As part of the first high resolution far-IR spectral survey of the Orion KL region ( Lerate et al .
2006 ) , we observed 20 CO emission lines with J _ { up } =16 to J _ { up } =39 ( upper levels from \approx 752 K to 4294 K above the ground state ) .
Observations were taken using the Long Wavelength Spectrometer ( LWS ) on board the Infrared Space Observatory ( ISO ) , in its high resolution Fabry-Pérot ( FP ) mode ( \approx 33 km s ^ { -1 } ) .
We present here an analysis of the final calibrated CO data , performed with a more sophisticated modelling technique than hitherto , including a detailed analysis of the chemistry , and discuss similarities and differences with previous results .
The inclusion of chemical modelling implies that atomic and molecular abundances are time-predicted by the chemistry .
This provides one of the main differences with previous studies in which chemical abundances needed to be assumed as initial condition .
The chemistry of the region is studied by simulating the conditions of the different known components of the KL region : chemical models for a hot core , a plateau and a ridge are coupled with an accelerated \Lambda -iteration ( ALI ) radiative transfer model to predict line fluxes and profiles .
We conclude that the CO transitions with 18 < J _ { up } < 25 mainly arise from a hot core of diameter 0.02 pc and a density of 10 ^ { 7 } cm ^ { -3 } rather from the plateau as previous studies had indicated .
The rest of the transitions originate from shocked gas in a region of diameter \approx 0.06 pc with densities ranging from 3 \times 10 ^ { 5 } –1 \times 10 ^ { 6 } cm ^ { -3 } .
The resulting CO fractional abundances are in the range X ( CO ) = ( 7.0–4.7 ) \times 10 ^ { -5 } .
A high temperature post-shock region at more than 1000 K is necessary to reach transitions with J _ { up } > 32 , whilst transitions with J _ { up } < 18 probably originate from the extended warm component .
Finally , we discuss the spatial origin of the CO emission compared with that of the next most abundant species detected by the far-IR survey towards Orion KL : H _ { 2 } O and OH .