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

Context. Structural parameters of model star clusters are measured in radial profiles built from number-density, mass-density and surface-brightness distributions, assuming as well different photometric conditions. Aims. We 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 massdensity 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 surfacebrightness 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