The interaction rates of dark-matter halos and subhalos , including collisions and mergers , are computed using high-resolution cosmological N -body simulations of the \Lambda CDM model .
Although the number fraction of subhalos of mass > 2 \times 10 ^ { 11 } h ^ { -1 } M _ { \odot } is only \sim 10 \% , we find that the interaction rate of such subhalos is relatively high because they reside in high density environments .
At low redshift , the subhalo collisions dominate the total collision rate , and even at z = 3 they are involved in more than 30 % of all collisions .
About 40 % of the “ major ” mergers ( those of mass ratio > 0.3 ) are between subhalos .
Therefore subhalo interactions must be incorporated in models of structure formation .

We find that the collision rate between halos in physical density units , is \propto ( 1 + z ) ^ { \delta } , with \delta = 3 - 4 , in agreement with earlier simulations and most observational data .

We test previous analytic estimates of the interaction rates of subhalos based on statistical models , which could be very inaccurate because of the small number of subhalos and the variation of conditions within small host halos .
We find that , while such statistical estimates may severely overestimate the rate within hosts < 10 ^ { 13 } h ^ { -1 } M _ { \odot } , typical of high redshifts , they are valid for larger hosts regardless of the number of subhalos in them .
We find the \citeN makino-hut estimate of the subhalo merger rate to be valid for hosts { { { { \mathrel { \mathchoice { \vbox { \offinterlineskip \halign { \cr } $ \displaystyle > $ \cr$% \displaystyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \textstyle > $ \cr$% \textstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptstyle > $ \cr$% \scriptstyle \sim$ } } } { \vbox { \offinterlineskip \halign { \cr } $ \scriptscriptstyle > $% \cr$ \scriptscriptstyle \sim$ } } } } 6 \times 10 ^ { 11 } h ^ { -1 } M _ { \odot } at all redshifts .

The collision rate between subhalos and the central object of their host halo is approximated relatively well using the timescale for dynamical friction in circular orbits .
This approximation fails in \sim 40 \% of the cases , partly because of deviations from the assumption of circular orbits ( especially at low redshift ) and partly because of the invalidity of the assumption that the subhalo mass is negligible ( especially at high redshift ) .