Quantifying the Detectability of Milky Way Satellites with Image Simulations: a Case Study with KiDS

Ultra-faint dwarf galaxies, which can be detected as resolved satellite systems of the Milky Way, are critical to understanding galaxy formation, evolution, and the nature of dark matter, as they are the oldest, smallest, most metal-poor, and most dark matter-dominated stellar systems known. Quantifying the sensitivity of surveys is essential for understanding their capability and limitations in searching for ultra-faint satellites. In this paper, we present the first study of the image-level observational selection function for Kilo-Degree Survey (KiDS) based on the Synthetic UniveRses For Surveys (surfs)-based KiDS-Legacy-Like Simulations. We generate mock satellites and simulate images that include resolved stellar populations of the mock satellites and the background galaxies, capturing realistic observational effects such as source blending, photometric uncertainties, and star-galaxy separation. The matched-filter method is applied to recover the injected satellites. We derive the observational selection function of the survey in terms of the luminosity, half-light radius, and heliocentric distance of the satellites. Compared to a catalogue-level simulation as used in previous studies, the image-level simulation provides a more realistic assessment of survey sensitivity, accounting for observational limitations that are neglected in catalogue-level simulations. The image-level simulation shows a detection loss for compact sources with a distance $d \gtrsim 100~\rm kpc$. We argue that this is because compact sources are more likely to be identified as single sources rather than being resolved during the source extraction process.