Tidal effects on the mass profile of galactic haloes

Most spiral galaxies are believed to be embedded in dark massive haloes^1,2. The main observational evidence for their presence is the rotation curves of edge-on disks at large radii measured both by optical^3,23 and radio (21cm)⁴ techniques: rotation velocities remain constant to distances of several tens of kiloparsecs, far beyond the main visible bodies of the galaxies. This suggests the existence of a dark halo whose mass, if spherical, varies linearly with distance R from the galactic centre and hence has a density profile which falls off as R^-2. The extended 'flat' shape of the haloes poses a problem for most theoretical hypotheses of galaxy formation because simulations of collapse^5-8 and of violent mergers⁹ predict a spherical density profile which is rather Hubble-like (ρ∝R^-3) or even steeper. The time scale for two-body relaxation, which can lead to a flatter, isothermal, density profile, is much larger than the Hubble time. If, as Gunn¹⁰ and Gott⁶ have suggested, secondary cosmological infall produces the ρ∝R^-2 haloes, special initial conditions are required: (1) the central perturbation, which is the progenitor of the galaxy, needs to be initially embedded in a bound homogeneous background - an assumption which might not be fully justified for relatively isolated galaxies; and, (2) the infall must be such that there is no dissipation so that most of the mass should already be in the form of compact objects before halo formation. We suggest, as an alternative mechanism, tidal interactions between haloes, or possibly between their smaller building blocks, while in the hierarchical gravitational clustering process. In this process typical tidal encounters are slow, such that relative orbital velocities of the interacting systems are comparable to the internal velocities of the stars in each system. The two systems are slightly unbound.