We study the dust properties of galaxies in the redshift range 0.1<z<2.8 observed by the Herschel Space Observatory in the field of the Great Observatories Origins Deep Survey-North as part of PEP and HerMES key programmes. Infrared (IR) luminosity (L_IR) and dust temperature (T_dust) of galaxies are derived from the spectral energy distribution (SED) fit of the far-infrared (FIR) flux densities obtained with PACS and SPIRE instruments onboard Herschel. As a reference sample, we also obtain IR luminosities and dust temperatures of local galaxies at z<0.1 using AKARI and IRAS data in the field of the Sloan Digital Sky Survey. We compare the L_IR-T_dust relation between the two samples and find that: the median T_dust of Herschel-selected galaxies at z>0.5 with L_IR>5x10^{10} L_odot, appears to be 2-5 K colder than that of AKARI-selected local galaxies with similar luminosities; and the dispersion in T_dust for high-z galaxies increases with L_IR due to the existence of cold galaxies that are not seen among local galaxies. We show that this large dispersion of the L_IR-T_dust relation can bridge the gap between local star-forming galaxies and high-z submillimeter galaxies (SMGs). We also find that three SMGs with very low T_dust (<20 K) covered in this study have close neighbouring sources with similar 24-mum brightness, which could lead to an overestimation of FIR/(sub)millimeter fluxes of the SMGs.
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