We study the far-infrared emission from the nearby spiral galaxy M33 in order to investigate the dust physical properties such as the temperature and the luminosity density across the galaxy. Taking advantage of the unique wavelength coverage (100, 160, 250, 350 and 500 micron) of the Herschel Space Observatory and complementing our dataset with Spitzer-IRAC 5.8 and 8 micron and Spitzer-MIPS 24 and 70 micron data, we construct temperature and luminosity density maps by fitting two modified blackbodies of a fixed emissivity index of 1.5. We find that the cool dust grains are heated at temperatures between 11 and 28 K with the lowest temperatures found in the outskirts of the galaxy and the highest ones in the center and in the bright HII regions. The infrared/submillimeter total luminosity (5 - 1000 micron) is estimated to be 1.9x10^9 Lsun. 59% of the total luminosity of the galaxy is produced by the cool dust grains (~15 K) while the rest 41% is produced by warm dust grains (~55 K). The ratio of the cool-to-warm dust luminosity is close to unity (within the computed uncertainties), throughout the galaxy, with the luminosity of the cool dust being slightly enhanced in the center of the galaxy. Decomposing the emission of the dust into two components (one emitted by the diffuse disk of the galaxy and one emitted by the spiral arms) we find that the fraction of the emission in the disk in the mid-infrared (24 micron) is 21%, while it gradually rises up to 57% in the submillimeter (500 micron). We find that the bulk of the luminosity comes from the spiral arm network that produces 70% of the total luminosity of the galaxy with the rest coming from the diffuse dust disk. The cool dust inside the disk is heated at a narrow range of temperatures between 18 and 15 K (going from the center to the outer parts of the galaxy).
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