How accurately can we detect the splashback radius of dark matter haloes and its correlation with accretion rate?

The splashback radius (R_sp) of dark matter haloes has recently been detected using weak gravitational lensing and cross-correlations with galaxies. However, different methods have been used to measure R_sp and to assess the significance of its detection. In this paper, we use simulations to study the precision and accuracy to which we can detect the splashback radius with 3D density, 3D subhalo, and weak lensing profiles. We study how well various methods and tracers recover R_sp by comparing it with the value measured directly from particle dynamics. We show that estimates of R_sp from density and subhalo profiles correspond to different percentiles of the underlying R_sp distribution of particle orbits. At low accretion rates, a second caustic appears and can bias results. Finally, we show that upcoming lensing surveys may be able to constrain the R_sp-Γ_dyn relation directly.