Impact parameter MI
Impact parameter MII
MAGIC I MAGIC II
Figure 2.31: Geometry of stereo event, where the impact parameters for both telescopes, impact point and shower axis are highlighted.
Shower axis: This axis can be calculated as the crossing of the enlarged major axes of the two images of the telescopes when they are superimposed in the same camera plane (Figure 2.33b). This is the so-calledcrossing point(Aharonian et al. 1997; Hofmann et al.
1999). This method cannot be used in mono observations, for which theDisp method is applied. The latter, more robust than the crossing point, is as well used for the current MAGIC stereo observations (see Section 2.4.3.7).
Impact point: The point in the ground that the shower axis reaches. It is determined by the crossing of the enlarged major axes of the image shower in each of the telescopes, taking into account their position (see Figure 2.33a).
Impact parameter: Perpendicular distance in the camera between the pointing direction and the shower axis. There is one impact parameter per telescope. See Figure 2.31.
Shower maximum height (Hmax): The altitude at which the number of particles in the cascade is maximum (Hmax) is determined, once the shower axis is known, with the angle at which the image of the center of gravity is viewed in each telescope. As shown in
Section 2.2, the Hmax depends on the energy of the primary particle: as higher is this energy, closer to the ground the cascade develops and hence,Hmaxis smaller. It can be used as an indicator for theγ/hadron separation, mainly at low energies: at that energy range, the Hmaxdistribution for the gamma ray-induced cascades follows a Gaussian, whilst the Hmax distribution for hadrons presents two peaks, the latter produced by muon events. A comparison ofHmax distribution for gamma- and hadron-induced showers is presented in Figure 2.32.
Figure 2.32: Shower maximum distribution height for EM (dotted lines) and hadronic cascades (solid line) for differentsizecuts (in phe). The MC distribution for hadronic shower is also shown (black points).
Images taken from Aleksi´c et al. (2012b).
Cherenkov radius (RC):Radius of the Cherenkov light pool produced by an electron with the bremsstrahlung critical energy 86 MeV at theHmax.
Cherenkov photon density:Density of Cherenkov radiation produced by an electron with the bremsstrahnlung critical energy 86 MeV at theHmax.
2.4.3.6 γ/hadron separation
As mentioned before, even for strong sources as the Crab Nebula, the ratio between hadronic and EM showers is 1000:1. Therefore, the hadronic images surviving the image cleaning is also around 3 orders of magnitude larger than the gamma ray-induced images. This is the reason why an optimal γ/hadron separation is key in the analysis. To perform this discrimination, we use RF, a multi-dimensional classification algorithm based on decision trees (Albert et al. 2008). In order to train the RF on how the gamma-ray events looks like compared to the hadronic ones, the algorithm uses two inputs: MC simulated gamma rays and a real background data (with no gamma-ray emitter, to avoid misleading the training of the RF algorithm). Both of them need to mimic the observational conditions under which the source data was taken, attending basically to weather conditions, moonlight and zenith range. The MC set applied here has to be different for the one used later on in the calculation of flux, in order to avoid being biased. Thus, the entire
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MC sample (simulated withCorsikafor different Zd ranges, see Section 2.4.3.1) is divided into two sub-sets, atrain sample, used for theγ/hadron separation, and atest sample, applied for the collection area and migration matrix computation.
The RF tree starts with the whole sample of events (containing both gamma rays from MC and hadrons from the background data), which provides a reliable image of the real scenario when observing. A randomly selected set of P parameters (such as size, length, arrival time, etc.) are used to discriminate between gamma rays and hadrons. The γ/hadron separation is obtained by dividing the initial sample into two subsamples of events, gamma rays and hadrons, based on optimized cuts of one Pparameter at a time. The optimization of the cuts is based on the minimization of theGini coeficient(Gini 1921):
QGini=4Nγ
N Nh
N (2.9)
whereNis the total number of events, Nγis the number of gamma rays andNhis the number of hadrons. The classification selects another parameter randomly and the subsequent division into gammas and hadrons takes place. If one of the subsamples contains only gamma rays or hadrons, the separation process stops in that branch. To evidence the discrimination, if the events from this subsample belongs to the gamma-ray population, they are assigned with a 0, whilst if they are hadrons the assignation is 1. The training of the RF grows up to a limit ofntrees, which in MAGIC is usuallyn= 100. In Figure 2.34 there is a graphical view of the RF classification.
This trained RF is afterwards applied to the real data from a source with the Melibea soft-ware. Each event of the data has to pass through all the trees previously trained, which allows to classify it into gamma ray or hadron. To quantify how likely an event is a gamma ray or hadron, each event is assigned a hadronnessvalue ranging from 0 to 1 (closer to 1 implies hadron-like event). The finalhadronnessvalue,h, of each event is determined by the mean of thehadronness
Lengthevent< Lengthcut?