Structural parameters of star clusters: relations among light, mass and star-count radial profiles and the dependence on photometric depth

Context. Structural parameters of model star clusters are measured in radial profiles built from number-density, massdensity and surface-brightness distributions, assuming as well different photometric conditions. Aims. Determine how the core, half-star count and tidal radii, as well as the concentration parameter, all of which are derived from number-density profiles, relate to the equivalent radii measured in near-infrared surface-brightness and mass-density profiles. We also quantify changes in the resulting structural parameters due to depth-limited photometry. Methods. Star clusters of different ages, structure and mass functions are modelled by assuming that the radial distribution of stars follows a pre-defined analytical form. Near-infrared surface brightness and mass-density profiles result from mass-luminosity relations taken from a set of isochrones. Core, tidal and half-light, half-mass and half-star count radii, together with the concentration parameter, are measured in the three types of profiles, which are built under different photometric depths. Results. While surface-brightness profiles are almost insensitive to photometric depth, radii measured in number-density and mass-density profiles change significantly with it. Compared to radii derived with deep photometry, shallow profiles result in lower values. This effect increases for younger ages. Radial profiles of clusters with a spatially-uniform mass function produce radii that do not depend on depth. With deep photometry, number-density profiles yield radii systematically larger than those derived from surface-brightness ones. Conclusions. In general, low-noise surface-brightness profiles result in uniform structural parameters that are essentially independent of photometric depth. For less-populous star clusters, those projected against dense fields and/or distant ones, which result in noisy surface-brightness profiles, this work provides a quantitative way to estimate the intrinsic radii by means of number-density profiles built with depth-limited photometry.