(Abridged) We perform dissipationless N-body simulations to elucidate the dynamical response of thin disks to bombardment by cold dark matter (CDM) substructure. Our method combines (1) cosmological simulations of the formation of Milky Way (MW)-sized CDM halos to derive the properties of substructure and (2) controlled numerical experiments of consecutive subhalo impacts onto an initially-thin, fully-formed MW type disk galaxy. The present study is the first to account for the evolution of satellite populations over cosmic time in such an investigation of disk structure. We find that accretions of massive subhalos onto the central regions of host halos, where the galactic disks reside, since z~1 should be common. One host halo accretion history is used to initialize the controlled simulations of satellite-disk encounters. We show that these accretion events severely perturb the thin galactic disk and produce a wealth of distinctive dynamical signatures on its structure and kinematics. These include (1) considerable thickening and heating at all radii, with the disk thickness and velocity ellipsoid nearly doubling at the solar radius; (2) prominent flaring associated with an increase in disk thickness greater than a factor of 4 in the disk outskirts; (3) surface density excesses at large radii, beyond ~5 disk scale lengths, resembling those of observed antitruncated disks; (4) lopsidedness at levels similar to those measured in observational samples of disk galaxies; and (5) substantial tilting. The interaction with the most massive subhalo drives the disk response while subsequent bombardment is much less efficient at disturbing the disk. We conclude that substructure-disk encounters of the kind expected in the LCDM paradigm play a significant role in setting the structure of disk galaxies and driving galaxy evolution.
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