1. Magnetogram Evolution Near Polarity Inversion Lines Brian Welsch and Yan Li Space Sciences Lab, UC-Berkeley, 7 Gauss Way, Berkeley, CA 94720-7450, USA A report on our work to address two questions: 1. How do strong gradients in B LOS form near PILs? 2. What are “typical” flow patterns near PILs?

2. Topic 1: Gradients near PILs. Why study strong gradients in fields along PILs? Studies have correlated strong gradients along PILs in LOS magnetograms with flares & CMEs. (Falconer et al., 2003, Falconer et al., 2006, Schrijver, 2007) 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

3. 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 tracking – not random sample! –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.

4. 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.)

5. 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/

6. 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, 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

7. Using positive & negative masks (black & white contours, resp.) that were dilated (red & blue contours, resp.), strong-field gradients near PILs were identified as points of overlap (white arrow).

8. Quantifying Flux Near Strong Gradients M OL was convolved with a normalized Gaussian, G  exp(-[x 2 +y 2 ]/2σ 2 ), with σ = 12.6 in pixel units (15 Mm at the equator). 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.

9. 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.

10. 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.

11. 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 |.

12. 216 371 671 363 R is the total unsigned flux along PILs near strong fields. We find increases in R are correlated with increases in unsigned flux --- a signature of emergence.

13. Conclusions Regarding Gradients 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.

14. Topic 2: Flows near PILs. Why study flows near PILs? Observations and theory suggest that converg- ing and shearing flows along PILs are relevant to prominence formation and eruption. (Martin 1998, Antiochos et al. 1999, Amari et al. 2003a/b, Li et al. 2004) How common are shearing and converging flows? OUR GOAL: Estimate flows in active regions, and quantify the strength of shearing and converging motions. Then, investigate correlations between solar activity and properties of estimated flows.

15. Shearing & Converging Flow Examples DeVore & Antiochos, 2000 Amari et al., 2003a, 2003b

16. Active Region (AR) Selection MDI full-disk, 96-minute cadence magnetograms from 1996-2007 were used -- - larger data set! N AR = 68 active regions were selected. –ARs were selected for easy tracking -- not random sample! –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.

17. Several techniques exist to estimate velocities. Time series of vector magnetograms can be used with: –FLCT, ILCT (Welsch et al. 2004, Fisher & Welsch 2007), –MEF (Longcope 2004), –MSR (Georgoulis & LaBonte 2006), –DAVE, DLCT (Schuck, 2006). We have been using FLCT, and have recently implemented versions of DAVE & DLCT. Flows discussed here were estimated with FLCT.

18. Fourier local correlation tracking (FLCT) finds v(x 1,x 2 ) by correlating image subregions. 1) for ea. (x i, y i ) above |B| threshold … 2) apply Gaussian mask at (x i, y i ) … 3) truncate and cross-correlate… * 4) v(x i, y i ) is inter- polated max. of correlation funct = = =

19. - We created “synthetic magnetograms” from ANMHD simulations of an emerging flux rope. - In these data, both v & B are known exactly. Recently, we conducted quantitative tests & comparisons of several available methods.

20. We tested several methods, with increasing time intervals Δt between the correlated images. % errors in magnitude showed biases – FLCT underestimates v.

21. However, FLCT did estimate the direction of v to better than 30º, on average. C VEC and C CS were as defined by Schrijver et al. (2005):

22. We found that flows along contours of B n are harder to estimate accurately than flows along  B n. Unfortunately, flows along contours of B n inject magnetic energy and helicity very efficiently!

23. How do we determine if shearing or convering flows are present?

24. First, we decompose velocities into parallel and perpendicular components…

29. At each pixel, a local right-hand coordinate system is defined, with +x along  B R.

30. We can then study the whole-AR properties of flows along gradients and contours. UNWEIGHTED FIELD-WEIGHTED (signed B!) These plots show the average flows along contours and gradients for each tracked magnetogram for this active region --- 50 velocity fields in this case.

31. …then we isolate regions near PILs…

32. We can then study the properties of flows along gradients and contours near PILs! UNWEIGHTED FIELD-WEIGHTED (signed B!) These plots show the average flows along contours and gradients for each tracked magnetogram for this active region --- 50 velocity fields in this case.

33. We can also compare the average flow properties of whole active regions with each other! This plot shows field-weighted, AR-averaged contour and gradient flows near PILs for all 68 of our ARs. Not all ARs show clear tendencies!

34. Conclusions Regarding Flows This work is still very much in progress! We have tracked N = 68 active regions, and are analyzing our tracking results. We must still correlate our derived flows’ properties with measures of coronal activity. We are also working to improve our flow estimates. We will probably apply “new & improved” methods to our data set, too!