1. Is there any relationship between photospheric flows & flares? Coupling between magnetic fields in the solar photosphere and corona implies that flows at the photosphere --- the only atmospheric layer where the magnetic field is routinely measured --- can inject magnetic energy and helicity into the coronal field. Fluxes of magnetic energy and helicity into the corona presumably play a central role in flares and coronal mass ejections (CMEs). Some flow patterns --- including shear flows, converging flows, and rotational flows --- have been proposed as particularly important processes leading to flares and CMEs. How common are these flow patterns? Which flows, if any, are statistically associated with flares? To answer these questions and others, we used the FLCT and DAVE methods to estimate flows in sequences of MDI full-disk magnetograms, with a nominal 96-minute cadence, from 46 active regions (ARs) that were tracked while within 45 degrees of disk center. Our AR sample includes both regions that produced many flares and CMEs, and regions that produced little activity. Based upon our preliminary analysis, we have not identified any flow properties that are as significantly correlated with average flare power as other AR properties: total unsigned flux; flux emergence; and previous flare activity. Hence, we conclude there is no simple or obvious relationship between photospheric flows and flares. by B.T. Welsch 1, Y. Li 1, P.W. Schuck 2, & G.H. Fisher 1 1: Space Sciences Lab, Univ. of California, Berkeley, CA 2: Plasma Physics Div., Naval Research Lab, Washington, DC

2. Active Region (AR) Selection N AR = 46 active regions were selected. See Table 1. –ARs were selected for easy tracking -- not a random sample! –Most were basically bipolar. > 2700 MDI full-disk, 96-min. cadence magnetograms (not recalibrated!) from 1996-1998 were used. The GOES catalog was used to ascribe flares to each AR, all of which had a NOAA active region #. An average flare flux, F, was computed after Abramenko (2006), F = (100S (X) + 10S (M) + 1.0S (C) + 0.1S (B) )/  where  is the time interval the AR was tracked across the disk (in days), and S (i) is the sum of GOES are signicands in the i-th GOES class over The units of F are  W m -2 day -1. (Some ARs had no flares.)

3. Magnetogram Data Handling Pixels were ~ 2’’, or ~1.4 Mm Pixels more than 45º from heliographic origin were ignored. To estimate the radial field, cosine corrections were used, B R = B LOS /cos(  ), where  is the angular distance from disk center. Mercator projections were used to conformally map the irregularly gridded B R (θ,φ) to a regularly gridded B R (x,y).

4. FLCT 1 and DAVE 2 methods were used to estimate flows. FLCT only tracked pixels with |B R | > 20 G. Windowing parameters of  = 8 & 9 pixels were set for FLCT & DAVE, resp. 1 Fisher, G. H. & Welsch, B. T. 2008, ASP Conf. Ser., v. 383, ed. R. Howe, R. W. Komm, K. S. Balasubramaniam, & G. J. D. Petrie, 373; also arXiv:0712.4289 2 Schuck, P. W. 2006, ApJ, 646, 1358 Fig. 1: FLCT and DAVE flows tend to be similar, as in these flow maps from AR 8038.

5. Fig. 2: Scatter plots comparing FLCT and DAVE flows from the maps above quantify correlations between the flows. Fig. 3: Speeds are higher where |B R | is weaker; DAVE speeds are higher than FLCT speeds. Fig. 4: The distribution of speeds declines steeply.

6. Fig. 5: Correlations between current-previous (thick) and current-initial for B R (black), and FLCT’s u x (blue) & u y (red) for three ARs. The flows have an e -folding correlation time of ~6 hr., while B R remains correlated for a few days or more.

7. We quantified photospheric magnetic evolution in several ways, including: 1. Summed unsigned flux, , and unsigned near strong field PILs, R (Schrijver 2007). 2. Signed & abs.change in flux, d  /dt & |d  /dt|. 3. Change in R with time, dR/dt 4. Change in center-of-flux separation, d(  x ± )/dt, where we have defined:  x ±  x + -x -, with x ±   ± da x B R   ± da B R 5. Moments of the flow, u, and the flux transport velocity, (u B R ). 6. Moments of divergence and vertical (radial) vorticity in the flow, (  u) & r (  x u), where r is the vertical unit vector. These were also computed for the flux-normed flux transport velocity.

8. 7. We also tried to quantify shearing converging flows near PILs. First, we dcomposed flows into components along gradients and contours of B R. Examples of flows decomposed in this way can be seen in Fig. 1. Since shearing & convergence require opposing flows across the PIL, we weight the flows by the signed radial field, B R. CONVERGING SHEARING

9. Fig. 6: Maps of divergence & curl (top row), B R -weighted divergence & curl (middle), and shear & convergence maps near the main PIL (bottom) for the flows from Fig. 1.

10. We first correlated disk-passage averaged flow properties & flare power. The field properties most strongly correlated with flares --- e.g.,  & increases in  --- are not related to flows. Average AR flow speeds are inversely proportional to , which introduces a flow-flare anti-correlation. This plot compares flow-flare CORRELATION COEF-FICIENTS from FLCT & DAVE --- hence, points on thediagonal (NOT a fit) Imply the two methods agree.

11. We also correlated flows with flare power in 6 & 24 hr windows around each of 2708 flow maps. As with the disk-passage correlations, the field properties most strongly correlated with flares do not involve flows. Again,  and increases in  are most strongly correlated with average flare power.

12. Finally, we correlated flows with flare power in 6 & 24 hr. windows after each of 2708 flow maps – to predict flares! Again,  and increases in  are most strongly correlated with flare power. Again, flow properties aren’t well correlated.

13. Conclusions We have estimated flows using the FLCT and DAVE methods in 46 ARs, to create 2708 flow maps. Flow patterns have an e -folding correlation time of ~6 hr. Flows tend to be slower in pixels with stronger magnetic fields. (Magnetic fields inhibit convection!) Total unsigned flux  and increases in  are most strongly correlated with average flare power. Many flow properties averaged over an AR are inversely proportional to , thereby introducing a flow-flare anti- correlation that hampers interpreting the flow-flare relationship.