Dust and star formation properties of a complete sample of local galaxies drawn from the Planck Early Release Compact Source Catalogue

We combine Planck High Frequency Instrument data at 857, 545, 353 and 217 GHz with data from Wide-field Infrared Survey Explorer (WISE), Spitzer, IRAS and Herschel to investigate the properties of a well-defined, flux-limited sample of local star-forming galaxies. A 545 GHz flux density limit was chosen so that the sample is 80 per cent complete at this frequency, and the resulting sample contains a total of 234 local, star-forming galaxies. We investigate the dust emission and star formation properties of the sample via various models and calculate the local dust mass function. Although single-component-modified blackbodies fit the dust emission longward of 80 mu m very well, with a median beta = 1.83, the known degeneracy between dust temperature and beta also means that the spectral energy distributions are very well described by a dust component with dust emissivity index fixed at beta = 2 and temperature in the range 10-25 K. Although a second, warmer dust component is required to fit shorter wavelength data, and contributes approximately a third of the total infrared emission, its mass is negligible. No evidence is found for a very cold (6-10 K) dust component. The temperature of the cold dust component is strongly influenced by the ratio of the star formation rate to the total dust mass. This implies, contrary to what is often assumed, that a significant fraction of even the emission from similar to 20 K dust is powered by ongoing star formation, whether or not the dust itself is associated with star-forming clouds or 'cirrus'. There is statistical evidence of a free-free contribution to the 217 GHz flux densities of less than or similar to 20 per cent. We find a median dust-to-stellar mass ratio of 0.0046; and that this ratio is anticorrelated with galaxy mass. There is good correlation between dust mass and atomic gas mass (median M-d/M-HI = 0.022), suggesting that galaxies that have more dust (higher values of M-d/M-*) have more interstellar medium in general. Our derived dust mass function implies a mean dust mass density of the local Universe (for dust within galaxies), of 7.0 +/- 1.4 x 10(5) M-circle dot Mpc(-3), significantly greater than that found in the most recent estimate using Herschel data.