The two main codes for performing -body simulations are Kira and NBODYx. The Kira
integrator is part of the Starlab environment which also includes
stellar evolution codes and other modules for doing
-body simulations [84]. The NBODYx
codes have been developed and improved by Aarseth since the early
1960’s. He has two excellent summmaries of the general properties
and development of the NBODYx codes [4, 3]. A good
summmary of general
-body applications can also be found at
the NEMO website [157]. Most large
-body calculations are done with a special purpose
computer called the GRAPE (GRAvity PipE) invented by
Makino [102]. The most recent
incarnation of the GRAPE is the GRAPE 6, which has a theoretical
peak speed of 100 Tflops [1]. The GRAPE
calculates the accelerations and jerks for the interaction between
each star in the cluster.
The main advantage of -body simulations is
the small number of simplifying assumptions which must be made
concerning the dynamical interactions within the cluster. The
specific stars and trajectories involved in any interactions during
the simulation are known. Therefore, the details for those specific
interactions can be calculated during the simulation. Within the
limits of the numerical errors that accumulate during the
calculation [61], one can have
great confidence in the results of
-body
simulations.
Obviously, one of the main computational
difficulties is simply the CPU cost necessary to integrate the
equations of motion for bodies. This scales roughly
as
[72
]. The other
computational difficulty of the direct
-body method is the
wide range of precision required [82, 72]. Consider the
range of distances, from the size of neutron stars (
) to the size of the globular cluster (
), spanning 14 orders of magnitude. If
the intent of the calculations is to determine the frequency of
interactions with neutron stars, we have to know the relative
position of every star to within 1 part in
. The range of time scales is worse yet. Considering
that the time for a close passage of two neutron stars is on the
order of milliseconds and that the age of a globular cluster is
, we find that the time scales span 20
orders of magnitude. These computational requirements coupled with
hardware limitations mean that the number of bodies which can be
included in a reasonable simulation is no more than
. This is about an order of magnitude less than the
number of stars in a typical globular cluster.
Although one has great confidence in the results
of an -body simulation, these simulations are generally for
systems that are smaller than globular clusters. Consequently,
applications of
-body simulations to globular cluster
dynamics involve scaling lower
simulations up to the
globular cluster regime. Although many processes scale with
, they do so in different ways. Thus, one scales the
results of an
-body simulation based upon the
assumption of a dominant process. However, one can never be certain
that the extrapolation is smooth and that there are no critical
points in the scaling with
. One can also scale other
quantities in the model, so that the quantity of interest is
correctly scaled [126].
An understanding of the nature of the scaling is crucial to
understanding the applicability of
-body simulations to
globular cluster dynamics (see Baumgardt [13] for an
example). The scaling problem is one of the fundamental
shortcomings of the
-body approach.