Smith [73] and Heggie [38] have noted
that *n* simulations each with *N*/*n* particles is much less expensive
than 1 simulation with *N* particles, and is also completely trivial to
parallelize. Such sets of simulations can also give better statistics
based on the larger sample size, as long as it is known how to scale
the statistics from smaller simulations to larger ones. Unfortunately,
this scaling is non-trivial because different processes scale differently
with *N*, so it is possible that they interact differently in current
simulations than they do in real clusters [38]. Again,
we are led to the conclusion that increasing *N* is the most desirable
way of increasing the reliability of *N*-body simulations.

Smith [73] continued his previous study ([74])
to ascertain the effects of different numbers of particles on
statistical measurements. He measured density profiles and binary star
formation rates for clusters with *N*=8,16,32,64 and found that,
although the scaled statistics for *N*=8 differed substantially from
those with higher *N*, the statistics for *N*=16 and higher agreed
quite well. Furthermore, the number of binaries formed scaled
as , consistent with a theoretical estimate
of . He didn't measure information on escapers, since
escapes happen sufficiently rarely that *N*=64 doesn't provide enough
of a sample. He concluded that better statistics can be taken with
many small simulations than with 1 large one.

Although this method is less effective at modelling some processes that
really do need a large *N*, such as gravothermal effects, it may be
reliable enough to study processes such as core collapse rates, escape
rates, binary star formation rates, density profiles, and gradients of
velocity dispersion with radius [38]. However, this
does not mean that we can learn everything there is to learn about
these statistics by running millions of simulations with *N*=64,
because discreteness noise is still a factor. What these results say
is that at any given time, if is the largest simulation one
is currently capable of running, it may be more productive to run 100
simulations with than a single simulation with
.

Fri Dec 27 17:41:39 EST 1996

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