Radiative Magnetohydrodynamic Simulation of Sunspot Structure

Abstract

Results of a 3D MHD simulation of a sunspot with a photospheric size of about 20 Mm are presented. The simulation has been carried out with the MURaM code, which includes a realistic equation of state with partial ionization and radiative transfer along many ray directions. The largely relaxed state of the sunspot shows a division in a central dark umbral region with bright dots and a penumbra showing bright filaments of about 2 to 3 Mm length with central dark lanes. By a process similar to the formation of umbral dots, the penumbral filaments result from magneto-convection in the form of upflow plumes, which become elongated by the presence of an inclined magnetic field: the upflow is deflected in the outward direction while the magnetic field is weakened and becomes almost horizontal in the upper part of the plume near the level of optical depth unity. A dark lane forms owing to the piling up of matter near the cusp-shaped top of the rising plume that leads to an upward bulging of the surfaces of constant optical depth. The simulated penumbral structure corresponds well to the observationally inferred interlocking-comb structure of the magnetic field with Evershed outflows along dark-laned filaments with nearly horizontal magnetic field and overturning perpendicular ('twisting') motion, which are embedded in a background of stronger and less inclined field. Photospheric spectral lines are formed at the very top and somewhat above the upflow plumes, so that they do not fully sense the strong flow as well as the large field inclination and significant field strength reduction in the upper part of the plume structures.

Solar Weather Event Modelling and Prediction

“…Advanced models have been developed for specific drivers and are quite promising as significant tiles in the development of effective predictive models suitable for space weather purposes, but in most cases they have been still science models and not operational models for space weather forecasting due to intrinsic limitations in the physics and to the highly demanding computing power required. In this context, we mention, e.g., the radiative magnetohydrodynamic 3D simulation of sunspot structure by Rempel et al (2009) and the analysis of sunspots observations and simulations from small-scale inhomogeneities towards a global theory carried out by Schlichenmaier (2009) where he concludes that the understanding of the smallscales will be the key to understanding the global structure and the large-scale stability of sunspots. Difficulties and prospects in understanding the coronal magnetic field are reviewed by Cargill (2009), who considered the key observational inputs expected from new generation instruments like the Advanced Technology Solar Telescope (ATST; Keil et al 2009) and the Frequency Agile Solar Radiotelescope (FASR; Bastian 2003), and states that global magnetic field models can provide information on the field in the corona, and towards the Earth through the solar wind, but major challenges for such modelling are the incorporation of small-scale plasma effects.…”

Properties of sunspot umbrae observed in cycle 24

“…Magnetohydrodynamic simulations of emerging flux tubes (Fan 2008), active regions (Cheung et al 2010), pores (Cameron et al 2007), and sunspots (Rempel et al 2009) became available recently. The flux emergence simulations model the rise of a twisted flux tube in the convection zone, its expansion, and fragments near the solar surface.…”

Solar surface magnetoconvection simulations: A brief review of solar dermatology

“…Similarly pores, which are the smallest features clearly associated with the solar cycle have been studied and compared to observations [18] . More recently sunspots have been tackled, including sunspot umbrae and umbral dots [19] , light bridges [20] , and penumbral filaments [21,22] . Figure 5 is an image from the simulation by Rempel et al [22] , showing a sunspot umbra including umbral dots, a rudimentary penumbra as well as the quietSun.…”

“…More recently sunspots have been tackled, including sunspot umbrae and umbral dots [19] , light bridges [20] , and penumbral filaments [21,22] . Figure 5 is an image from the simulation by Rempel et al [22] , showing a sunspot umbra including umbral dots, a rudimentary penumbra as well as the quietSun. More recent simulations are even more impressive and include complete spots.…”

“…An intensity image from a calculation designed to study penumbral filaments [22] . The simulation encompasses quiet Sun, penumbral and umbral regions.…”