The infrared compactness-temperature relation for quiescent and   starburst galaxies
  IRAS observations show the existence of a correlation between the infrared luminosity Lir and dust temperature Td in star-forming galaxies, in which larger Lir leads to higher dust temperature. The Lir-Td relation is commonly seen as reflecting the increase in dust temperature in galaxies with higher star formation rate. Even though the correlation shows a significant amount of dispersion, a unique relation has been commonly used to construct spectral energy distributions of galaxies in distant universe studies, such as source number counting or photometric redshift determination. In this work, we introduce a new parameter, namely the size of the star-forming region Rir and lay out the empirical and modelled relation between the global parameters Lir, Td and Rir of IR-bright non-AGN galaxies. IRAS 60-to-100um color is used as a proxy for the dust temperature and the 1.4GHz radio contiuum emission for the infrared spatial distribution. The analysis has been carried out on two samples. The first one is made of the galaxies from the 60um flux-limited IRAS Revised Bright Galaxy Samples which have a reliable RC size estimate from the VLA follow-ups of the IRAS Bright Galaxy Samples. The second is made of the sources from the 170um ISOPHOT Serendipity Sky Survey which are resolved by the NVSS or FIRST surveys. We show that the dispersion in the Lir-Td diagram can be reduced to a relation between the infrared surface brightness and the dust temperature, a relation that spans 5 orders of magnitude in surface brightness. We explored the physical processes giving rise to the Sir-Td relation, and show that it can be derived from the Schmidt law, which relates the star formation rate to the gas surface density. 
Pierre Chanial, Hector Flores, Bruno Guiderdoni, David Elbaz, Francois   Hammer, and Laurent Vigroux