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.
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