Estimate of blow-up and relaxation time for self-gravitating Brownian particles and bacterial populations

We determine an asymptotic expression of the blow-up time t_coll for self-gravitating Brownian particles or bacterial populations (chemotaxis) close to the critical point. We show that t_coll=t_{*}(eta-eta_c)^{-1/2} with t_{*}=0.91767702..., where eta represents the inverse temperature (for Brownian particles) or the mass (for bacterial colonies), and eta_c is the critical value of eta above which the system blows up. This result is in perfect agreement with the numerical solution of the Smoluchowski-Poisson system. We also determine the asymptotic expression of the relaxation time close but above the critical temperature and derive a large time asymptotic expansion for the density profile exactly at the critical point

Unstable Disk Galaxies. I. Modal Properties

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear eigenvalue problem which is solved using standard numerical methods. I apply the method to the dynamics of a model stellar disk which is embedded in the field of a soft-centered logarithmic potential. The outcome is the full spectrum of eigenfrequencies and their conjugate normal modes for prescribed azimuthal wavenumbers. The results show that the fundamental bar mode is isolated in the frequency space while spiral modes belong to discrete families that bifurcate from the continuous family of van Kampen modes. The population of spiral modes in the bifurcating family increases by cooling the disk and declines by increasing the fraction of dark to luminous matter. It is shown that the variety of unstable modes is controlled by the shape of the dark matter density profile.Comment: Accepted for publication in The Astrophysical Journa

Clustering in gravitating N-body systems

We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of thermodynamic limit can be defined for the transient regime of cluste ring. Structure formation proceeds along two paths: (i) fluid-like evolution of density perturbations at large scales and (ii) shift of the granular (non fluid) properties from small to large scales. The latter mechanism finally dominates at all scales and it is responsible for the self-similar characteristics of the clustering.Comment: 7 pages, 3 figures. Accepted for publication in Europhys. Let

A rigorous implementation of the Jeans--Landau--Teller approximation

Rigorous bounds on the rate of energy exchanges between vibrational and translational degrees of freedom are established in simple classical models of diatomic molecules. The results are in agreement with an elementary approximation introduced by Landau and Teller. The method is perturbative theory ``beyond all orders'', with diagrammatic techniques (tree expansions) to organize and manipulate terms, and look for compensations, like in recent studies on KAM theorem homoclinic splitting.Comment: 23 pages, postscrip

Morphology of Galactic Open Clusters

We analyzed the shapes of Galactic open clusters by the star counting technique with the 2MASS star catalog database. Morphological parameters such as the ellipticity and size have been derived via stellar density distribution, weighed by clustering probability. We find that most star clusters are elongated, even for the youngest star clusters of a few million years old, which are located near to the Galactic disk. The shapes of young star clusters must reflect the conditions in the parental molecular clouds and during the cluster formation process. As an open cluster ages, stellar dynamics cause the inner part of the cluster to circularize, but the overall radius gets larger and the stellar density becomes sparser. We discuss how internal relaxation process competes with Galactic external perturbation during cluster evolution.Comment: 13 pages; 10 pages; accepted Astronomical Journa

The Formation of the First Stars. I. The Primordial Star Forming Cloud

To constrain the nature of the very first stars, we investigate the collapse and fragmentation of primordial, metal-free gas clouds. We explore the physics of primordial star formation by means of three-dimensional simulations of the dark matter and gas components, using smoothed particle hydrodynamics, under a wide range of initial conditions, including the initial spin, the total mass of the halo, the redshift of virialization, the power spectrum of the DM fluctuations, the presence of HD cooling, and the number of particles employed in the simulation. We find characteristic values for the temperature, T ~ a few 100 K, and the density, n ~ 10^3-10^4 cm^-3, characterising the gas at the end of the initial free-fall phase. These values are rather insensitive to the initial conditions. The corresponding Jeans mass is M_J ~ 10^3 M_sun. The existence of these characteristic values has a robust explanation in the microphysics of H2 cooling, connected to the minimum temperature that can be reached with the H2 coolant, and to the critical density at which the transition takes place betweeb levels being populated according to NLTE, and according to LTE. In all cases, the gas dissipatively settles into an irregular, central configuration which has a filamentary and knotty appearance. The fluid regions with the highest densities are the first to undergo runaway collapse due to gravitational instability, and to form clumps with initial masses ~ 10^3 M_sun, close to the characteristic Jeans scale. These results suggest that the first stars might have been quite massive, possibly even very massive with M_star > 100 M_sun.Comment: Minor revisions. 26 pages, including 24 figures and 5 tables. ApJ, in press. To appear in the Dec. 20, 2001 issue (v563

Singular Isothermal Disks: II. Nonaxisymmetric Bifurcations and Equilibria

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M=1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M=2, 3, 4, ... separate bodies. On the basis of our experience in this paper, and the preceding Paper I, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.Comment: 49 pages, 11 figures, LaTeX, needs aaspp4.sty. The Astrophysical Journal, in pres

Measurement of the W-pair Production Cross-section and W Branching Ratios at s\sqrt{s}=205 and 207 GeV

The cross-section for the process e+e-->W+W- was measured with the data sample collected by DELPHI at centre-of-mass energies up to 209 GeV and corresponding to a total integrated luminosity of about 209 pb^-1. The branching ratios of the W decay were also measured; from them the value of |Vcs| was extracted. The results are compared with the most recent calculations in the frame of the Standard Model