Day 4 - Statistics
Responsible: Rolf Bühler, Markus Ackermann
4.1 Event Statistics
Estimate signal and background event statistics for the dark matter scenario derived on day 3 for measurements with the future Cherenkov Telescope Array (CTA). The assumed WIMP mass was 0.5 TeV and the gamma-ray spectrum is assumed to follow Fornengo et al., 2004 (arXiv:0407342).
Solve the following problems either using ROOT or by coding in “human language”, e.g.:
get effective area histogram
loop over energy bins:
multiply bin value with observation time
The script “DAY4_statistics.py” shows one implementation in python.
Familiarize yourself with the instrument response of CTA: effective area, background rate, accuracy of angular and energy resolution. Browse the file “CTA_response.root”.
Assume that the CTA observation was taken with an offset of 2.5°. Use an ON region of 2° radius. What is your expected number of signal events between 0.1 and 1 TeV be in 50 hours of CTA observations? (Ignore errors in the direction and energy reconstruction of photons, is this a good approximation? Also assume that the effective area is homogeneous over the ON region at the value in its center.)
Determine expected number of background using 3 reflected background regions. (The background from cosmic-rays misclassified as gamma-rays, no astrophysical gamma-ray background. Assume a homogeneous background rate over the OFF region, at the value in its center )
Randomly throw one signal and background measurement realization for the obtained expected values and estimate the significance of the detection following equation 9 in Li & Ma, ApJ 272. 1983
Determine the 90% confidence interval for your measurement realization following Rolke et al. NIM 551, 2005 (arXiv:0403059) (use the TRolke module of ROOT)
4.2 Systematic Errors
Discuss possible systematic errors of the measurement, how would you take them into account in your results?
4.3 Coverage (extra task if there is time)
Test the coverage of the TRolke for 90% and 99% confidence intervals.