4 research outputs found
A universal velocity distribution of relaxed collisionless structures
Several general trends have been identified for equilibrated,
self-gravitating collisionless systems, such as density or anisotropy profiles.
These are integrated quantities which naturally depend on the underlying
velocity distribution function (VDF) of the system. We study this VDF through a
set of numerical simulations, which allow us to extract both the radial and the
tangential VDF. We find that the shape of the VDF is universal, in the sense
that it depends only on two things namely the dispersion (radial or tangential)
and the local slope of the density. Both the radial and the tangential VDF's
are universal for a collection of simulations, including controlled collisions
with very different initial conditions, radial infall simulation, and
structures formed in cosmological simulations.Comment: 13 pages, 6 figures; oversimplified analysis corrected; changed
abstract and conclusions; significantly extended discussio
The Efficiency of Globular Cluster Formation
(Abridged): The total populations of globular cluster systems (GCSs) are
discussed in terms of their connection to the efficiency of globular cluster
formation---the mass fraction of star-forming gas that was able to form bound
stellar clusters rather than isolated stars or unbound associations---in galaxy
halos. Observed variations in GCS specific frequencies (S_N=N_gc/L_gal), both
as a function of galactocentric radius in individual systems and globally
between entire galaxies, are reviewed in this light. It is argued that trends
in S_N do not reflect any real variation in the underlying efficiency of
cluster formation; rather, they result from ignoring the hot gas in many large
ellipticals. This claim is checked and confirmed in each of M87, M49, and NGC
1399, for which existing data are combined to show that the volume density
profile of globular clusters, rho_cl, is directly proportional to the sum of
(rho_gas+rho_stars) at large radii. The constant of proportionality is the same
in each case: epsilon=0.0026 +/- 0.0005 in the mean. This is identified with
the globular cluster formation efficiency. The implication that epsilon might
have had a universal value is supported by data on the GCSs of 97 early-type
galaxies, on the GCS of the Milky Way, and on the ongoing formation of open
clusters. These results have specific implications for some issues in GCS and
galaxy formation, and they should serve as a strong constraint on more general
theories of star and cluster formation.Comment: 36 pages with 11 figures; accepted for publication in The
Astronomical Journa
The velocity anisotropy - density slope relation
One can solve the Jeans equation analytically for equilibrated dark matter
structures, once given two pieces of input from numerical simulations. These
inputs are 1) a connection between phase-space density and radius, and 2) a
connection between velocity anisotropy and density slope, the \alpha-\beta
relation. The first (phase-space density v.s. radius) has already been analysed
through several different simulations, however the second (\alpha-\beta
relation) has not been quantified yet. We perform a large set of numerical
experiments in order to quantify the slope and zero-point of the \alpha-\beta
relation. We find strong indication that the relation is indeed an attractor.
When combined with the assumption of phase-space being a power-law in radius,
this allows us to conclude that equilibrated dark matter structures indeed have
zero central velocity anisotropy \beta_0 = 0, central density slope of \alpha_0
= -0.8, and outer anisotropy of \beta_\infty = 0.5.Comment: 15 pages, 7 figure