of the simple form of the matter distribution in this model, we can compute all of the relevant quantities in a semi-analytic fashion, and the main features of the model can be easily understood, thereby providing an important reference point for investigating more elaborate models. Moreover, by working out in detail a simple analytic model, our results provide an ideal test bed for more involved numerical codes, which would then allow us to investigate how our conclusions are changed as more complicated models are allowed (Chen et al. 2007, in preparation).

Semi-Analytical Modeling
------------------------

Our analytical halo model is that of a simple triaxial isothermal profile of the form $$\rho(\bar{\mathbf{x}}) = N(q_1,q_2)\frac{\sigma_v^2}{2\pi G}
    \frac{1}{x^2/q_1^2+y^2+z^2/q_2^2}
\label{eq:3dsie}$$ where $q_1$ and $q_2$ are the axis ratios of the profile and we have chosen a coordinate system that is aligned with the halo’s principal axes, and such that $1\geq q_1 \geq q_2$.[^3] The normalization constant $N(q_1,q_2)$ is chosen to ensure that the mass contained within a sphere of radius $r$ be independent of the axis ratios for fixed velocity dispersion $\sigma_v^2$, the latter being the velocity dispersion of the Singular Isothermal Sphere (SIS) obtained when $q_1=q_2=1$.

Let then $(\theta,\phi)$ denote a line of sight. 