A&A 410, 389-396 (2003)
DOI: 10.1051/0004-6361:20031194
G. P. Rowell
Max Planck Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany
Received 21 May 2003 / Accepted 30 July 2003
Abstract
A new method is described that permits quickly and easily, a 2-dimensional search for TeV -ray
sources over large fields of view (
)
with instruments utilising the imaging atmospheric Cerenkov
technique. It employs as a background estimate,
events normally rejected according to a cosmic-ray background rejection criterion based on image shape,
but with reconstructed directions overlapping the source of interest.
This so-called template background model is demonstrated using example data taken with the stereoscopic HEGRA System of Cerenkov Telescopes. Discussion includes comparisons with a conventional background estimate and limitations of the model. The template model is well suited to the search for point-like, moderately extended sources and combinations thereof, and compensates well
for localised systematic changes in cosmic-ray background response.
Key words: methods: data analysis - gamma rays: observations
Described here is the template background model (an earlier version is described in Rowell 2000), designed to provide a background estimate for sources of interest at all positions in the FoV. The model is demonstrated on archival data from the HEGRA System of Cerenkov telescopes (HEGRA CT-System). For detailed descriptions of this instrument and its performance see Daum et al. (1997) and Pühlhofer et al. (2003). Comparisons are made between results of the template model and those taken from a conventional background model presently in use in HEGRA CT-System data analysis. Some features and limitations of the template model are described.
Present ground-based instruments utilising the imaging atmospheric Cerenkov technique (100 GeV to 30 TeV),
must detect
-ray initiated events against a background of vastly outnumbering isotropic
cosmic-ray (CR) initiated events. First, a set of so-called
-ray cuts are employed to
preferentially select events conforming to a
-ray
hypothesis. These are a priori chosen, and based primarily on Cerenkov image shape parameters, for
example width, length (Hillas 1985), and mean-scaled-width (
)
(Konopelko 1995; Daum et al. 1997).
Second, event arrival directions are also reconstructed based on
the orientation of recorded Cerenkov images (see e.g. Buckley et al. 1998;
Hofmann et al. 1999) and a so-called directional cut made on the
distance
(or analogous parameters) between the reconstructed and assumed arrival directions.
To assess the statistical
significance of any region in the FoV, an estimate of the CR background surviving both
-ray and
directional cuts must be made.
This background estimate can be derived from separate observations of different OFF tracking positions
(ON/OFF tracking), or control regions displaced within the same FoV containing the source region.
The latter types of background models are termed here displacement backgrounds, and a number of different
displacement background geometries are available.
Background regions are chosen so that their CR response matches as closely
as possible, that of the source region (see Fig. 1).
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Figure 1: Illustration of some conventional background estimation methods. (1) Separate OFF source observations are taken at matching zenith angles to those of ON source data. (2) Discrete background regions within the same FoV at a common source-to-tracking distance so as to match background response. (3) A continuous version of (2), ring or ring segments may be used instead. Regions adjacent to the source (shaded) may be preferred to avoid global systematic changes in response. (4) A ring region completely surrounding the source. Methods 2, 3 and 4 are termed displacement background models. Method 4 is used when the source is too close to the tracking position to implement methods 2 and 3, or over the entire FoV. |
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For a given region in the FoV, the source events s are derived from within a nominal source region
according to some directional cut
and
-ray cuts on image shape parameters.
The number of background events b are
derived according to the above-described displacement background methods, after also applying the same
-ray cuts.
The statistical significance S of excess counts
is then estimated from Eq. (17) of Li & Ma (1983):
In 2D skymap generation, the above procedure is repeated over
the FoV at a series of grid positions. Directional parameters such
as
and those necessary to form the background estimate are then re-calculated with respect to each
grid position, and excesses and significances are calculated accordingly.
The template background model invokes a different philosophy to that
of displacement background models. Instead of selecting spatially different
regions in the FoV for background estimates, template model background
events are comprised of those with their
arrival directions reconstructed in the same region as that for the
source, yet separated in image shape parameter space. Such events can
form a suitable template of response for -ray-like CR events over the FoV.
As applied to data of the HEGRA CT-System, the shape parameter mean-scaled-width (
) is used
to construct the template background estimate.
is the image scaled-width, averaged over all
images accepted for analysis. The scaled-width is the image width scaled according to a
-ray
hypothesis. This scaling is dependent upon the total photoelectron
yield of the image, the zenith angle of observations, and the impact parameter or distance to the air-shower core. By design (see Fig. 2), true
-ray events have
values centred at unity, leaving the generally broader CR events to fill higher
values.
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Figure 2:
Normalised distributions of ![]() ![]() |
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Figure 3:
Illustration of the template background geometry with the
FoV and normalisation region (defined by radius R) in
relation to various source positions. The template background and "![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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2D skymaps of excess significance are shown in Fig. 4, illustrating the template model
performance
at various stages of correction. About 50 hours of CT-System exposure on Tycho's SNR out
to a radius
(
)
were used in generating these skymaps. Previous analysis of these
data are described in Aharonian et.al (2001b).
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Figure 4:
2D Skymaps and 1D distributions of significance Susing the template background estimate after various correction levels.
a) no correction, wi=1.0
b) radial correction only,
![]() ![]() ![]() ![]() ![]() ![]() |
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Table 1:
Event excesses
and significances S derived using the template and displacement background models for a number of established TeV
-ray sources. The source region is defined by the cut
.
s:
-ray-like events; b: background estimate;
:
normalisation. Datasets are from the HEGRA CT-System archive; Cas A (212 hours),
H1426+428 (42 hours, 1999/2000), 1ES1959+650 (94 hours, 2000/2001),
Crab (33 hours).
The template model was also tested with a number of a priori
chosen positions in the FoV corresponding to established -ray sources.
Presented in Table 1 are the excess significances for a representative
sample of TeV
-ray sources with a variety of
signal to CR background ratios. Results using background estimates from both the template and
displacement background models are given for comparison.
In all cases a normalisation radius for the
template background model of
and minimum number of images
have been used.
The template model provides derived excesses
quite consistent with those obtained from the
displacement model. Since the example sources of
Table 1 lie quite close to their respective tracking positions,
the zenith-correlated correction term of the template background has little effect, and hence results
only for the fully corrected template background are shown.
For the Crab, a slight modification regarding the template correction is made to the fit limits of the
polynomials ps and pb, to exclude regions containing
this strong source. The polynomial fits are affected by strong sources near (<
)
the tracking position
and these should be avoided.
It should be stressed that the derived excesses and significances for
the Cas A and H1426+428 and 1ES1959+650
here are generally lower than those of presently published
analyses (Aharonian et al. 2001a,2002; Horns et al. 2002),
which employed the more sensitive reconstruction algorithms #2 and #3
(Hofmann et al. 1999), and in some cases a higher minimum
.
The template model does reproduce published results when employing the corresponding analyses.
Finally, a particularly useful feature of the template model is demonstrated against a
problematic systematic effect arising when camera pixels view bright stars in the FoV.
Increased noise fluctuations (and corresponding anode currents) in camera pixels viewing bright stars
can distort derived image parameters.
Affected pixels, usually the same for all five cameras, are therefore removed
from a camera trigger dynamically during data taking and also from image analysis at a software level.
Any pixel with anode current A is not considered in estimation of image parameters and consequent
event direction reconstruction (Bulian et al. 1998; Daum et al. 1997).
A residual effect of this latter step is to leave
a systematic deficit of reconstructed event directions in a region broadly centred on the offending star.
This effect was verified by artificially removing certain pixels before image parametrisation.
In practise, up to two to three pixels may be removed during data taking at any given time depending on the
star brightness. The Crab field, with
-Taurii (mB=2.9)
and the Cas-A field with AR-Cas (mB=4.8),
are ideal examples to illustrate such star deficits.
Quantitatively, star deficits amount to a
reduction in CR events up to
20% over a diameter
.
Table 2 summarises
the template (after full correction only) and displacement background model performance at the
-Taurii and
AR-Cas positions. Since the template background closely follows the CR background response of gamma-ray-like
events, star deficits are considerably reduced when
using the template model. The displacement background however, which does not include the
star region, produces a strong negative bias. Conversely, if displacement
background regions (applied to another source region) were to overlap star deficit(s), some positive
biases could be introduced. A large number of bright stars in the FoV would in general
render application of displacement background models problematic.
Table 2:
Event excesses
and significances S at star positions within the Crab (
-Taurii, 161 hrs) and Cas-A (AR-Cas, 212 hrs) fields of view. Compared are results using the template and displacement background models.
The Tycho's SNR dataset is representative of many in the CT-System archive of order 50 hrs exposure,
with 4 telescopes of the CT-System in operation.
Such an exposure is generally found not sufficient to reveal higher-order systematic effects.
The Cas A dataset comprises a deeper exposure (>200 hrs).
The fully corrected template model skymap of these data (Fig. 5) shows
a strong deviation from Gaussian behaviour (1D
)
already when searching for point
sources (
). A "hotter'' group of bins is seen at
h, Dec
58
to
,
representing an additional systematic excess of order few percent in units of
normalised background. The source of this systematic is as yet not fully understood. It may be linked to a
"missing'' telescope (CT2 is not present in large fraction of these data) which is uncovering inhomogeneities
in trigger response correlating with certain telescopes, although this gradient does not align with the
CT-System geometry. It is seen in these data that artificial removal of other telescopes for example,
can also introduce further similar-scale effects which may or may not be related. Changes in average
skynoise across the FoV may also contribute. Care should
therefore be taken when searching for sources in affected regions, employing alternative background
estimates such as displacement backgrounds as a check. All background methods will of course also be
affected by large-scale systematics of various types and so the above-mentioned problem is not particular to
the template model.
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Figure 5:
Skymap (2D and 1D) of significance S
using the fully corrected template background estimate for Cas-A data.
White star: Nominal
position (SIMBAD) of Cas-A, White dots: tracking positions.
Dashed line: Gaussian (![]() ![]() |
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The estimation of energy spectra from source excesses requires that the background estimate be comprised
of events with a similar distribution of estimated energies to that of events from the source region.
The template background estimate however does not meet this criterion since the
values comprising the background estimate will differ in estimated energy from those in the
-ray-like
regime. Thus alternative background models should be used for spectral analysis.
Described in this paper is a new method to estimate the CR background in 2D searches for sources of
TeV -ray emission with ground-based detectors. This so-called template background estimate, demonstrated
here with HEGRA CT-System data, employs a subset of CR events normally rejected according to
the Cerenkov image shape parameter mean-scaled-width
.
These template events spatially and temporally overlap with CR events considered "gamma-ray-like'',
and thus no dedicated OFF source observations are required.
Applying the template model successfully to HEGRA CT-System data involves correction over of the field
of view for:
(1) differences in radial response and (2) differences in a zenith-correlated gradient, both
between the CR events of the two
regimes.
A particularly useful feature of the template model is its ability to
compensate well for localised systematic changes in CR event density due to the presence of stars in the
field of view. It is well suited to cases where many stars and TeV sources are present.
The template model applicability is limited by the presence of systematic
gradients in CR event density which are presently not corrected. All background models
will however suffer to various extent from weak, large scale systematics. Further
investigation of these aspects is ongoing.
Systematic uncertainties in the derived event excess of less than 4% of the
normalised background are achieved when searching for sources of size less than
radius in
many datasets.
It should be possible to extend the template model philosophy to analyses which use
other means to reject CR background, for example
maximum likelihood methods, multi-dimensional cluster analyses, applied to either single or
multi-telescope systems.
Issues relating to systematic gradients over the FoV and star deficits
will be important for the next generation IACTs
such as H.E.S.S., VERITAS, CANGAROO III and MAGIC. In these new systems, CR event rates of order 500 Hz
are expected, likely revealing higher-order systematic gradients in response after observation times
significantly shorter than that required in HEGRA CT-System data.
Furthermore, the larger mirror areas of these future experiments will also increase considerably the number
of stars that could cause detrimental systematics in the FoV response. The template
background model could therefore be quite useful in 2D skymap construction, in future searches for
TeV -ray sources.
Acknowledgements
HEGRA colleagues are thanked for advice with CT-System data analysis and valuable discussions on this topic (in particular Niels Götting, Dieter Horns and Gerd Pühlhofer). GPR acknowledges receipt of a von Humboldt Fellowship.
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(A.1) |
ps | pb | |
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(A.2) |
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This gradient actually comprises two components: (1) the naturally expected event
rate dependence upon zenith angle for a Cerenkov detection instrument, and (2) using in the construction
of the
parameter which employs a zenith-dependent scaling, the tracking zenith angle instead of
that for each individual event. Here, the template model is demonstrated for a type of
worst-case-scenario, without removing component (2). Component (1) is usually of order few percent
per degree for data taken at zenith angles such in the Tycho's SNR dataset.
It should also be noted that Eq. (1) takes no account of statistical errors in the
normalisation ,
and the template correction terms. These errors are however generally less than one
percent (for obs. time >10 h) and can be
neglected given the high significance levels to which these parameters are estimated.