Appendix A: Cleaning of data for soft proton solar flares

Various methods have been used to remove background flares from XMM-Newton and Chandra data sets. For XMM-Newton observations, perhaps the most simple is direct visual inspection of the binned high-energy (10-12) keV light curve over the whole field of view, the adoption of a threshold level, and the exclusion of any intervals above the selected threshold (see e.g., Arnaud et al. 2001). For Chandra data, an $n\sigma$ clipping is used, where the average count rate in the (3-6) keV band over the field of view is calculated, thresholds are set depending on this value, and the light curve cleaned for any intervals where the thresholds are not met.

It is known that the XMM-Newton quiescent background level is variable by $\sim$$\pm 10\%$, and so it is not possible to set a rigid threshold level for flare rejection because of the risk of losing good data. The threshold level should ideally be dependent on the quiescent rate of the observation in question.

Figure A.1: Top: The MOS 1 (10-12 keV) light curve of A1413 before (black) and after (red) cleaning for flares. Dashed lines show the $\pm$$3 \sigma$ thresholds. Bottom: The Poisson fit to the histogram of the light curve, from which the thresholds are calculated. The upper threshold is 14 cts/104 s.

Figure A.2: Top: The MOS 1 (10-12 keV) light curve of MKW9 before (black) and after (red) cleaning for flares. Dashed lines show the $\pm$$3 \sigma$ thresholds. Note the y-axis is in log units. Bottom: The Poisson fit to the histogram of the light curve, from which the thresholds are calculated. The x-axis has been zoomed to emphasise the fit. The upper threshold is 19 cts/104 s.

For the A1413 observation, we extracted the MOS (10-12) keV light curves in the field of view in 104 s bins (chosen as this is an integral multiple of the frame readout time). Similar light curves were made for the pn, but in the (12-14) keV band. We then made a histogram of each light curve and fitted this histogram with a Poisson distribution

$$y = \frac{\lambda^x e^{-\lambda}}{x!}$$ (A.1)

where the mean of the distribution, $\lambda$, is the free parameter of the fit. Following Poisson statistics, the error on the mean, $\sigma = \sqrt{\lambda}$. We found that the Poisson distribution was, without exception, a better fit than a Gaussian distribution. We then defined thresholds at the $\pm$$3 \sigma$ level, and rejected any time intervals outside these thresholds. We show the Poisson fit and the original and cleaned light curves for A1413, which is a quiet observation, and for comparison, the observation of MKW9 (Neumann et al., in preparation), which shows several solar flares, in Figs. A.1 and A.2.

This method is effective at finding the quiescent periods, even for data strongly affected by flares. As such it is not prone to the overestimation of the mean rate, the main problem with the $n\sigma$ clipping method.