We suggest here a simple improvement. Replace 
with
a new parameter, , and only accept halos that have at least one
particle with at least friends.
The advantage of over is that diffuse, relatively
low-density linked groups
are more likely to be rejected,
while small but compact clumps
may still be accepted as real halos.
The effects of in Model 3 are shown
in the left hand panels of Figure 3,
using 
.
Figure:
As Figure 2, but using the two alternative methods
for rejecting spurious halos as discussed in the text.
On the left are results for , and on the right
are results using the evaporative method. The evaporative
method finds 11 halos, all of which are guaranteed (by construction)
to be gravitationally bound. In contrast the method with
requires much less computation, but finds only 8 halos (not as good
as the evaporative method, but better than the conventional method,
see Figure 2).
In this case all of the spurious halos are rejected,
and more real halos are accepted than for = 30.