Tufts/CfA/MIT Cosmology Seminar, at CfA:

                     Tuesday March 11, 1997
                             2:30 pm
                       Pratt Conference Room (NOTE!!!)

                  "Self-Similarity, Mixing, and Violent 
                         Relaxation in N-body Systems"

                          Larry Widrow
                         Queens University

Abstract: 
In the standard cosmological model structure formation occurs when
linear density perturbations become unstable and collapse to form
objects such as galaxies, clusters, and filaments.  While most of our
understanding of how this process occurs comes from numerical
simulation there are certain special situations in which exact
analytic solutions can be obtained, even in the nonlinear regime.  In
the mid 1980's, Fillmore \& Goldreich and Bertschinger found
similarity solutions which describe the evolution of a spherical
density perturbation after collapse.  While these solutions are fully
time-dependent they represent an eternally collapsing system (this is
necessary for their to be similarity solutions) and so do not explain
how systems enter or exit the self-similar phase.

I will begin by formulating the problem of self-similar collapse in a
novel way working directly with the distribution function rather than
particle orbits.  I will then describe numerical simulations of
spherical radial collapse.  Early on the distribution of ``particles''
(i.e., spherical shells) exhibits the characteristics of the
similarity solutions.  However an instability soon develops.  Large
irregular fluctuations lead to mixing between neighboring phase space
streams erasing much of the spiral pattern present at earlier times.

It is not known whether the halo of our Galaxy is truly mixed.  Indeed
fine-grained structure in the distribution function of the dark matter
may effect the outcome of dark matter search experiments.  My talk will
conclude with a discussion of some of these issues.