Top: Total mass of cold rapidly infalling gas within the central 500 pc as a function of time in the control (red), L0.5 (blue), L1.0 (green), and L2.0 (magenta) simulations. We added the mass accreted by the SMBH particle to this total. Solid lines show the mean of the four stochastically different simulations; shading encompasses their full range. Squares mark the times when the mean mass reaches its minimum value. Bottom: Minimum value of cold rapidly infalling gas mass in all simulations (circles) as a function of luminosity, with colours denoting the time when the minimum is reached. The solid red line is the best linear fit between log M and L_AGN of all simulations except the control and L0.1; the dashed lines indicate 95% confidence limits on the line parameters, estimated via bootstrapping.