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The fundamental properties of stellar clusters, such as the age or the total initial mass in stars, are often inferred from population synthesis models. The predicted properties are then used to constrain the physical mechanisms involved in the formation of such clusters in a variety of environments. Population synthesis models cannot, however, be applied blindy to such systems. We show that synthesis models cannot be used in the usual straightforward way to small-mass clusters (say, M < few times 10**4 Mo). The reason is that the basic hypothesis underlying population synthesis (a fixed proportionality between the number of stars in the different evolutionary phases) is not fulfilled in these clusters due to their small number of stars. This incomplete sampling of the stellar mass function results in a non-gaussian distribution of the mass-luminosity ratio for clusters that share the same evolutionary conditions (age, metallicity and initial stellar mass distribution function). We review some tests that can be carried out a priori to check whether a given cluster can be analysed with the fully-sampled standard population synthesis models, or, on the contrary, a probabilistic framework must be used. This leads to a re-assessment in the estimation of the low-mass tail in the distribution function of initial masses of stellar clusters.
Young stellar clusters across nearly five orders of magnitude in mass appear to follow a power-law mass-radius relationship (MRR), $R_{star} propto M_{star}^{alpha}$, with $alpha approx 0.2 - 0.33$. We develop a simple analytic model for the cluster
Galaxy formation entails the hierarchical assembly of mass, along with the condensation of baryons and the ensuing, self-regulating star formation. The stars form a collisionless system whose orbit distribution retains dynamical memory that can const
We analyse Spitzer images of 30 long-duration gamma-ray burst (GRB) host galaxies. We estimate their total stellar masses (M*) based on the rest-frame K-band luminosities (L_Krest) and constrain their star formation rates (SFRs, not corrected for dus
Observations of young open clusters show a bimodal distribution of stellar rotation. Sun-like stars in those clusters group into two main sub-populations of fast and slow rotators. Beyond an age of about 500 Myrs, the two populations converge towards
We provide a review of the current status of several topics on the ages, distances, and mass functions of open clusters, with a particular emphasis on illuminating the areas of uncertainty. Hipparcos has obtained parallaxes for nearby open clusters t