Getting in shape with minimal energy. A variational principle for protohaloes

Abstract

In analytical models of structure formation, protohalos are routinely assumed to be peaks of the smoothed initial density field, with the smoothing filter being spherically symmetric. This works reasonably well for identifying a protohalo's center of mass, but not its shape. To provide a more realistic description of protohalo boundaries, one must go beyond the spherical picture. We suggest that this can be done by looking for regions of fixed volume, but arbitrary shape, that minimize the enclosed energy. Such regions are surrounded by surfaces over which (a slightly modified version of) the gravitational potential is constant. We show that these equipotential surfaces provide an excellent description of protohalo shapes, orientations and associated torques.

5 pages, 6 figures

References in corpus (4)

• Universality of dark matter haloes shape over six decades in mass: Insights from the Millennium XXL and SBARBINE simulations
• Ellipsoidal halo finders and implications for models of triaxial halo formation
• Perturbation theory and excursion set estimates of the probability distribution function of dark matter, and a method for reconstructing the initial distribution function
• Angular momentum evolution can be predicted from cosmological initial conditions