Calibrating mid-infrared emission as a tracer of obscured star formation on HII-region scales in the era of JWST

Measurements of the star formation activity on cloud scales are fundamental to uncovering the physics of the molecular cloud, star formation, and stellar feedback cycle in galaxies. Infrared (IR) emission from small dust grains and polycyclic aromatic hydrocarbons (PAHs) are widely used to trace the obscured component of star formation. However, the relation between these emission features and dust attenuation is complicated by the combined effects of dust heating from old stellar populations and an uncertain dust geometry with respect to heating sources. We use images obtained with NIRCam and MIRI as part of the PHANGS--JWST survey to calibrate dust emission at 21$\rm \mu m$, and the emission in the PAH-tracing bands at 3.3, 7.7, 10, and 11.3$\rm \mu m$ as tracers of obscured star formation. We analyse $\sim$ 16000 optically selected HII regions across 16 nearby star-forming galaxies, and benchmark their IR emission against dust attenuation measured from the Balmer decrement. We model the extinction-corrected H$\alpha$ flux as the sum of the observed H$\alpha$ emission and a term proportional to the IR emission, with $a_{IR}$ as the proportionality coefficient. A constant $a_{IR}$ leads to extinction-corrected H$\alpha$ estimates which agree with those obtained with the Balmer decrement with a scatter of $\sim$ 0.1 dex for all bands considered. Among these bands, 21$\rm \mu m$ emission is demonstrated to be the best tracer of dust attenuation. The PAH-tracing bands underestimate the correction for bright HII regions, since in these environments the ratio of PAH-tracing bands to 21$\rm \mu m$ decreases, signalling destruction of the PAH molecules. For fainter HII regions all bands suffer from an increasing contamination from the diffuse infrared background.