Weekly Notes from the Yohkoh Soft X-Ray Telescope

(Week 32, 2002)

Science Nugget: August 9, 2002

Setting the Record Straight on Big Flares


This nugget hopes to answer some of the questions raised by previous science nuggets, "One of the missing X flares appears" and When do big flares happen?"  Please see these nuggets for background information, but do not blindly accept their conjectures!

The main point that this nugget hopes to address is whether or not there is a need to incorporate new physics in our view of the occurrence distribution of solar flares. What dictates the X to M flare ratio, and does this vary significantly with time? X flares and M flares differ by a factor of 10 in energy, so this ratio defines the distribution of flare energies over a wide range. The previous nuggets depended upon a database renewed each week. Using a more complete database, also from NOAA, we were able to get data that were much more reliable then that used in the previous nuggets. Additionally, whereas before only data from 1992 to early 2002 were used, now we can use data starting from 1979. With this new insight, it is easy to say that the idea that there is some set variational pattern in the X to M ratio is at best a tenuous proposition.

The idea that there is a set variation in the X to M ratio is rooted in the huge variation that can be seen in the years starting with 1991 to early 2002.  If one looks at the X to M ratio, most years lie close to the expected ratio value, which has a remarkable persistence - the number of flares falls off slightly slower than their energy ([1], [2]).  However, there are some years that seem odd; apples that fell far from the tree.  The previous nugget noted that there are years in which many M flares were observed, but very few X class events .  Why does this happen, is there anything  meaningful that causes this?  Let's see if we can shed some light on this.

Our new database contains 35,877 C-class events, 5104 M-class, and 382 X-class. The X/M ratio is therefore 0.075, corrsponding to a power-law distribution with a slope of -1.13: appreciably steeper than that found in many studies of smaller events. We are seeing fewer X-class flares than the usual distribution, with a power-law exponent of -0.7 or so, predicts.

Flare Statistics

The plots below cover the years from 1979-2002.  The first plot gives the number events observed versus the year.  The solar cycle is clearly outlined in the flare counts.

The three sets of points plotted represent the number of events per class, starting with C at the top (dotted), M in the middle (green), and X at the bottom (red).  Each class differs by one factor of ten from the next in total energy. Nobody knows what C, M, and X stand for, except that they are like logarithms. The number of events occurring within each class all follow the solar cycle, with the number of X events dropping to zero for some years at sunspot minimum.  There nothing unexpected in this graph.   Now we can plot the M/X ratio:

What does this graph mean?  Here we have the X/M ratio with simple error bars (root-N error estimation).  The dashed line represents the ratio averaged over the whole period.  In this case we can see that many of the years fall within the mean.  The really interesting years turn out to be 1998 and 1999.  In 1987,1993,1994 and 1995 there were no X class flares observed at all.  This however is not so strange because in 1987 the sunspot cycle was at a minimum, and in the years between 1993-1995 the cycle was coming off its maximum and approaching the minimum again.  At the times when the original nuggets were written, 2002 was turning out to be an interesting year because of the lack of X class flares at the time of writing.  However, since that time, there have been several X class events, which has yielded a reasonable ratio.

Looking through several cycles it seems that the cases in 1998 and 1999 are not the norm.  In the authors' opinion this is just noise.  The original nuggets were based on a shorter (and error-prone) database,. containing just the years beginning in 1991 and ending at the start of 2002.  When viewed in this context it did seem that something strange was going on.  However, when we zoom out a little bit, and look at more of the years, this effect is not as pronounced.  Clearly the years between 1979 and 1990 fall well within the mean ratio. The years that follow show some variation from this, but it's difficult to be convinced that anything special is really happening here.

For a normal error distribution we would expect that about 2/3 of the cases should lie within the error range of the average (dashed line).  In this case we have 14 of the 23 years falling within this range.  This is 61%, not quite 2/3, but very close.  Moreover, if we discount the years in which no X class events were recorded at all, we find that 14 of 19 years fall within this range. This is again close enough to the 2/3 value not to raise suspicions unduly. The point for 1999, viewed out of context, still looks odd - only four X-class events versus 170 M-class. However "one swallow does not make a summer" seems to be a good rule to apply here.

How about the pattern of large flares relative to the phase of the solar cycle? It is conventional wisdom that the biggest flares actually avoid the peaks of sunspot number. The plots above seem to lay this superstition to rest; just during sunspot maxima, the X/M ratio seems quite well-behaved and obeying its mean value.


It is very difficult to draw any definite conclusions from what we have here, except that flare occurrence rates of all classes seem similar. The conjectures in the original nuggets regarding a variable X/M ratio do not seem so plausible in the light of the improved database. However it would be foolish to ignore the fact that there is some fundamental physics determining this ratio, and the entire distribution of flare occurrence. The large database seems to show a steepening of the distribution function, as anticipated from an analysis of fossil cosmic-ray tracks in lunar rocks.

[Topical index] -o- [Chronological index]

August 9, 2002

H. Jabran Zahid, Hugh Hudson (hudson@isass1.solar.isas.ac.jp)