12CO 1-0,2-1,4-3,7-6, and 13CO 1-0, 2-1, and 3-2 line was mapped with angular resolutions of 13 - 22 toward the nuclear region of starburst galaxy M82. The difference of lobe spacings in submillimeter (~15) and millimeter (~26) lines indicates the presence of a `low and a `high CO excitation component. An LVG excitation analysis of the submillimeter lines leads to inconsistencies, since area and volume filling factors are almost the same, resulting in cloud sizes along the lines-of-sight that match the entire size of the M82 starburst region. Nevertheless, LVG column densities agree with estimates derived from the dust emission in the far infrared and at submillimeter wavelengths. Accounting for high UV fluxes and variations in kinetic temperature and assuming that the observed emission arises from photon dominated regions (PDRs) resolves the problems related to an LVG treatment of the radiative transfer. 12CO/13CO line intensity ratios > 10 indicate that the bulk of the CO emission arises in UV-illuminated diffuse cloud fragments of small column density and sub-parsec cloud sizes with area filling factors >> 1. Thus CO arises from quite a different gas component than the classical high density tracers. The dominance of such a diffuse molecular interclump medium also explains observed high [CI}/CO line intensity ratios. PDR models do not allow a determination of the relative abundances of 12CO to 13CO. Ignoring magnetic fields, the CO gas appears to be close to the density limit for tidal disruption. A warm diffuse ISM not only dominates the CO emission in the starburst region of M82 but is also ubiquitous in the central region of our Galaxy, where tidal stress, cloud-cloud collisions, shocks, high gas pressure, and high stellar densities may all contribute to the formation of a highly fragmented molecular debris.
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