Beschreibung:
The ratio of the [C ii ] ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn1.gif] $158\,\mu \rmm$ emission line over the total infrared emission (TIR) is often used as a proxy for the photoelectric (PE) heating efficiency ( ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn2.gif] $\epsilon _\mathrmPE$ ) of the far-ultraviolet (FUV) photons absorbed by dust in the interstellar medium. In the nearby galaxy M31, we measure a strong radial variation of [C ii ]/TIR that we rule out as being due to an intrinsic variation in ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn3.gif] $\epsilon _\mathrmPE$ . [C ii ]/TIR fails as a proxy for ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn4.gif] $\epsilon _\mathrmPE$ , because the TIR measures all dust heating, not just the contribution from FUV photons capable of ejecting electrons from dust grains. Using extensive multi-wavelength coverage from the FUV to far-infrared, we infer the attenuated FUV emission ( ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn5.gif] $\mathrmUV_\mathrmatt$ ), and the total attenuated flux ( ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn6.gif] $\mathrmTOT_\mathrmatt$ ). We find [C ii ]/TIR to be strongly correlated with ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn7.gif] $\mathrmUV_\mathrmatt$ / ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn8.gif] $\mathrmTOT_\mathrmatt$ , indicating that, in M31 at least, one of the dominant drivers for [C ii ]/TIR variation is the relative hardness of the absorbed stellar radiation field. We define ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn9.gif] $\epsilon _\mathrmPE^\mathrmUV$ , [C ii ]/ ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn10.gif] $\mathrmUV_\mathrmatt$ which should be more closely related to the actual PE efficiency, which we find to be essentially constant ( ##IMG## [http://ej.iop.org/images/0004-637X/842/2/128/apjaa7265ieqn11.gif] $1.85\pm 0.8 % $ ) in all explored fields in M31. This suggests that part of the observed variation of [C ii ]/TIR in other galaxies is likely due to a change in the relative hardness of the absorbed stellar radiation field, caused by a combination of variations in the stellar population, dust opacity, and galaxy metallicity, though PE efficiency may also vary across a wider range of environments.