Detection of satellite remnants in the Galactic Halo with Gaia - I. The effect of the Galactic background, observational errors and sampling

We address the problem of identifying remnants of satellite galaxies in the halo of our galaxy with Gaia data. The remnants have to be extracted from a very large data set (of order 10^9 stars) in the presence of observational errors and against a background population of Galactic stars. We address this issue through a numerical simulation of the Gaia catalogue with a realistic number of entries. The Galaxy model includes separate light distributions and kinematics for the bulge, disc and stellar halo. Our catalogue contains 3.5x10^8 stars. We perform tree code 10^6-body simulations of satellite dwarf galaxies in orbit around a rigid mass model of the Galaxy. The shrinking satellite cores and tidal tails are added to the Monte Carlo simulation of the Gaia catalogue. When combining the Milky Way and dwarf galaxy models we include the complication that the luminosity function of the satellite is probed at various depths as a function of position along the tidal tails. The combined models are converted to a synthetic Gaia catalogue using a detailed model for the expected astrometric and radial velocity errors, depending on magnitude, colour and sky position of the stars. We explore the feasibility of detecting tidal streams in the halo using the energy versus angular momentum plane. A straightforward search in this plane will be very challenging. The background population and the observational errors make it difficult to detect tidal streams as discrete structures in the E-Lz plane. The propagation of observational errors leads to apparent caustic structures in the integrals of motion space that may be mistaken for physical entities. Any practical search strategy will have to use a combination of pre-selection of high-quality data and complementary searches using the photometric data from Gaia. (abridged)