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Distribution and excitation of thermal methanol in 6.7 GHz maser bearing star-forming regions - I. The nearby source Cepheus A

Context. Candidate high-mass star-forming regions can be identified through the occurrence of 6.7 GHz methanol masers. In these sources the methanol abundance of the gas must be enhanced, because the masers require a considerable methanol path length. The place and time of origin of this enhancement is not well known. Similarly, it is debated in which of the physical components of the high-mass star-forming region the masers are located. Aims. The aim of this study is to investigate the distribution and excitation of the methanol gas around Cep A and to describe the physical conditions of the region. In addition the large-scale abundance distribution is determined to understand the morphology and kinematics of star-forming regions in which methanol masers occur. Methods. The spatial distribution of methanol is studied by mapping the line emission, as well as the column density and excitation temperature, which are estimated using rotation diagrams. For a limited number of positions the parameters are checked with non-LTE models. Furthermore, the distribution of the methanol abundance is derived in comparison with archival dust continuum maps. Results. Methanol is detected over a 0.3x0.15 pc area centred on the Cep A HW2 source and shows an outflow signature. Most of the gas can be characterized by a moderately warm rotation temperature (30-60 K). At the central position two velocity components are detected with different excitation characteristics, the first related to the large-scale outflow. The second component, uniquely detected at the central location, is probably associated with the maser emission on much smaller scales of 2 ''. A detailed analysis reveals that the highest densities and temperatures occur for these inner components. In the inner region the dust and gas are shown to have different physical parameters. Conclusions. Abundances of methanol in the range 10(-9)-10(-7) are inferred, with the abundance peaking at the maser position. The geometry of the large-scale methanol is in accordance with previous determinations of the Cep A geometry, in particular those from methanol masers. The dynamical and chemical time-scales are consistent with a scenario where the methanol originates in a single driving source associated with the HW2 object and the masers in its equatorial region.