The infrared compactness-temperature relation for quiescent and starburst galaxies

Context. IRAS observations show the existence of a correlation between the infrared luminosity L-IR and dust temperature T-d in star-forming galaxies, in which larger L-IR leads to higher dust temperature. The L-IR-T-d relation is commonly seen as reflecting the increase in dust temperature in galaxies with higher star formation rate (SFR). Even though the correlation shows a significant amount of dispersion, a unique relation has been commonly used to construct spectral energy distributions (SEDs) of galaxies in distant universe studies, such as source number counting or photometric redshift determination. Aims. In this work, we introduce a new parameter, namely the size of the star-forming region r(IR) and lay out the empirical and modelled relation between the global parameters L-IR, T-d and r(IR) of IR-bright non-AGN galaxies. Methods. IRAS 60- to- 100 mu m color is used as a proxy for the dust temperature and the 1.4GHz radio contiuum ( RC) 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 60 mu m flux-limited IRAS Revised Bright Galaxy Samples (RBGS) 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 170 mu m ISOPHOT Serendipity Sky Survey (ISOSSS) which are resolved by the NRAO VLA Sky Survey (NVSS) or by the Faint Images of the Radio Sky at Twenty-cm survey ( FIRST). Results. 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. Conclusions. We explored the physical processes giving rise to the Sigma(IR)-T-d relation, and show that it can be derived from the Schmidt law, which relates the star formation rate to the gas surface density.