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The interstellar medium of the Milky Way and nearby disk galaxies harbourslarge-scale coherent magnetic fields of Microgauss strength, that can beexplained via the action of a mean-field dynamo. As in our previous work, weaim to quantify dynamo effects that are self-consistently emerging in realisticdirect magnetohydrodynamic simulations, but we generalise our approach to thecase of a non-local (non-instantaneous) closure relation, described by aconvolution integral in space (time). To this end, we leverage ourcomprehensive simulation framework for the supernova-regulated turbulentmulti-phase interstellar medium. By introducing spatially (temporally)modulated mean fields, we extend the previously used test-field method to thespectral realm -- providing the Fourier representation of the convolutionkernels. The resulting spectra of the dynamo mean-field coefficients that weobtain broadly match expectations and allow to rigorously constrain the degreeof scale separation in the Galactic dynamo. A surprising result is found forthe diamagnetic pumping term, which increases in amplitude when going tosmaller scales. Our results amount to the most comprehensive description ofdynamo mean-field effects in the Galactic context to date. Surveying therelevant parameter space and quenching behaviour, this will ultimately enablethe development of assumption-free sub-grid prescriptions for otherwiseunresolved global galaxy simulations.

On the spatial and temporal non-locality of dynamo mean-field effects in supersonic interstellar turbulence