Motivated by the presence of numerous dark matter clumps in the Milky Way's halo, as expected from the cold dark matter cosmological model, we conduct numerical simulations to examine the heating of the disk. We construct a fairly realistic initial Galaxy model with a stable thin disk. The disk interacts with dark matter clumps for about 5 Gyr. Three physical effects are examined: the mass spectrum of the dark matter clumps, the initial thickness of the galactic disk, and the spatial distribution of the clumps. We find that the massive end of the mass spectrum determines the amount of disk heating. Thicker disks suffer less heating. There is a certain thickness at which the heating due to the interaction with the clumps is saturated. The spatial distribution of the clumps plays an important role in disk heating. We adopt two different spatial distributions of the clumps. The first, which mimics the primordial distribution of the clumps at the epoch of the collapse of the halo, is proportional to the underlying halo density distribution. Recent cosmological simulations, however, yield depletion of the clumps within the extent of the disk in the present-day galaxies. Therefore, we construct the second distribution, which has the same number density of the clumps as the prediction for the cosmological simulations within the disk region. Our numerical simulations show that the first distribution produces considerable disk heating, while the latter does not. These results suggest that at early epochs, or in cases where many clumps are surviving until the present, the disk should have suffered considerable heating in the earlier epochs of their evolution.
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