1 Introduction

The present paper is the third in a series presenting the observations and the results of the first IRAM key-project "small-scale structure of pre-star-forming regions''. Fully sampled maps had been obtained for three nearby ($d\sim 150$pc) quiescent molecular clouds (MCLD 123.5+24.9, L1512 and L134A) with high spatial and spectral resolution with the IRAM 30m telescope. The data set covers observations in both lowest rotational transitions of ¹²CO and ¹³CO, and in C¹⁸O $J=1\rightarrow$ 0. A detailed description of the key-project, the presentation of the data and first results are published by Falgarone et al. (1998), hereafter Paper I. The discussion of the data reduction procedure will be given by Panis et al. (in preparation; Paper II). Here, we present a detailed study of the influence and the correction of the error beam pick-up and discuss the factors limiting the accuracy of the intensity calibration for the corrected data. An independently reduced data set is presented with the error beam correction based on the beam pattern measurements by Greve et al. (1998, GKW). This data set is compared to the released data from Paper I, where the correction was done using the earlier beam pattern measurements by Garcia-Burillo et al. (1993, GGC).

With the increasing number of surveys covering spatially extended emission, such as those needed to study the structure of the interstellar medium (ISM), it has become clear that a significant fraction of the detected intensity can be due to pick-up in beam pattern components outside the main beam. Early studies of the influence of the stray radiation pick-up and methods for its correction have been done for HI observations (cf. Heiles & Hoffman 1968; Westerhout et al. 1973; Hartmann et al. 1996), based on accurate beam pattern measurements (cf. Baars & Mezger 1964; Hartsuijker et al. 1972; Harten 1973). Kalberla et al. (1980) have shown, that the pick-up in a relatively weak but spatially constrained stray pattern can significantly contribute to the observed intensity. For (sub-)mm wave telescopes, studies of the error beam pick-up were done by e.g. Schneider et al. (1998) for IRAM 30m observations, and Dame & Thaddeus (1994) for observations made with CfA 1.2m telescope.

Measurements of the IRAM 30 m beam pattern show that the error beam accounts for a substantial fraction of the beam pattern (GGC and GKW), more than 50% for observations at wavelengths $\le1.3$mm (frequencies $\nu \ge 230$GHz). This demonstrates that an error beam correction is essential, in particular for observations of spatially extended sources, such as those of the key-project.

For the correction of the key-project data set we use observations made with the KOSMA telescope. Smeared to the spatial resolution of the error beam (appropriately scaled to account for the relative contribution of the error beam to the full beam pattern), they provide an estimate of the error beam pick-up. In Sect. 2 we summarize the beam pattern parameters of the IRAM 30 m and the correction method applied. In Sect. 3 the original and corrected maps are compared. The accuracy of the correction method and of the corrected data set is discussed in Sect. 4. In Sect. 5 we describe the self-consistent error beam correction, which is applied to the released data set (Paper I) and the data set presented here. Both independently reduced data sets are compared. A summary of our results is given in Sect. 6.

For the error beam corrected data we use the corrected main beam temperature scale $T_{\rm mb,c}$. The rigorous definition of $T_{\rm mb,c}$ is given in a supplementary paper (Bensch et al. 2001) where we compare two correction methods and provide a guideline for observers wishing to correct their own data.