Eventdisplay6, one of the two VERITAS data analysis packages, was used for the search for gamma-ray emission from star-forming galaxies, see Chapter 8. The standard VERITAS data analysis is described in Daniel et al., (2007). In this subsection, I will discuss some aspects of the analysis relevant for the estimation of the Ćux (and upper limits on the Ćux) of gamma-ray point sources.
5.7.1 Background Estimation from Off-Source Counts
Except for observations of the Galactic center region, difuse gamma-ray emission is negligible in the VHE regime. For the star-forming galaxies studied in this work, the dominant contri- bution to the background after gamma-ray selection cuts is due to cosmic ray events, whose arrival directions are distributed nearly isotropically. Thus, simultaneous of-source data from the same Ąeld of view as the source can be used to estimate the remaining background in the source region (Fomin et al., 1994). When possible, this approach is preferred over the method described in Section 5.5 because it does not rely on simulations of the background.
6https://znwiki3.ifh.de/CTA/Eventdisplay%20Software
5.7 Gamma-Ray Point Source Analysis
For the study presented here, data were taken in wobble mode, with the center of the camera ofset from the source by 0.5◦. The source region or ON region is then deĄned as a circular region, centered on the source position, with a radius of 0.09◦ (comparable to the angular resolution for gamma rays). For the background estimate, six circular OFF regions were used with the same radius and the same ofset from the camera center as the source region. The acceptance of the VERITAS camera has been found to be radially symmetric, so the background rate is expected to be the same for each region. In the ON region, there may be an additional (unknown) contribution from signal events.
The actual event counts in the ON and OFF regions after gamma-ray selection cuts and possible cuts on the reconstructed energy, NON and NOFF, are expected to follow Poissonian distributions with mean values λON = NS+NBand λOF F = NαB, where NS(NB) corresponds
to the expected number of signal (background) events in the ON region, and α = 1 6 is the ratio between the area of the ON and OFF regions.
Given the event counts NON and NOFF, the statistical signiĄcance of the signal is evaluated according to Eqn. 17 in Li & Ma, (1983). The threshold for a signiĄcant detection is set at the customary value of 5σ.
5.7.2 Flux Estimation (Point Source)
Given a signiĄcant excess, the best estimate for the number of signal events in the ON region is given by ˆNS = NON− α · NOFF (Li & Ma, 1983). and the Ćux is then estimated as F =ˆ NˆS
Aeff·T, where Aeff is the efective collection area of the array, weighted according
to the energy spectrum and T is the observing time after corrections for dead time due to detector readout. The efective collection area takes into account the eiciencies of the trigger system, reconstruction algorithm, and gamma-ray selection cuts as well as losses due to mis- reconstruction of the arrival direction. This expression is can be used for point sources and sources with an extension smaller than the Ąeld of view of the instrument.
If no signiĄcant excess over the background expectation is found, an upper limit on the number of source counts, NUL
S , is calculated following the formalism of Rolke et al., (2005)
method 4 (background from sidebands, known eiciency τ = 1
α) and reported at 99% conĄ-
dence level. The upper limit on the Ćux is then given by FUL = NSUL
Aeff·T.
5.7.3 Expected Flux Limits
Eventdisplay provides several sets of gamma-ray selection cuts, optimized for diferent source strengths and spectral indices. The energy threshold for the calculation of the Ćux (or upper limits) can be set independently of the cuts, although a lower limit on the energy threshold is deĄned by the reconstruction algorithm and selection cuts. It is necessary to compare the sensitivity of the diferent cut sets and to chose the optimal energy threshold in an un-biased way. Expected limits, calculated under the assumption that there is no source as described
5 Data Analysis Methods
below, are used for this purpose. These only depend on the background counts, which have smaller statistical Ćuctuations that the ON counts.
Given the number of background events (above a certain energy threshold) NOFF and the ON/OFF ratio α, the best estimate for the background rate NBisNˆB= α ·NOFF. Assuming
there is no gamma-ray source (NS = 0), the number of ON events follows a Poissonian
distribution with mean NB.
To calculate the expected limits, I perform toy Monte-Carlo experiments in which I draw ON and OFF events according to Poissonian distributions with mean parameters λON = NB
and λOF F = NαB. For each draw, the upper limit on the signal events according to (Rolke
et al., 2005) is calculated. The expected limit on the signal count is then given by median of the distribution of limits over a large number (typically 100000) random draws. The 1σ and 2σ error bars are derived from the 2.5 %, 16 %, 84 %, and 97.5 % quantiles of the distribution. The expected limits on the Ćux are calculated in the same way as described above.
These expected limits and their associated uncertainties provide an estimate on the mean value and on the statistical Ćuctuations to expect on the actual upper limits. In roughly 95 % of all observations of non-sources, the upper limit derived from background counts should be within the 2σ band around the expected limit. The actual limit can be lower than the expected limit due to downward Ćuctuation of the background.