The movies below show the secondary infall of collisionless dark matter shells onto a point perturbation, following the equations of Bertschinger 1985 (see also Fillmore & Goldreich 1984). The beauty of this solution is that it is self-similar, meaning that all shells follow the same trajectory in units of the turn-around radius and logarithmic turn-around time.

In the movies, the turn-around radius is indicated as the gray, outermost shell. All shells at larger radii expand with the Hubble flow, and are not shown here. Time proceeds in units of physical time. We note that the shells do not have equal mass, but are rather equally spaced in time for a better visualization. There are two versions of the movie, namely one with radii in physical units (i.e., a turn-around radius that expands with time) and one with radii re-scaled to the turn-around radius.

The visualizations highlight the pile-up of shells at the apocenter of their first orbit. This “splashback radius” has recently been proposed as a physically motivated halo boundary that separates infalling from orbiting material, evenĀ in realistic dark matter halosĀ (Diemer & Kravtsov 2014, Adhikari et al. 2014, and More et al. 2015).


Secondary infall model (with physical radii)
Low quality, 30s
High quality, 30s
mp4 (9 MB)
mp4 (27 MB)
shell model
Secondary infall model (with radii re-scaled to the turn-around radius)
Low quality, 20s
High quality, 20s
mp4 (5 MB)
mp4 (16 MB)
shell model