We use a semianalytic galaxy catalogue constructed from the Millennium Simulation(MS) to study the satellites of isolated galaxies in theCDM cosmogony. The large volume surveyed by the MS (500 3 h 3 Mpc 3 ), together with its unprecedented numerical resolution, e nable the compilation of a large sample of � 80,000 bright (Mr < 20.5) primaries, surrounded by � 178,000 satellites down to the faint magnitude limit (Mr = 17) of our catalogue. This sample allows the characterization, with minimal statistical uncertainty, of the dynam- ical properties of satellite/primary galaxy systems in aCDM universe. The details of this characterization are sensitive to the details of the modeli ng, such as its assumptions on galaxy merging and dynamical friction timescales, but many of its general predictions should be ap- plicable to hierarchical formation models such asCDM. We find that, overall, the satellite population traces the dark matter rather well: its spatial d istribution and kinematics may be approximated by an NFW profile with a mildly anisotropic velo city distribution. Their spatial distribution is also mildly anisotropic, with a well-define d anti-Holmberg effect that reflects the misalignment between the major axis and angular momentum of the host halo. Our anal- ysis also highlights a number of difficulties afflicting stud ies that rely on satellite velocities to constrain the primary halo mass. These arise from variations in the star formation efficiency and assembly history of isolated galaxies, which result in a scatter of up to � 2 decades in halo mass at fixed primary luminosity. Our isolation criteri on (primaries may only have com- panions at least 2 mag fainter within 1 h 1 Mpc) contributes somewhat to the scatter, since it picks not only galaxies in sparse environments, but also a number of primaries at the centre of fossil groups. We find that the abundance and luminosity fu nction of these unusual systems are in reasonable agreement with the few available observational constraints. Much tighter halo mass-luminosity relations are found when splitting the sample by colour: red primaries inhabit halos more than twice as massive as those surrounding blue primaries, a difference that vanishes, however, when considering stellar mass instead of luminosity. The large scat- ter in the halo mass-luminosity relation hinders the interp retation of the velocity dispersion of satellites stacked according to the luminosity of the pri mary. We find L / σ 3 (the natu- ral scaling expected forCDM) for truly-isolated primaries, i.e., systems where the central galaxy contributes more than 85% of the total luminosity within its virial radius. Less stric t primary selection, however, leads to substantial modificat ion of the scaling relation: blindly stacking satellites of all primaries results in a much shall ower L-σ relation that is only poorly approximated by a power law.
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