Improved energy resolution for VHE gamma-ray astronomy with systems of Cherenkov telescopes

We present analysis techniques to improve the energy resolution of stereoscopic systems of imaging atmospheric Cherenkov telescopes, using the HEGRA telescope system as an example. The techniques include (i) the determination of the height of the shower maximum, which is then taken into account in the energy determination, and (ii) the determination of the location of the shower core with the additional constraint that the direction of the gamma rays is known a priori. This constraint can be applied for gamma-ray point sources, and results in a significant improvement in the localization of the shower core, which translates into better energy resolution. Combining both techniques, the HEGRA telescopes reach an energy resolution between 9% and 12%, over the entire energy range from 1 TeV to almost 100 TeV. Options for further improvements of the energy resolution are discussed. Imaging atmospheric Cherenkov telescopes (IACTs) represent the prime instruments for gamma-ray astronomy in the TeV energy range [1]. With a number of sources established as TeV gamma-ray emitters in IACT observations, emphasis is starting to shift from the pure detection of sources to the precise determination of gamma-ray spectra. The energy of gamma rays is determined from the intensity of IACT images, taking into account the radial distribution of Cherenkov light within the light pool. In case of stereoscopic systems of multiple IACTs, which observe an air shower from different viewing angles, the location of the shower axis and hence the distance of a given telescope from this axis can be obtained by a simple geometrical reconstruction. For single IACTs, the impact distance can be estimated based on the location and shape of the Cherenkov image within the camera, albeit with larger uncertainty. Energy resolutions quoted around 1 TeV for single telescopes vary between 29%-36% [2,3], ≈ 30-35% [4] and 20-28% [5]. The HEGRA systems of IACTs provides a resolution of about 20% [6]. Sources such as the Crab Nebula or the AGN Mkn 421 show spectra which are consistent Preprint submitted to Elsevier Preprint 1 February 2008 with pure power laws, dN/dE ∼ E−α, with spectral indices α ranging between 2.5 and about 4. In the determination of power-law energy spectra, energy resolution is not a very critical parameter. Convolution of a power-law spectrum with a resolution function of constant width ∆E/E will result in a spectrum with the identical spectral index. A correction is required in the determination of the flux at or above a certain energy, but this correction is modest even for instruments with a poor resolution ∆E/E ≈ 40%. The situation changes once sources exhibit a cutoff in the energy spectrum, such as observed for Mkn 501 [3,7,8,4,6]. For the interpretation of the cutoff phenomenon, e.g. in terms of absorption of gamma rays in interactions with the infrared/optical background, it is important to precisely map the shape of cutoff. Smearing of the spectrum with an energy resolution in the 20% range may distort its shape significantly. In principle, the original spectrum can be recovered by unfolding techniques (see, e.g., [4] and refs. given there). However, all such techniques result in rapidly increasing statistical errors, once the bin size of the unfolded spectrum approaches the energy resolution of the instrument – after all, the loss of information cannot be recovered and leads to this penalty. It is therefore of significant importance to improve the energy resolution of IACTs. In this article, we will demonstrate that with new analysis techniques, a significant improvement of the energy resolution of stereoscopic systems of IACTs can be achieved, in particular if the source of gamma rays can be considered a point source with known position. The results are based on Monte-Carlo simulations of the HEGRA IACT system, but they should apply in similar form to the various new systems of IACTs which are currently planned or in construction. 1 Factors governing the energy resolution of Cherenkov telescopes The energy resolution of Cherenkov telescopes is governed by a number of factors, among them Statistical fluctuations in the image. Since the number of photoelectrons in a typical image is O(100), statistical fluctuations in the number of photoelectrons limit the resolution to O(10%). Additional fluctuations arise from the amplification process in the photomultiplier and from night-sky background under the image. In case of the HEGRA telescopes, the amplification noise increases the fluctuations by a about a factor 1.2 compared to the Poisson fluctuations alone, and the night-sky noise in a typical image corresponds to about 4-5 p.e. rms. Image truncation. In order to reduce the influence of the night-sky background, the image intensity is usually summed only over ‘image pixels’ above a minimum intensity, cutting away the tail of the image. The sum over image pixel amplitudes provides the so-called size parameter used to derive the shower energy. Such a ‘tail cut’ introduces both additional noise as well as systematic nonlinearities; for low-intensity images a larger fraction of the image is cut than for intense images. An additional truncation occurs for images which extend beyond the edge of the camera. At the 10%-level, edge effects start to matter at distances as large as 0.8◦ between the image centroid and the edge of the camera.