The effect of measurement uncertainties on the inferred stability of planes of satellite galaxies

Context. Observations have revealed that the Milky Way, Andromeda, Centaurus A, and possibly other galaxies host spatially thin and kinematically coherent planes of satellites. Such structures are highly improbable within the standard ΛCDM cosmological model, and the dynamical stability of these planes has long been debated. Accurately determining their stability requires a thorough understanding of orbital parameters such as proper motion, distance, and line-of-sight velocity, in addition to as the gravitational potential of the host galaxy. However, many of these parameters remain poorly constrained, leading to significant uncertainties in analyses. Aims. This study explores the impact of measurement errors in the proper motions and distances of the satellite galaxies and in the adopted host halo mass on the inferred stability of satellite planes in Milky Way-like potentials. Methods. We simulated mock-observed test satellite galaxies orbiting a host galaxy by adding various degrees and types of observational errors, and then backward-integrated the orbits. We analyzed trends and correlations between the initial conditions and the uncertainties applied on the inferred orbital stability of the satellite systems. We also considered the effects of adopting incorrect potentials and the impact of different orbital eccentricities. Results. Uncertainties in proper motions lead to an apparent widening of an intrinsically stable satellite plane, with its width increasing linearly with the uncertainties in the adopted proper motion. Even uncertainties at the level of Gaia systematics strongly affect the plane’s inferred past width. Moreover, the potential with a low halo mass has a significant impact on the stability of these planes, whereas the remaining two host models show similar effects. Uncertainties in satellite distance also contribute noticeably to the inferred instability.