We estimate the energy input into the solar corona from photospheric footpoint motions, using observations of a plage region by the Hinode Solar Optical Telescope. Assuming a perfectly ideal coronal evolution, two alternative lower bounds for the Poy
nting flux are computed based on field line footpoint trajectories, without requiring horizontal magnetic field data. When applied to the observed velocities, a bound based solely on displacements between the two footpoints of each field line is tighter than a bound based on relative twist between field lines. Depending on the assumed length of coronal magnetic field lines, the higher bound is found to be reasonably tight compared with a Poynting flux estimate using an available vector magnetogram. It is also close to the energy input required to explain conductive and radiative losses in the active region corona. Based on similar analysis of a numerical convection simulation, we suggest that observations with higher spatial resolution are likely to bring the bound based on relative twist closer to the first bound, but not to increase the first bound substantially. Finally, we put an approximate upper bound on the magnetic energy by constructing a hypothetical ``unrelaxed magnetic field with the correct field line connectivity.
Coronal mass ejections (CMEs) are powered by magnetic energy stored in electric currents in coronal magnetic fields, with the pre-CME field in balance between outward magnetic pressure of the proto-ejecta and inward magnetic tension from confining ov
erlying fields. In studies of global, current-free coronal magnetic field models --- Potential-Field Source-Surface (PFSS) models --- it has been reported that model field strengths above flare sites tend to be weaker in when CMEs occur than when eruptions fail to occur. This suggests that potential field models might usefully quantify magnetic confinement. An implication of this idea is that a decrease in model field strength overlying a possible eruption site should correspond to diminished confinement, implying an eruption is more likely. We have searched for such an effect by {em post facto} investigation of the time evolution of model field strengths above a sample of 10 eruption sites, which included both slow and fast CMEs. In most events we study, we find no statistically significant evolution in either: (i) the rate of magnetic field decay with height; (ii) the strength of overlying magnetic fields near 50 Mm; (iii) or the ratio of fluxes at low and high altitudes (below 1.1$R_{odot}$, and between 1.1--1.5$R_{odot}$, respectively). Instead, we found that overlying field strengths and overlying flux tend to increase slightly, and their rates of decay with height become slightly more gradual, consistent with increased confinement. Since CMEs occur regardless of whether the parameters we use to quantify confinement are increasing or decreasing, either: (i) these parameters do not accurately characterize confinement in CME source regions; or (ii) systematic evolution in the large-scale magnetic environment of CME source regions is not, by itself, a necessary condition for CMEs to occur; or both.
Aims. We show how the build-up of magnetic gradients in the Suns 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 fie
ld 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 hour 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.
Sequences of line-of-sight (LOS) magnetograms recorded by the Michelson-Doppler Imager are used to quantitatively characterize photospheric magnetic structure and evolution in three active regions that rotated across the Suns disk during the Whole He
liosphere Interval (WHI), in an attempt to relate the photospheric magnetic properties of these active regions to flares and coronal mass ejections (CMEs). Several approaches are used in our analysis, on scales ranging from whole active regions, to magnetic features, to supergranular scales, and, finally, to individual pixels. We calculated several parameterizations of magnetic structure and evolution that have previously been associated with flare and CME activity, including total unsigned magnetic flux, magnetic flux near polarity inversion lines, amount of cancelled flux, the proxy Poynting flux, and helicity flux. To catalog flare events, we used flare lists derived from both GOES and RHESSI observations. By most such measures, AR 10988 should have been the most flare- and CME-productive active region, and AR 10989 the least. Observations, however, were not consistent with this expectation: ARs 10988 and 10989 produced similar numbers of flares, and AR 10989 also produced a few CMEs. These results highlight present limitations of statistics-based flare and CME forecasting tools that rely upon line-of-sight photospheric magnetic data alone.
Determining the electric field (E-field) distribution on the Suns photosphere is essential for quantitative studies of how energy flows from the Suns photosphere, through the corona, and into the heliosphere. This E-field also provides valuable input
for data-driven models of the solar atmosphere and the Sun-Earth system. We show how Faradays Law can be used with observed vector magnetogram time series to estimate the photospheric E-field, an ill-posed inversion problem. Our method uses a poloidal-toroidal decomposition (PTD) of the time derivative of the vector magnetic field. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD E-field without affecting consistency with Faradays Law. We present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this E-field is also not a unique solution to Faradays Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique E-field, similar to Longcopes Minimum Energy Fit. The PTD technique, the iterative technique, and the variational technique are used to estimate E-fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these E-fields are compared with the simulations known electric fields. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data.
We estimated photospheric velocities by separately applying the Fourier Local Correlation Tracking (FLCT) and Differential Affine Velocity Estimator (DAVE) methods to 2708 co-registered pairs of SOHO/MDI magnetograms, with nominal 96-minute cadence a
nd ~2 pixels, from 46 active regions (ARs) from 1996-1998 over the time interval t45 when each AR was within 45^o of disk center. For each magnetogram pair, we computed the average estimated radial magnetic field, B; and each tracking method produced an independently estimated flow field, u. We then quantitatively characterized these magnetic and flow fields by computing several extensive and intensive properties of each; extensive properties scale with AR size, while intensive properties do not depend directly on AR size. Intensive flow properties included moments of speeds, horizontal divergences, and radial curls; extensive flow properties included sums of these properties over each AR, and a crude proxy for the ideal Poynting flux, the total |u| B^2. Several magnetic quantities were also computed, including: total unsigned flux; a measure of the amount of unsigned flux near strong-field polarity inversion lines, R; and the total B^2. Next, using correlation and discriminant analysis, we investigated the associations between these properties and flares from the GOES flare catalog, when averaged over both t45 and shorter time windows, of 6 and 24 hours. We found R and total |u| B^2 to be most strongly associated with flares; no intensive flow properties were strongly associated with flares.
We describe the computational techniques employed in the recently updated Fourier local correlation tracking (FLCT) method. The FLCT code is then evaluated using a series of simple, 2D, known flow patterns that test its accuracy and characterize its errors.
Several studies have correlated observations of impulsive solar activity -- flares and coronal mass ejections (CMEs) -- with the amount of magnetic flux near strong-field polarity inversion lines (PILs) in active regions photospheric magnetic fields,
as measured in line-of-sight (LOS) magnetograms. Practically, this empirical correlation holds promise as a space weather forecasting tool. Scientifically, however, the mechanisms that generate strong gradients in photospheric magnetic fields remain unknown. Hypotheses include: the (1) emergence of highly twisted or kinked flux ropes, which possess strong, opposite-polarity fields in close proximity; (2) emergence of new flux in close proximity to old flux; and (3) flux cancellation driven by photospheric flows acting fields that have already emerged. If such concentrations of flux near strong gradients are formed by emergence, then increases in unsigned flux near strong gradients should be correlated with increases in total unsigned magnetic flux -- a signature of emergence. Here, we analyze time series of MDI line-of-sight (LOS) magnetograms from several dozen active regions, and conclude that increases in unsigned flux near strong gradients tend to occur during emergence, though strong gradients can arise without flux emergence. We acknowledge support from NSF-ATM 04-51438.
Estimates of velocities from time series of photospheric and/or chromospheric vector magnetograms can be used to determine fluxes of magnetic energy (the Poynting flux) and helicity across the magnetogram layer, and to provide time-dependent boundary
conditions for data-driven simulations of the solar atmosphere above this layer. Velocity components perpendicular to the magnetic field are necessary both to compute these transport rates and to derive model boundary conditions. Here, we discuss some possible approaches to estimating perpendicular flows from magnetograms. Since Doppler shifts contain contributions from flows parallel to the magnetic field, perpendicular velocities are not generally recoverable from Doppler shifts alone. The induction equations vertical component relates evolution in $B_z$ to the perpendicular flow field, but has a finite null space, meaning some ``null flows, e.g., motions along contours of normal field, do not affect $B_z$. Consequently, additional information is required to accurately specify the perpendicular flow field. Tracking methods, which analyze $partial_t B_z$ in a neighborhood, have a long heritage, but other approaches have recently been developed. In a recent paper, several such techniques were tested using synthetic magnetograms from MHD simulations. Here, we use the same test data to characterize: 1) the ability of the induction equations normal component, by itself, to estimate flows; and 2) a tracking methods ability to recover flow components that are perpendicular to $mathbf{B}$ and parallel to contours of $B_z$. This work has been supported by NASA Heliophysics Theory grant NNG05G144G.
