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With the newly available SPIRE images at 250 and 500 micron from HerschelSpace Observatory, we study quantitative correlations over a sub-kpc scaleamong three distinct emission components in the interstellar medium of thenearby spiral galaxy M 81 (NGC 3031): (a) $I_{8}$ or $I_{24}$, the surfacebrightness of the mid-infrared emission observed in the Spitzer IRAC 8 or MIPS24 micron band, with $I_8$ and $I_{24}$ being dominated by the emissions fromPolycyclic Aromatic Hydrocarbons (PAHs) and very small grains (VSGs) of dust,respectively; (b) $I_{500}$, that of the cold dust continuum emission in theHerschel SPIRE 500 micron band, dominated by the emission from large dustgrains heated by evolved stars, and (c) $I_{{\rm H}\alpha}$, a nominal surfacebrightness of the H$\alpha$ line emission, from gas ionized by newly formedmassive stars. The results from our correlation study, free from any assumptionon or modeling of dust emissivity law or dust temperatures, present solidevidence for significant heating of PAHs and VSGs by evolved stars. In the caseof M 81, about 67% (48%) of the 8 micron (24 micron) emission derives itsheating from evolved stars, with the remainder attributed to radiation heatingassociated with ionizing stars.

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