SOLARNET Conference: The Many Scales of the Magnetic Sun

More than 20 years ago most photospheric MHD simulations focused primarily on small patches of granulation with moderate numerical resolution. Over the past 2 decades advances in computing infrastructure have enabled photospheric MHD simulations to cover most magnetic environments from quiet Sun to active Sun. In this talk I review these recent developments and focus primarily on simulations that cover the extreme ends of the spectrum: (1) Small-scale dynamo simulations of quiet Sun magnetism and (2) Simulations of active region scales. (1) Recent research (observations and modeling) supports the view that the origin of small-scale magnetism is mostly due to a small-scale dynamo that operates independently from the large-scale dynamo responsible for the solar cycle. Recent simulations have shown that the saturation field strength and structure of the resulting magnetic field in the photosphere depend critically on the contributions from deep and shallow recirculation within the strongly stratified convection zone. Therefore, the small-scale dynamo is not restricted to the photosphere and involves a wide range of scales. Recent research suggests that small-scale magnetic fields may play a critical role for convection zone dynamics. Outstanding questions concern the role of the magnetic Prandtl number, which will require in the future simulations with better resolution (< 1km) to be addressed properly. (2) Active region-scale simulations have provided a comprehensive picture of how sunspot fine structure from umbral dots to penumbral filaments arises from overturning magneto convection. Larger-scale simulations have addressed the connection to the moat region and studied sunspot decay. However, the presence of penumbra in simulations is found to be critically dependent on boundary conditions and the subsurface structure of sunspots. To date none of these simulations have provided penumbra with the “robustness” solar observations indicate, and no simulations of flux emergence have led to the formation of a penumbra as part of the spot formation process (although certain aspects are captured). Ultimately progress may require a more comprehensive simulations flux emergence and active region formation that are fully coupled to large-scale dynamo simulations.