The high latitude translucent molecular cloud L1642 has been mapped in the J=1-0 and J=2-1 transitions of 12CO, 13CO and C18O using the SEST radio telescope. We have analysed the morphology and velocity structure of the cloud using the Positive Matrix Factorization (PMF) method. The results show that L1642 is composed of a main structure at radial velocity 0.2 km/s while the higher velocity components at ~0.5 and 1.0 km/s form an incomplete ring around it, suggesting an expanding shell structure. Fainter emission extends to the north with a still higher velocity of up to 1.6 km/s. Such a velocity structure suggests an elongated morphology in the line of sight direction. The physical properties of the cloud have been investigated assuming LTE conditions, but non-LTE radiative transfer models are also constructed for the 13CO observations. We confirm that L1642 follows an r^-1 density distribution in its outer parts while the distribution is considerably flatter in the core. The cloud is close to virial equilibrium. In an Appendix the PMF results are compared with the view obtained through the analysis of channel maps and by the use of Principal Component Analysis (PCA). Both PMF and PCA present the observations as a linear combination of basic spectral shapes that are extracted from the data. Comparison of the methods shows that the PMF method in particular is able to produce a presentation of the complex velocity that is both compact and easily interpreted.
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