  Understanding the numerical dependencies that act on the galactic dynamo is a
crucial step in determining what resolution and what conditions are required to
properly capture the magnetic fields observed in galaxies. Here, we present an
extensive study on the numerical dependencies of the galactic dynamo in
isolated spiral galaxies using smoothed particle magnetohydrodynamics (SPMHD).
We performed 53 isolated spiral galaxy simulations with different initial
setups, feedback, resolution, Jeans floor and dissipation parameters. The
results show a strong mean-field dynamo occurring in the spiral-arm region of
the disk, likely produced by the classical alpha-omega dynamo or the recently
described gravitational instability dynamo. The inclusion of feedback is seen
to work in both a destructive and positive fashion for the amplification
process. Destructive interference for the amplification occurs due to break
down of filament structure in the disk, increase of turbulent diffusion and the
ejection of magnetic flux from the central plane to the circumgalactic medium.
The positive effect of feedback is the increase in vertical motions and the
turbulent fountain flows that develop, showing a high dependence on the
small-scale vertical structure and the numerical dissipation within the galaxy.
Galaxies with an effective dynamo saturate their magnetic energy density at
levels between 10-30% of the thermal energy density. The density averaged
numerical Prandtl number is found to be below unity throughout the galaxy for
all our simulations, with an increasing value with radius. Assuming a turbulent
injection length of 1 kpc, the numerical magnetic Reynolds number are within
the range of $Re_{mag}=10-400$, indicating that some regions are below the
levels required for the small-scale dynamo ($Re_{mag,crit}=30-2700$) to be
active.
