The transport of gas towards the centre of galaxies is critical for black hole feeding and, indirectly, it can control active galactic nucleus (AGN) feedback. We have quantified the molecular gas inflow in the central R<1kpc of M51 to be 1 Msun/yr, using a new gravitational torque map and the molecular gas traced by the PdBI Arcsecond Whirlpool Survey (PAWS). The nuclear stellar bar is responsible for this gas inflow. We have also used torque profiles to estimate the location of dynamical resonances, suggesting a corotation for the bar at R~20, and a corotation for the spiral at R~100. We demonstrate how important it is to correct 3.6um images for dust emission in order to compute gravitational torques, and we carefully examine further sources of uncertainty. Our observational measurement of gas inflow can be compared with nuclear molecular outflow rates and provide useful constraints for numerical simulations.
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