Denition Sample Clauses

Denition. ‌ For halos that continuously amass matter, material close to its rst apocenter piles up next to the edge of the multi-stream region, where collapsed and infalling material meets (Adhikari et al., 2014). A sudden drop in density, i.e. the feature visible in the proles of Figure 4.1, is associated with this process. This intuitive picture leads to three characterizations of the splashback radius, de- pending on the approach used to measure or model it: 1. The location of the outermost phase-space caustic. 2. The point of steepest slope in the density prole. 3. The apocenter of recently accreted material. While these denitions have all been previously hinted at in the introduction, in this section, we explicitly present them and discuss the connections existing between them. This also justies our adopted denition, based on the density prole. The rst denition is clearly motivated in the spherical case but fails once it is applied to realistic halos. The presence of angular momentum and tidal streams from disrupted subhalos (see e.g. Vogelsberger and White, 2011), smooth out this feature and make its description murky. The second denition was the rst suggested in the literature. Introduced by Diemer and Kravtsov (2014), it is based on the study of dark matter proles in N-body simulations and has been linked to the rst, more dynamical, denition (Adhikari et al., 2014; Shi, 2016). The third was rst suggested by Diemer (2017), who showed that this location can be calibrated to the second one (Diemer et al., 2017) by choosing specic percentiles of the apocenter distribution. To clarify the relationship between the outermost caustic and apocenter, it is ed- ucational to use a self-similar toy model based on Adhikari et al. (2014) to show the phase-space distribution of a constantly accreting halo with an NFW-like mass prole (Navarro et al., 1997). GM (< r, t) 4.1) r2 between their rst and second turnaround in the mass prole: