The star cluster - field star connection in nearby spiral galaxies. II. Field star and cluster formation histories and their relation

Context. Recent studies have started to cast doubt on the assumption that most stars are formed in clusters. Observational studies of field stars and star cluster systems in nearby galaxies can lead to better constraints on the fraction of stars forming in clusters. Ultimately this may lead to a better understanding of star formation in galaxies, and galaxy evolution in general. Aims. We aim to constrain the amount of star formation happening in long-lived clusters for four galaxies through the homogeneous, simultaneous study of field stars and star clusters. Methods. Using HST/ACS and HST/WFPC2 images of the galaxies NGC 45, NGC 1313, NGC 5236, and NGC 7793, we estimate star formation histories by means of the synthetic CMD method. Masses and ages of star clusters are estimated using simple stellar population model fitting. Comparing observed and modeled luminosity functions, we estimate cluster formation rates. By randomly sampling the stellar initial mass function (SIMF), we construct artificial star clusters and quantify how stochastic effects influence cluster detection, integrated colors, and age estimates. Results. Star formation rates appear to be constant over the past 107−108 years within the fields covered by our observations. The number of clusters identified per galaxy varies, with a few detected massive clusters (M ≥ 105 M ) and a few older than 1 Gyr. Among our sample of galaxies, NGC 5236 and NGC 1313 show high star and cluster formation rates, while NGC 7793 and NGC 45 show lower values.We find that stochastic sampling of the SIMF has a strong impact on the estimation of ages, colors, and completeness for clusters with masses ≤103−104 M , while the effect is less pronounced for high masses. Stochasticity also makes size measurements highly uncertain at young ages (τ 108 yr), making it difficult to distinguish between clusters and stars based on sizes. Conclusions. The ratio of star formation happening in clusters (Γ) compared to the global star formation appears to vary for different galaxies. We find similar values to previous studies (Γ ≈ 2%–10%), but we find no obvious relation between Γ and the star formation rate density (ΣSFR) within the range probed here (ΣSFR ∼ 10−3−10−2 M yr−1 kpc−2). The Γ values do, however, appear to correlate with the specific U-band luminosity (TL(U), the fraction of total light coming from clusters compared to the total U-band light of the galaxy).