Figure 5 shows the halos found by IsoDen in Model 1. The halo finder ran for approximately 20 minutes on a 512 node Paragon at Caltech, and required over 5 gigabytes of memory. This computation would have been prohibitively time-consuming on a uniprocessor system -- assuming we could have found one with sufficient memory!

**Figure:**
The positions of halo centers as found by IsoDen from Model 1,
projected into an arbitrary plane; the box is 250 Mpc on a side.
Only halos with central density at least 178 times the background
density of the system are shown, since lower density halos are
poorly resolved for astrophysical purposes.
There are 43,727 halos shown, and a further 16,631
low density halos were identified.

Figure 6 shows some additional timing results from halo finding on a Paragon.

**Figure:**
Timing results for the IsoDen method. The *time* is the average CPU time
on each processor, *Npart* is the total number of particles, and
*Nproc* the number of processors.
The different point shapes indicate different models
(in particular, different Npart),
from table 1:
stars are model 1,
triangles are model 2,
and
squares are model 3.
The dashed line indicates the slope for constant time independent
of Nproc.
The top panel shows the time for all calculations up to
and including the calculation of the overlaps of preliminary
halos (see Section 5).
The lower panel shows the time for the remaining steps:
the construction of the tree of halos,
the application of noise suppression tests,
and the calculation of genuine halo numbers.

Most of the calculations are shown in the top panel, and show good scaling, which is expected since for these calculations most of the parallelization is done effectively via the tree library. The last few steps of the method, which are more difficult to implement in parallel, are shown separately in the lower panel. Even for these steps the scaling is reasonable.

Sat Sep 27 18:44:36 PDT 1997