Using high resolution cosmological hydrodynamical simulations of Milky Way-massed disk galaxies, we demonstrate that supernovae feedback and tidal stripping lower the central masses of bright (-15 < M_V < -8) satellite galaxies. These simulations resolve high density regions, comparable to giant molecular clouds, where stars form. This resolution allows us to adopt a prescription for H_2 formation and destruction that ties star formation to the presence of shielded, molecular gas. Before infall, supernova feedback from the clumpy, bursty star formation captured by this physically motivated model leads to reduced dark matter (DM) densities and shallower inner density profiles in the massive satellite progenitors (Mvir > 10^9 Msun, Mstar > 10^7 Msun) compared to DM-only simulations. The progenitors of the lower mass satellites are unable to maintain bursty star formation histories, due to both heating at reionization and gas loss from initial star forming events, preserving the steep inner density profile predicted by DM-only simulations. After infall, tidal stripping acts to further reduce the central densities of the luminous satellites, particularly those that enter with cored dark matter halos, increasing the discrepancy in the central masses predicted by baryon+DM and DM-only simulations. We show that DM-only simulations, which neglect the baryonic effects described in this work, produce denser satellites with larger central velocities. We provide a simple correction to the central DM mass predicted for satellites by DM-only simulations. We conclude that DM-only simulations should be used with great caution when interpreting kinematic observations of the Milky Ways dwarf satellites.
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