A Two-Component Probability Distribution Function Describes the mid-IR Emission from the Disks of Star-Forming Galaxies

High-resolution JWST-MIRI images of nearby spiral galaxies reveal emission with complex substructures that trace dust heated both by massive young stars and the diffuse interstellar radiation field. We present high angular (0."85) and physical resolution (20-80 pc) measurements of the probability distribution function (PDF) of mid-infrared (mid-IR) emission (7.7-21 $\mu$m) from 19 nearby star-forming galaxies from the PHANGS-JWST Cycle-1 Treasury. The PDFs of mid-IR emission from the disks of all 19 galaxies consistently show two distinct components: an approximately log-normal distribution at lower intensities and a high-intensity power-law component. These two components only emerge once individual star-forming regions are resolved. Comparing with locations of HII regions identified from VLT/MUSE H$\alpha$-mapping, we infer that the power-law component arises from star-forming regions and thus primarily traces dust heated by young stars. In the continuum-dominated 21 $\mu$m band, the power-law is more prominent and contains roughly half of the total flux. At 7.7-11.3 $\mu$m, the power-law is suppressed by the destruction of small grains (including PAHs) close to HII regions while the log-normal component tracing the dust column in diffuse regions appears more prominent. The width and shape of the log-normal diffuse emission PDFs in galactic disks remain consistent across our sample, implying a log-normal gas column density $N$(H)$\approx10^{21}$cm$^{-2}$ shaped by supersonic turbulence with typical (isothermal) turbulent Mach numbers $\approx5-15$. Finally, we describe how the PDFs of galactic disks are assembled from dusty HII regions and diffuse gas, and discuss how the measured PDF parameters correlate with global properties such as star-formation rate and gas surface density.