1. On the Origin of Strong Gradients in Photospheric Magnetic Fields Brian Welsch and Yan Li Space Sciences Lab, UC-Berkeley, 7 Gauss Way, Berkeley, CA 94720-7450, USA

2. Abstract Several studies correlated observations of impulsive solar activity — flares and coronal mass ejections (CMEs) — with the amount of magnetic flux near strong angular gradients in active regions’ radial magnetic field, as measured in photospheric 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, and (2) 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.

3. Studies have correlated gradients in photospheric LOS magnetograms with flares & CMEs. Falconer et al., 2003, JGR, v. 108, #A10, 1380 Falconer et al., 2006, ApJ, v. 644,1258 Schrijver, 2007, ApJ, v. 655, 117 But how do these gradients arise? –From convergence of flux, and cancellation? –From flux emergence? OUR GOAL: Correlate changes in gradients with changes in flux, to see if the occurrence of gradients is correlated with increases in total unsigned flux

4. Active Region (AR) Selection MDI full-disk, 96-minute cadence magnetograms from 1996-98 were used. N AR = 64 active regions were selected. –ARs were selected for an LCT tracking study. –Each had a single, well-defined neutral line. –Hence, most were bipolar. –ARs both with & without CMEs were selected. –Several ARs were followed over multiple rotations; some lacked NOAA AR designation. Here, we analyze N mag = 4062 AR magnetograms.

5. Data Handling Pixels more that 45º from heliographic origin were ignored. To estimate the radial field, cosine corrections were used, B R = B LOS /cos(Θ) Mercator projections were used to conformally map the irregularly gridded B R (θ,φ) to a regularly gridded B R (x,y). (While this projection preserves shapes, it distorts spatial scales – but this distortion can be corrected.)

6. Fig. 1: A typical, deprojected AR magnetogram. Each AR was tracked over 3 - 5 days, and cropped with a moving window. A list of tracked ARs, as well as mpegs of the ARs, are online. 1 1 http://sprg.ssl.berkeley.edu/~yanli/lct/

7. Finding Strong-Gradients Near PILs We used the gradient identification technique of Schrijver (2007). Positive/negative maps M ± — where B R > 150 G & B R < -150 G, resp.— were found (Fig. 2), then dilated by a (3x3) kernel. Regions of overlap, where M OL = M + M -  0, were identified as sites of strong-field gradients near PILs. 2

8. Fig. 2: Using positive & negative masks (black & white contours, resp.) that were dilated (red & blue contours, resp.), strong-field gradients near PILs 2 were identified as points of overlap (white arrow). 2 Polarity Inversion Lines

9. Quantifying Flux Near Strong Gradients M OL was convolved with a normalized 3 Gaussian, G = G 0 -1 exp(-[x 2 +y 2 ]/2σ 2 ), with σ = 12.6 in pixel units (15 Mm at the equator). Fig. 3 shows a map of B R x C MG, where C MG = convol( M OL, G). Following Schrijver (2007), we summed the unsigned magnetic field in |B R | x C MG, to get a measure, R, of the flux near strong-field PILs. 3 with G 0 = ∫ ∫ dx dy exp(-[x 2 +y 2 ]/2σ 2 )

10. Fig. 3: A map of the product of B R with C MG, the convolution of the overlap map M OL and a normalized Gaussian, G. Schrijver (2007) showed that the integral R of unsigned magnetic field |B R | over such maps is correlated with large flares.

11. Changes in R vs. Total Unsigned Field, Σ|B R | For the N R =1621 magnetograms with R  0, we used the product of the previous B R with same C MG to compute the backwards-difference ΔR. (When the overlap map M OL is identically zero, R is also zero, and no ΔR is computed.) We also computed the difference in summed, unsigned |B R | between the current and previous magnetograms.

12. What factors can cause changes in R? And/or in the total unsigned field, Σ|B R |? Flux can emerge or submerge, which only happens at PILs. Either process could increase or decrease R. Horizontal flows could compress or disperse field, which could increase or decrease R. Flux emergence can only increase Σ|B R |, and flux cancellation can only decrease Σ|B R |. Flux could cross into or out of the field of view, thereby increasing or decreasing Σ|B R |.

13. With these ambiguities in mind, how are changes in R and Σ|B R | related? Table of N with… d(Σ|B R |)/dt < 0 (“cancellation”) d(Σ|B R |)/dt > 0 (“emergence”) ΔR > 0 216671 ΔR < 0 363371

14. Fig. 4: Change in R vs. change in summed, unsigned B R.

15. Fig. 5: A slight zoom of Fig. 4.

16. Conclusions Increases in R, the measure of unsigned flux near strong-field PILs, defined by Schrijver (1997), are associated with increases in total unsigned flux. With caveats, this supports Schrijver’s contention that flux emergence creates the strong field gradients that he found to be correlated with impulsive energy release. Our active region sample was not unbiased with respect to active region morphology and age. Hence, this bears further study, with a larger sample of active regions.

17. Comment: Is Space Weather Forecasting simply a matter of tracking R, or emerging flux? Simply put, “NO!” Fig. 6: A geomagnetic storm occurred for the May 12, 1997 CME, though it occurred without flux emergence! CME