Most simulations of stellar *N*-body systems are done for the purpose
of observing global evolution or for taking statistics of global
measurements. The microscopic details of which star goes where are rarely
of interest. On this basis, a sufficient condition for simulation
reliability is that all global measurements of interest from the real
system should be reproduced by the simulation. In fact, the assumption
that macroscopic measurements are valid (the *MMV* assumption), even
though the microscopic details are possibly wrong, is a necessary
working assumption for practicing *N*-body researchers. It is
difficult to see how this assumption could be verified conclusively
without an understanding of how the simulation treats microscopic
details (for example, a set of self-consistent simulations may contain
systematic errors such that they are all wrong in the same way), but
most practitioners of stellar *N*-body simulation take the MMV
hypothesis as a working assumption anyway. Heggie [36]
states that this assumption ``is little better than an article of
faith.'' Nonetheless, we are led to the question of what accuracy
level is necessary in order for us to collect undistorted statistics.

When measuring statistical quantities, we must keep in mind that even
if we had a perfect *N*-body simulator, we could only run it a finite
number of times, so there would still be the fundamental noise that
is present in any finite-sized statistical sample. Thus, there is
little use in attempting to measure statistics any more accurately than
this limit dictates
[74, 73, 35, 38]. Also, a
disadvantage of using direct *N*-body simulation to collect statistics
is that only a small amount of the wealth of information in a full
*N*-body simulation is ever extracted.
Thus direct *N*-body simulation
is not a particularly information-efficient method of gathering
statistics [35].

Smith [74] used a 2nd order variable timestep
predictor/corrector with no regularization and double precision
arithmetic to test the hypothesis that some statistics are relatively
insensitive to integration accuracy. The statistics he measured in
globular cluster simulations were the first and third quartic mean
stellar density, energy, and radius, as well
as the median radius. He compared simulations with varying degrees of
accuracy using various statistical tests and found the statistics to
disagree at only the 10% level, *i.e., * there was little evidence to
conclude that the simulations gave different results according to
integration accuracy. He concluded that the statistics taken are
reliable unless energy conservation is grossly violated.
However, Lecar [53] chose to measure different statistics,
and found them to vary widely depending on which machine or
algorithm was used to integrate the problem. This will be further
discussed below.

Fri Dec 27 17:41:39 EST 1996

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