Deriving physical parameters of unresolved star clusters

Context. The aperture photometry method is a powerful tool that enables us to study large star cluster systems efficiently. However, its accuracy depends on various factors, including the stochasticity of the stellar initial mass function and variations in the sky background. Previously, in the eighth paper of this series, we established the best achievable limits of the aperture photometry method for star cluster studies in the local Universe. Aims. The aim of this study is to determine how the sky background affects the limits and applicability of the aperture photometry method in star cluster analysis. Methods. We used a large sample of star cluster models spanning the parameter space of M 31 clusters. Synthetic images were generated to match the Panchromatic Hubble Andromeda Treasury (PHAT) survey observations. To determine how the background affects star cluster photometry, we placed images of simulated clusters into five background fields of different stellar densities from the PHAT survey and measured them using aperture photometry. Results. We determined age and mass limits for the M 31 disc star clusters at which photometric uncertainties are low enough to enable the determination of cluster parameters using the aperture photometry method. We demonstrated that for typical-size clusters, optimal aperture diameters are of ∼3 half-light radii. We assessed cluster detection completeness in relation to varying sky background densities, based on the M 31 PHAT survey data. Our results suggest that a significant selection bias towards more compact clusters may exist in the PHAT survey. We derived low-mass limits of the cluster mass function (CMF) in the PHAT survey, reaching down to masses of ∼500 M ⊙ in outer disc areas, ∼1500 M ⊙ in middle disc or star-forming regions, and ∼3000 M ⊙ in inner disc regions. Therefore, we stress the necessity of careful accounting for selection effects arising due to sky background variations when studying the CMF.