The many boundaries of the stratified dark matter halo

Abstract

We review the physics of halo collapse giving rise to various halo boundaries, as well as their identification, observation, and applications. The classical halo is typically defined as a monolithic, virialized object enclosed within its virial radius -- a definition which, however, does not account for ongoing halo growth. Continuous accretion causes the orbits of infalling particles to shrink over time, confining newly accreted material in a growing layer outside the virialized region. Several novel halo boundaries, such as the splashback and depletion radii, have recently been proposed to characterize this growth layer from different perspectives. Along with the turnaround radius, which operates on an even larger scale to enclose the entire infall region, these multiple boundaries comprise an extended view of a dark matter halo as a stratified structure. Theoretical models can largely explain the existence of various boundaries, while challenges remain in providing unified and quantitative predictions of their properties. The multiple boundaries open new avenues for observing halo growth and may substantially improve our understanding and modeling of cosmic structure formation. We provide a python package, SpheriC, implementing the key spherical collapse models.

Figures (9)

• Figure 1: The layers and boundaries around a cluster-size dark matter halo at $z=0$ from a cosmological $N$-body simulation. Left: Projected dark matter distribution in a $2\mathrm{Mpc}\,h^{-1}$ slice along the $z$ direction. The color-bar indicates the projected particle count in each pixel. Right: The dark matter particle distribution in phase space (halo-centric radius versus radial velocity) around the same halo. The black solid curve shows the average radial velocity profile. The vertical colored lines mark the virial ($R_{\rm vir}$), depletion ($R_{\rm id}$), and turnaround radius ($R_{\rm ta}$), respectively. These boundaries divide the space around the halo into the virialized, growing, depleting and expanding regions. The short solid lines on the top axis mark the locations of the splashback radius, $R_{\rm sp}$, and the edge radius, $R_{\rm edge}$. The cyan dotted line illustrates the approximate separation between the orbiting and infalling particles. Some of these radii are also shown in the left panel. In both panels, the orange arrows indicate the mass flow pattern.
• Figure 2: Monolithic spherical collapse solution. The shell oscillates periodically in the monolithic spherical collapse model, but will evolve towards virialization in reality, as indicated by the dotted curve. The black solid curve shows the solution in the EdS universe. For comparison, the red dashed curve shows the solution in a flat universe with parameters $\Omega_{\rm m}=0.3$ and $\Omega_{\Lambda}=0.7$ at the turnaround time.
• Figure 3: The total potential for a spherical shell of mass $M$ in presence of the cosmological constant. The contributions from the Newtonian gravity and from the cosmological constant are shown by the green and magenta curves respectively. The total potential reaches its maximum at $r_\Lambda$, and the shell can ever turnaround (i.e., is bound) only when its total energy is below $\Phi_{\rm max}$.
• Figure 4: Evolution of shell size compared with model predictions. The data points show the evolution of the size of a spherical region of a fixed enclosed mass in simulation. The solid and dashed curves are the predicted size evolution from the top-hat spherical collapse model and the non-stationary Jeans equation, respectively. The left and right panels are two different example halos. Figure reproduced from Suto16.
• Figure 5: The dynamical structure of a halo formed from a $\epsilon=0.3$ peak. Top left: distance evolution of a shell, normalized by its own turnaround radius and time. Top right: the phase space structure of the halo at a given time. The red crosses mark the locations of the first few caustics. The orange dashed curve shows the classical spherical collapse solution. Bottom left: the density profile normalized by the average density within the turnaround radius. Note some irregularities in the pattern of the caustics (density spikes) are due to the finite sampling of the profile when plotting. Bottom right: the mass flow rate profile (normalized by $\mu_{\rm ta}\equiv M_{\rm ta}/t$). Caustics corresponding to those in the density profile are observed in the outer halo, while the rate in the inner halo approaches zero.