Dynamical flows through dark matter haloes: inner perturbative dynamics, secular evolution and applications

We investigate statistically the dynamical consequences of cosmological fluxes of matter and related moments on progenitors of today's dark matter haloes. These haloes are described as open collisionless systems which do not undergo strong interactions anymore. Their dynamics is described via canonical perturbation theory which accounts for two types of perturbations: the tidal field corresponding to flybys and accretion of dark matter through the outer boundary of the halo. The non-linear evolution of both the entering flux and the particles of the halo is followed perturbatively. The dynamical equations are solved linearly, order by order, projecting on a bi-orthogonal basis to consistently satisfy the field equation. Since our perturbative solution of the Boltzmann–Poisson is explicit, we obtain, as a result, expressions for the N-point correlation function of the response of the halo to the perturbative environment. It allows statistical predictions for the ensemble distribution of the inner dynamical features of haloes. We demonstrate the feasibility of the implementation via a simple example in Appendix B. We argue that the fluid description accounts for the dynamical drag and the tidal stripping of incoming structures. We discuss the realm of non-linear problems which could be addressed statistically by such a theory, such as differential dynamical friction, tidal stripping and the self-gravity of objects within the virial sphere. The secular evolution of open galactic haloes is investigated: we derive the kinetic equation which governs the quasi-linear evolution of dark matter profile induced by infall and its corresponding gravitational correlations. This yields a Fokker–Planck-like equation for the angle-averaged underlying distribution function. This equation has an explicit source term accounting for the net infall through the virial sphere. Under the assumption of ergodicity we then relate the corresponding source, drift and diffusion coefficients for the ensemble-average distribution to the underlying cosmic two-point statistics of the infall and discuss possible applications. The internal dynamics of substructures within galactic haloes (distortion, clumps as traced by Xray emissivity, weak lensing, dark matter annihilation, tidal streams, etc.), and the implication for the disc (spiral structure, warp, etc.) are then briefly discussed. We show how this theory could be used to (i) observationally constrain the statistical nature of the infall, (ii) predict the observed distribution and correlations of substructures in upcoming surveys, (iii) predict the past evolution of the observed distribution of clumps and finally (iv) weight the relative importance of the intrinsic (via the unperturbed distribution function) and external (tidal and/or infall) influence of the environment in determining the fate of galaxies. We stress that our theory describes the perturbed distribution function (mean profile removed) directly in phase space.