Stability, instability, and "backward" transport in stratified fluids
Astrophysical Journal 534:1 PART 1 (2000) 420-427
Abstract:
The stratification of entropy and the stratification of angular momentum are closely analogous. The analogy has been developed for a number of different problems in the fluid literature, but its consequences for the behavior of turbulent accretion disks are less appreciated. Of particular interest is the behavior of disks in which angular momentum transport is controlled by convection, and heat transport by dynamical turbulence. In both instances we argue that the transport must proceed "backward" relative to the sense one would expect from a simple enhanced diffusion approach. Reversed angular momentum transport has already been seen in numerical simulations; contragradient thermal diffusion should be amenable to numerical verification as well. These arguments also bear on the observed nonlinear local stability of isolated Keplerian disks: locally generated turbulence in such a disk would require simultaneous inward and outward angular momentum transport, which is, of course, impossible. We also describe a diffusive instability that is the entropy analogue to the magnetorotational instability. It affects thermally stratified layers when Coulomb conduction and a weak magnetic field are present. The plasma must be sufficiently dilute that heat is channeled only along field lines. The criterion for convective instability goes from one of upwardly decreasing entropy to one of upwardly decreasing temperature. The instability remains formally viable if radiative heat transport is also present, but the equilibrium is much more unstable if Coulomb transport is dominant. In that case, the maximum growth rate is of the order of the inverse sound crossing time, independent of the thermal conductivity. The indifference of the growth rate to the conduction coefficient, its simple dynamical scaling, and the replacement in the stability criterion of a conserved quantity (entropy) gradient by a free energy (temperature) gradient are properties similar to those exhibited by the magnetorotational instability.Microlensing and Galactic Structure
ArXiv astro-ph/0004362 (2000)
Abstract:
Because we know little about the Galactic force-field away from the plane, the Galactic mass distribution is very ill-determined. I show that a microlensing survey of galaxies closer than 50 Mpc would enable us to map in three dimensions the Galactic density of stellar mass, which should be strictly less than the total mass density. A lower limit can be placed on the stellar mass needed at RThe Age of the Solar Neighbourhood
ArXiv astro-ph/0003479 (2000)
Abstract:
High-quality Hipparcos data for a complete sample of nearly 12000 main-sequence and subgiant stars, together with Padua isochrones, are used to constrain the star-formation history of the solar neigbourhood and the processes that stochastically accelerate disk stars. The velocity dispersion of a coeval group of stars is found to increase with time from ~8 kms at birth as t^{0.33}. In the fits, the slope of the IMF near 1 Msun proves to be degenerate with the rate at which the star-formation rate declines. If the slope of the IMF is to lie near Salpeter's value, -2.35, the star-formation rate has to be very nearly constant. The age of the solar neighbourhood is found to be 11.2+/-0.75 Gyr with remarkably little sensitivity to variations in the assumed metallicity distribution of old disk stars. This age is only a Gyr younger than the age of the oldest globular clusters when the same isochrones and distance scale are employed. It is compatible with current indications of the redshift of luminous galaxy formation only if there is a large cosmological constant. A younger age is formally excluded because it provides a poor fit to the number density of red stars. Since this density is subject to a significantly uncertain selection function, ages as low as 9 Gyr are plausible even though they lie outside our formal error bars.Is Galactic Structure Compatible with Microlensing Data?
ArXiv astro-ph/0003330 (2000)
Abstract:
We generalize to elliptical models the argument of Kuijken (1997), which connects the microlensing optical depth towards the Galactic bulge to the Galactic rotation curve. When applied to the latest value from the MACHO collaboration for the optical depth for microlensing of bulge sources, the argument implies that the Galactic bar cannot plausibly reconcile the measured values of the optical depth, the rotation curve and the local mass density. Either there is a problem with the interpretation of the microlensing data, or our line of sight to the Galactic centre is highly atypical in that it passes through a massive structure that wraps only a small distance around the Galactic centre.Dark Matter Problem in Disk Galaxies
ArXiv astro-ph/0003199 (2000)