Adriaan A. van Ballegooijen

Sustaining the Quiet Photospheric Network: The Balance of Flux Emergence, Fragmentation, Merging, and Cancellation

The magnetic field in the solar photosphere evolves as flux concentrations fragment in response to sheared flows, merge when they collide with others of equal polarity, or (partially) cancel against concentrations of opposite polarity. Newly emerging flux replaces the canceled flux. We present a quantitative statistical model that is consistent with the histogram of fluxes contained in concentrations of magnetic flux in the quiet network for fluxes exceeding ≈ 2 × 1018 Mx, as well as with estimated collision frequencies and fragmentation rates. This model holds for any region with weak gradients in the magnetic flux density at scales of more than a few supergranules. We discuss the role of this dynamic flux balance (i) in the dispersal of flux in the photosphere, (ii) in sustaining the network-like pattern and mixed-polarity character of the network, (iii) in the formation of unipolar areas covering the polar caps, and (iv) on the potential formation of large numbers of very small concentrations by incomplete cancellation. Based on the model, we estimate that as much flux is cancelled as is present in quiet-network elements with fluxes exceeding ≈ 2 × 1018 Mx in 1.5 to 3 days, which is compatible with earlier observational estimates. This timescale is close to the timescale for flux replacement by emergence in ephemeral regions, so that this appears to be the most important source of flux for the quiet-Sun network; based on the model, we cannot put significant constraints on the amount of flux that is injected on scales that are substantially smaller than that of the ephemeral regions. We establish that ephemeral regions originate in the convection zone and are not merely the result of the reemergence of previously cancelled network flux. We also point out that the quiet, mixed-polarity network is generated locally and that only any relatively small polarity excess is the result of flux dispersal from active regions.

Steady Flows Detected in Extreme-Ultraviolet Loops

Recent Transition Region and Coronal Explorer (TRACE) observations have detected a class of active region loops whose physical properties are inconsistent with previous hydrostatic loop models. In this Letter we present the first co-aligned TRACE and the Solar Ultraviolet Measurement of Emitted Radiation (SUMER) observations of these loops. Although these loops appear static in the TRACE images, SUMER detects line-of-sight flows along the loops of up to 40 km s-1. The presence of flows could imply an asymmetric heating function; such a heating function would be expected for heating that is proportional to (often asymmetric) footpoint field strength. We compare a steady flow solution resulting from an asymmetric heating function to a static solution resulting from a uniform heating function in a hypothetical coronal loop. We find that the characteristics associated with the asymmetrically heated loop better compare with the characteristics of the loops observed in the TRACE data.

NONLINEAR FORCE-FREE MODELING OF A LONG-LASTING CORONAL SIGMOID

A study of the magnetic configuration and evolution of a long-lasting quiescent coronal sigmoid is presented. The sigmoid was observed by Hinode/XRT and Transition Region and Coronal Explorer (TRACE) between 2007 February 6 and 12 when it finally erupted. We construct nonlinear force-free field models for several observations during this period, using the flux-rope insertion method. The high spatial and temporal resolution of the X-Ray Telescope (XRT) allows us to finely select best-fit models that match the observations. The modeling shows that a highly sheared field, consisting of a weakly twisted flux rope embedded in a potential field, very well describes the structure of the X-ray sigmoid. The flux rope reaches a stable equilibrium, but its axial flux is close to the stability limit of about 5 × 1020 Mx. The relative magnetic helicity increases with time from February 8 until just prior to the eruption on February 12. We study the spatial distribution of the torsion parameter α in the vicinity of the flux rope, and find that it has a hollow-core distribution, i.e., electric currents are concentrated in a current layer at the boundary between the flux rope and its surroundings. The current layer is located near the bald patch separatrix surface (BPSS) of the magnetic configuration, and the X-ray emission appears to come from this current layer/BPSS, consistent with the Titov and Demoulin model. We find that the twist angle Φ of the magnetic field increases with time to about 2π just prior to the eruption, but never reaches the value necessary for the kink instability.

OBSERVATIONS AND NONLINEAR FORCE-FREE FIELD MODELING OF ACTIVE REGION 10953

We present multiwavelength observations of a simple bipolar active region (NOAA 10953), which produced several small flares ( mostly B class and one C8.5 class) and filament activations from April 30 to May 3 in 2007. We also explore nonlinear force-free field (NLFFF) modeling of this region prior to the C8.5 flare on May 2, using magnetograph data from SOHO/MDI and Hinode/SOT. A series of NLFFF models are constructed using the flux-rope insertion method. By comparing the modeled field lines with multiple X-ray loops observed by Hinode/XRT, we find that the axial flux of the flux rope in the best-fit models is ( 7 +/- 2) x 10(20) Mx, while the poloidal flux has a wider range of (0.1-10) x 10(10) Mx cm(-1). The axial flux in the best-fit model is well below the upper limit (similar to 15 x 10(20) Mx) for stable force-free configurations, which is consistent with the fact that no successful full filament eruption occurred in this active region. From multiwavelength observations of the C8.5 flare, we find that the X-ray brightenings ( in both RHESSI and XRT) appeared about 20 minutes earlier than the EUV brightenings seen in TRACE 171 angstrom images and filament activations seen in MLSO H alpha images. This is interpreted as an indication that the X-ray emission may be caused by direct coronal heating due to reconnection, and the energy transported down to the chromosphere may be too low to produce EUV brightenings. This flare started from nearly unsheared flare loop, unlike most two-ribbon flares that begin with highly sheared footpoint brightenings. By comparing with our NLFFF model, we find that the early flare loop is located above the flux rope that has a sharp boundary. We suggest that this flare started near the outer edge of the flux rope, not at the inner side or at the bottom as in the standard two-ribbon flare model.

OBSERVATIONS AND MAGNETIC FIELD MODELING OF A SOLAR POLAR CROWN PROMINENCE

We present observations and magnetic field modeling of the large polar crown prominence that erupted on 2010 December 6. Combination of Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) and STEREO_Behind/EUVI allows us to see the fine structures of this prominence both at the limb and on the disk. We focus on the structures and dynamics of this prominence before the eruption. This prominence contains two parts: an active region part containing mainly horizontal threads and a quiet-Sun part containing mainly vertical threads. On the northern side of the prominence channel, both AIA and EUVI observe bright features which appear to be the lower legs of loops that go above then join in the filament. Filament materials are observed to frequently eject horizontally from the active region part to the quiet-Sun part. This ejection results in the formation of a dense-column structure (concentration of dark vertical threads) near the border between the active region and the quiet Sun. Using the flux rope insertion method, we create nonlinear force-free field models based on SDO/Helioseismic and Magnetic Imager line-of-sight magnetograms. A key feature of these models is that the flux rope has connections with the surroundings photosphere, so its axial flux varies along the filament path. The height and location of the dips of field lines in our models roughly replicate those of the observed prominence. Comparison between model and observations suggests that the bright features on the northern side of the channel are the lower legs of the field lines that turn into the flux rope. We suggest that plasma may be injected into the prominence along these field lines. Although the models fit the observations quiet well, there are also some interesting differences. For example, the models do not reproduce the observed vertical threads and cannot explain the formation of the dense-column structure.

Is the Quiet-Sun Corona a Quasi-steady, Force-free Environment?

We model a coronal volume over a quiet, mixed-polarity solar network as an ensemble of quasi-steady loop atmospheres. These are contained by an assumed potential field, including the associated variations in the loop cross section through the coronal volume and the loop flows induced by such asymmetries. The average temperature and density stratifications are close to those of the quiet-Sun corona for a coronal heating flux density into the corona of FH = 8 × 1014B/L (ergs cm-2 s-1) for loop-base field strengths B (G) and loop half-lengths L (cm). Earlier, that heating parameterization was shown to be consistent with the appearance and radiative losses of a solar corona in which active regions dominated the emission. This study thus supports the hypothesis that the same, likely braiding-driven, heating dominates throughout the quiescent corona. The average ratio β of gas to magnetic pressure lies close to unity throughout the modeled coronal height range of 22 Mm, with β > 1 in ~30% of the volume and β > 0.4 in ~90% of the volume, perhaps indicating that the quiet-Sun corona is driven to near its maximum heating capacity by the random walk of its footpoints. Our findings that the solar corona has β close to unity, and that our model corona exhibits insufficient fine structure and no significant spatially averaged Doppler shifts, imply that the quiet-Sun corona is often neither quasi-steady nor force free and thus that dynamic magnetohydrodynamics (MHD) models are essential to furthering our understanding of the quiet solar corona.

THE EFFECT OF PROTON TEMPERATURE ANISOTROPY ON THE SOLAR MINIMUM CORONA AND WIND

A semiempirical, axisymmetric model of the solar minimum corona is developed by solving the equations for conservation of mass and momentum with prescribed anisotropic temperature distributions. In the high-latitude regions, the proton temperature anisotropy is strong and the associated mirror force plays an important role in driving the fast solar wind; the critical point where the outflow velocity equals the parallel sound speed (v = c∥) is reached already at 1.5 R☉ from Sun center. The slow wind arises from a region with open-field lines and weak anisotropy surrounding the equatorial streamer belt. The model parameters were chosen to reproduce the observed latitudinal extent of the equatorial streamer in the corona and at large distance from the Sun. We find that the magnetic cusp of the closed-field streamer core lies at about 1.95 R☉. The transition from fast to slow wind is due to a decrease in temperature anisotropy combined with the nonmonotonic behavior of the nonradial expansion factor in flow tubes that pass near the streamer cusp. In the slow wind, the plasma β is of order unity and the critical point lies at about 5 R☉, well beyond the magnetic cusp. The predicted outflow velocities are consistent with O5+ Doppler dimming measurements from UVCS/SOHO. We also find good agreement with polarized brightness (pB) measurements from LASCO/SOHO and H I Lyα images from UVCS/SOHO.

PROTON, ELECTRON, AND ION HEATING IN THE FAST SOLAR WIND FROM NONLINEAR COUPLING BETWEEN ALFVÉNIC AND FAST-MODE TURBULENCE

In the parts of the solar corona and solar wind that experience the fewest Coulomb collisions, the component proton, electron, and heavy ion populations are not in thermal equilibrium with one another. Observed differences in temperatures, outflow speeds, and velocity distribution anisotropies are useful constraints on proposed explanations for how the plasma is heated and accelerated. This paper presents new predictions of the rates of collisionless heating for each particle species, in which the energy input is assumed to come from magnetohydrodynamic (MHD) turbulence. We first created an empirical description of the radial evolution of Alfven, fast-mode, and slow-mode MHD waves. This model provides the total wave power in each mode as a function of distance along an expanding flux tube in the high-speed solar wind. Next, we solved a set of cascade advection-diffusion equations that give the time-steady wavenumber spectra at each distance. An approximate term for nonlinear coupling between the Alfven and fast-mode fluctuations is included. For reasonable choices of the parameters, our model contains enough energy transfer from the fast mode to the Alfven mode to excite the high-frequency ion cyclotron resonance. This resonance is efficient at heating protons and other ions in the direction perpendicular to the background magnetic field, and our model predicts heating rates for these species that agree well with both spectroscopic and in situ measurements. Nonetheless, the high-frequency waves comprise only a small part of the total Alfvenic fluctuation spectrum, which remains highly two dimensional as is observed in interplanetary space.

On the Support of Solar Prominence Material by the Dips of a Coronal Flux Tube

The dense prominence material is believed to be supported against gravity through the magnetic tension of dipped coronal magnetic field. For quiescent prominences, which exhibit many gravity-driven flows, hydrodynamic forces are likely to play an important role in the determination of both the large- and small-scale magnetic field distributions. In this study, we present the first steps toward creating a three-dimensional magneto-hydrostatic prominence model where the prominence is formed in the dips of a coronal flux tube. Here 2.5D equilibria are created by adding mass to an initially force-free magnetic field, then performing a secondary magnetohydrodynamic relaxation. Two inverse polarity magnetic field configurations are studied in detail, a simple o-point configuration with a ratio of the horizontal field (Bx ) to the axial field (By ) of 1:2 and a more complex model that also has an x-point with a ratio of 1:11. The models show that support against gravity is either by total pressure or tension, with only tension support resembling observed quiescent prominences. The o-point of the coronal flux tube was pulled down by the prominence material, leading to compression of the magnetic field at the base of the prominence. Therefore, tension support comes from the small curvature of the compressed magnetic field at the bottom and the larger curvature of the stretched magnetic field at the top of the prominence. It was found that this method does not guarantee convergence to a prominence-like equilibrium in the case where an x-point exists below the prominence flux tube. The results imply that a plasma β of ~0.1 is necessary to support prominences through magnetic tension.

MAGNETIC STRUCTURE AND DYNAMICS OF THE ERUPTING SOLAR POLAR CROWN PROMINENCE ON 2012 MARCH 12

We present an investigation of the polar crown prominence that erupted on 2012 March 12. This prominence is observed at the southeast limb by SDO/AIA (end-on view) and displays a quasi vertical-thread structure. Bright U-shape/horn-like structure is observed surrounding the upper portion of the prominence at 171 angstrom before the eruption and becomes more prominent during the eruption. The disk view of STEREO-B shows that this long prominence is composed of a series of vertical threads and displays a half loop-like structure during the eruption. We focus on the magnetic support of the prominence vertical threads by studying the structure and dynamics of the prominence before and during the eruption using observations from SDO and STEREO-B. We also construct a series of magnetic field models (sheared arcade model, twisted flux rope model, and unstable model with hyperbolic flux tube (HFT)). Various observational characteristics appear to be in favor of the twisted flux rope model. We find that the flux rope supporting the prominence enters the regime of torus instability at the onset of the fast rise phase, and signatures of reconnection (post-eruption arcade, new U-shape structure, rising blobs) appear about one hour later. During the eruption, AIA observes dark ribbons seen in absorption at 171 angstrom corresponding to the bright ribbons shown at 304 angstrom, which might be caused by the erupting filament material falling back along the newly reconfigured magnetic fields. Brightenings at the inner edge of the erupting prominence arcade are also observed in all AIA EUV channels, which might be caused by the heating due to energy released from reconnection below the rising prominence.