We analyze the effect of dissipation on the shapes of dark matter (DM) halos using high-resolution cosmological gasdynamics simulations of clusters and galaxies in the LCDM cosmology. We find that halos formed in simulations with gas cooling are significantly more spherical than corresponding halos formed in adiabatic simulations. Gas cooling results in an average increase of the principle axis ratios of halos by ~ 0.2-0.4 in the inner regions. The systematic difference decreases slowly with radius but persists almost to the virial radius. We argue that the differences in simulations with and without cooling arise both during periods of quiescent evolution, when gas cools and condenses toward the center, and during major mergers. We perform a series of high-resolution N-body simulations to study the shapes of remnants in major mergers of DM halos and halos with embedded stellar disks. In the DM halo-only mergers, the shape of the remnants depends only on the orbital angular momentum of the encounter and not on the internal structure of the halos. However, significant shape changes in the DM distribution may result if stellar disks are included. In this case the shape of the DM halos is correlated with the morphology of the stellar remnants.
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