Detectability of Satellite Planes in Mock Observations of Isolated <i>L</i> * Galaxies

The existence and prevalence of planar, co-rotating distributions of satellite galaxies around L* host galaxies in the local universe remains a subject of ongoing debate. Despite numerous observational efforts over the past decade, a statistically robust sample of ”satellite planes” across the diversity of host galaxy environments is lacking. To guide future observing strategies, we construct a controlled suite of mock observations of on-sky positions and line-of-sight (LOS) velocities of isolated L* host galaxies and their satellite systems, based on samples drawn from the Illustris TNG100-1 cosmological simulation to build a statistical sample. In these mock systems, satellite planes are defined by three key parameters: the number of satellites (Nsat), the fraction residing in a thin co-rotating plane (fp), and the orientation angle relative to the observer (θrot). We evaluate the sensitivity of three observational metrics, Ncor (number of co-rotating satellites), b/a (projected flattening of the satellite distribution), and vlos (mean absolute LOS velocity), to the presence of such planes. Our results show that detection rates are strongly dependent on θrot and Nsat. Satellite planes that are viewed nearly edge-on or face-on, are the most readily detected. In contrast, intermediate orientations and systems with fewer satellites yield low detection success rates. Generally, only satellite planes with Nsat > 20 have high chances of being detected. These findings provide a practical framework for prioritising observational targets and designing future surveys aimed at detecting and characterising satellite planes.