Building Big FlaresConstraining Generating Processes of Solar Flare DistributionsThomas Wyse Jackson[1], Vinay Kashyap[2], Sean McKillop[2]

[1] Trinity College, Dublin [2] Harvard-Smithsonian Center for Astrophysics, Cambridge, MA

Solar FlaresNOAA

Daily solar weather report [6]We extracted the sunspot area and magnetic classification.

GOES, AIA 131Å & 193ÅFlare Detective [7], XRT Flare Catalog [8]

We gathered properties of flares, such as flare duration, peak luminosity, the active region number of the flare, and the start, peak, and end times of the flare.

Data

Evolution of Active RegionsWe tracked the evolution of active regions with time.

Figure 3) Evolution of active region 11726

We can identify when a flare occurred during an active region’s growth or decay.

We flagged flares depending on whether they occurred before or after the peak area of the active region.

This work was supported by the NSF grant AGS 1263241 to the REU Solar Physics Program at SAO and the Smithsonian Competitive Grants Fund 40488100HH0043.VLK acknowledges support from NASA contract NAS8-03060 to the Chandra X-ray Center. SMK acknowledges support from Hinode/XRT grant NNM07AB07C to SAO.

Slicing of Flare ParametersWe looked at how various parameters of the flares affected the flare distributions. We selected the characteristics of:

Duration of the Flare

Evolutionary status of active region - Before or after peak sunspot area

Area of the sunspot at the time of flare

Ratio of the area at the time, to the peak area

Ratio of the 131Å to the 193Å wavelength flux

Number DistributionsPlotting a histogram of number of flares against the energy of the solar flares results in a power law, where 𝑁 𝐸 ∝𝐸−𝛼 where N is number of flares, and E is the energy of the flares.

,

noise. The missing high energy flares suggests that there is a hindering effect.

If we extrapolate for the occurrence of superflares (energy releases > 1036 ergs) we expect to observe one every 100,000 years. We are unaware of any geological records for such an event, which suggests that there is a hard physical limit beyond which, the power law becomes invalid.

We are interested in where this turnover occurs. Is the observed deficit of flares an indicator that this limit is within observational reach? Is the deficit explained by a small sample size & small number statistics? Or is it due to the suggested waiting time due to magnetic field wind up?

Before and after the peak

We compared our solar flare dataset to the stellar superflares found in the Kepler data (Maehara et al. [9]).

We found that 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 ∝ 𝐸𝑛𝑒𝑟𝑔𝑦0.36±0.01. This is close to the relationship for stellar superflares which is, 𝐷𝑢𝑟𝑎𝑡𝑖𝑜𝑛 ∝ 𝐸𝑛𝑒𝑟𝑔𝑦0.4.

Figure 7a) Energy of the flare against durationFigure 7b) Energy of flare against area of active region

Maehara et al also derived a theoretical relationship between the Energy of the flares and the area of the active

region to be 𝐸𝑛𝑒𝑟𝑔𝑦 ∝ 𝐴𝑟𝑒𝑎3

2, which was not the case for our data.

Solar vs Stellar Superflares

Line of best fitEnergy ∝ Area0.3

Energy ∝ Area1.5

We looked at the energy of solar flares which occurred in an active region, and compared it to the maximum area the active region achieved.

Flares vs Active Region

We normalized the timing of the flares to when they occurred in the active region, with the start of the active region being at time 0, the peak at time 0.5, and the end being a time of 1.

We then investigated how the value of α changed as we went further along the normalized time.

We found the value of α decreased as we included flares from later in the normalized time, and that the distribution tended to fill out at higher energies as the active region ages.

This meant comparatively more high energy flares were occurring later in the active regions, implying that there is a deviation from the simple SOC process. This is consistent with there being a winding up effect whereby longer lasting ARs have the time to store excess energy that can be released in larger flares.

Figure 8) Flare Distributions over normalized time. Darker curves denote later times

Distributions over time

• The energy released in an active region, duration of the active region and number of flares in an active region are correlated with the maximal active region size.

• Energy of flares ∝ Area0.28±0.03

• Flare durations ∝ Energy0.36±0.01

• Solar flares have no discernible effect on active region evolution.

• There is a tendency for more higher energy flares to occur later in the evolution of the active region.

• The number distributions of the before peak and after peak flares are statistically indistinguishable.

Conclusions

• [1] - Lu & Hamilton 1991 Astrophys. J. 380 L89-92

• [2] - Aschwanden 2011, Solar Physics 274 L119-129

• [3] - Lin et al. 1984 Astrophys. J. 283 L421-425

• [4] - Hudson et al. 1991 Solar Phys. 133 L357-369

• [5] - Crawford et al. 1972 Astrophys. J 162 L405

• [6] - swpc.noaa.gov/products/solar-region-summary

• [7] - Grigis et al. 2010 Bull. Amer. Astron. Soc. 41 L874

• [8] - xrt.cfa.harvard.edu/flare_catalog/• [9] - Maehara et al. 2015 Earth Planets

& Space 67 L59

References

# Flares before peak vs # after peak

Figure 6a) Energy released from an active region vs maximum area of the active regionFigure 6b) Scatter of the maximum areas

around the line of best fit.

Figure 2) Extrapolated number distribution for 100,000 years

Figure 5) Number of flares before peak vs after peak

From the large scatter seen for the maximum area achieved by an active region regardless of the energy lost in pre-peak flares, we conclude that flaring is energetically unimportant to the evolution of sunspots.

An extrapolated distribution for 100,000 years

Energy of flare (ergs)

Nu

mb

er o

f fl

ares

Figure 1) A number distribution of solar flares for the year 2013

We measure α using the fitting method pioneered by Crawford et al [5] for Log N – Log S curves.

There are deviations from the power-law at high and low energies. The deficit in low energy solar flares can be attributed to difficulties in detecting them in the presence of

When we compared the number of flares which occurred before the peak of the active region, to the number which occurred afterwards, we found a significant difference. We found far more flares occur before the peak of the active region than after.

Solar flares are thought to occur due to self organisedcriticality (SOC; see Lu & Hamilton [1]; Aschwanden [2]).

The events draw upon a reservoir of energy much greater than that of the events themselves and are not characterized by a specific physical length-, time- or energy-scale. This results in power law number distributions. Lin et al. [3], Hudson et al. [4]. This means that solar flares should follow scale-free distributions for parameters such as solar flare energy.

We compared the value of α for different slices of each of these characteristics. Flares with shorter durations tend to have steeper distributions, with fewer higher energy flares

α for different slices of flare duration

Nu

mb

er o

f fl

ares

in t

he

slic

ing

α

Figure 4) α for various slicings of flares

Cumulative Energy vs Max Area

Scatter in sunspot areas

American Geophysical Union Fall Meeting 2015December 14th – 18thhttp://www.maths.tcd.ie/~wysejact/