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Quantifying the Heating Sources for Mid-infrared Dust Emissions in Galaxies: The Case of M 81

With the newly available SPIRE images at 250 and 500 micron from Herschel Space Observatory, we study quantitative correlations over a sub-kpc scale among three distinct emission components in the interstellar medium of the nearby spiral galaxy M 81 (NGC 3031): (a) $I_{8}$ or $I_{24}$, the surface brightness of the mid-infrared emission observed in the Spitzer IRAC 8 or MIPS 24 micron band, with $I_8$ and $I_{24}$ being dominated by the emissions from Polycyclic Aromatic Hydrocarbons (PAHs) and very small grains (VSGs) of dust, respectively; (b) $I_{500}$, that of the cold dust continuum emission in the Herschel SPIRE 500 micron band, dominated by the emission from large dust grains heated by evolved stars, and (c) $I_{{\rm H}α}$, a nominal surface brightness of the H$α$ line emission, from gas ionized by newly formed massive stars. The results from our correlation study, free from any assumption on or modeling of dust emissivity law or dust temperatures, present solid evidence for significant heating of PAHs and VSGs by evolved stars. In the case of M 81, about 67% (48%) of the 8 micron (24 micron) emission derives its heating from evolved stars, with the remainder attributed to radiation heating associated with ionizing stars.