Context. The forbidden fine structure transition of C+ at 158 μm is one of the major cooling lines of the interstellar medium (ISM).
Aims: We aim to understand the contribution of the ionized, atomic, and molecular phases of the ISM to the [C II] emission from clouds near the dynamical center and the BCLMP302 H II region in the north of the nearby galaxy M 33 at a spatial resolution of 50 pc.
Methods: We combine high-resolution [C II] spectra taken with the HIFI spectrometer onboard the Herschel satellite with [C II] Herschel-PACS maps and ground-based observations of CO(2-1) and H I. All data are at a common spatial resolution of 50 pc. Correlation coefficients between the integrated intensities of [C II], CO(2-1) and H I are estimated from the velocity-integrated PACS data and from the HIFI data. We decomposed the [C II] spectra in terms of contribution from molecular and atomic gas detected in CO(2-1) and H I, respectively. At a few positions, we estimated the contribution of ionized gas to [C II] from the emission measure observed at radio wavelengths.
Results: In both regions, the center and BCLMP302, the correlation seen in the [C II], CO(2-1) and H I intensities from structures of all sizes is significantly higher than the highest correlation in intensity obtained when comparing only structures of the same size. The correlations between the intensities of tracers corresponding to the same velocity range as [C II], differ from the correlation derived from PACS data. Typically, the [C II] lines have widths intermediate between the narrower CO(2-1) and broader H I line profiles. A comparison of the spectra shows that the relative contribution of molecular and atomic gas traced by CO(2-1) and H I varies substantially between positions and depends mostly on the local physical conditions and geometry. At the positions of the H II regions, the ionized gas contributes between 10-25% of the observed [C II] intensity. We estimate that 11-60% and 5-34% of the [C II] intensities in the center and in BCLMP302, respectively, arise at velocities showing no CO(2-1) or H I emission and could arise in CO-dark molecular gas. The deduced strong variation in the [C II] emission not associated with CO and H I cannot be explained in terms of differences in AV, far-ultraviolet radiation field, and metallicity between the two studied regions.
Conclusions: The relative amounts of diffuse (CO-dark) and dense molecular gas possibly vary on spatial scales smaller than 50 pc. In both regions, a larger fraction of the molecular gas is traced by [C II] than by the canonical tracer CO. Correlations between observed intensities of [C II], CO, and H I crucially depend on the spatial and spectral resolution of the data and need to be used carefully, in particular, for extragalactic studies. These results emphasize the need for velocity-resolved observations to discern the contribution of different components of the ISM to [C II] emission.
