Supervisors - Professor Dana Longcope and Professor Jiong Qiu A Presentation Regarding the Evolution of Flare Temperatures (or PREFT for short) Thomas Howson Supervisors - Professor Dana Longcope and Professor Jiong Qiu N.B. This is not identical to the presentation delivered as extra annotations are added to aid with clarity. Any new text (including this note) is shown in purple.

Solar Flares Solar flares are huge releases of energy associated with a sudden brightening of the solar surface observed across the electromagnetic spectrum. During a flare event, plasma is heated to many millions of Kelvins Occur around sun-spots Often associated with coronal mass ejections and can have consequences for Earth (ie disruption of telecommunications).

Energy Transfer Magnetic reconnection is believed to be responsible for the transfer of magnetic energy observed during flaring. Flares occur near active regions where magnetic fields are non-potential Magnetic energy released in the corona Energy transported to the dense chromosphere

Shocks and Evaporation Heating of chromosphere observed as bright ribbons Heat transferred through retracting loops by the process of evaporation Movement faster than the local sound speed causes the plasma to be shocked New larger loops appear that cause the ribbons to separate from each other.

My Boxing Day Flare 26th December 2011 211 Å Video of flare as observed at 211Å

My Boxing Day Flare Video of flare in 171 Å Video of flare in 1600 Å

Characteristic Temperature K AIA Data Tracing was completed using 171Å data. However AIA data is available for 6 other wavelengths. Wavelength Å Source Characteristic Temperature K 94 Fe XVIII 6.3 x 106 131 Fe VIII, XX, XXIII 4 x 105, 107, 1.6 x 107 171 Fe IX 6.3 x 105 193 Fe XII, XXIV 1.2 x 106, 2 x 107 211 Fe XIV 2 x 106 335 Fe XVI 2.5 x 106 1600 C IV (+ continuum) 105, 5000

Wavelength Alignment Wavelengths were aligned by comparing the co-ordinates of physical features visible in each wavelength with those in a reference image. The shift in features caused by solar rotation had already been accounted for.

Loop Selection Out of the 250 loops traced, loops with light curves similar to the one shown above were selected for further analysis. Desirable features included a sharp, impulsive rise in UV intensity paired with a sharp rise in each wavelength at the footprint of the loop (this corresponds to energy reaching the chromosphere). Furthermore, distinct rises and decays in intensity should be visible in each wavelength at different times corresponding to the loop cooling.

Loop Selection Here is an example of a light curve for a loop that was rejected. Whilst a small impulsive rise in intensity is viewed in UV, it is not always paired with a rise in foot point intensity when viewed in other wavelengths. In addition, the intensity signature at the footprints is noisy throughout the duration of the flare.

Group 1 or Group 2? Most of the loops selected fell into one of two categories that were labelled as Group 1 and Group 2. Group 1 loops tended to appear earlier in the flare process with the (in general) slightly longer Group 2 loops appearing later in the flare. It was decided that these loops were sufficiently different for it to be sensible to model them separately.

PREFT PREFT (Post-Reconnection Evolution of a Flux Tube) was used to model the loops observed during the flare. Given reasonably limited time, I chose to focus on how the temperatures produced by PREFT compared to those observed. In order to do this light curves were produced from PREFT runs.

Loop Modelling An example PREFT run Input Parameter Selected Value Final Loop Length 60 - 80 Mm Reconnection Angle 90-120˚ Minimum Initial Temperature 0.01 MK Maximum Initial Temperature 2-4MK Magnetic Field Strength 25 - 40 G Energy Input 2 x 1010 erg/cm^2

Simulating Light Curves In order to compare the results of a PREFT run to observations, theoretical light curves were generated. Using the evolution of temperature found in a PREFT run, it is possible to predict the expected intensity of a particular wavelength

Example Theoretical Light Curve The light curves of different wavelengths as simulated by a PREFT run. The number density, volume and a temperature response function were used to calculate expected intensities of different wavelengths through time. As expected each wavelength peaks in intensity at different times and this plot can be compared to the light curves generated from observations in order to see how well the PREFT runs agree with the flare.

Light Curves of One Pixel within a Loop Here, the light curves generated by one pixel on one loop are shown. The time used for peak intensity is highlighted. Whilst on this plot the peaks are obvious, occasionally a smaller local peak was identified as the largest peak corresponded to a lower characteristic temperature than the one being considered.

Considering Emission by Pixels This plot was used to determine whether the delay times were a function of the pixel’s location on a loop. The approximate horizontal bands show that (as expected) this is not the case. They suggest that peak intensities at each wavelength are delayed by a similar time no matter whereabouts on a loop a pixel is located. This plot includes all non-chromospheric pixels from loops that are being analysed.

Delays in Peak Emission This plot shows the delays in peak intensity as observed in different wavelengths for the pixels on one loop. The red stars refer to the average delays for all the pixels in the loop. As expected peak intensities in wavelengths corresponding to cooler temperatures occur later than peak intensities in wavelengths corresponding to higher temperatures.

Comparing Observed Delays to Modelled Delays This plot shows how delays in peak intensities as predicted by an initial PREFT run correspond to those observed. Delays from 75% of the observed pixels fall within the purple error bars and so it is clear that the results of this PREFT run (shown by the green stars) are not a good fit. Subsequently different initial parameters were used in PREFT runs in order to produce a better fit.

Comparing the Results of Multiple PREFT runs This is a repeat of the previous plot with the results of additional PREFT runs also included. Whilst none of these runs produce perfect results, the predicted delays certainly fit the observed delays more accurately than those found by the initial PREFT run.

Zoom This is a zoom of the previous plot. The pale blue stars refer to the observed delays and the vertical lines show the interquartile ranges of the observed data at each wavelength.

Equating 94Å Delays Based on the tendency for the modelled 94Å delays to be too low and the hypothesis that during PREFT runs, the temperature never reached the highest characteristic for 131Å, simulated and observed cooling was compared by equating 94Å delays and examining subsequent peak times (previously 131Å delays were equated in order to find a common flare start time). Now simulated cooling was found to be too slow as opposed to being too rapid as it had been previously.

Best Fit The sum of the distances between simulated and observed delays for each PREFT run was calculated. The run for which this sum was smallest was selected to be the best fit. The delays found by this run are compared to observed data in this plot. As has been seen previously, the 94Å and 335Å delays are too low in the PREFT model but the 211Å, 193Å and 171Å delays all fit the observed delays remarkably well.

Lightcurve Comparison 30G 70Mm 120º 211 Å 193 Å 171 Å Using the PREFT run that was determined to be the best fit for the observed data, simulated light curves (dashed lines) for the three wavelengths that were seen to be the most agreeable in the previous plot were generated. These are compared to the observed light curves (solid lines) in the above plot. Whilst there are noticeable differences, the observed and simulated curves do indeed have similar shapes. The spiky nature of the 193Å lightcurve is probably due to an error in correcting the intensity for exposure time and this will need to be investigated.

Future Work? Complete analysis of different groups identified i.e. group 2 and long and sheared loops. A study into how the modelled density compares to that observed would be interesting. I never got onto this due to the relative difficulty of estimating plasma density from AIA observations (in comparison to producing light curves).

Thank you for a Wonderful Summer