Detection of the Milky Way Reflex Motion Caused by the Magellanic Clouds in Different Observation Accuracy

Motivated by recent studies of the perturbation of the Magellanic Clouds (MCs) on the Milky Way (MW) and the planned multi-band wide-field deep survey named Chinese Space Station Telescope (CSST), we explore the detection limit of the MW reflex motion due to the MCs infall in different observation precision using an MW-MCs-mass galaxy from magpie simulation to provide a reference for the CSST survey. By involving different errors of distance, proper motion, and radial velocity, we investigate the reflex motion characterized by the velocity shift in each velocity component. We find the strongest shifts in the tangential velocities, which align with the motion direction of the MCs. In the ideal case that distance errors dominate, we find a relative distance error of 10% can allow the reliable detection of velocity shifts in tangential velocities within 100 kpc, and a relative distance error of 30% is the minimum requirement to detect the reliable tangential velocity shifts of about 40 km s(-1) within 50 kpc. Different errors of proper motions in combination with a relative distance error of 10% or 20% show an error of 0.1 mas yr(-1) in proper motions can guarantee the reliable detection of velocity shifts in V ( l ) and V ( b ) up to 80-100 kpc and an error of 0.15 mas yr(-1) is the minimum requirement. In the other ideal case that radial velocity errors dominate, we find a radial velocity error of 20 km s(-1) can present reliable reflex motion in line-of-sight velocity up to 70 kpc, while the detection volume will be reduced to 50 kpc as the radial velocity error increases to 40 km s(-1). When the radial velocity error is larger than 60 km s(-1), the velocity shifts cannot be detected anymore. In addition, we find that reliable detection of reflex motion requires at least 20% of the whole sample.