1. Flare Flux vs. Magnetic Flux …extending previous studies to new regimes

2. Fisher et al. (1998) found that active region (AR) non-flare soft X-ray luminosity is L SXR   1.19.  is total unsigned magnetic flux r s is the Spearman rank-order coefficient They did a principle components analysis, including L SXR vs. properties of B, J, and other aspects of photospheric fields; the correlation with  was the most significant.

3. Building upon this work, Pevtsov et al. (2003) looked at non-flare L SXR vs.  beyond AR fields. Our group has taken to referring to this relationship as “Pevtsov’s Law”. L SXR   1.15

4. Building upon this work, Pevtsov et al. (2003) looked at non-flare L SXR vs.  beyond AR fields. Our group has taken to referring to this relationship as “Pevtsov’s Law”. G,K,M dwarfs T-Tauri stars whole Sun ARs X-ray bright points quiet sun L SXR   1.15

5. Pevtsov et al. (2003) correlated non-flare soft X- ray luminosity L SXR vs. magnetic flux over 12 dex. Our group has taken to referring to this relationship as “Pevtsov’s Law”. G,K,M dwarfs T-Tauri stars whole Sun ARs X-ray bright points quiet sun L SXR   1.15

6. Q: How does GOES flare flux vary with  ? Slope differs! (but N is low) AR GOES flux is averaged over disk-passage time  (see below)  = whole-AR

7. RHESSI can do MUCH BETTER than my sophomoric approach! One could spatially bin RHESSI flare emission, and correlate that emission with MDI’s  from the same bins. There might be considerable scatter in RHESSI emission vs. MDI’s , since flares have a power- law distribution. But perhaps less  “participates” in smaller flares.

8. We’ve got the entire MDI full-disk magnetogram archive, through fall 2007, on local machines. We can easily copy the RHESSI-era data from the archive to a machine that’s cross-mounted with RHESSI data.

9. A Couple of Slides on Flare Statistics Follow…

10. ASIDE: It’s been known since the dark ages that flares obey a power-law distribution. From Hudson (1991), this plot shows results from several studies. Power laws (a.k.a., polynomials) are scale invariant – i.e., there is no characteristic or average flare energy.

11. Schrijver (2007) found a rough maximum GOES flare flux vs. magnetic flux near polarity inversion lines (PILs). R is the summed  near PILs As expected, there are more weak flares than strong flares.

12. It might be that the spectral index  in the flare power-law N(E) ~ E  varies with . Here, I’ve added a 3 rd dimension to a Schrijver-like plot.