Constrained Violent Relaxation to a Spherical Halo

Abstract

Violent relaxation during the collapse of a galaxy halo is known to be incomplete in realistic cases such as cosmological infall or mergers. We adopt a physical picture of strong but short-lived interactions between potential fluctuations and particle orbits, using the broad framework outlined earlier for incorporating incompleteness of the relaxation. We are guided by results from plasma physics, viz., the quasilinear theory of Landau damping, but allow for significant differences in our case. Crucially, wave particle scattering does not drive the system to an equilibrium distribution function of the exponential type, even in regions of phase space allowed by the constraints. The physical process is mixing without friction in ``action'' space, for which the simplest possible model is a constant phase space density modulated by the constraints. Our distribution function does not use the exponential functions of the energy prevalent in other work, which we regard as inappropriate to collisionless systems. The dynamical constraint of a finite short period of the relaxation process is argued to lead to a 1/T_r factor in the distribution function, where T_r is the radial period. The notion of strong potential fluctuations in a core is built in as a cutoff in pericenter (which we find preferable to one angular momentum, the other alternative we explored). The halo of the self-consistent, parameter-free solutions show an r^-4 behavior in density at large r, an r^1/4 surface brightness profile in the region 0.1r_e-8r_e, and a radially anisotropic velocity dispersion profile outside an isotropic core. The energy distribution seen in simulations N(E) singles out the pericenter cutoff model as the most realistic among the variants we have explored. The results are robust to modifications of the period dependence keeping the same asymptotic behavior or to the use of binding energy raised to the power of 3/2 in place of 1/T_r.