Detectability of Satellite Planes in Mock Observations of Isolated L* 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 ($N_{\mathrm{sat}}$), the fraction residing in a thin co-rotating plane ($f_{p}$), and the orientation angle relative to the observer ($\theta_{\mathrm{rot}}$). We evaluate the sensitivity of three observational metrics, $N_{\mathrm{cor}}$ (number of co-rotating satellites), $b/a$ (projected flattening of the satellite distribution), and $v_\mathrm{los}$ (mean absolute LOS velocity), to the presence of such planes. Our results show that detection rates are strongly dependent on $\theta_{\mathrm{rot}}$ and $N_{\mathrm{sat}}$. 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 $N_{\mathrm{sat}}>20$ 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.