When do powerful flares occur?
By way of background, the distribution function of total flare energies has been well studied. A distribution function represents the frequency at which events occur, distributed over some parameter: in our application, it is the total flare energy as represented by its soft Xray peak flux. This is a powerlaw distribution over the observable range, almost an inversesquare law, such that there are roughly 1/10 as many events of 10 times the total energy. This is the solar equivalent of the astronomer's logN/logS curve, for those interested in something entirely different (the example linked here is for cosmic gammaray bursts, but stars, galaxies, quasars, etc., all have their intrinsic occurrence distributions).


Now for the key question. Look at the year 1998 in the upper panel: only three Xclass flares occurred, but an amazing 161 Mclass flares popped off. This epoch, plus 1993 (with no Xclass flares, plus the recent RHESSI epoch with one Xclass flare and 45 Mclass flares, seem different. The average ratio of X to M for the entire epoch (not counting RHESSI's 2002 experience) is 1:17 or so, so that a naive view of the statistics would say that we could multiply Mflare numbers by 0.059 + 0.007 to get predicted Xflare numbers. Hence the table below for the odd epochs:
Interesting epoch  Xflares predicted  Xflares observed 
1993  4.4 + 0.5  0 
1998  9.4 + 1.3  3 
Early 2002  2.6 + 0.3  1 
The above table, depending upon whether you are an optimist or a pessimist, provides convincing evidence of a changing distribution function, or not. The red entries refer to the RHESSI epoch, which lay outside the tenyear Yohkoh interval used for the predictions. In the latter case the skeptic would just shrug and say that there are too few events to deal with statistically. The author of this nugget would disagree with that sort of skeptic, though. In terms of the primitive view of the statistics presented here, the 1998 result is a "threesigma" result, of which we can be confident at the 99% level. In a horse race this would be a very good bet indeed. The simple approach works better for the RHESSI epoch, but any interested reader is invited to apply some fancypants technique such as a KolmogorovSmirnov test, which I am sure would be decisive. Ask if you want detailed lists of flare magnitudes.
Meanwhile, here is another look at the statistics, the time variation of the X/M count ratio with primitive error bars. The 1998 epoch stands out clearly (but note 1996, where a single Xclass flare occurred, and only 3 Mclass flare):
Well, this has been a dull nugget because there have been no pretty pictures, so here is a preflare view of the Xclass flare of July 7, 1996:
The flare occurred in the righthand region. It is only interesting in this context (since Yohkoh missed the main part of it) because it was the unique Xclass flare during solar minimum. In 1996 only 3 Mclass flares occurred, plus this Xclass one. So... is this an example of another distortion of the flare distribution, ie a time when there was a deficit of middlesized flares and not great flares?
May 3, 2002
Hugh Hudson (hudson@isass1.solar.isas.ac.jp)