We study the thermalization of excitations generated by spontaneous emission events for cold bosons in an optical lattice. Computing the dynamics described by the many-body master equation, we characterize equilibration timescales in different parameter regimes. For simple observables, we find regimes in which the system relaxes rapidly to values in agreement with a thermal distribution, and others where thermalization does not occur on typical experimental timescales. Because spontaneous emissions lead effectively to a local quantum quench, this behavior is strongly dependent on the low-energy spectrum of the Hamiltonian, and undergoes a qualitative change at the Mott Insulator-superfluid transition point. These results have important implications for the understanding of thermalization after localized quenches in isolated quantum gases, as well as the characterization of heating in experiments.
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