Characterization of magneto-convection in sunspots

The Gough-Tayler stability criterion in MURaM sunspot simulations^⋆

¹ Leibniz-Institut für Sonnenphysik (KIS), Schöneckstr. 6, 79104 Freiburg im Breisgau, Germany
e-mail: schmassmann@leibniz-kis.de, nbello@leibniz-kis.de, schliche@leibniz-kis.de
² High Altitude Observatory, NCAR, PO Box 3000 Boulder, CO, 80307 USA
³ Astronomical Institute, Czech Academy of Sciences, Fričova 298, 25165 Ondřejov, Czech Republic

Received: 21 June 2021
Accepted: 13 September 2021

Abstract

Context. Observations have shown that in stable sunspots, the umbral boundary is outlined by a critical value of the vertical magnetic field component. However, the nature of the distinct magnetoconvection regimes in the umbra and penumbra is still unclear.

Aims. We analyse a sunspot simulation in an effort to understand the origin of the convective instabilities giving rise to the penumbral and umbral distinct regimes.

Methods. We applied the criterion from Gough & Tayler (1966, MNRAS, 133, 85), accounting for the stabilising effect of the vertical magnetic field, to investigate the convective instabilities in a MURaM sunspot simulation.

Results. We find: (1) a highly unstable shallow layer right beneath the surface extending all over the simulation box in which convection is triggered by radiative cooling in the photosphere; (2) a deep umbral core (beneath −5 Mm) stabilised against overturning convection that underlies a region with stable background values permeated by slender instabilities coupled to umbral dots; (3) filamentary instabilities below the penumbra nearly parallel to the surface and undulating instabilities coupled to the penumbra which originate in the deep layers. These deep-rooted instabilities result in the vigorous magneto-convection regime characteristic of the penumbra; (4) convective downdrafts in the granulation, penumbra, and umbra develop at about 2 km s⁻¹, 1 km s⁻¹, and 0.1 km s⁻¹, respectively, indicating that the granular regime of convection is more vigorous than the penumbra convection regime, which, in turn, is more vigorous than the close-to-steady umbra; (5) the GT criterion outlines both the sunspot magnetopause and peripatopause, highlighting the tripartite nature of the sub-photospheric layers of magnetohydrodynamic (MHD) sunspot models; and, finally, (6) the Jurčák criterion is the photospheric counterpart of the GT criterion in deep layers.

Conclusions. The GT criterion as a diagnostic tool reveals the tripartite nature of sunspot structure with distinct regimes of magneto-convection in the umbra, penumbra, and granulation operating in realistic MHD simulations.