We study the effect of newly emerged solar active regions (ARs) on the large-scale magnetic environment of pre-existing ARs (PEARs). We first present a theoretical approach to quantify the interaction energy between new ARs and PEARs as the differenc
e between (i) the summed magnetic energies of their individual potential fields and (ii) the energy of their superposed potential fields. We expect that this interaction energy can, depending upon the relative arrangements of newly emerged and PEAR magnetic flux, indicate the existence of topological free magnetic energy in the global coronal field that is independent of any internal free magnetic energy due to coronal electric currents flowing within the newly emerged and PEAR flux systems. We then examine the interaction energy in two well-studied cases of flux emergence, but find that the predicted energetic perturbation is relatively small compared to energies released in large solar flares. Next, we present an observational study on the influence of the emergence of new ARs on flare statistics in PEARs, using NOAAs Solar Region Summary and GOES flare databases. As part of an effort to precisely determine the emergence time of ARs in a large event sample, we find that emergence in about half of these regions exhibits a two-stage behavior, with an initial gradual phase followed by a more rapid phase. Regarding flaring, we find that the emergence of new ARs is associated with a significant increase in the occurrence rate of X- and M-class flares in PEARs. This effect tends to be more significant when PEARs and new emerging ARs are closer. Given the relative weakness of the interaction energy, this effect suggests that perturbations in the large-scale magnetic field, such as topology changes invoked in the breakout model of coronal mass ejections, might play a significant role in the occurrence of some flares.
Researchers have reported (i) correlations of coronal mass ejection (CME) speeds and the total photospheric magnetic flux swept out by flare ribbons in flare-associated eruptive events, and, separately, (ii) correlations of CME speeds and more rapid
decay, with height, of magnetic fields in potential coronal models above eruption sites. Here, we compare the roles of both ribbon fluxes and the decay rates of overlying fields in a set of 16 eruptive events. We confirm previous results that higher CME speeds are associated with both larger ribbon fluxes and more rapidly decaying overlying fields. We find the association with ribbon fluxes to be weaker than a previous report, but stronger than the dependence on the decay rate of overlying fields. Since the photospheric ribbon flux is thought to approximate the amount of coronal magnetic flux reconnected during the event, the correlation of speeds with ribbon fluxes suggests that reconnection plays some role in accelerating CMEs. One possibility is that reconnected fields that wrap around the rising ejection produce an increased outward hoop force, thereby increasing CME acceleration. The correlation of CME speeds with more rapidly decaying overlying fields might be caused by greater downward magnetic tension in stronger overlying fields, which could act as a source of drag on rising ejections.
The minimum-energy configuration for the magnetic field above the solar photosphere is curl-free (hence, by Amperes law, also current-free), so can be represented as the gradient of a scalar potential. Since magnetic fields are divergence free, this
scalar potential obeys Laplaces equation, given an appropriate boundary condition (BC). With measurements of the full magnetic vector at the photosphere, it is possible to employ either Neumann or Dirichlet BCs there. Historically, the Neumann BC was used with available line-of-sight magnetic field measurements, which approximate the radial field needed for the Neumann BC. Since each BC fully determines the 3D vector magnetic field, either choice will, in general, be inconsistent with some aspect of the observed field on the boundary, due to the presence of both currents and noise in the observed field. We present a method to combine solutions from both Dirichlet and Neumann BCs to determine a hybrid, least-squares potential field, which minimizes the integrated square of the residual between the potential and actual fields. This has advantages in both not overfitting the radial field used for the Neumann BC, and maximizing consistency with the observations. We demonstrate our methods with SDO/HMI vector magnetic field observations of AR 11158, and find that residual discrepancies between the observed and potential fields are significant, and are consistent with nonzero horizontal photospheric currents. We also analyze potential fields for two other active regions observed with two different vector magnetographs, and find that hybrid potential fields have significantly less energy than the Neumann fields in every case --- by more than 10^(32) erg in some cases. This has major implications for estimates of free magnetic energy in coronal field models, e.g., non-linear force-free field extrapolations.
Some models of coronal heating suppose that convective motions at the photosphere shuffle the footpoints of coronal magnetic fields and thereby inject sufficient magnetic energy upward to account for observed coronal and chromospheric energy losses i
n active regions. Using high-resolution observations of plage magnetic fields made with the Solar Optical Telescope aboard the Hinode satellite, we investigate this idea by estimating the upward transport of magnetic energy --- the vertical Poynting flux, S_z --- across the photosphere in a plage region. To do so, we combine: (i) estimates of photospheric horizontal velocities, v_h, determined by local correlation tracking applied to a sequence of line-of-sight magnetic field maps from the Narrowband Filter Imager, with (ii) a vector magnetic field measurement from the SpectroPolarimeter. Plage fields are ideal observational targets for estimating energy injection by convection, because they are: (i) strong enough to be measured with relatively small uncertainties; (ii) not so strong that convection is heavily suppressed (as within umbrae); and (iii) unipolar, so S_z in plage is not influenced by mixed-polarity processes (e.g., flux emergence) unrelated to heating in stable, active-region fields. In this plage region, we found that the average S_z varied in space, but was positive (upward) and sufficient to explain coronal heating, with values near (5 +/- 1) x 10^7 erg/cm^2/s. We find the energy input per unit magnetic flux to be on the order of 10^5 erg/s/Mx. A comparison of intensity in a Ca II image co-registered with the this plage shows stronger spatial correlations with both total field, B, and unsigned vertical field, |B_z|, than either S_z or horizontal field, B_h. The observed Ca II brightness enhancement, however, probably contains a strong contribution from a near-photosphere hot-wall effect unrelated to atmospheric heating.
The zero point of measured photospheric Doppler shifts is uncertain for at least two reasons: instrumental variations (from, e.g., thermal drifts), and the convective blueshift, a known correlation between intensity and upflows. Calibrated Doppler ve
locities would be useful for (i) improving estimates of the Poynting flux of magnetic energy across the photosphere, and (ii) constraining processes underlying flux cancellation, the mutual apparent loss of magnetic flux in closely spaced, opposite-polarity magnetogram features. We present a method to absolutely calibrate line-of-sight (LOS) velocities in solar active regions (ARs) near disk center using three successive vector magnetograms and one Dopplergram coincident with the central magnetogram. It exploits the fact that Doppler shifts measured along polarity inversion lines (PILs) of the LOS magnetic field determine one component of the velocity perpendicular to the magnetic field, and optimizes consistency between changes in LOS flux near PILs and the transport of transverse magnetic flux by LOS velocities, assuming ideal electric fields govern the magnetic evolution. We apply our method to vector magnetograms of AR 11158, observed by the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory, and find clear evidence of offsets in the Doppler zero point, in the range of 50 -- 550 m s$^{-1}$. In addition, we note that a simpler calibration can be determined from an LOS magnetogram and Dopplergram pair from the median Doppler velocity among all near-disk-center PIL pixels. We briefly discuss shortcomings in our initial implementation, and suggest ways to address these. In addition, as a step in our data reduction, we discuss use of temporal continuity in the transverse magnetic field direction to correct apparently spurious fluctuations in resolution of the 180$^circ$ ambiguity.
We use autocorrelation to investigate evolution in flow fields inferred by applying Fourier Local Correlation Tracking (FLCT) to a sequence of high-resolution (0.3 arcsec), high-cadence ($simeq 2$ min) line-of-sight magnetograms of NOAA active region
(AR) 10930 recorded by the Narrowband Filter Imager (NFI) of the Solar Optical Telescope (SOT) aboard the {em Hinode} satellite over 12--13 December 2006. To baseline the timescales of flow evolution, we also autocorrelated the magnetograms, at several spatial binnings, to characterize the lifetimes of active region magnetic structures versus spatial scale. Autocorrelation of flow maps can be used to optimize tracking parameters, to understand tracking algorithms susceptibility to noise, and to estimate flow lifetimes. Tracking parameters varied include: time interval $Delta t$ between magnetogram pairs tracked, spatial binning applied to the magnetograms, and windowing parameter $sigma$ used in FLCT. Flow structures vary over a range of spatial and temporal scales (including unresolved scales), so tracked flows represent a local average of the flow over a particular range of space and time. We define flow lifetime to be the flow decorrelation time, $tau$. For $Delta t > tau$, tracking results represent the average velocity over one or more flow lifetimes. We analyze lifetimes of flow components, divergences, and curls as functions of magnetic field strength and spatial scale. We find a significant trend of increasing lifetimes of flow components, divergences, and curls with field strength, consistent with Lorentz forces partially governing flows in the active photosphere, as well as strong trends of increasing flow lifetime and decreasing magnitudes with increases in both spatial scale and $Delta t$.
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.
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.
