A spatially resolved study of photoelectric heating and [CII] cooling in the LMC

(abridged) We study photoelectric heating throughout the Large Magellanic Cloud. We quantify the importance of the [CII] cooling line and the photoelectric heating process of various environments in the LMC and investigate which parameters control the extent of photoelectric heating. We use the BICE [CII] 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. We correlate the photoelectric heating efficiency and the emission from various dust constituents and study the variations as a function of Hαemission, dust temperatures, and the total infrared luminosity. From this we estimate radiation field, gas temperature, and electron density. 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 (~1.4 times lower). The [CII] line emission constitutes 1.32% of the far infrared luminosity across the whole of the LMC. We find correlations between the [CII] 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 [CII] surface brightness can be described as: S_{[CII]}=1.25 S_{TIR}^{0.69} [10^{-3} erg s^{-1} cm^{-2} sr^{-1}]. The [CII] emission is well-correlation with the 8 micrometer emission, suggesting that the polycyclic aromatic hydrocarbons play a dominant role in the photoelectric heating process.