The parametrization of gas flows in discs in the Auriga simulations.

We study the radial motions of cold, star-forming gas in the secular evolution phase of a set of 14 magnetohydrodynamical cosmological zoom-in simulations of Milky Way-mass galaxies. We study the radial transport of material within the disc plane in a series of concentric rings. For the gas in each ring at a given time we compute two quantities as a function of time and radius: 1) the radial bulk flow of the gas; and 2) the radial spread of the gas relative to the bulk flow. Averaging the data from all the halos, we find that the radial spread increases with radius in the form of a power law with strong secondary dependencies on the fraction of accreted material and the local radial velocity dispersion of the gas. We find that the bulk motion of gas is well described in the inner disc regions by a radially-independent mean inward flow speed of $-$2.4 km s$^{-1}$. The spread around this value relates to the change in angular momentum of the gas and also the amount of accreted material. These scalings from fully cosmological, MHD simulations of galaxy formation can then be used in semi-analytic models to better parameterise the radial flow of gas in discs.