The Greatest GOES Flares

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Nugget
Number:	456
1st Author:	Hugh HUDSON
2nd Author:	Ed CLIVER
Published:	September 25, 2023
Next Nugget:	TBD
Previous Nugget:	Introducing SunSketcher
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Contents 1 Background 2 The GOES soft X-rays 3 Conclusions 4 Acknowledgements 5 References

Background

Solar flares appear as isolated bursts of soft X-rays, and powerful ones are distinctly less frequent than weaker ones. In this property they share the power-law occurrence character of earthquakes and many other natural (and man-made) phenomena. In the case of the Sun, this power law is so "flat" that, if extrapolated up into the domain of infrequent but powerful events, the total energy required appears to be infinite. This cannot be! See an earlier Nugget on this issue. Accordingly it was reassuring when Ref. [1] surveyed solar radio bursts and suggested an upper limit to the power law, which otherwise is scale-free.

The GOES soft X-rays

Since the 1970s there have been systematic observations of the solar soft X-ray flux, which varies continuously and shows flare activity very well. Indeed, estimates suggest that a solar flare devotes several percent of its total energy release in just the standard GOES 1-8 Å spectral band. Other estimates suggest that a similar fraction goes into MeV "solar cosmic rays", meaning that the flare process is wildly non-thermal in its nature.

Do the soft X-ray bursts, a relatively close proxy for total flare energy, truly follow the flat power law that we're familiar with? The answer to this question is hidden in a dozen GOES events that "saturated" their X-ray flux estimations. In Ref. [2] we have now analyzed these events systematically, as shown for test examples in Figure 1. We applied the same techniques to the 12 saturated events in the database and believe that the estimates of their peak fluxes thus derived have uncertainties well within the absolute calibrations of the GOES measurements.

We can now present a complete occurrence distribution function (Figure 2), based on our new estimates of peak soft X-ray fluxes. The left panel shows a best effort in defining the linear part of the distribution function, based on a maximum-likelihood fit to an assumed power law. The fitted power law has an index of -2.0, within uncertainties, a good fit over a limited range of event magnitudes. We chose the M1-X3 class range here to avoid overlapping small events, and below what the right panel shows: a clear downwards break.

Conclusions

The turn-over we see, if it scales with total event energy or other manifestations, suggests that extreme events may be less probable than previously thought. In particular the remarkable tree-ring radioisotope events (Ref. [2]) seem less consistent with our current understanding of the physics of solar flares. This is also an interesting development for "superflares" on other stars. However our understanding of the physics is sufficiently weak that eventually a common theoretical basis for solar flare, solar extreme events, and stellar superflares may develop.

Acknowledgements

The authors of Ref. [2] and this Nugget include Stephen WHITE, Janet MACHOL, Courtney PECK, Kim TOLBERT, Rodney VIERECK, and Dominic ZARRO.

References

[1] "The Peak Flux Distribution of Solar Radio Bursts"

[2] Xflares in arXiv soon

[3] "A signature of cosmic-ray increase in AD 774-775 from tree rings in Japan"