Anisotropy and characteristic scales in halo density gradient profiles

We use a large N-body simulation to study the characteristic scales in density gradient profiles and around halos with masses ranging from $10^{12}$ $10^{15} h^{-1}{\rm M_\odot}$. investigate separately along major (T_1) minor (T_3) axes of local tidal tensor how depend on halo mass, formation time, environment. find two kinds prominent features profiles, deep `valley' `peak'. Gaussian Process Regression fit identify extrema determine associate these features. Around valley, we three types distinct minima, corresponding caustics particles orbiting halos. The appearance depth significantly direction defined by field, time environment first caustic is located at radius r>0.8R_{200}, splashback feature, dominated their apocenter after infall. second third caustics, 0.6R_{200} 0.4R_{200} respectively, can be determined reliably only for old always most feature T_3, but may not case T_1 or azimuthally-averaged suggesting that caution must taken when using averaged radius. approximately isotropic proper separations are made between other caustics. also peak $\sim$ 2.5R_{200} profile. This produced mass accumulations structure outside discuss origins observational implications.