| Abstract
| - We study the wavelength dependence of the dust emission as a function of position and environment across the disk of M 33 using Spitzer and Herschel photometric data. M 33 is a Local Group spiral with slightly subsolar metallicity, which makes it an ideal stepping-stone to less regular and lower-metallicity objects such as dwarf galaxies and, probably, young-universe objects. Expressing the emissivity of the dust as a power law, the power-law exponent ( β) was estimated from two independent approaches designed to properly treat the degeneracy between β and the dust temperature ( T). Both β and T are higher in the inner than in the outer disk, contrary to reported β − T anti-correlations found in other sources. In the cold + warm dust model, the warm component and the ionized gas (H α) have a very similar distribution across the galaxy, demonstrating that the model separates the components in an appropriate way. Both cold- and warm-dust column densities are high in star-forming regions and reach their maxima toward the giant star-forming complexes NGC 604 and NGC 595. β declines from close to 2 in the center to about 1.3 in the outer disk. β is positively correlated with star formation and with the molecular gas column, as traced by the H α and CO emission. The lower dust-emissivity index in the outer parts of M 33 is most likely related to the reduced metallicity (different grain composition) and possibly to a different size distribution. It is not due to the decrease in stellar radiation field or temperature in a simple way because the far-infrared-bright regions in the outer disk also have a low β. Like most spirals, M 33 has a (decreasing) radial gradient in star formation and molecular-to-atomic gas ratio such that the regions bright in H α or CO tend to trace the inner disk, which makes it difficult to distinguish between their effects on the dust. The assumption of a constant emissivity index β is obviously not appropriate.
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