spiral arm tips. (abridged)Comment: 20 pages, 15 figures, accepted for publication in A&A, included changes based on referee comment

D-branes as a Bubbling Calabi-Yau

We prove that the open topological string partition function on a D-brane configuration in a Calabi-Yau manifold X takes the form of a closed topological string partition function on a different Calabi-Yau manifold X_b. This identification shows that the physics of D-branes in an arbitrary background X of topological string theory can be described either by open+closed string theory in X or by closed string theory in X_b. The physical interpretation of the ''bubbling'' Calabi-Yau X_b is as the space obtained by letting the D-branes in X undergo a geometric transition. This implies, in particular, that the partition function of closed topological string theory on certain bubbling Calabi-Yau manifolds are invariants of knots in the three-sphere.Comment: 32 pages; v.2 reference adde