on the sources of grain heating [e.g. @takagi03; @takeuchi05; @dopita05]. Dust temperature is determined by the intensity of interstellar radiation field (ISRF) and the optical properties of dust (i.e. how it absorbs and emits light). Since dust grains absorb UV light efficiently, the FIR luminosity and the dust temperature mostly reflect the UV radiation field [@buat96].

Observationally, dust temperature can be estimated from FIR colour, which is defined as the flux ratio between two FIR wavelengths. If more than two ($\geq 3$) bands are available in FIR, we can take two independent FIR colours and examine a FIR colour–colour relation. A colour–colour relation, because of increased information compared with a single FIR colour, enables us to obtain not only the dust temperature but also the wavelength dependence of dust emissivity. @nagata02, adopting 60 $\mu$m, 100 $\mu$m, and 140 $\mu$m as three wavelengths, show that there is a tight relation in the FIR colour–colour diagram. This tightness implies a common wavelength dependence of FIR emissivity among various galaxies. Their work has been developed by @hibi06, who show that a tight FIR colour–colour relation found for the Milky Way dust emission, called “main correlation”, is also consistent with the FIR colour–colour relation 