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Will new evidence emerge for the frequency of solar superflares?

Question

The Carrington Event, the strongest solar storm on record, was no joke.

Shortly before Noon on September 1, 1859, amateur solar observers in England noticed an intense burst of light from a large sunspot group. Less than 20 hours later, a cloud of hot plasma ejected by the flare slammed into Earth's magnetosphere. Auroras were visible down to tropical latitudes, and telegraphs failed in spectacular fashion, reportedly delivering electric shocks to their operators. As discussed in a previous question, solar storms have the potential to impact power and communications systems, and storms at or above the Carrington level would have devastating effects. A 2013 assessment by Lloyd's estimates that if such an event were to occur today, damages to the US economy alone would range from 0.6 to 2.6 trillion dollars.

Solar flares occur in association with magnetic field reconnection near the Sun's surface, and are most frequent during the active period of the solar cycle. The occurrence rate of solar storm energies follows a relatively well-defined power-law distribution, and the Carrington event was estimated to have had energy ~ erg. The frequency of trans-Carrington storms, however, depends on how far the distribution extends, which is unknown.

Some constraint comes from geological records. Evidence from an overabundance of radioactive 14C detected in tree rings suggests the Sun might have produced a small "superflare" in AD 775 and again in AD 993, although alternate explanations for the anomalies are also viable.

Additional insight is gained by monitoring of the flares of nearby stars. Researchers using the LAMOST telescope have reported regular eruptions 10,000 times larger than the Carrington event on other stars. The team showed that these superflares are likely formed via the same mechanism as solar flares, and unexpectedly, they found ~10% of the superflaring stars have magnetic fields either comparable to or weaker than the Sun's, implicitly raising the possibility that our Sun could go amok with a massive flare.

Superflaring stars generally have short rotation periods (which generate higher levels of magnetic activity), but stars with rotation as slow as the Sun can apparently also produce superflares. A study published in Nature showed a total of 187 superflares on 23 solar-type stars (5600-6000 K, rotational period > 10 d) having energies in the erg range. A consideration of theoretical estimates in conjunction with the observations generated a published hypothesis that superflares of erg occur once in ~800 yr on our present Sun.

An analysis of Kepler photometry showed that superflares on solar-type stars (with rotational periods greater than 10 days) exhibit similar occurrence frequency distribution of those for solar flares. The analysis suggests, however, that all superflaring stars have starspot complexes substantially larger than those presently occurring during solar maxima.

A reasonable summary of the current evidence suggests that the Sun can produce flares up to ~1000x the strength of the Carrington event, but such flares would require sunspot activity at levels substantially larger than those seen in the historical record. Given the stakes, it would be nice to have a better handle on the odds.

By July 2018, will additional significant evidence emerge suggesting that our Sun experiences erg or larger flares on a time scale shorter than 1000 years?

Positive resolution requires a paper in the peer-reviewed literature by July 2018 in which a "most likely" or "fiducial" estimate of solar flares with energy erg exceeds 1 per 1000 years. In addition, in order to add a specious bit of flair to the question, positive resolution will also occur in the unlikely event that a flare with energy exceeding ergs occurs prior to July 2018.

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