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We develop a simple dynamical model for the evolution of gas in the centres of barred spiral galaxies, using the Milky Way's Central Molecular Zone (CMZ, i.e. the central few hundred pc) as a case study. We show that, in the presence of a galactic bar, gas in a disc in the central regions of a galaxy will be driven inwards by angular momentum transport induced by acoustic instabilities within the bar's inner Lindblad resonance. This transport process drives turbulence within the gas that temporarily keeps it strongly gravitationally stable and prevents the onset of rapid star formation. However, at some point the rotation curve must transition from approximately flat to approximately solid body, and the resulting reduction in shear reduces the transport rates and causes gas to build up, eventually producing a gravitationally unstable region that is subject to rapid and violent star formation. For the observed rotation curve of the Milky Way, the accumulation happens 100 pc from the centre of the Galaxy, in good agreement with the observed location of gas clouds and young star clusters in the CMZ. The characteristic time-scale for gas accumulation and star formation is of the order of 10-20 Myr. We argue that similar phenomena should be ubiquitous in other barred spiral galaxies.
Krumholz et al. (Mon,) studied this question.