  We perform the first self-consistent measurement of the rate of interactions
between stellar tidal streams created by disrupting satellites and dark
subhalos in a cosmological simulation of a Milky-Way-mass galaxy. Using a
retagged version of the Aquarius A dark-matter-only simulation, we selected 18
streams of tagged star particles that appear thin at the present day and
followed them from the point their progenitors accrete onto the main halo,
recording in each snapshot the characteristics of all dark-matter subhalos
passing within several distance thresholds of any tagged star particle in each
stream. We considered distance thresholds corresponding to constant impact
parameters (1, 2, and 5 kpc), as well as those proportional to the region of
influence of each subhalo (one and two times its half-mass radius $r_{1/2}$).
We then measured the age and present-day, phase-unwrapped length of each stream
in order to compute the interaction rate in different mass bins and for
different thresholds, and compared these to analytic predictions from the
literature. We measure a median rate of $1.5^{+3.0}_{-1.1}\
(9.1^{+17.5}_{-7.1},\ 61.8^{+211}_{-40.6})$ interactions within 1 (2, 5) kpc of
the stream per 10 kpc of stream length per 10 Gyr. Resolution effects (both
time and particle number) affect these estimated rates by lowering them.
