Numerical simulations of sunspot decay: On the penumbra-evershed flow-moat flow connection

Abstract

We present a series of high-resolution sunspot simulations that cover a timespan of up to 100 hr. The simulation domain extends about 18 Mm in depth beneath the photosphere and 98 Mm horizontally. We use open boundary conditions that do not maintain the initial field structure against decay driven by convective motions. We consider two setups: a sunspot simulation with penumbra, and a "naked-spot" simulation in which we removed the penumbra after 20 hr through a change in the magnetic top boundary condition. While the sunspot has an Evershed outflow of 3-4 km s-1, the naked spot is surrounded by an inflow of 1-2 km s-1 in close proximity. However, both spots are surrounded by an outflow on larger scales with a few 100 m s-1 flow speed in the photosphere. While the sunspot has an almost constant magnetic flux content for the simulated timespan of three to four days, the naked spot decays steadily at a rate of 1021 Mx day-1. A region with reduced downflow filling factor, which is more extended for the sunspot, surrounds both spots. The absence of downflows perturbs the upflow/downflow mass flux balance and leads to a large-scale radially overturning flow system; the photospheric component of this flow is the observable moat flow. The reduction of the downflow filling factor also inhibits the submergence of magnetic field in the proximity of the spots, which stabilizes them against decay. While this effect is present for both spots, it is more pronounced for the sunspot and explains the almost stationary magnetic flux content.