Within the framework of the DustPedia project we investigate the properties of cosmic dust and its interaction with the stellar radiation (originating from different stellar populations) for 814 galaxies in the nearby Universe, all observed by the Herschel Space Observatory. We take advantage of the widely used galaxy SED fitting code CIGALE, properly adapted to include the state-of-the-art dust model THEMIS. Using the DustPedia photometry we determine the physical properties of the galaxies, such as, the dust and stellar mass, the star-formation rate, the bolometric luminosity as well as the unattenuated and the absorbed by dust stellar light, for both the old (> 200 Myr) and young (<= 200 Myr) stellar populations. We show how the mass of stars, dust, and atomic gas, as well as the star-formation rate and the dust temperature vary between galaxies of different morphologies and provide recipes to estimate these parameters given their Hubble stage (T). We find a mild correlation between the mass fraction of the small a-C(:H) grains with the specific star-formation rate. On average, young stars are very efficient in heating the dust, with absorption fractions reaching as high as ~77% of the total, unattenuated luminosity of this population. On the other hand, the maximum absorption fraction of old stars is ~24%. Dust heating in early-type galaxies is mainly due to old stars, up to a level of ~90%. Young stars progressively contribute more for `typical spiral galaxies and they become the dominant source of dust heating for Sm type and irregular galaxies, donating up to ~60% of their luminosity to this purpose. Finally, we find a strong correlation of the dust heating fraction by young stars with morphology and the specific star-formation rate.
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