The Photon Dominated Region in the IC 348 molecular cloud

In this paper we discuss the physical conditions of clumpy nature in the IC 348 molecular cloud. We combine new observations of fully sampled maps in [C I] at 492 GHz and 12CO 4--3, taken with the KOSMA 3 m telescope at about 1' resolution, with FCRAO data of 12CO 1--0, 13CO 1--0 and far-infrared continuum data observed by HIRES/IRAS. To derive the physical parameters of the region we analyze the three different line ratios. A first rough estimate of abundance is obtained from an LTE analysis. To understand the [C I] and CO emission from the PDRs in IC 348, we use a clumpy PDR model. With an ensemble of identical clumps, we constrain the total mass from the observed absolute intensities. Then we apply a more realistic clump distribution model with a power law index of 1.8 for clump-mass spectrum and a power law index of 2.3 for mass-size relation. We provide detailed fits to observations at seven representative positions in the cloud, revealing clump densities between 4 10$^{4}$ cm$^{-3}$ and 4 10$^{5}$ cm$^{-3}$ and C/CO column density ratios between 0.02 and 0.26. The derived FUV flux from the model fit is consistent with the field calculated from FIR continuum data, varying between 2 and 100 Draine units across the cloud. We find that both an ensemble of identical clumps and an ensemble with a power law clump mass distribution produce line intensities which are in good agreement (within a factor ~ 2) with the observed intensities. The models confirm the anti-correlation between the C/CO abundance ratio and the hydrogen column density found in many regions.