The splashback radius

Traditionally, halo radii have been defined based on the spherical overdensity criterion where the halo radius encloses some overdensity with respect to the critical or mean density of the universe, leading to definitions such as R200c, R200m, and Rvir. There are, however, a number of issues with these definitions: the halo mass and radius undergo pseudo-evolution, a significant number of satellites orbit outside the virial radius (e.g., Wetzel et al. 2014), and infalling subhalos begin to get stripped far outside Rvir (Behroozi et al. 2014).

To remedy these issues, we have proposed the splashback radius (Rsp) as a physically motivated definition of the halo boundary (Diemer & Kravtsov 2014, Adhikari et al. 2014, More et al. 2015). Rsp is the radius where particles reach the apocenter of their first orbit. The theoretical motivation for this definition is provided by the self-similar spherical infall model (Fillmore & Goldreich 1984, Bertschinger 1985): in spherical symmetry, this radius cleanly separates infalling material from matter orbiting in the halo, and by definition includes the orbits of all satellites in the halo (see figure).

In perfect spherical symmetry, the splashback radius would be marked by a caustic, an infinitely sharp drop in density. This feature is smoothed out in realistic halos but we detected it in stacked density profiles in simulations. While conventional definitions depend only on the static density profile, the location of Rsp depends on the mass accretion rate because a rapidly growing potential well reduces the apocenters of particles’ orbits. Overall, Rsp is significantly larger than spherical overdensity radii, roughly between about 1 and 2.5 Rvir. This is illustrated in the figure below: the left panel shows a slowly accreting halo where Rsp is significantly larger than R200m, the right panel shows a quickly accreting halo where Rsp is slightly smaller than R200m.

While the location of the density caustic is obvious in the above examples, identifying it in individual halos is non-trivial due to non-sphericity, sub-structure, and the complex nature of orbits in LCDM halos. We have presented two algorithms for measuring Rsp. The first, SHELLFISH, finds sharp drops in the 3D density field around halos and fits their locations with non-spherical shells (Mansfield et al. 2017). The second, SPARTA, analyzes the orbits of individual particles and assigns the halo a splashback radius based on the distribution of the orbit apocenters (Diemer 2017). The figure below shows the classical virial radii (orange) of halos with at least 1000 particles in a simulation, the white circles show the splashback radii identified by SPARTA. 

Observationally, the splashback radius has been detected in the density profiles of satellite galaxies around stacked clusters as well as in weak lensing (see references below). Initially, these observations found slightly lower splashback radii than expected from simulations but this difference has likely been tracked to projection effects and systematics in the cluster selection. 

Most recently, we have provided publicly available halo catalogs and merger trees for the Erebos N-body simulations that contain both conventional and splashback masses and radii, as well as subhalo relations for each definition. The relationship between spherical overdensity and splashback radii has also been summarized in a fitting function that is included in the Colossus python code.

Literature on the splashback radius

In the following list, I will try to give an overview of particularly relevant, splashback-related publications. They are crudely split into theoretical and observational work and sorted chronologically within those groups. Pre-prints are marked as (pp). This list is probably incomplete, out of date, or biased by my particular view of the topic. If you feel that I missed or mischaracterized any papers, please let me know!

Simulations and theoretical modeling

Observations of splashback

Related work