Speaker
Description
There are many observations of sunspots, but few attempts at sunspot simulations. Rempel (2012) presented realistic magneto-hydrodynamic (MHD) sunspot simulations. Jurčák et al. (2020) showed that the magnetic field of such simulations differs from observations; in particular, the $B_\mathrm{ver}$ at the umbral boundary is too low.
Using the MURaM MHD code and a potential field top boundary condition, we simulated a set of sunspots with different box widths and potential initial fields. The fields were defined by setting $B_\mathrm{ver}$ at the bottom boundary to a Gaussian with different parameters and subtracting uniform vertical fields. If the field subtracted is strong enough, this corresponds to embedding the spot into a region with opposite polarity flux.
Initial field strengths at the bottom of less than 160kG result in much too narrow penumbrae. Those extreme field strengths at 7.4Mm beneath the photosphere decay quickly, to below 45kG in the time range we studied. In general, the penumbra-to-spot ratios in potential field simulations are smaller than those of observed sunspots. Simulations with fluxes $>10^{22}\,$Mx in the Gaussian produce unrealistic strong magnetic fields in the umbra. Widening the box and decreasing the overall flux through the box has minimal effect on the dynamics and magnetic field distribution within the spot, but allows control over the average vertical field outside the spot. The potential field simulations do not show a pure Evershed (radially outward) flow. The $B_0=160\,$kG and $F_\mathrm{Gauss}=10^{22}\,$Mx simulations show bi-directional flows: inflows in the inner penumbra and outflows in the outer penumbra, as observed in high-resolution observations of penumbra formation by García-Rivas et al. (2024).
The potential field initialized simulations provide an excellent scenario for the little-investigated processes of penumbra formation.
