Unveiling hidden properties of young star clusters: differential reddening, star-formation spread, and binary fraction

Context. Usually, important parameters of young, low-mass star clusters are very difficult to obtain by means of photometry, especially when differential reddening and/or binaries occur in large amounts. Aims. We present a semi-analytical approach (ASAmin) that, when applied to the Hess diagram of a young star cluster, is able to retrieve the values of mass, age, star-formation spread, distance modulus, foreground and differential reddening, and binary fraction. Methods. The global optimisation method known as adaptive simulated annealing (ASA) is used to minimise the residuals between the observed and simulated Hess diagrams of a star cluster. The simulations are realistic and take the most relevant parameters of young clusters into account. Important features of the simulations are a normal (Gaussian) differential reddening distribution, a time-decreasing star-formation rate, the unresolved binaries, and the smearing effect produced by photometric uncertainties on Hess diagrams. Free parameters are cluster mass, age, distance modulus, star-formation spread, foreground and differential reddening, and binary fraction. Results. Tests with model clusters built with parameters spanning a broad range of values show that ASAmin retrieves the input values with a high precision for cluster mass, distance modulus, and foreground reddening, but they are somewhat lower for the remaining parameters. Given the statistical nature of the simulations, several runs should be performed to obtain significant convergence patterns. Specifically, we find that the retrieved (absolute minimum) parameters converge to mean values with a low dispersion as the Hess residuals decrease. When applied to actual young clusters, the retrieved parameters follow convergence patterns similar to the models. We show how the stochasticity associated with the early phases may affect the results, especially in low-mass clusters. This effect can be minimised by averaging out several twin clusters in the simulated Hess diagrams. Conclusions. Even for low-mass star clusters, ASAmin is sensitive to the values of cluster mass, age, distance modulus, star-formation spread, foreground and differential reddening, and to a lesser degree, binary fraction. Compared with simpler approaches, including binaries, a decaying star-formation rate, and a normally distributed differential reddening appears to yield more constrained parameters, especially the mass, age, and distance from the Sun. A robust determination of cluster parameters may have a positive impact on many fields. For instance, age, mass, and binary fraction are important for establishing the dynamical state of a cluster or for deriving a more precise star-formation rate in the Galaxy