H II region filling factors in NGC 628: Luminosity-size relation and connection with polycyclic aromatic hydrocarbon emission

Abstract: Understanding the internal structure of H II regions is fundamental for constraining star formation processes in galaxies. We investigated how the filling factor (FF) relates to luminosity, size, electron density, and H$α$ equivalent width (EW(H$α$)) in H II regions, and explored its connection with polycyclic aromatic hydrocarbon (PAH)-to-dust emission as a possible tracer of evolutionary stages. We analyzed 622 H II regions in NGC~628, combining 475 regions from SIGNALS and 147 from PHANGS-MUSE. We derived their luminosities, emission-line fluxes, radii, electron densities, and FF, and used PHANGS-JWST/MIRI imaging to quantify the PAH-to-dust ratio $R_{\rm PAH}$ from the 7.7, 11.3, and 21~$μ$m bands. Higher FF and EW(H$α$) values are found in luminous regions, whereas more extended regions with lower EW(H$α$) exhibit lower FF. We show that the H II region radius definition significantly affects the $L_{\rm Hα}$--$R$ relation. Low-luminosity compact H II regions appear to mark a transition from cluster-powered regions to nebulae ionized by single massive stars, around $\log(L_{\rm Hα}) \sim 37~{\rm erg \ s<sup>{-1}}$. The PAH-to-dust ratio correlates with the volumetric H$α$ luminosity density, $L_{\rm Hα}/R<sup>3$, with a transition around $$\log(L_{\rm Hα}/R³⁾ \sim 32~{\rm erg \ s<sup>{-1}}$$, corresponding to $\log({\rm FF}) \approx -4.4$. Regions with lower FF exhibit higher $R_{\rm PAH}$, suggesting less efficient PAH processing in more porous structures. These results are consistent with an evolutionary scenario in which FF decreases with stellar cluster age as giant H II regions evolve toward fainter and more extended states. The volumetric H$α$ luminosity density reduces covariance between $L_{\rm Hα}$ and $R$ induced by region-definition methods, enabling more consistent cross-catalog comparisons.