Aims: We aim to better understand the heating of gas by observing the prominent gas cooling line [C ii] at 158 {$μ$}m in the low-metallicity environment of the Local Group spiral galaxy M 33 on... Show moreAims: We aim to better understand the heating of gas by observing the prominent gas cooling line [C ii] at 158 {$μ$}m in the low-metallicity environment of the Local Group spiral galaxy M 33 on scales of 280 pc. In particular, we describe the variation of the photoelectric heating efficiency with the galactic environment. Methods: In this study, we present [C ii] observations along the major axis of M 33 using the Infrared Space Observatory in combination with Herschel continuum maps, IRAM 30 m CO 2-1, and VLA H i data to study the variation in velocity integrated intensities. The ratio of [C ii] emission over the far-infrared continuum is used as a proxy for the heating efficiency, and models of photon-dominated regions are used to study the local physical densities, far-ultraviolet radiation fields, and average column densities of the molecular clouds. Results: The heating efficiency stays constant at 0.8% in the inner 4.5 kpc radius of the galaxy, where it increases to reach values of ~{}3% in the outskirts at about a 6 kpc radial distance. The rise of efficiency is explained in the framework of PDR models by lowered volume densities and FUV fields for optical extinctions of only a few magnitudes at constant metallicity. For the significant fraction of H i emission stemming from PDRs and for typical pressures found in the Galactic cold neutral medium (CNM) traced by H i emission, the CNM contributes ~{}15% to the observed [C ii] emission in the inner 2 kpc radius of M 33. The CNM contribution remains largely undetermined in the south, while positions between radial distances of 2 and 7.3 kpc in the north of M 33 show a contribution of ~{}40% {plusmn} 20%. Herschel is an ESA space observatory with science instruments provided by European-led PrincipalInvestigator consortia and with important participation from NASA.Appendices are available in electronic form at http://www.aanda.orgShow less
