On the life and death of satellite haloes

We study the evolution of dark matter satellites orbiting inside more massive haloes using semi-analytical tools coupled with high-resolution N-body simulations. We select initial satellite sizes, masses, orbital energies, and eccentricities as predicted by hierarchical models of structure formation. Both the satellite (of initial mass Ms,0) and the main halo (of mass Mh) are described by a Navarro, Frenk & White density profile with various concentrations. We explore the interplay between dynamic friction and tidal mass loss/evaporation in determining the final fate of the satellite. We provide a user-friendly expression for the dynamic friction time-scale τdf,live and for the disruption time for a live (i.e. mass-losing) satellite. This can be easily implemented into existing semi-analytical models of galaxy formation improving considerably the way they describe the evolution of satellites. Massive satellites (Ms,0 > 0.1Mh) starting from typical cosmological orbits sink rapidly (irrespective of the initial circularity) toward the centre of the main halo where they merge after a time τdf,rig, as if they were rigid. Satellites of intermediate mass (0.01Mh < Ms,0 < 0.1Mh) suffer severe tidal mass losses as dynamic friction reduces their pericentre distance. In this case, mass loss increases substantially their decay time with respect to a rigid satellite. The final fate depends on the concentration of the satellite, cs, relative to that of the main halo, ch. Only in the unlikely case where cs/ch≲ 1 are satellites disrupted. In this mass range, τdf,live gives a measure of the merging time. Among the satellites whose orbits decay significantly, those that survive must have been moving preferentially on more circular orbits since the beginning as dynamical friction does not induce circularization. Lighter satellites (Ms,0 < 0.01Mh) do not suffer significant orbital decay and tidal mass loss stabilizes the orbit even further. Their orbits should map those at the time of entrance into the main halo. After more than a Hubble time satellites have masses Ms∼ 1–10 per cent Ms,0, typically, implying Ms < 0.001Mh for the remnants. In a Milky-Way-like halo, light satellites should be present even after several orbital times with their baryonic components experimenting morphological changes due to tidal stirring. They coexist with the remnants of more massive satellites depleted in their dark matter content by the tidal field, which should move preferentially on tightly