Background Modelling in Very-High-Energy Gamma-Ray Astronomy Page: 3 of 13
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Berge, Funk, Hinton: Background modelling in y-ray astronomy
The task of a background model is to provide the quantities
Noff and a. A choice of background regions such that a < 1
(achievable, e.g., by choosing much larger OFF than ON re-
gions) results generally in higher statistical significance, be-
cause background fluctuations are reduced, but may also result
in increased systematic errors. The principle difficulty in deriv-
ing a background estimate is the determination of the correct
value of a. Since proper control over the system acceptance is
crucial for this purpose, we investigate below the acceptance of
H.E.S.S..
2.1. Cosmic-Ray System Acceptance after y-ray Cuts
The system acceptance is defined as the probability of accept-
ing, after triggering, analysis cuts and y-ray selection, a back-
ground event reconstructed at a certain position in the system
FoV and with a certain energy. For most background models
some knowledge of the system acceptance is required to gen-
erate an image of y-ray excess events or calculate significances
of arbitrary positions in the FoV. In general, the acceptance de-
pends on:
E the position in the FoV, particularly the distance to the op-
tical axis
E the zenith (#z) and azimuth 0,, angle of observations, due
to the influence of the Earth's magnetic field on the shower
development in the atmosphere and the rotational asymme-
try of the telescope system.
E the reconstructed primary energy
E the time of observation, due to possible changes in the sys-
tem configuration and aging of mirrors
E the sky coordinates viewed, due to the night-sky back-
ground light level.
In most cases it is a reasonable assumption that the accep-
tance is radially symmetric (the validity of this assumption
is discussed later). It is generated in a one-dimensional fash-
ion as the number of background events as a function of the
(squared) angular distance between reconstructed event direc-
tion and system pointing direction. It can either be determined
on a run-by-run basis from the data set under analysis or be
extracted from observations without significant y-ray emission
in the FoV (OFF runs). In the latter case it is assumed that the
system acceptance is identical for the ON and OFF runs. In the
former case one may face two problems, y-ray contamination
by a source, and lack of statistics. For a typical data run lasting
28 minutes, recorded at moderate zenith angles, the number of
events after y-ray selection cuts (available for the determination
of the acceptance) is 0(104) with cuts for spectral analysis, and
as low as 0(103) with cuts for morphology studies (see below
for a description of the analysis cuts).
Here we use 220 hours of H.E.S.S. observations without
significant y-ray sources in the FoV to obtain a model of the ra-
dial system acceptance. These reference observations are sub-
divided into zenith-angle bands. Events passing y-ray cuts (i.e.
y-ray-like background events) are then binned according to the
squared angular distance between the reconstructed event di-
rection and the system's pointing direction. Figure 1 illustratesthe dependence of the acceptance on the zenith angle of obser-
vations and analysis cuts. The shallow central peak and rapid
decline towards larger distances, stems from the analysis based
on image (Hillas) parameters, where a cut on the distance be-
tween image centre-of-gravity and the camera centre is applied
to avoid truncation effects at the camera edge. Due to the finite
camera size, edge effects are inherent and will always appear
independent of the exact analysis applied.
As can be seen from Fig. 1, 20 away from the system cen-
tre, the y-ray acceptance at moderate zenith angles decreases
to 20% - 50% of the peak value, depending on analysis cuts.
In addition a smooth variation with zenith angle is apparent.
With increasing zenith angle, the system acceptance broadens,
an increasing fraction of events with directions further away
from the system pointing direction is detected. This is a direct
consequence of the fact that with increasing zenith angle the
shower maximum is increasingly further away from the tele-
scope system causing a broadening of the Cherenkov light-pool
on ground and hence an enlarged phase space for events with
large inclination angles. When comparing the average curve for
any given zenith-angle band to the radial acceptance in differ-
ent fields of view, observed at the same altitude, the scatter is
relatively small, less than 3% within 1 of the observation po-
sition and less than 10% out to 30. It is therefore justifiable to
use OFF data taken in different fields of view to determine a
model of the system acceptance.
The influence of analysis cuts is also apparent in Fig. 1.
The two sets of cuts used throughout this paper are labelled
std and hard. The first set includes a cut on the minimum am-
plitude of each camera image at 80 photo-electrons (p.e.) and
is optimised for the determination of source spectra. The sec-
ond set uses a cut on the image amplitude at 200 p.e., and pro-
vides better background suppression and superior angular res-
olution. It is therefore normally used for source searches and
image generation (more detailed descriptions of the H.E.S.S.
analysis techniques may be found in Aharonian et al. (2005d)
and Aharonian et al. (2006b)). The larger cut on the minimum
image size results in curves which exhibit a generally less pro-
nounced peak and a less rapid decline towards large distances.
There is an increased fraction of events with large inclination
angles with respect to the system pointing direction.
The azimuth dependence of the radial system acceptance
is small and therefore neglected here: when sub-dividing data
taken in a narrow zenith-angle band into azimuth bins (say
North, East, South, and West), only marginal differences occur
at the few-percent level. The energy dependence of the accep-
tance is much stronger, greatly complicating the use of back-
ground models that require an acceptance correction for spec-
tral analysis. This is illustrated in Fig. 2 (left) where the energy
dependence for a zenith angle range from 00 to 200 is plotted.
The curves shown correspond to three different energy bands,
E < 0.6 TeV , 0.6 TeV <E < 1.4 TeV, and 1.4 TeV <E. For
relatively small energies the acceptance declines rapidly with
increasing offset. For large energies the shape is completely
different. High-energy showers result in large Cherenkov light-
pool radii on ground. Therefore, as already mentioned, more
events with large angular offsets start to trigger the array. In ef-3
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Berge, David; /Heidelberg, Max Planck Inst. /CERN; Funk, S.; /Heidelberg, Max Planck Inst. /KIPAC, Menlo Park; Hinton, J. & /Heidelberg, Max Planck Inst. /Heidelberg Observ. /Leeds U. Background Modelling in Very-High-Energy Gamma-Ray Astronomy, article, November 7, 2006; [Menlo Park, California]. (https://digital.library.unt.edu/ark:/67531/metadc879443/m1/3/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.