  Previous models of galactic disk heating in interactions invoke restrictive
assumptions not necessarily valid in modern LCDM contexts: that satellites and
orbits are rigid and circular, with slow decay over many orbital times from
dynamical friction. This leads to a linear scaling of disk heating with
satellite mass: disk heights and velocity dispersions scale ~M_sat/M_disk. In
turn, observed disk thicknesses present strong constraints on merger histories:
the implication for the Milky Way is that <5% of its mass could come from
mergers since z~2, in conflict with cosmological predictions. More
realistically, satellites merge on nearly radial orbits, and once near the
disk, resonant interactions efficiently remove angular momentum while tidal
effects strip mass, leading to rapid merger/destruction in a couple of
free-fall plunges. Under these conditions the proper heating efficiency is
non-linear in mass ratio, ~(M_sat/M_disk)^2. We derive the scaling of disk
scale heights and velocity dispersions as a function of mass ratio and disk gas
content in this regime, and show this accurately describes the results of
simulations with proper 'live' halos and disks. Under realistic circumstances,
disk heating in minor mergers is suppressed by an order of magnitude relative
to expectations of previous models. We show that the Milky Way disk could have
absorbed ~5-10 1:10 mass-ratio mergers since z=2, in agreement with
cosmological models. These distinctions lead to dramatic differences in which
mass ratios are most important for disk heating and in the isophotal shapes of
disk+bulge systems.
