Numerical experiments of the emergence of magnetic flux from the uppermost layers of the solar interior to the photosphere and its further eruption into the low atmosphere and corona are carried out. We use idealized models for the initial stratification and magnetic field distribution below the photosphere similar to those used for multidimensional flux emergence experiments in the literature. The energy equation is adiabatic except for the inclusion of ohmic and viscous dissipation terms, which, however, become important only at interfaces and reconnection sites. Three-dimensional experiments for the eruption of magnetic flux both into an unmagnetized corona and into a corona with a preexisting ambient horizontal field are presented. The shocks preceding the rising plasma present the classical structure of nonlinear Lamb waves. The expansion of the matter when rising into the atmosphere takes place preferentially in the horizontal directions: a flattened (or oval) low plasma-β ball ensues, in which the field lines describe loops in the corona with increasing inclination away from the vertical as one goes toward the sides of the structure. Magnetograms and velocity field distributions on horizontal planes are presented simultaneously for the solar interior and various levels in the atmosphere. Since the background pressure and density drop over many orders of magnitude with increasing height, the adiabatic expansion of the rising plasma yields very low temperatures. To avoid this, the entropy of the rising fluid elements should be increased to the high values of the original atmosphere via heating mechanisms not included in the present numerical experiments. The eruption of magnetic flux into a corona with a preexisting magnetic field pointing in the horizontal direction yields a clear case of essentially three-dimensional reconnection when the upcoming and ambient field systems come into contact. The coronal ambient field is chosen at time t = 0 perpendicular to the direction of the tube axis and thus, given the twist of the magnetic tube, almost anti-parallel to the field lines at the upper boundary of the rising plasma ball. A thin, dome-shaped current layer is formed at the interface between the two flux systems, in which ohmic dissipation and heating are taking place. The reconnection proceeds by merging successive layers on both sides of the reconnection site; however, this occurs not only at the cusp of the interface, but, also, gradually along its sides in the direction transverse to the ambient magnetic field. The topology of the magnetic field in the atmosphere is thereby modified: the reconnected field lines typically are part of the flanks of the tube below the photosphere but then join the ambient field system in the corona and reach the boundaries of the domain as horizontal field lines.

/pdf/emergence-of-magnetic-flux-from-the-convection-zone-into-the-1dztltn565.pdf

Emergence of magnetic flux from the convection zone into the corona

The magnetic field of the Sun is the underlying cause of the many diverse phenomena combined under the heading of solar activity. Here we describe the magnetic field as it threads its way from the bottom of the convection zone, where it is built up by the solar dynamo, to the solar surface, where it manifests itself in the form of sunspots and faculae, and beyond into the outer solar atmosphere and, finally, into the heliosphere. On the way it transports energy from the surface and the subsurface layers into the solar corona, where it heats the gas and accelerates the solar wind.

https://iopscience.iop.org/article/10.1088/0034-4885/69/3/R02/pdf

The solar magnetic field

The evolution of active regions (AR) from their emergence through their long decay process is of fundamental importance in solar physics. Since large-scale flux is generated by the deep-seated dynamo, the observed characteristics of flux emergence and that of the subsequent decay provide vital clues as well as boundary conditions for dynamo models. Throughout their evolution, ARs are centres of magnetic activity, with the level and type of activity phenomena being dependent on the evolutionary stage of the AR. As new flux emerges into a pre-existing magnetic environment, its evolution leads to re-configuration of small-and large-scale magnetic connectivities. The decay process of ARs spreads the once-concentrated magnetic flux over an ever-increasing area. Though most of the flux disappears through small-scale cancellation processes, it is the remnant of large-scale AR fields that is able to reverse the polarity of the poles and build up new polar fields. In this Living Review the emphasis is put on what we have learned from observations, which is put in the context of modelling and simulation efforts when interpreting them. For another, modelling-focused Living Review on the sub-surface evolution and emergence of magnetic flux see Fan (2009). In this first version we focus on the evolution of dominantly bipolar ARs.

/pdf/evolution-of-active-regions-46suhkd8xu.pdf

Evolution of Active Regions

A dynamo model of the Babcock-Leighton type having the following features is studied. The toroidal fieldB

 φ
 is generated in a thin layer (the GL), located at the lower solar convection zone, by a shear in the angular velocity acting on the poloidal fieldB

 p
 (= ∇ × [0, 0,A

 φ
 ].) If, in this layer, and for a certain value of the polar angle,θ, |B

 O
 | exceeds a critical field,B

 cr
 , then the eruption of a flux tube occurs. This flux tube, which is assumed to rise radially, generates, when reaching the surface, a bipolar magnetic region (BMR) with fluxes Φ
 p
 and Φ
 f
 for the preceding and following spot respectively. For the purpose of the numerical calculations this BMR is replaced by its equivalent axisymmetrical magnetic ring doublet. The ensemble of these eruptions acts as the source term for the poloidal field. This field, generated in the surface layers, reaches the lower solar convection by transport due to meridional motions and by diffusion. The meridional motions are the superpositions of a one-cell velocity field that rises at the equator and sinks at the poles and of a two-cell circulation that rises at the equator and poles and sinks at mid latitudes. The toroidal field andA

 O
 were expanded in Legendre polynomials, and the coupled partial differential equations (int andr; time and radial coordinate) satisfied by the coefficients in these expansions were solved by a finite difference method. In the expansions, Legendre polynomials up to order thirty were included. In spite of an exhaustive search no solutions were found with Φ
 p
 = −Φ
 f
 . The solutions presented in this paper were obtained with Φp = −0.5 Φ
 f
 . In this case, the northern and southern hemisphere are not entirely decoupled since lines of force join both hemispheres. Most of the solutions found were periodic. For the one-cell meridional flow described above and for a purely radial shear in the GL (the angular velocity increasing inwards) the dynamo wave propagates from the pole towards the equator. The new cycle starts at the poles while the old cycle is still present in the equatorial regions.

On a Babcock-Leighton dynamo model with a deep-seated generating layer for the toroidal magnetic field

Recent observational studies suggest that active region magnetic flux emerges in a twisted state and that the sense of twist depends weakly on solar hemisphere. We propose that this twist is imparted to the flux through its interaction with turbulent velocities in the convection zone. This process, designated the Σ-effect, operates on isolated magnetic flux tubes subjected to buffeting by turbulence with a nonvanishing kinetic helicity ${b u}$ --> ∇ × ${b u}$ -->. The Σ-effect leads to twist of the same sense inferred from observation and opposite to that predicted by the α-effect. A series of numerical calculations are performed to estimate the magnitude of the Σ-effect in the solar convective zone. The results compare favorably with observations in both mean value and statistical dispersion. We find a further relationship with total magnetic flux that can be tested in future observations. The model also predicts that twist is uncorrelated with the tilt angle of the active region.

Flux-Tube Twist Resulting from Helical Turbulence: The Σ-Effect

The buoyant rise of a magnetic flux loop arising from a single perturbed segment of a toroidal flux ring lying slightly beneath the base of the convection zone is studied by way of numerical simulations. We have considered flux loop evolution assuming both solid-body rotation, and differential rotation consistent with recent results from helioseismology. Our major results are presented, and we offer some speculations on the decay of active regions, based on the results of our studies. We speculate that as plasma in the tube attempts to establish hydrostatic equilibrium along the field lines after the flux emergence has taken place, the tube field strength at some intermediate depths below the surface becomes sufficiently small at the surface portions of the tube (which have cooled and undergone convective collapse) become dynamically disconnected from those portions near the base of the convection zone. The surface proportions of the emerged flux tubes are then transported by motions near the photosphere, such as supergranular convection and meridional flow.

Dynamics of emerging active region flux loops

The evolution of the unstable solar atmosphere into the nonlinear phase, in response to various perturbations, is followed. The initial dynamic evolution of the atmosphere follows the predictions of linear stability analysis. In the nonlinear phase, rapid changes are confined to the transition region; these changes are manifested as a propagation of the transition region through the plasma, i.e., chromospheric evaporation or condensation. Global evolution therefore proceeds on the coronal conductive time scale. The rate of propagation of the transition region is determined by the imbalance between the energy supplied by thermal conduction from the corona and radiative cooling within the transition region itself. Flow velocities in the lower corona during evaporation or condensation are, in the cases studied, of order 3 km/s. The observed dynamic evolution is consistent with the existence of relatively long-lived coronal loops whose brightnesses vary on the evaporative time scale.

A. N. Mcclymont

Papers

Dynamics of emerging active region flux loops

Flare loop radiative hydrodynamics. IV - Dynamic evolution of unstable semiempirical loop models