One of the limitations of IsoDen is that there are several parameters
whose value is somewhat arbitrary: , , and the
``significance'' parameter *n*.

The parameter is particularly important since it determines how much smoothing is done to the particle density field. In particular, IsoDen is unlikely to detect halos which have fewer particles than . Also, the peak densities and overlap densities, which are used in the noise suppression method, will be affected by changing . Notice that only enters the density estimation step. An alternative density estimator might have different parameters, but generally, some free parameter(s) in the density estimator will govern the minimum size of peaks that are discovered in the density field.

The parameter has an effect similar to . If, is too large, then a bona fide peak whose central particle is an -neighbor of a higher density particle will be overlooked by the method. If is too small, then overlaps are not detected at all, and halos are detected in isolation rather than as part of a hierarchy. Our limited experience is that the results are not strongly sensitive to in the range 12 to 24.

The ``significance'' parameter, *n*,
represents a tradeoff between failing to detect small halos and wrongly
``detecting'' spurious halos. Since the test is not actually
a rigorous statistical test, an appropriate value of *n* needs to be
empirically determined, and the best value may depend in a subtle
way on the other parameters. It is even possible that the best value
could vary for different simulations or for different spatial or
temporal regions of a single simulation.
One option could be to use the evaporative method, which is motivated
by the discipline-specific knowledge about the problem, to
determine an appropriate
value of *n* in various circumstances.

Both methods for noise suppression make some assumptions about the
nature of the particle position and velocity distributions in *N*-body
simulations -- e.g. specific sorts of randomness.
While these assumptions are based on experience with the simulation data,
and seem reasonable, it is possible that they
could be violated under some conditions.

The method used by IsoDen to estimate densities has been chosen from a practical point of view as an effective way to deal with resolution in regions of vastly different density. However there are alternative methods available for density estimation which we have not examined, and would could ultimately prove even more effective.

Sat Sep 27 18:44:36 PDT 1997