A gas bubble trapped in water by an oscillating acoustic field can emit visible bursts of light. Currently the energy focusing of this phenomenon (sonoluminescence) is understood as the converging of a shock toward the interior of the bubble. A complementary but alternative possibility is presented which stems from a linear hydrodynamic instability of the entire gas inside the bubble, leading to the storage of acoustic energy inside the bubble. This mechanism suggests a qualitatively different method for estimating the light intensities from the bubble than those given previously, identifying the hydrodynamic parameters which are important for determining the light intensity. A natural consequence of the theory is the presence of abrupt transitions in the light intensity as a function of experimental parameters, such as those previously observed by Weninger et al. [J. Phys. Chem. 99, 14195 (1995)]. These transitions are where energy input during the bubble collapse exactly balances energy dissipation throughout a cycle.