IRC + 10 216 revisited II . The circumstellar CO shell ?

12 CO and 13 CO J = 6-5 observations of IRC +10 216 with the JCMT are presented. A spherically symmetric radia-tive transfer code is used to model these and other CO observations of the carbon star IRC +10 216/CW Leo. Compared to previously published model calculations a much larger set of observational data is used as constraints; on-source 12 CO and 13 CO J = 1-0 up to J = 6-5 and mapping data taken with various telescopes, most of which are obtained from the literature. The gas temperature in the envelope is calculated taking into account heating and cooling. The heating by dust-gas collisions and various other parameters (such as luminosity over distance squared) are constrained from our previous modeling of the circumstellar dust shell. Photoelectric heating is taken into account. A grid of models is calculated with the following parameters: luminosity (in the range 10 000 – 30 000, in steps of 5 000 L), mass loss rate, dust-togas ratio, dust opacity and CO abundance. For each of the considered luminosities a good fit to the on-source data can be obtained. A comparison with CO J = 1-0 data obtained from the literature points towards a preferred luminosity of 10-15 000 L. Notwithstanding the overall good agreement, there remain discrepancies. The different observed 12 CO J = 3-2 observations appear to be always larger than the model predictions. The observed 13 CO J = 6-5 is almost flat-topped, while the model gives a slight double-peaked profile. There is a large discrepancy with the single existing 12 CO J = 7-6 observation. The best fitting models (for each of the considered luminosi-ties) cannot accommodate the more extended emission seen in the mapping data. This is not due to an underestimate of the photoelectric effect. To fit the data for radial offsets >50 the mass loss rate must be a factor of 5 higher in the outer envelope. Because the various sets of data for offsets > ∼ 150 are not consistent with each other it is unclear if the enhancement in the mass loss rate extends beyond that radius. Visibility curves are calculated for comparison with future interferometric observations. These appear to be insensitive to luminosity and mass loss variations but should be good tracers of the geometry of the CO shell. A comparison is made between the mass loss rates and dust-togas ratios derived from the CO …