Stellar crowding and the science case for extremely large telescopes

We present a study of the effect of crowding on stellar photometry. We develop an analytical model through which we are able to predict the error in magnitude and color for a given star for any combination of telescope resolution, stellar luminosity function, background surface brightness, and distance. We test our predictions with Monte Carlo simulations of the Large Magellanic Cloud globular cluster NGC 1835, for resolutions corresponding to a seeing-limited telescope, the Hubble Space Telescope, and an adaptive optics (AO) corrected 30 m ( nearly diffraction-limited) telescope. Our analytically predicted magnitude errors agree with the simulation results to within similar to20%. The analytical model also predicts that errors in color are strongly affected by the correlation of crowding-induced photometric errors between bands, as is seen in the simulations. Using additional Monte Carlo simulations and our analytical crowding model, we investigate the photometric accuracy that 30 m and 100 m extremely large telescopes (ELTs) will be able to achieve at distances extending to the Virgo Cluster. We argue that for stellar-populations work, ELTs quickly become crowding-limited, suggesting that low-Strehl AO systems may be sufficient for this type of science.