Solar magnetic carpet I: simulation of synthetic magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×1016 - 1019 Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×1016 Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.

Solar magnetic carpet III: coronal modelling of synthetic magnetograms

This article is the third in a series working towards the construction of a realistic, evolving, non-linear force-free coronal-field model for the solar magnetic carpet. Here, we present preliminary results of 3D time-dependent simulations of the small-scale coronal field of the magnetic carpet. Four simulations are considered, each with the same evolving photospheric boundary condition: a 48-hour time series of synthetic magnetograms produced from the model of Meyer et al. ( Solar Phys. 272, 29, 2011). Three simulations include a uniform, overlying coronal magnetic field of differing strength, the fourth simulation includes no overlying field. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. In particular, we study their dependence upon the evolution of the photospheric magnetic field and the strength of the overlying coronal field. We also consider where energy is stored and dissipated within the coronal field. The free magnetic energy built up is found to be more than sufficient to power small-scale, transient phenomena such as nanoflares and X-ray bright points, with the bulk of the free energy found to be stored low down, between 0.5 - 0.8 Mm. The energy dissipated is currently found to be too small to account for the heating of the entire quiet-Sun corona. However, the form and location of energy-dissipation regions qualitatively agree with what is observed on small scales on the Sun. Future MHD modelling using the same synthetic magnetograms may lead to a higher energy release.

The storage and dissipation of magnetic energy in the quiet sun corona determined from SDO/HMI magnetograms

In recent years, higher cadence, higher resolution observations have revealed the quiet-Sun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the small-scale coronal magnetic field exhibits similar complexity. For the first time, the quiet-Sun coronal magnetic field is continuously evolved through a series of non-potential, quasi-static equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain small-scale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex small-scale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona.