A spatially resolved study of photoelectric heating and [C II] cooling in the LMC Comparison with dust emission as seen by SAGE

Context. Photoelectric heating is a dominant heating mechanism for many phases of the interstellar medium. We study this mechanism throughout the Large Magellanic Cloud (LMC).Aims. We aim to quantify the importance of the [C II] cooling line and the photoelectric heating process of various environments in the LMC and to investigate which parameters control the extent of photoelectric heating.Methods. We use the BICE [C II] map and the Spitzer/SAGE infrared maps. We examine the spatial variations in the efficiency of photoelectric heating: photoelectric heating rate over power absorbed by grains, i.e. the observed [C II] line strength over the integrated infrared emission. We correlate the photoelectric heating efficiency and the emission from various dust constituents and study the variations as a function of Ha emission, dust temperatures, and the total infrared luminosity. The observed variations are interpreted in a theoretical framework. From this we estimate radiation field, gas temperature, and electron density.Results. We find systematic variations in photoelectric efficiency. The highest efficiencies are found in the diffuse medium, while the lowest coincide with bright star-forming regions (similar to 1.4 times lower). The [C II] line emission constitutes 1.32% of the far infrared luminosity across the whole of the LMC. We find correlations between the [C II] emission and ratios of the mid infrared and far infrared bands, which comprise various dust constituents. The correlations are interpreted in light of the spatial variations of the dust abundance and by the local environmental conditions that affect the dust emission properties. As a function of the total infrared surface brightness, S-TIR, the [C II] surface brightness can be described as: S [C II] = 1.25 S-TIR(0.69) [10(-3) erg s(-1) cm(-2) sr(-1)], for S-TIR greater than or similar to 3.2 x 10(-4) erg s(-1) cm(-2) sr(-1). We provide a simple model of the photoelectric efficiency as a function of the total infrared luminosity. We find a power-law relation between radiation field and electron density, consistent with other studies. The [ C II] emission is well-correlated with the 8 mu m emission, suggesting that the polycyclic aromatic hydrocarbons play a dominant role in the photoelectric heating process.