2 Instrument description and data analysis

COMPTEL was designed to operate in the energy range 0.75 to 30 MeV. It has a large field-of-view of about 1 steradian, and different sources within this field can be resolved, if they are more than about 3 to 5 degrees away from each other (energy dependent). The resulting source location accuracy is of the order of 1$^{\circ}$. The COMPTEL energy resolution of 5% to 10% FWHM is an important feature for gamma-ray line investigations. A detailed description of COMPTEL is given by [Schönfelder et al. (1993)].

COMPTEL consists of two detector assemblies, an upper one of liquid scinitillator NE213, and a lower one of NaI (Tl). A gamma-ray is detected by a Compton collision in the upper detector and a subsequent interaction in the lower detector.

The arrival direction of a detected gamma ray is known to lie on a circle on the sky. The center of each circle is the direction of the scattered gamma-ray, and the radius of the circle is determined by the energy losses E1 and E2 in both interactions. The detected photons are binned in a 3-dimensional (3-D) data space, consisting of the scatter direction (defined by the two angular coordinates $\chi$ and $\psi$) and by the scatter angle $\bar{\varphi}$ (derived from the measured energy losses in both interactions). Each detected photon is represented by a single point in the 3-D dataspace. The signature of a point source with celestial coordinates ( $\chi_{\rm o}$, $\psi_{\rm o}$) is a cone of 90$^{\circ}$ opening angle with its axis parallel to the $\bar{\varphi}$-axis. The apex of the cone is at ( $\chi_{\rm o}$, $\psi_{\rm o}$). Imaging with COMPTEL involves recognizing the cone patterns in the 3-D dataspace. Two main techniques are applied: one is a maximum-entropy method that generates model-independent images ([Strong et al. 1992]) and the other one is a maximum-likelihood method that is used to determine the statistical significance, flux and position uncertainty of a source ([de Boer et al. 1992]). Significances are derived in this method from the quantity $\rm -2\,ln$ $\lambda$, where $\lambda$ is the maximum likelihood ratio L(B) / L(B+S); B represents the background model and S the source model (or sky intensity model). In a point-source search, $\rm -2\,ln$ $\lambda$formally obeys a $\chi_{3}^{2}$ distribution; in studies of a given source, $\chi_{1}^{2}$ applies. [This allows to translate a measured Lvalue into a corresponding probability for it being a noise fluctuation, equivalent to a Gaussian $\sigma$ description of significances. In studies of a "known'' source, $\sigma = \sqrt{-2 {\rm ln} \lambda}$ applies.]

We verified by simulation that the shape of the probability density distribution for our application of the likelihood analysis to the COMPTEL data is indeed Gaussian. Furthermore, we calibrated by the same simulations the number of independent "trials'' we make in a search for source, taking into account the total sky area searched (see [de Boer et al. 1992]).

Our threshold for detection is a chance probability of 99.7%, corresponding to a $3\sigma$ Gaussian significance. The applicable statistics, i.e. the relevant trails, are discussed for each source in the original publication.

The sensitivity of COMPTEL is significantly determined by the instrumental background. A substantial suppression is achieved by the combination of effective charged-particle shield detectors, time-of-flight measurement techniques, pulse-shape discrimination, Earth-horizon angle cuts and proper event selections in energy and $\bar{\varphi}$-space.

The application of the imaging techniques requires an accurate knowledge of the instrumental and cosmic COMPTEL background. A variety of background models has been investigated and is being used. In one method, the background is derived from averaging high-latitude observations. This assumes that the background has a constant shape in the instrumental system in at least the spatial coordinates (but not in Compton scatter angle) for all observations, and it also assumes that the extragalactic source contribution is small and smeared out by the averaging process (see [Strong et al. 1999]). A second method derives the background from the data that are being studied itself. This is accomplished by applying a low-pass filter to the 3-D data, which smooths the photon distribution and eliminates (in the first approximation) the source signatures (e.g. [Bloemen et al. 1994]). By applying iterations of this process the background estimate can be improved, further. All viewing periods have to be handled separately to account for changes of the background during the mission ([Bloemen et al. 1999a]). For line studies, we estimate the background below an underlying cosmic gamma-ray line by averaging the count rate from neighbouring energy intervals ([Diehl et al. 1994]).

For sources within the Galactic plane the global diffuse emission from the Galaxy is modelled by fitting a bremsstrahlung, and an inverse Compton component to the data. Also an isotropic component is added to these fits to represent the cosmic gamma-ray background. The amplitude of each of these components is obtained as free parameter from the fits. It has to be admitted, however (see above), that the modelling of the plane, at present, does not yet achieve the required degree of accuracy.

In addition to the normal double-scatter mode of operation, two of the NaI crystals in the lower detector assembly of COMPTEL are also operated simultaneously as burst detectors. These two modules are used to measure the time history and energy spectra of cosmic gamma-ray bursts and solar flares.

Hence, solar flares and cosmic gamma-ray bursts can be measured in the telescope mode (provided the event was within the field-of-view of the instrument), and in the burst mode.

In its telescope mode COMPTEL has an unprecedented sensitivity. Within a 2-week observation period it can detect sources, which are about 10-times weaker than the Crab. By adding up all data from a certain source that were obtained over the entire duration of the mission, higher sensitivities can be obtained. Table 1 summarizes the achieved point-source sensitivities for a 2-week exposure in Phase-I of the mission ( $t_{{\rm eff}}\sim 3.5 \ 10^{5}$ s), and for the ideal cases, when all data from a certain source in the Galactic center or anticenter (where the exposure is highest) are added from either Phase-I to III ( $t_{{\rm eff}}\sim 2.5 \ 10^{6}$ s) or Phase-I to IV/Cycle-5 ( $t_{{\rm eff}}\sim 6 \ 10^{6}$ s).

From this table rough upper limits can be derived for those objects, which are not contained in the later tables 10 to 12 by deriving the effective exposure from Fig. 1.