Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

In the presence of a strong   m = 2  component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L ₁ or L ₂. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern.     

Kinematic properties and stellar populations of faint early-type galaxies – I. Velocity dispersion measurements of central Coma galaxies

We present velocity dispersion measurements for 69 faint early-type galaxies in the core of the Coma cluster, spanning  −22.0 ≲ M_R ≲−17.5 mag  . We examine the   L –σ  relation for our sample and compare it to that of bright elliptical galaxies (Es) from the literature. The distribution of the the faint early-type galaxies in the   L –σ  plane follows the relation   L ∝σ^2.01±0.36  , which is significantly shallower from   L ∝σ⁴  as defined for the bright Es. While increased rotational support for fainter early-type galaxies could account for some of the difference in slope, we show that it cannot explain it. We also investigate the colour–σ relation for our Coma galaxies. Using the scatter in this relation, we constrain the range of galaxy ages as a function of their formation epoch for different formation scenarios. Assuming a strong coordination in the formation epoch of faint early-type systems in Coma, we find that most had to be formed at least 6 Gyr ago and over a short 1-Gyr period.     

A three-dimensional model of moist convection for the giant planets II: Saturn's water and ammonia moist convective storms

Moist convective storms constitute a key aspect in the global energy budget of the atmospheres of the giant planets. Among them, Saturn is known to develop the largest scale convective storms in the Solar System, the Great White Spots (GWS) which occur rarely and have been detected once every 30 years approximately. On the average, Saturn seems to show much less convective storms than Jupiter with smaller size and reduced frequency and intensity. Here we present detailed simulations of the onset and development of storms at the Equator and mid-latitudes of Saturn. These are the regions where most of the recent convective activity of the planet has been observed. We use a 3D anelastic model with parameterized microphysics (Hueso and Sánchez-Lavega, 2001, Icarus 151, 257) studying the onset and evolution of water and ammonia moist convective storms up to sizes of a few hundred km. Water storms, while more difficult to initiate than in Jupiter, can be very energetic, arriving to the 150 mbar level and developing vertical velocities on the order of 150 m s⁻¹. Ammonia storms develop easier but with a much smaller intensity unless very large abundances of ammonia (10 times solar) are present in Saturn's atmosphere. The Coriolis forces play a major role in the morphology and properties of water based storms.     

Effect of property variation and modelling on convection in a fluid overlying a porous layer

An accurate computational analysis is presented for the onset of thermal convection in a two‐layer system which is comprised of a saturated layer of porous material described by Darcy's law, over which lies a layer of the same saturating fluid. The two‐layer system is heated from below and the upper (fluid) surface is allowed to be fixed or stress free. The onset of convection may have a bi‐modal nature in which convection may be dominated by the porous medium or by the fluid depending on the depths of the relative layers, but this is strongly controlled by material parameters. The effect of variation of relevant fluid and porous material properties is investigated in detail, as is the effect of the interface boundary condition between the fluid and the porous medium. Copyright © 2001 John Wiley & Sons, Ltd.     

Cuspy dark matter haloes and the Galaxy

The microlensing optical depth to Baade's Window constrains the minimum total mass in baryonic matter within the Solar circle to be greater than ∼     , assuming the inner Galaxy is barred with viewing angle ∼20°. From the kinematics of solar neighbourhood stars, the local surface density of dark matter is ∼     . We construct cuspy haloes normalized to the local dark matter density and calculate the circular-speed curve of the halo in the inner Galaxy. This is added in quadrature to the rotation curve provided by the stellar and ISM discs, together with a bar sufficiently massive so that the baryonic matter in the inner Galaxy reproduces the microlensing optical depth. Such models violate the observational constraint provided by the tangent-velocity data in the inner Galaxy (typically at radii     . The high baryonic contribution required by the microlensing is consistent with implications from hydrodynamical modelling and the pattern speed of the Galactic bar. We conclude that the cuspy haloes favoured by the cold dark matter cosmology (and its variants) are inconsistent with the observational data on the Galaxy.