In shape with minimal energy. A variational principle for protohaloes

Analytical models of structure formation routinely assume that dark matter halos form from peaks of the initial density field, smoothed with some spherically symmetric filter. This works reasonably well for identifying the center of mass of protohaloes, but gives no information about their shapes. To provide a more realistic description of protohalo boundaries, one must go beyond the spherical picture. I suggest that this can be done with a simple variational principle, solving for shapes of fixed given mass that minimize the enclosed potential energy. Such regions are delimited by isosurfaces of (a slightly modified version of) the gravitational potential. I will show that these equipotential surfaces provide an excellent description of protohalo shapes, orientations, and associated torques.