Relation between ﹩r_{\mathrm{peri}\,}/ r_{\mathrm{apo}\,}﹩ and ﹩j_{\theta }/ j_{r}﹩ for shells in our halos. In spite of the dispersion in individual shell properties (shown in Fig. 2), all shells in all halos obey this well‐defined relation, which can be understood in terms of the model presented in § 5. The three solid lines are predictions of this model for noncircular orbits in halos with ﹩\alpha =1.99,﹩ 1, and 0.5 (top to bottom). The dotted line is the relation ﹩r_{\mathrm{peri}\,}/ r_{\mathrm{apo}\,}=j_{\theta }/ j_{r}﹩. Circular orbits will lie at ﹩r_{\mathrm{peri}\,}/ r_{\mathrm{apo}\,}=1﹩ and ﹩j_{\theta }/ j_{r}\rightarrow \infty ﹩. There are two sets of points: the upper right set belongs to the reference halo (§ 4.3), while the lower left set belongs to the halo with almost no random motions, shown as the dotted line in Fig. 6. See § 5.4 for details.