5 The released data set and comparison to the independently reduced data set presented here

   
5.1 Self-consistent error beam correction

Irrespective of the possible reasons which result in a systematically under-(or over-) estimated error beam pick-up, we now assume that the $\mu_x\ne1$ is due to systematic errors in the intensity calibration of the KOSMA data. In this case a correction can be done by scaling the KOSMA spectra by $(\mu_x)^{-1}$. This is reasonable because the distributions in Fig. 11 are narrow with a distinct maximum (except for the ¹³CO $J=2\rightarrow$ 1 map of MCLD 123.5+24.9). The thus corrected key-project spectra give a better estimate for the corrected main beam brightness temperature scale.

This procedure was applied to the released data set of the key-project (Paper I) and the data set presented here. However, one has to keep in mind that this is an ad hoc correction. The residual difference between the KOSMA and the corrected, smoothed IRAM spectra is not solely due to the KOSMA error beam pick-up, as shown above.

5.2 Correction of the CO $\mathsfsl{J}\ \mathsf{=1 \rightarrow 0}$ observations

No observations from a smaller telescope are available to correct the CO $J=1\rightarrow$ 0 maps of the key-project, except for the ¹²CO $J=1\rightarrow$ 0 map of MCLD 123.5+24.9. An alternative correction method is therefore applied, based on the assumption that the intensity ratio CO $J=2\rightarrow$ 1 to CO $J=1\rightarrow$ 0 (hereafter ${{\cal R}_{21}}$) is constant on the angular scale of the error beam pattern. We can then use the KOSMA CO $J=2\rightarrow$ 1 observations, scaled by ${{\cal R}_{21}}^{-1}$, to estimate the error beam pick-up in the CO $J=1\rightarrow$ 0 maps. A constant ratio ${{\cal R}_{21}}$ has been noted for a large number of cold molecular clouds (e.g. Falgarone & Phillips 1996).

For an application to the key-project maps we merge the ratio ${{\cal R}_{21}}$ and the ad hoc scaling factor for the KOSMA data to a single scaling factor, which is determined for each map with the x-distribution. This is done for the ¹²CO $J=1\rightarrow$ 0 map of L1512 and L134A, and for the ¹³CO $J=1\rightarrow$ 0 map of MCLD 123.5+24.9 and L134A. The signal-to-noise ratio of the remaining maps (C¹⁸O $J=1\rightarrow$ 0 maps, and the ¹³CO $J=1\rightarrow$ 0 map of L1512) is too small to reliably determine the scaling factor. For these maps the correction is done using the KOSMA CO $J=2\rightarrow$ 1 data, assuming a constant ratio of ${{\cal R}_{21}}=0.65$ (Paper I).

The accuracy of this correction method is estimated by using the ¹²CO $J=1\rightarrow$ 0 map of MCLD 123.5+24.9, where KOSMA observations of both lower CO transitions are available. The key-project map, corrected with the KOSMA ¹²CO $J=1\rightarrow$ 0 data, and the same map, corrected with the KOSMA ¹²CO $J=2\rightarrow$ 1 observations scaled by ${{\cal R}_{21}}^{-1}=1/0.65$, differ by no more than 15% if the correction is done according to Eq. (2), and 7% if the correction is done self-consistently.

   
5.3 Accuracy of the final data set

For the ¹²CO and ¹³CO $J=2\rightarrow$ 1 key-project maps we estimate an overall accuracy of the intensity calibration of 10-15%, judged from the $\sigma _x$ in Fig. 11. Only for two data sets (the ¹³CO $J=2\rightarrow$ 1 map of MCLD 123.5+24.9 and L1512) we determine larger uncertainties of 22% and 18%, respectively. For these maps the accuracy is limited by the uncorrected first error beam. For the CO J= $1\rightarrow$ 0 data we deduce an overall accuracy of 11%, using the 7% accuracy estimated in the previous section with the 9% accuracy of the relative intensity calibration (Panis 1995) being added in quadrature.

The data reduction of key-project maps was done independently in Paris and Cologne. For the released data set (Paper I), the correction was done using the beam pattern parameters determined by GGC. The correction of the independently reduced data set presented here is done using the more recent beam measurements by GKW. The comparison of both data sets show that the integrated spectral line maps differ by no more than 10%, consistent with the estimated accuracy.

The released maps of the key-project, the data set presented with this paper and the complementary 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