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Mixing and transport of metals by gravitational instability-driven turbulence in galactic discs

Metal production in galaxies traces star formation, and is highly concentrated toward the centers of galactic discs. This suggests that galaxies should have inhomogeneous metal distributions with strong radial gradients, but observations of present-day galaxies show only shallow gradients with little azimuthal variation, implying the existence of a redistribution mechanism. We study the role of gravitational instability-driven turbulence as a mixing mechanism by simulating an isolated galactic disc at high resolution, including metal fields treated as passive scalars. Since any cylindrical field can be decomposed into a sum of Fourier-Bessel basis functions, we set up initial metal fields characterized by these functions and study how different modes mix. We find both shear and turbulence contribute to mixing, but the mixing strongly depends on the symmetries of the mode. Non-axisymmetric modes have decay times smaller than the galactic orbital period because shear winds them up to small spatial scales, where they are erased by turbulence. The decay timescales for axisymmetric modes are much greater, though for all but the largest-scale inhomogeneities the mixing timescale is still short enough to erase chemical inhomogeneities over cosmological times. These different timescales provide an explanation for why galaxies retain metallicity gradients while there is almost no variation at a fixed radius. Moreover, the comparatively long timescales required for mixing axisymmetric modes may explain the greater diversity of metallicity gradients observed in high redshift galaxies as compared to local ones: these systems have not yet reached equilibrium between metal production and diffusion.