The resolved star formation law in NGC 7469 from JWST, ALMA and VLA

We investigate the star formation process within the central 3.3 kpc region of the nearby luminous infrared Seyfert NGC 7469, probing scales ranging from 88 to 330 pc. We combine JWST/MIRI imaging with the F770W filter, with CO(2-1) and the underlying 1.3 mm dust continuum data from ALMA, along with VLA radio continuum observations at 22 GHz. NGC 7469 hosts a starburst ring which dominates the overall star formation activity. We estimate a global star formation rate SFR $\sim 11.5$ $\rm M_{\odot}~yr^{-1}$ from the radio at 22 GHz, and a cold molecular gas mass M(H2) $\sim$ 6.4 $\times$ $\rm 10^9 M_{\odot}$ from the CO(2-1) emission. We find that the 1.3 mm map shows a morphology remarkably similar to those traced by the 22 GHz and the 7.7 $\rm \mu m$ polycyclic aromatic hydrocarbon (PAH) emission observed with JWST. The three tracers reproduce the morphology of the starburst ring with good agreement. We further investigate the correlations between the PAHs, the star formation rate and the cold molecular gas. We find a stronger correlation of the PAHs with the star formation than with the CO, with steeper correlations within the starburst ring ($n > 2$) than in the outer region ($n < 1$). We derive the correlation between the star formation rate and the cold molecular gas mass surface densities, the Kennicutt-Schmidt star formation law. Comparisons with other galaxy populations, including starburst galaxies and active galactic nuclei, highlighted that NGC 7469 exhibits an intermediate behavior to the Kennicutt-Schmidt relations found for these galaxy populations.