B. T. Welsch

Global Energetics of Thirty-Eight Large Solar Eruptive Events

We have evaluated the energetics of 38 solar eruptive events observed by a variety of spacecraft instruments between 2002 February and 2006 December, as accurately as the observations allow. The measured energetic components include: (1) the radiated energy in the Geostationary Operational Environmental Satellite 1-8 A band, (2) the total energy radiated from the soft X-ray (SXR) emitting plasma, (3) the peak energy in the SXR-emitting plasma, (4) the bolometric radiated energy over the full duration of the event, (5) the energy in flare-accelerated electrons above 20 keV and in flare-accelerated ions above 1 MeV, (6) the kinetic and potential energies of the coronal mass ejection (CME), (7) the energy in solar energetic particles (SEPs) observed in interplanetary space, and (8) the amount of free (non-potential) magnetic energy estimated to be available in the pertinent active region. Major conclusions include: (1) the energy radiated by the SXR-emitting plasma exceeds, by about half an order of magnitude, the peak energy content of the thermal plasma that produces this radiation; (2) the energy content in flare-accelerated electrons and ions is sufficient to supply the bolometric energy radiated across all wavelengths throughout the event; (3) the energy contents of flare-accelerated electrons and ions are comparable; (4) the energy in SEPs is typically a few percent of the CME kinetic energy (measured in the rest frame of the solar wind); and (5) the available magnetic energy is sufficient to power the CME, the flare-accelerated particles, and the hot thermal plasma.

A POWER-LAW DISTRIBUTION OF SOLAR MAGNETIC FIELDS OVER MORE THAN FIVE DECADES IN FLUX

Solar flares, coronal mass ejections, and indeed phenomena on all scales observed on the Sun, are inextricably linked with the Sun’s magnetic field. The solar surface is covered with magnetic features observed on many spatial scales, which evolve on differing timescales: the largest features, sunspots, follow an 11-year cycle; the smallest seem to follow no cycle. Here, we analyze magnetograms from Solar and Heliospheric Observatory (SOHO)/Michelson Doppler Imager (full disk and high resolution) and Hinode/Solar Optical Telescope to determine the fluxes of all currently observable surface magnetic features. We show that by using a “clumping” algorithm, which counts a single “flux massif” as one feature, all feature fluxes, regardless of flux strength, follow the same distribution—a power law with slope −1.85 ± 0.14—between 2 × 10 17 and 10 23 Mx. A power law suggests that the mechanisms creating surface magnetic features are scale-free. This implies that either all surface magnetic features are generated by the same mechanism, or that they are dominated by surface processes (such as fragmentation, coalescence, and cancellation) in a way which leads to a scale-free distribution.

Tests and Comparisons of Velocity-Inversion Techniques

Recently, several methods that measure the velocity of magnetized plasma from time series of photospheric vector magnetograms have been developed. Velocity fields derived using such techniques can be used both to determine the fluxes of magnetic energy and helicity into the corona, which have important consequences for understanding solar flares, coronal mass ejections, and the solar dynamo, and to drive time-dependent numerical models of coronal magnetic fields. To date, these methods have not been rigorously tested against realistic, simulated data sets, in which the magnetic field evolution and velocities are known. Here we present the results of such tests using several velocity-inversion techniques applied to synthetic magnetogram data sets, generated from anelastic MHD simulations of the upper convection zone with the ANMHD code, in which the velocity field is fully known. Broadly speaking, the MEF, DAVE, FLCT, IM, and ILCT algorithms performed comparably in many categories. While DAVE estimated the magnitude and direction of velocities slightly more accurately than the other methods, MEFs estimates of the fluxes of magnetic energy and helicity were far more accurate than any other methods. Overall, therefore, the MEF algorithm performed best in tests using the ANMHD data set. We note that ANMHD data simulate fully relaxed convection in a high-β plasma, and therefore do not realistically model photospheric evolution.

Solar Magnetic Tracking. I. Software Comparison and Recommended Practices

Feature tracking and recognition are increasingly common tools for data analysis, but are typically implemented on an ad hoc basis by individual research groups, limiting the usefulness of derived results when selection effects and algorithmic differences are not controlled. Specific results that are affected include the solar magnetic turnover time, the distributions of sizes, strengths, and lifetimes of magnetic features, and the physics of both small scale flux emergence and the small-scale dynamo. In this paper, we present the results of a detailed comparison between four tracking codes applied to a single set of data from SOHO/MDI, describe the interplay between desired tracking behavior and parameterization tracking algorithms, and make recommendations for feature selection and tracking practice in future work.

Magnetic Helicity Injection by Horizontal Flows in the Quiet Sun. I. Mutual-Helicity Flux

The flux of magnetic helicity through the solar photosphere has implications in diverse areas of current solar research, including solar dynamo modeling and coronal heating. In this work, we focus on the flux of magnetic helicity from quiet-Sun magnetic fields. We express the total helicity flux in terms of mutual and self-helicities, which arise from relative motions of separate flux elements and from internal motions within individual magnetic flux elements, respectively. Using a novel labeling algorithm and a tracking algorithm applied to high-cadence, high-resolution Solar and Heliospheric Observatory Michelson Doppler Imager magnetograms, we determine the observed mutual-helicity flux density in the quiet Sun to be ~5 × 1012 Mx2 cm-2 s-1 and compare this value with a simple theoretical prediction. The observed rate corresponds to a whole-cycle, hemispheric mutual-helicity flux of ~1043 Mx2 from the quiet Sun, meaning that helicity injection by surface motions in quiet-Sun fields is negligible compared to the active region helicity flux rate.

Magnetic Flux Cancellation and Coronal Magnetic Energy

I investigate the processes at work in the cancellation of normal magnetic flux in solar magnetograms and study the relationships between cancellation and the budget of free magnetic energy in the coronal magnetic field that can power solar flares and CMEs. After defining cancellation mathematically, I derive equations that quantify the evolution of free magnetic energy in response to arbitrary plasma flows on the boundary, including flows consistent with cancellation. While cancellation can reduce the magnetic energy in both the actual coronal field and the potential field matching the same normal field boundary condition, cancellation can, in the process, increase the difference between the two; i.e., cancellation can increase the free magnetic energy in the corona. By making simple assumptions based upon typical observed field configurations in filament channels, I show that cancellation tends to add free energy to these fields. Finally, I discuss the implications of this fact, as well as wider applications of the free energy flux formalism developed here. I also briefly address related issues, including the relationship of cancellation to Taylors hypothesis.

THE SOLAR MAGNETIC FIELD AND CORONAL DYNAMICS OF THE ERUPTION ON 2007 MAY 19

The solar eruption on 2007 May 19, from AR 10956 near solar disk center, consisted of a B9.5 flare (12:48 UT), a filament eruption, an EUV dimming, a coronal wave, and a multifront CME. The eruption was observed by the twin STEREO spacecraft at a separation angle of 8.5°. We report analysis of the source region photospheric magnetic field and its preeruption evolution using MDI magnetograms, the coronal magnetic field topology estimated via PFSS modeling, and the coronal dynamics of the eruption through STEREO EUVI wavelet-enhanced anaglyph movies. Despite its moderate magnitude and size, AR 10956 was a complex and highly nonpotential active region with a multipolar configuration, and hosted frequent flares, multiple filament eruptions, and CMEs. In the 2 days prior to the May 19 eruption, the total unsigned magnetic flux of the region decreased by ~17%. We interpret the photospheric magnetic field evolution, the coronal field topology, and the observed coronal dynamics in the context of current models of CME initiation and discuss the prospects for future MHD modeling inspired by these analyses.

SOLAR MAGNETIC TRACKING. IV. THE DEATH OF MAGNETIC FEATURES

The removal of magnetic flux from the quiet-Sun photosphere is important for maintaining the statistical steady state of the magnetic field there, for determining the magnetic flux budget of the Sun, and for estimating the rate of energy injected into the upper solar atmosphere. Magnetic feature death is a measurable proxy for the removal of detectable flux, either by cancellation (submerging or rising loops, or reconnection in the photosphere) or by dispersal of flux. We used the SWAMIS feature tracking code to understand how nearly 2 ? 104 magnetic features die in an hour-long sequence of Hinode/SOT/NFI magnetograms of a region of the quiet Sun. Of the feature deaths that remove visible magnetic flux from the photosphere, the vast majority do so by a process that merely disperses the previously detected flux so that it is too small and too weak to be detected, rather than completely eliminating it. The behavior of the ensemble average of these dispersals is not consistent with a model of simple planar diffusion, suggesting that the dispersal is constrained by the evolving photospheric velocity field. We introduce the concept of the partial lifetime of magnetic features, and show that the partial lifetime due to Cancellation of magnetic flux, 22?hr, is three times slower than previous measurements of the flux turnover time. This indicates that prior feature-based estimates of the flux replacement time may be too short, in contrast with the tendency for this quantity to decrease as resolution and instrumentation have improved. This suggests that dispersal of flux to smaller scales is more important for the replacement of magnetic fields in the quiet Sun than observed bipolar cancellation. We conclude that processes on spatial scales smaller than those visible to Hinode dominate the processes of flux emergence and cancellation, and therefore also the quantity of magnetic flux that threads the photosphere.

DETECTION OF COHERENT STRUCTURES IN PHOTOSPHERIC TURBULENT FLOWS

We study coherent structures in solar photospheric flows in a plage in the vicinity of the active region AR 10930 using the horizontal velocity data derived from Hinode/Solar Optical Telescope magnetograms. Eulerian and Lagrangian coherent structures (LCSs) are detected by computing the Q-criterion and the finite-time Lyapunov exponents of the velocity field, respectively. Our analysis indicates that, on average, the deformation Eulerian coherent structures dominate over the vortical Eulerian coherent structures in the plage region. We demonstrate the correspondence of the network of high magnetic flux concentration to the attracting Lagrangian coherent structures (aLCSs) in the photospheric velocity based on both observations and numerical simulations. In addition, the computation of aLCS provides a measure of the local rate of contraction/expansion of the flow.

Lagrangian coherent structures in photospheric flows and their implications for coronal magnetic structure

Aims. We show how the build-up of magnetic gradients in the Sun’s corona may be inferred directly from photospheric velocity data. This enables computation of magnetic connectivity measures such as the squashing factor without recourse to magnetic field extrapolation. Methods. Assuming an ideal evolution in the corona, and an initially uniform magnetic field, the subsequent field line mapping is computed by integrating trajectories of the (time-dependent) horizontal photospheric velocity field. The method is applied to a 12 h high-resolution sequence of photospheric flows derived from Hinode/SOT magnetograms. Results. We find the generation of a network of quasi-separatrix layers in the magnetic field, which correspond to Lagrangian coherent structures in the photospheric velocity. The visual pattern of these structures arises primarily from the diverging part of the photospheric flow, hiding the effect of the rotational flow component: this is demonstrated by a simple analytical model of photospheric convection. We separate the diverging and rotational components from the observed flow and show qualitative agreement with purely diverging and rotational models respectively. Increasing the flow speeds in the model suggests that our observational results are likely to give a lower bound for the rate at which magnetic gradients are built up by real photospheric flows. Finally, we construct a hypothetical magnetic field with the inferred topology, that can be used for future investigations of reconnection and energy release.