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| - III. Influence of and correction for the error beam pick-up
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| - The IRAM key-project: Small-scale structure of pre-star forming regions
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| - The goal of the IRAM key-project "Small-scale structure of pre-star forming regions"is to map three nearby ( $d\sim 150 {\rm pc}$), quiescent molecular clouds with a high angular and spectral resolution to study the molecular cloud structure down to the smallest linear scales currently accessible by single dish radio telescopes. Here, we give a detailed discussion of the influence and the correction of the error beam pick-up. A new set of corrected data is presented using the beam pattern parameters of the IRAM 30 m telescope recently published by Greve et al. (1998). For the correction we use observations made at lower angular resolution with the KOSMA 3 m telescope. Smeared to the resolution of the error beam, they provide an estimate of the pick-up therein. The error beam pick-up accounts for a significant fraction of the observed intensity in the key-project maps: on average 31% to 50% for the 12CO $J=2\rightarrow$ 1 maps, 10% to 35% for the 13CO $J=2\rightarrow$ 1 maps, and 16.5% in the 12CO $J=1\rightarrow$ 0 map of MCLD 123.5+24.9. In addition, the line profiles are significantly modified by the error beam pick-up. The large data set available with the IRAM key-project allows us to investigate the accuracy of the correction method and its limitations in detail. For the corrected maps, we determine the overall accuracy of the temperature scale to be better than 15% , except for the 13CO $J=2\rightarrow$ 1 map of MCLD123.5+24.9 and L1512 where we estimate an accuracy of 22% and 18% . The key-project maps presented here and the released maps published by Falgarone et al. (1998) (with the correction done using the previous beam pattern parameters determined by Garcia-Burillo et al. 1993) differ by no more than 10% and only in localized regions. Both data sets and the supplementary observations made with the KOSMA telescope are available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html The "error beam problem"is not limited to observations obtained with the IRAM 30 m. Similar beam pattern are found for other large single dish (sub-)mm telescopes, although few quantitative studies exist. In particular, for observations of spatially extended sources, the error beam contribution has to be considered and corrected for if necessary.
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