Roberto Lionello

Magnetohydrodynamic modeling of the global solar corona

A three-dimensional magnetohydrodynamic model of the global solar corona is described. The model uses observed photospheric magnetic fields as a boundary condition. A version of the model with a polytropic energy equation is used to interpret solar observations, including eclipse images of the corona, Ulysses spacecraft measurements of the interplanetary magnetic field, and coronal hole boundaries from Kitt Peak He 10 830 A maps and extreme ultraviolet images from the Solar Heliospheric Observatory. Observed magnetic fields are used as a boundary condition to model the evolution of the solar corona during the period February 1997–March 1998. A model with an improved energy equation and Alfven waves that is better able to model the solar wind is also presented.

A Comparison between Global Solar Magnetohydrodynamic and Potential Field Source Surface Model Results

The large-scale, steady-state magnetic field configuration of the solar corona is typically computed using boundary conditions derived from photospheric observations. Two approaches are typically used: (1) potential field source surface (PFSS) models, and (2) the magnetohydrodynamic (MHD) models. The former have the advantage that they are simple to develop and implement, require relatively modest computer resources, and can resolve structure on scales beyond those that can be handled by current MHD models. However, they have been criticized because their basic assumptions are seldom met. Moreover, PFSS models cannot directly incorporate time-dependent phenomena, such as magnetic reconnection, and do not include plasma or its effects. In this study, we assess how well PFSS models can reproduce the large-scale magnetic structure of the corona by making detailed comparisons with MHD solutions at different phases in the solar activity cycle. In particular, we (1) compute the shape of the source surface as inferred from the MHD solutions to assess deviations from sphericity, (2) compare the coronal hole boundaries as determined from the two models, and (3) estimate the effects of nonpotentiality. Our results demonstrate that PFSS solutions often closely match MHD results for configurations based on untwisted coronal fields (i.e., when driven by line-of-sight magnetograms). It remains an open question whether MHD solutions will differ more substantially from PFSS solutions when vector magnetograms are used as boundary conditions. This will be addressed in the near future when vector data from SOLIS, the Solar Dynamics Observatory, and Solar-B become incorporated into the MHD models.

Multispectral Emission of the Sun during the First Whole Sun Month: Magnetohydrodynamic Simulations

We demonstrate that a three-dimensional magnetohydrodynamic (MHD) simulation of the corona can model its global plasma density and temperature structure with sufficient accuracy to reproduce many of the multispectral properties of the corona observed in extreme ultraviolet (EUV) and X-ray emission. The key ingredient to this new type of global MHD model is the inclusion of energy transport processes (coronal heating, anisotropic thermal conduction, and radiative losses) in the energy equation. The calculation of these processes has previously been confined to one-dimensional loop models, idealized two-dimensional computations, and three-dimensional active region models. We refer to this as the thermodynamic MHD model, and we apply it to the time period of Carrington rotation 1913 (1996 August 22 to September 18). The form of the coronal heating term strongly affects the plasma density and temperature of the solutions. We perform our calculation for three different empirical heating models: (1) a heating function exponentially decreasing in radius; (2) the model of Schrijver et al.; and (3) a model reproducing the heating properties of the quiet Sun and active regions. We produce synthetic emission images from the density and temperature calculated with these three heating functions and quantitatively compare them with observations from EUV Imaging Telescope on the Solar and Heliospheric Observatory and the soft X-ray telescope on Yohkoh. Although none of the heating models provide a perfect match, heating models 2 and 3 provide a reasonable match to the observations.

A Model for the Sources of the Slow Solar Wind

Models for the origin of the slow solar wind must account for two seemingly contradictory observations: the slow wind has the composition of the closed-field corona, implying that it originates from the continuous opening and closing of flux at the boundary between open and closed field. On the other hand, the slow wind also has large angular width, up to ~60?, suggesting that its source extends far from the open-closed boundary. We propose a model that can explain both observations. The key idea is that the source of the slow wind at the Sun is a network of narrow (possibly singular) open-field corridors that map to a web of separatrices and quasi-separatrix layers in the heliosphere. We compute analytically the topology of an open-field corridor and show that it produces a quasi-separatrix layer in the heliosphere that extends to angles far from the heliospheric current sheet. We then use an MHD code and MDI/SOHO observations of the photospheric magnetic field to calculate numerically, with high spatial resolution, the quasi-steady solar wind, and magnetic field for a time period preceding the 2008 August 1 total solar eclipse. Our numerical results imply that, at least for this time period, a web of separatrices (which we term an S-web) forms with sufficient density and extent in the heliosphere to account for the observed properties of the slow wind. We discuss the implications of our S-web model for the structure and dynamics of the corona and heliosphere and propose further tests of the model.

Flux cancellation and coronal mass ejections

Time dependent magnetohydrodynamic computations of the flux cancellation mechanism are presented. Previous authors have discussed this mechanism as a possible cause for the formation of prominences and the trigger for prominence eruptions and coronal mass ejections (CMEs). This paper shows that flux cancellation in an energized two-and-one-half-dimensional helmet streamer configuration first leads to the formation of stable flux rope structures. When a critical threshold of flux reduction is exceeded, the configuration erupts violently. Significant amounts of stored magnetic energy are released through magnetic reconnection. The ejected flux rope propagates out into the solar wind and forms an interplanetary shock wave. A similar eruption occurs for a three-dimensional calculation where the ends of the flux rope field lines are anchored to the Sun. The flux cancellation mechanism unifies the processes of prominence formation, prominence eruption, and CME initiation, and thus provides an attractive hypothesis for explaining the cause of these dynamic events.Time dependent magnetohydrodynamic computations of the flux cancellation mechanism are presented. Previous authors have discussed this mechanism as a possible cause for the formation of prominences and the trigger for prominence eruptions and coronal mass ejections (CMEs). This paper shows that flux cancellation in an energized two-and-one-half-dimensional helmet streamer configuration first leads to the formation of stable flux rope structures. When a critical threshold of flux reduction is exceeded, the configuration erupts violently. Significant amounts of stored magnetic energy are released through magnetic reconnection. The ejected flux rope propagates out into the solar wind and forms an interplanetary shock wave. A similar eruption occurs for a three-dimensional calculation where the ends of the flux rope field lines are anchored to the Sun. The flux cancellation mechanism unifies the processes of prominence formation, prominence eruption, and CME initiation, and thus provides an attractive hypothe...

Magnetohydrodynamic modeling of prominence formation within a helmet streamer

We present a 2.5-D axisymmetric MHD model to self-consistently describe the formation of a stable prominence that supports cool, dense material in the lower corona. The upper chromosphere and transition region are included in the calculation. Reducing the magnetic flux along the neutral line of a sheared coronal arcade forms a magnetic field configuration with a flux rope topology. The prominence forms when dense chromospheric material is brought up and condenses in the corona. The prominence sits at the base of a helmet streamer structure. The dense material is supported against gravity in the dips of the magnetic field lines in the flux rope. Further reduction in magnetic flux leads to an eruption of the prominence, ejecting material into the solar wind.

Calculating the Thermal Structure of Solar Active Regions in Three Dimensions

We describe a technique to obtain the temperature and density distribution in an active region for a specified plasma heating model. The technique can be applied in general to determine the magnetic field and thermal structure self-consistently. For simplicity, we illustrate the application of this technique in the limit of small plasma β, in which the plasma dynamics decouples from that of the magnetic field, a good approximation in active regions, in which the magnetic field is strong. We select a particular active region, observed in 1996 August, to demonstrate the methodology. We apply the technique to a force-free magnetic field with a plasma heating model in which the volumetric coronal heating rate is directly proportional to the strength of the local magnetic field, and we compute the expected extreme-ultraviolet and soft X-ray emissions from the resulting thermal structure. We compare our solutions with one-dimensional loop models and analytic loop scaling laws. In the future, we plan to compare these emission images with those obtained by the SOHO EUV Imaging Telescope (EIT) and the Yohkoh Soft X-Ray Telescope (SXT) and to explore the relationship between coronal emission and various coronal heating models.

Magnetic Topology of Coronal Hole Linkages

In recent work, Antiochos and coworkers argued that the boundary between the open and closed field regions on the Sun can be extremely complex with narrow corridors of open flux connecting seemingly disconnected coronal holes from the main polar holes and that these corridors may be the sources of the slow solar wind. We examine, in detail, the topology of such magnetic configurations using an analytical source surface model that allows for analysis of the field with arbitrary resolution. Our analysis reveals three new important results. First, a coronal hole boundary can join stably to the separatrix boundary of a parasitic polarity region. Second, a single parasitic polarity region can produce multiple null points in the corona and, more important, separator lines connecting these points. It is known that such topologies are extremely favorable for magnetic reconnection, because they allow this process to occur over the entire length of the separators rather than being confined to a small region around the nulls. Finally, the coronal holes are not connected by an open-field corridor of finite width, but instead are linked by a singular line that coincides with the separatrix footprint of the parasitic polarity. We investigate how the topological features described above evolve in response to the motion of the parasitic polarity region. The implications of our results for the sources of the slow solar wind and for coronal and heliospheric observations are discussed.

Magnetic Field Topology in Prominences

We present a study of the magnetic field lines of a prominence using MHD and thermodynamic/hydrodynamic (TH) models. Previous modeling of prominences has tended to emphasize either magnetic field modeling or TH modeling in isolation. In this paper, we combine these approaches to model a long-lived filament observed in 1996 August-September. In our new approach, we (1) use magnetograms to prescribe the boundary conditions for the magnetic flux in three-dimensional MHD simulations, (2) show that observed magnetic flux changes can produce a fluxrope and that the dipped (concave upward) portion of the field lines form in the approximate location of the observed prominence, and (3) show that TH computations, using the computed geometry of magnetic field lines that are in three-dimensional MHD equilibrium, have condensations forming in the dipped portions of the field lines.

The Effects of Differential Rotation on the Magnetic Structure of the Solar Corona: Magnetohydrodynamic Simulations

Coronal holes are magnetically open regions from which the solar wind streams. Magnetic reconnection has been invoked to reconcile the apparently rigid rotation of coronal holes with the differential rotation of magnetic flux in the photosphere. This mechanism might also be relevant to the formation of the slow solar wind, the properties of which seem to indicate an origin from the opening of closed magnetic field lines. We have developed a global MHD model to study the effect of differential rotation on the coronal magnetic field. Starting from a magnetic flux distribution similar to that of Wang and coworkers, which consists of a bipolar magnetic region added to a background dipole field, we applied differential rotation over a period of 5 solar rotations. The evolution of the magnetic field and of the boundaries of coronal holes are in substantial agreement with the findings of Wang and coworkers. We identified examples of interchange reconnection and other changes of topology of the magnetic field. Possible consequences for the origin of the slow solar wind are also discussed.