Data Selection and Reduction
4.5 Background Reduction – γ-Hadron-Separation
Even for a strong VHE γ-ray source, such as the Crab Nebula, the typical H.E.S.S. event rate estimated from simulations is only≈ 0.1 Hz. The typical acquisition rate during observations of ≈ 300 Hz indicates a signal-to-noise ratio of < 10−3 requiring an efficient background re-duction method in order to detect fainterγ-ray sources. In Section 3.1.1, the characteristics of the Cherenkov emission of air showers were discussed and it was suggested that for IACTs a discrimination should be possible based on image morphology.
4.5.1 Event Selection based on Image Shape
Showers initiated by hadronic cosmic rays have a much broader lateral extent than electromag-netic showers. As a consequence, it is possible to distinguish primaryγ-rays from hadrons by applying a cut on the image parameter Width. Since the image shape depends on the shower energy and impact distance, the efficiency of such a cut on the absolute image width depends on the energy and impact distance as well. In order to avoid such an effect, so-called “scaled”
image parameters were introduced [based on HEGRA collaboration, 1997], scaling the shape parameters Width and Length with their expectation value derived from simulatedγ-rays.
Scaling of Shape Parameters with Expectation Values
For each telescope image, the scaled image parameter psis defined as:
ps= p− hpiMC σMC .
The expectation value and its RMS σMC were derived, as for the energy reconstruction pro-cedure, as a function of impact parameter β, zenith angle Θ, and image amplitude Size, i.e.
hpiMC=hpiMC(β,Θ,Size).
A scaled parameter is assigned to each shower event by averaging the parameter of each telescope passing the image quality cuts, resulting in a “Mean Reduced Scaled Parameter”
(MRSP):
MRSP= 1 Ntels
tmax
X
t
ps(t).
The scaled image parameters corresponding to Width and Length are referred to as MRSW and MRSL, respectively, and represent the deviation of the parameters from their expectation value.
Cuts on Scaled Parameters
Figure 4.22 shows the distribution of the MRSW parameter for simulated γ-rays, simulated protons, and data from H.E.S.S. observations of a field of view containing no known γ-ray sources. The distribution forγ-rays is symmetric around zero, corresponding to the expectation value, with a width of ≈ 1σ. The distribution for simulated protons is very similar to that measured for cosmic rays, and is much broader, with a mean 1σ. The γ-hadron-separation was performed by rejecting all events with MRSW> MRSWminand MRSW< MRSWmax, and similarly for MRSL. Most rejection power is provided by the cut parameter MRSWmax.
Simulated vs. Measuredγ-Rays
In order to verify that the measuredγ-rays conform to expectations, the scaled parameter dis-tributions of measured and simulated γ-ray events were compared. For this purpose, events obtained from observations of the Crab Nebula, a “standard candle” for VHEγ-ray astronomy, were used. Figure 4.23 shows the resulting distribution of MRSW for simulated γ-rays and events from the Crab data after background subtraction. The distributions are found to be in reasonable agreement.
4.5.2 Event Selection based on Shower Direction
An additional efficient background rejection – especially when searching for point sources of γ-rays – is given by selecting events based on their reconstructed shower direction. By consid-ering only events contained within a solid angle corresponding to a circle of radiusθcutaround a candidate source position, it is possible to reject a large fraction of the isotropic cosmic ray background. Furthermore, γ-ray events originating from the source but with a poorly recon-structed shower direction, and thus a large energy uncertainty are also rejected.
4.5.3 Cut Optimisation and Performance
The cuts for the selection of γ-ray events were optimised using the complete sample of sim-ulated γ-rays as signal and several off-source runs as background. The selection cuts Sizemin (image quality), MRSWmin,MRSWmax,MRSLmin,MRSLmax(image shape), andθcut(shower di-rection) were varied, and for each possible combination, the number of events containing the γ-ray signal plus backgroundNon = Nγ +Ndata,onand background only Noff = Ndata,off were de-rived according to the “7-background” model (see Sec. 5.1.2) using a background normalisation of α = 1/7. Subsequently, the cut values were chosen such that the significance [Li and Ma, 1983]
S = √ 2
"
Nonln 1+α α
Non Non+Noff
!
+Noffln (1+α) Noff Non+Noff
!#1/2
(4.2) of theγ-ray excess was maximal. The excess was scaled to a source strength of 10% of the flux of the Crab Nebula in order to optimise for rather faintγ-ray sources.
Table 4.2 lists the cut values which were found in the optimisation process. These cuts retain 41.2% of the simulated γ-ray events whilst rejecting more than 99.9% of background events from data and were used for the analysis of the PSR B1259−63 dataset described in the next chapter.
σ] MRSW [
−2 0 2 4 6 8
σ] MRSWmax
MRSW [
MRSWmin Data
MC raysγ MC protons
Entries [a.u.]
0 0.02 0.04 0.06 0.08 0.1 0.12
MRSW, −Rays and Background
γ
Figure 4.22: Distribution of the mean reduced scaled width for simulatedγ-rays (filled) and protons (solid line), and H.E.S.S. off-source data (points). The vertical dashed lines show the cut values used in the analysis. The distributions are normalised to unity.
σ] MRSW [ Data
MC −raysγ
−2 0 2 4 6 8
Entries [a.u.]
−0.02 0 0.02 0.04 0.06 0.08 0.1 0.12
MRSW, MC −Rays and Excess from Crab Nebulaγ
Figure 4.23:Normalised distribution of the mean reduced scaled width for simulatedγ-rays (histogram) and measuredγ-rays from the Crab Nebula (points).
Cut Category Selection Cut Value dmaxlocal 0.525 m∗ image quality
Sizemin 80 p.e.
MRSWmin −2.0
MRSWmax 0.9
image shape
MRSLmin −2.0
MRSLmax 1.3
direction θ2cut 0.02 deg2
∗not included in the optimisation process
Table 4.2: Optimisedγ-ray selection cuts for point sources with a flux of 0.1 Crab.