Working Group 1: Solar Flux Origins, Emergence and Eruptions

Comprehensive models of sunspot formation

Sunspots are the centerpieces of solar magnetic activity; however, their origin has remained one of the large unsolved mysteries in solar physics. High resolution observation in the solar photosphere strongly suggest a process in which magnetic field produced in the deeper convection zone is transported towards the surface and forms a pair of sunspots with opposite polarity when the magnetic field threads through the photosphere. Modeling this process has remained a challenge, mostly due to the strong million-fold density drop from the base of the convection zone into the photosphere. As a consequence, models of sunspot formation could never address the complete picture: Global models that address the formation of magnetic field through a dynamo process do not include the surface layers where we actually observe sunspots; local models of the surface layers do not go deep enough to address the origin of magnetic flux bundles that give rise to sunspot formation in the photosphere.

Schematic highlighting the coupling of the global FSAM dynamo model and the local MURaM radiative MHD simulation covering the upper convection zone and photosphere of the sun. A rising magnetic field bundle produced by 3D convection and rotational shear in the global FSAM dynamo simulations is imposed as lower boundary condition for the local MURaM radiative MHD simulation. The magnetic field continues to rise into the photosphere, where it eventually forms a group of sunspots. The strong magnetic field concentrations in the photosphere exceeding 3000 Gauss have a dark appearance in intensity and show asymmetries similar to those of sunspots observed on the sun.

Over the past few years both classes of models have seen substantial improvements: Global models advanced to the point where they self-consistently produce a significant amount of strong flux bundles that rise upward and are good candidates for those fields that could form sunspot groups; local models of the photosphere and upper convection zone evolved to the point where they can simulate regions with an extent of typical solar active regions over a time span of several days to weeks. These improvements set the stage for the next big step forward that was taken by HAO scientists and published in 2017 in the Astrophysical Journal: Two models, a global FSAM solar dynamo simulation and a local MURaM radiative MHD simulation of the photosphere and upper convection zone, were coupled and lead to a comprehensive model of sunspot formation that captures the full vertical extent of the solar convection zone.

The model demonstrated for the first time that the flux bundles that are produced in global dynamo simulations indeed produce sunspots in the photosphere after rising through the last 30,000 km of solar convection zone that were missing in previous models, but comprise actually most of the million-fold density drop of the convection zone. While the rising magnetic field initially spreads out and weakens substantially, amplification in the near surface layers, where radiative cooling is important, does lead to re-amplification and formation of sunspots with a field strength exceeding 3000 Gauss and a dark appearance in synthetic intensity images. Furthermore, it was found that large scale flows that are present in the upper layers of the global FSAM simulation play a critical role in further shaping the appearance of the sunspot group in terms of asymmetries with respect to the direction of solar rotation. The sunspots that lead in the direction of rotation form above a coherent downflow lane that leads to stronger and deeper rooted magnetic field and also a faster formation of the leading sunspots. The trailing sunspots form later and remain less coherent and consequently decay more rapidly. This asymmetry is a well-known observed property of solar active regions.

Coupling the FSAM and MURaM code is a first step towards comprehensive models of flux emergence that help to understand not only how sunspots form in the photosphere, but also how they energize the overlying solar corona and trigger flares and coronal mass ejections. An extension of the flux emergence models into the solar corona is work in progress.