Rejection based on binding energy

  An alternative approach to rejecting spurious halos is to use the actual particle velocities to directly calculate whether putative halos are gravitationally bound. We do this using an ``evaporative'' method which is almost the same as that used in the DENMAX algorithm [3, 6]. In this method each putative halo is considered in isolation, and the total energy of each particle is calculated: its gravitational potential energy in the field of the other particles, plus its kinetic energy relative to the center of mass of the halo. Then the particle with the highest energy is considered. If the particle's total energy is negative then so are all particles with lower energy, so the ensemble is guaranteed to be gravitationally bound, and the halo is accepted. Otherwise the particle's energy is positive -- meaning that it is on an orbit that will eventually remove it from the neighborhood of the halo. The particle is removed from the halo (``evaporated'') and the process is repeated, recalculating the energies of the remaining particles to account for the loss of the removed particle. The process continues until either the halo is accepted, or the number of particles remaining drops below some minimum, in which case the halo is rejected. (In the results included in this paper the minimum number of particles is set to 10.)

The evaporative method can be considered more correct that the simple and methods (in terms of directly addressing our definition of a halo), but it does involve significantly more computation. For each halo containing bodies, evaporation requires operations. To save time, we assume that halos with very many particles (say ) are bound, since this is almost certainly the case. Results using the evaporative method in Model 3 are shown in the right hand panels of Figure 3. The method is very good at discriminating between genuine and spurious halos, and finds eleven genuine halos compared with only eight found by .