Deep into the core of dense star clusters: an astrometric and photometric test case for {ELT}

We present a novel analysis of a young star cluster in the Large Magellanic cloud, R136-like, as seen by the Extremely Large Telescope (ELT). The main aim of this study is to quantify precision and accuracy of stellar proper motion measurements in crowded field when using an ELT working at its diffraction limit. This can serve as a reference study for future development of ELT scientific cases. In particular, we investigate our future ability to detect the dynamical signature of intermediate-mass black holes (IMBHs) with mass similar to 10(4) M-circle dot through detailed measurements of stellar proper motions. We have simulated two N-body dynamical cluster models with and without an IMBII. For each model, we have chosen two snapshots temporally spaced by 5 yr. Stellar fluxes in IJHK filters and star positions have been used to create ELT mock images for both single- and multiconjugate adaptive optics observing modes following the requierements given by ESO technical specifications for the first light imager. These images have been analysed using a classical software for seeing-limited data reduction, DAOPHOT/ALLSTAR. We make accurate photometry till the very faint pre-main-sequence stars, i.e. depending on the adaptive optics (AO) mode, magnitudes down to K similar to 24 mag (single-conjugate AO) or K similar to 22 mag (multiconjugate AO) in a total integration time of 20 min on target. Although DAOPHOT suite of programs is not devoted to precise astrometry, the astrometric accuracy is impressive, reaching few mu as yr(-1) or km s(-1). In these assumptions, we are able to detect the IMBH signature at the centre of the cluster.