Quantifying the scale of star formation across the Perseus spiral arm using young clusters around Cas OB5

Cas OB5 is an OB association located at a distance of 2.5-3 kpc that intercepts the Perseus spiral arm. It carries a moderate amount of reddening ($A_V \sim$ 2-3 mag) and contains several well-known open clusters within its boundaries, such as King 12, NGC 7788, and NGC 7790. The availability of modern clustering algorithms, together with \textit{Gaia} DR3 kinematics and complementary spectroscopic data, makes it a suitable site for studies of Galactic structure. We seek to quantify the spatial scale of star formation in the spiral arms, using Cas OB5 as a pilot target before extending our study to more distant and extinguished regions of the Galaxy. We selected 129,695 candidate OBA stars in a 6x8 deg$^2$ region around Cas OB5. We applied a spectral energy distribution (SED) fitting process to this sample to derive the physical parameters. Through this process, we found 56 379 OBA stars, which we then clustered using HDBSCAN. We identified 17 open clusters inside this area, four of which appear to form a coherent structure that we identify as Cas OB5. Nevertheless, our findings suggest that these clusters belong to two different age groups despite sharing a similar position and kinematics. Spectroscopic observations confirm the youth of NGC 7788 (10-15 Myr) compared to NGC 7790 ($110\pm15\:$Myr). We have determined a spatial scale for star formation of a few tens of pc to a few hundreds of pc, comparing the clustered to the diffuse population of Cas~OB5 across this part of the Perseus arm. A spectroscopic analysis was required to complement the clustering algorithm, so that we could separate younger OCs (tracers of the spiral arm) from older ones. These results highlight the need to combine these techniques to fully disentangle the Milky Way structure.