Computing Our Universe 1998, Student Project
Why is Angular Momentum interesting
The Simulations We Used
For our project we analyzed the simulation described in the
paper by Ben Moore
et al.
In short, they ran a large scale structure simulation at a low resolution
and picked a halo cluster of interest in that simulation. The particles
of that halo cluster were traced back to their initial conditions to identify
the originating region, which was then resimulated at a higher resolution.
The data we treat
is an attempt to simulate a "Virgo" cluster of galaxies.
Angular Momentum Within A Galaxy Halo
Part of our project was to analyze the angular momentum distribution and
alignment within the halos found in the simulation described above. The
alignment was analyzed measuring the angle between the particle angular
momentum and the halo angular momentum, where each particle was a member of
the halo. A plot of the particle angular momentum
versus the cosine of the angle
between the particle and halo angular momentum vectors
implies that there is no trend towards alignment of particle
and halo angular momentum.
A plot of the distribution of (the absolute value) of the
particle angular momentum
implies that for
this halo there is a trend for the particles to have a certain value for their
angular momentum. Although other halos showed the same trend, few of the
halos in the simulation were analyzed due to time constraints. So from
this quick analysis
it appears that there is no alignment in the halo but a trend towards a
certain value for the particle angular momentum. A more complete
analysis would involve analysing
all the halos in the simulation and as a function of time.
Group Finding in N-Body Simulations
We used two algorithms to find groups in existing N-Body simulations.
The Friends-of-Friends algorithm groups particles
that are within a certain "linking length" of each other. Thus the name, which evokes
the adage "A friend of yours is a friend of mine." The SKID algorithm
uses a more sophisticated method, by finding density gradients in the simulation
and evolving the orbits of particles along these gradients to create groups of
gravitationally bound particles. SKID also performs a procedure called "unbinding"
which removes particles that fall into density wells of a true group but are not
in fact gravitationally bound to the rest of the particles in the group.
Angular Momentum Alignment in Cluster Simulations
We looked for indication of alignment of angular momenta within a cluster simulation.
The net angular momentum of each group, or galaxy halo, was calculated as the sum
of its constituent parts. This vector was then plotted with respect to radial distance
from the center of the cluster. Two types of angular alignment were also investigated.
We investigated the magnitude of the angular momentum
versus the distance from the center of the cluster. The halos at less
than 0.005 (500 kpc) are
located at the very center of the cluster. A trend towards lower angular momentum at the center is seen. Galaxies at the center of the cluster will feel the strongest gravitational force, which will strip away some of the dark matter halo of the galaxy, which contains a significant portion of the galaxy's angular momentum.
We did not find any angular correlation at the galaxy level in the cluster
simulation, as seen in a plot of
cos(theta) versus radial distance, where
theta is the angle between the angular momentum vector and the radial
vector. The plot
at the bottom is a closeup of the inner region of the cluster. Note that the distribution
is fairly isotropic over the range of the polar angle theta. We thus cannot draw any
conclusions about angular alignment as a function of radius.
An "all-sky" type plot was used to picture the
direction component of
the angular momentum vectors for the cluster. In this plot, theta is
plotted against phi times the sine of theta, where the cosine of theta
is the z component of the angular momentum vector, and the tangent
of phi is the ratio of the y and x components. Again
we see a fairly even distibution. A larger sized point near the center of
the plot indicates the total angular momentum of the entire
cluster, found using the Friends-of-Friends algorithm. This probes for
some sort of correlation between the net angular momentum of the
cluster and the halos' individual components. We also examined a
larger simulation of a filament, and
used the same "all-sky" method to look for net
alignment, perhaps along
the axis of the filament, but none is evident in the plot.
Computing Our
Universe, 1998
