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The splashback radius $R_{\rm sp}$, the apocentric radius of particles ontheir first orbit after falling into a dark matter halo, has recently beensuggested as a physically motivated halo boundary that separates accreting fromorbiting material. Using the SPARTA code presented in Paper I, we analyze theorbits of billions of particles in cosmological simulations of structureformation and measure $R_{\rm sp}$ for a large sample of halos that span a massrange from dwarf galaxy to massive cluster halos, reach redshift 8, and includeWMAP, Planck, and self-similar cosmologies. We analyze the dependence of$R_{\rm sp}/R_{\rm 200m}$ and $M_{\rm sp}/M_{\rm 200m}$ on the mass accretionrate $\Gamma$, halo mass, redshift, and cosmology. The scatter in theserelations varies between 0.02 and 0.1 dex. While we confirm the known trendthat $R_{\rm sp}/R_{\rm 200m}$ decreases with $\Gamma$, the relationships turnout to be more complex than previously thought, demonstrating that $R_{\rm sp}$is an independent definition of the halo boundary that cannot trivially bereconstructed from spherical overdensity definitions. We present fittingfunctions for $R_{\rm sp}/R_{\rm 200m}$ and $M_{\rm sp}/M_{\rm 200m}$ as afunction of accretion rate, peak height, and redshift, achieving an accuracy of5% or better everywhere in the parameter space explored. We discuss thephysical meaning of the distribution of particle apocenters and show that thepreviously proposed definition of $R_{\rm sp}$ as the radius of the steepestlogarithmic density slope encloses roughly three-quarters of the apocenters.Finally, we conclude that no analytical model presented thus far can fullyexplain our results.

The splashback radius of halos from particle dynamics. II. Dependence on mass, accretion rate, redshift, and cosmology