Isolated and non-isolated dark matter halos and the NFW profile

We compare the conclusions reached using the coarse-graining technique employed by Henriksen (2004) for a one degree of freedom (per particle) collisionless system, to those presented in a paper by Binney (2004) based on an exact one degree of freedom model. We find agreement in detail but in addition we show that the isolated 1D system is self-similar and therefore unrelaxed. Fine graining of this system recovers much less prominent wave-like structure than in a spherically symmetric isotropic 3D system. The rate of central flattening is also reduced in the 1D system. We take this to be evidence that relaxation of collisionless systems proceeds ultimately by way of short wavelength Landau damping. N-body systems, both real and simulated, can be trapped in an incompletely relaxed state because of a break in the cascade of energy to small scales. This may be due to the rapid dissipation of the small scale oscillations in an isolated system, to the existence of conserved quantities such as angular momentum, or to the failure in simulations to resolve sub-Jeans length scales. Such a partially relaxed state appears to be the NFW state, and is to be expected especially in young systems. The NFW core is shown to be isolated. In non-isolated systems continuing coarse-grained relaxation should be towards a density core in solid body rotation.Comment: 14 pages, MNRAS, submitted 21 June 200

Distribution of Gamma-Ray Bursts in Halo Neutron Star-Comet Models

The motions of comets and neutron stars have been integrated over five billion years in the Galactic potential to determine a gamma-ray burst distribution, presuming that bursts are the result of interactions between these two families of objects. The comets originate in two distinct populations - one from ejection by stars in the Galactic disk, and the other from ejection by stars in globular clusters. No choice of the free parameters resulted in agreement with both the isotropy data and the $\log(N>F) - \log(F)$ data.Comment: 4 pages LaTex and two style files, tarred, compressed, and uuencoded. One postscript figure. To appear in Astrophysics and Space Science as part of the proceedings of the 29th ESLAB Symposium 'Toward the Source of Gamma-Ray Bursts' held in Noordwijk, 1995. A postscript version can be found at http://astro.queensu.ca/~mark/preprints.htm

On Stationary, Self-Similar Distributions of a Collisionless, Self-Gravitating, Gas

We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution functions where the mass density and gravitational potential are strict power laws in $r$, the distance from the symmetry point. We treat as special cases, systems built from purely radial orbits and systems that are isotropic in velocity space. We then discuss systems with arbitrary velocity space anisotropy finding a new and very general class of distribution functions. These distributions may prove useful in modelling galaxies. Distribution functions in cylindrical and planar geometries are also discussed. Finally, we study spatially spheroidal systems that again exhibit strict power-law behaviour for the density and potential and find results in agreement with results published recently.Comment: 23 pages, regular Tex, figures in separate .uu file to follo

Cored Apple Bipolarity : A Global Instability to Convection in Radial Accretion?

We propose that the prevalence of bipolarity in Young Stellar Objects is due to the fine tuning that is required for spherical accretion of an ambient medium onto a central node.It is shown that there are two steady modes that are more likely than radial accretion, each of which is associated with a hyperbolic central point in the meridional stream lines, and consequently with either an equatorial inflow and an axial ejection or vice versa. In each case the stream lines pass through a thick accretion torus, which is better thought of as a standing pressure wave rather than as a relatively inert Keplerian structure.We base our arguments on a simple analytic example,which is topologi cally generic,wherein each bipolarmode is created by the rebound of accreting matter under the action of the thermal,magnetic,turbulent and centrifugal pressures created in the flow. In both bipolar modes the presence of non-zero angular momentum implies axial regions wherein the pressure is first reduced below the value at infinity and then becomes negative, where the solution fails because rotating material can not enter this region without suction.The model thus has empty stems where the activity of the central source must dominate.So the basic engine of the bipolar flow discussed here is simply the rebound of freely falling material from a thick pressure disc into an axial low pressure region.The low mass,high velocity outflow must be produced in this region by an additional mechanism. This is reminiscent of the cored apple structure observed recently in the very young bipolar source VLA 1623.Comment: PostScript, 10 page

Relaxing and Virializing a Dark Matter Halo

Navarro, Frenk, and White have suggested that the density profiles of simulated dark matter halos have a ``universal'' shape so that a given halo can be characterized by a single free parameter which fixes its mass. In this paper, we revisit the spherical infall model in the hope of recognizing in detail the existence and origin of any such universality. A system of particles is followed from linear perturbation, through first shell crossing, then through an accretion or infall phase, and finally to virialization. During the accretion phase, the system relaxes through a combination of phase mixing, phase space instability, and moderate violent relation. It is driven quickly, by the flow of mass through its surface, toward self-similar evolution. The self-similar solution plays its usual role of intermediate attractor and can be recognized from a virial-type theorem in scaled variables and from our numerical simulations. The transition to final equilibrium state once infall has ceased is relatively gentle, an observation which leads to an approximate form for the distribution function of the final system. The infall phase fixes the density profile in intermediate regions of the halo to be close to r^{-2}. We make contact with the standard hierarchical clustering scenario and explain how modifications of the self-similar infall model might lead to density profiles in agreement with those found in numerical simulations.Comment: 26 pages, Latex, plus 11 figure