(CO)-C-12 and (CO)-C-13 J = 6-5 observations of IRC +10 216 with the J
CMT are presented. A spherically symmetric radiative transfer code is
used to model these and other CO observations of the carbon star IRC 10 216/CW Lee. Compared to previously published model calculations a m
uch larger set of observational data is used as constraints; on-source
(CO)-C-12 and (CO)-C-13 J = 1-0 UP to J = 6-5 and mapping data taken
with various telescopes, most of which are obtained from the literatur
e. The gas temperature in the envelope is calculated taking into accou
nt heating and cooling. The heating by dust-gas collisions and various
other parameters (such as luminosity over distance squared) are const
rained from our previous modeling of the circumstellar dust shell. Pho
toelectric heating is taken into account. A grid of models is calculat
ed with the following parameters: luminosity (in the range 10 000 - 30
000, in steps of 5 000 L.), mass loss rate, dust-to-gas ratio, dust o
pacity and CO abundance. For each of the considered luminosities a goo
d 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 lumin
osity of 10-15 000 L.. Notwithstanding the overall good agreement, the
re remain discrepancies. The different observed (CO)-C-12 J = 3-2 obse
rvations appear to be always larger than the model predictions. The ob
served (CO)-C-13 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 (CO)-C-12 J = 7-6 observation. The best fitting models
(for each of the considered luminosities) cannot accommodate the more
extended emission seen in the mapping data. This is not due to an und
erestimate of the photoelectric effect. To fit the data for radial off
sets >50 '' the mass loss rate must be a factor of 5 higher in the out
er envelope. Because the various sets of data for offsets greater than
or similar to 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 interferom
etric observations. These appear to be insensitive to luminosity and m
ass 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-to
-gas ratios derived from the CO modelling and those derived from our p
revious dust modelling. To do this we make use of the relation (M) ove
r dot v(infinity) = tau(F) L/c (1 - 1/Gamma), which is valid for radia
tion pressure driven outflows. The best agreement is obtained for the
model with 15 000 L.. This agrees well with the luminosity range 7 700
-12 500 L. based on the period-luminosity relation for carbon miras. I
n summary, we conclude that the likely luminosity of IRC +10 216 is be
tween 10 000 and 15 000 L. and that its distance is between 110 and 13
5 pc. The present-day mass loss rate is (1.5 +/- 0.3) x 10(-5) M. yr(-
1) and the gas-to-dust ratio is a 700 +/- 100. The dust opacity at 60
mu m is found to be of order of 250 cm(2)gr(-1). The CO abundance is 1
.1 x 10(-3) relative to H-2.