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Hinode 5 Conference, Oct 2011, Cambridge MA : Poster #96

Detecting Bright Points in Hinode XRT Lightcurves
Jennifer Posson-Brown, Vinay Kashyap, and Paolo Grigis (Harvard-Smithsonian Center for Astrophysics)

Abstract
One of the greatest challenges in solar coronal physics is to obtain a statistically complete sample of short duration events like coronal brigh t points. Such samples are necessary to fully characterize the properties of these events and understand the physical basis of such phenomena. Datasets are best acquired automatically, without manual intervention, in order to avoid introducing observer biases. We evaluate several algorithms for detecting flare events in ti me series data. One algorithm determines where derivatives of the Gaussian-smoo thed lightcurve cross certain thresholds. A second algorithm segments the Loess- smoothed lightcurve between consecutive minima, then joins adjacent segments if their extrema are not statistically distinguishable. A third algorithm is a hybrid of the first two. We generate simulated datasets with similar properties to obs erved Hinode XRT quiet Sun lightcurves and test each algorithm on these datasets. The performance of each algorithm on the simulated lightcurves is scored accor ding to the rates of false positive (Type I) and false negative (Type II) errors. We use these results to optimize the parameter values of each algorithm. We compare the performances of the algorithms and evaluate the efficiency with which they are able to detect small events. Such evaluations are relevant to properly int erpret the observed steepening of the slope of the solar flare energy distributio n at small energies.

II. Simulated Lightcurves
To test the performance of the event detection algorithms an d find optimal values for the algorithm parameters, we make simulated lightcu rves with 0, 1, 2, 4, 8, 16, 32, and 64 events in 1896 time bins (to match the length of our observed lightcurves). The events are the product of a slanted line and a modified Lorentzian (PINTofALE mk_slant routine). The event peaks are chosen randomly from a powerlaw distribution with index 1.8, and the co re widths are chosen randomly from a Gaussian distribution. The other event para meters (position of peak, rising angle, and beta-profile index) are chosen rando mly from uniform distributions. The events are added to a constant background. T he mean value of the lightcurve is set to match that of the observed data, and Poisson noise is added. For each number of events we have 1000 simulated lightcurves . An example with 64 events is shown in Figure 2.

IV. Algorithm Performance
Using the optimal parameter values determined in Figure 3, w e run the algorithms on a set of 15 lightcurves observed with Hinode XRT (Figure 4, left), and on the set of simulated lightcurves with 64 events (Figure 4, ri ght). The observed lightcurves were manually selected based on the occurrence of one event, but we have extended the analysis to include all possible events. Each of the 15 bright points is widely separated, so the events are indepen dent. Fitting the logdistributions of observed events, we find powerlaw indices o f 1.6-1.8.

I. Event Detection Algorithms
Goal Event detection in presence of variable background (e.g. Fi gure 1), without knowledge of background. Identify start and end time of event. Three IDL event detection codes: 1. Detect Peak Smooths lightcurve with fixed-width Gaussian, looks at where lightcurve derivative crosses given thresholds to find even t. 2. Segment Finder Multi-scale Loess smoothing on lightcurve, segments lightcurve between consecutive minima, then merges adjacent segments if adjacent extrema are statistically indistinguishable. 3. Combined A combination of the first two methods: uses multi-scale Loess smoothing and identifies events with derivative threshold crossing method.
Figure 2 Simulated lightcurve with 64 events added to a constant background. Events are modeled as the product of a slanted line and a modified Lorentzian, and event intensities are chosen randomly from a powerlaw di stribution with index 1 .8 .

Figure 4 Performance of the algorithms on observed and simulated ligh tcurves. Left Number versus luminosity (DN/s) of detected events in 15 lightcurves observed with Hinode XRT, with sensitivity parameters in each algorithm set to optimize false positives. Fitting the curves above DN/s = 0.3 gives the following powerlaw index values: 1.81 (Segment Finder), 1.77 (Detect Peak), 1.59 (combined). Right Number versus peak intensity of detected events in 1000 simulated lightcurves, with sensitivity parameters in each algorith m set to optimize false positives. The black line shows the histogram of all peak intensities in the simulated data set. The algorithms perform equally well for bri ght events, but the probability of detection decreases for weaker events. This decrease is due to a decrease in sensitivity to weak events (for Detect Peak and the combined algorithm), and also because weak events are undetected when they occur over the same time interval as a stronger event.

III. Calibrating with False Positives
Each of the three event detection codes has one parameter pri marily controlling the sensitivity: for Detect Peak and the combined algorithm it is a normalization applied to the threshold values, and for Segment Finder it is the difference threshold S/N for deciding if adjacent extrema are statistically d istinguishable. (For Detect Peak and the combined algorithm, increasing the threshold normalization results in a looser detection criteria and therefore more fa lse positives.) To find the values of these parameters which optimize false positives, we run each code on the simulated lightcurves with zero events, varying the p arameter values. The results are shown in Figure 3. Based on the length of the simul ated lightcurves, we would expect 2 false positives at the 99.7% significance level. Therefore, we choose optimal values for the event detection codes of · Detect Peak: threshold normalization = 6 в 10 · Segment Finder: difference threshold S/N = 3
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V. Summary & Future Work
· We develop a set of simulated lightcurves to test three event detection algorithms. · Simulated lightcurves with zero events are used to calibrat e the algorithms to optimize false positives. · Compared to the other two algorithms, Segment Finder appear s more sensitive to small (peak < 10 counts) events. · In our sample of 15 observed Hinode XRT lightcurves, quiet Sun bright point events are distributed as a powerlaw with measured ind ex between 1.6 and 1.8. · To do: investigate the use of a robust Bayesian wavelet-based event detection method, developed by Alex Blocker.

Figure 1 Observed solar lightcurves from flaring region (red asteris ks) and nearby background region (black crosses). XRT data provided by P. G rigis.

· Combined: threshold normalization = 5 в 10

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References
· Aschwanden, M.J., Nightingale, R.W. Tarball, T.D., & Wolfson, C.J. 2000, Ap J , 5 3 5 , 1 0 2 7 · Hudson, H.S. 1991, SoPh, 133, 357
Figure 3 Calibrating the event detection algorithms to optimize false positives, using the simulated lightcurves with zero events. We expect 2 false positives at the 99.7% significance level. Right Average number of false positives versus threshold normalization for Detect Peak. Middle Average number of false positives versus difference threshold S/N for Segment Finder. Left Average number of false positives versus threshold normalization for the c ombined algorithm.

· Kashyap, V.L., & Drake, J.J. 2000, BASI, 28, 475 · Lu, E.T., & Hamilton, R.J. 1991, ApJ, 380, 89 · Parnell, C.E., & Jupp, P.E. 2000 ApJ, 529, 554 · Winebarger, A.R, Emslie, A.G., Mariska, J.T., & Warren, H.P. 2002, ApJ, 565, 1298

contact: jpossonbrown@cfa.harvard.edu