Low-J CO line emission from PDRs: A natural explanation for the narrow range of observed line ratios

We argue that the surprisingly narrow range of low-J ¹²CO, ¹³CO and C¹⁸O line ratios observed in massive star-formation regions is naturally explained if the CO emission is understood to arise in an ensemble of dense clumps which are embedded in a lower-density interclump medium which is pervaded by stellar radiation. We demonstrate this by presenting PDR computations which focus explicitly on the ¹²CO, ¹³CO and C¹⁸O J = 1 → 0, J = 2 → 1 and J = 3 → 2 rotational line emission for a wide range of cloud conditions. We consider spherical clouds which are illuminated by isotropic far-ultraviolet (FUV) radiation fields. Our models provide a self-consistent treatment of the chemical and thermal balance together with the radiative transfer of the CO line emission. We present results for clouds with power-law density gradients with average hydrogen particle densities 〈n〉 ranging from 10⁴ to 10⁷ cm^-3 and total average hydrogen column densities 〈N〉 between 2.5 × 10²¹ and 4.0 × 10²² cm^-2. We consider clouds exposed to FUV fields (χ) 10² to 10⁴ times more intense than the mean interstellar radiation field. We find that the resulting line ratios are insensitive to the cloud conditions and reproduce the observed values of the relative CO line strengths.