Tracers, halos and anisotropy

This reference covers profile-specific scale, deprojection and cutoff conventions. Use the model tutorial to compose or extend components and the spherical API catalogue for available classes in each backend. Shared units and parameter interfaces are defined in the model contract.

Tracer scales and three-dimensional support

The NumPy/SciPy Plummer, projected exponential and Sersic profiles have three-dimensional deprojections. Uniform2dModel supplies only a projected disk and cannot be passed to a three-dimensional Jeans calculation. ProjectedExponentialModel(r_exp_pc=...) uses the scale inside exp(-R/r_exp_pc). Its read-only re_pc property returns the projected half-light radius, 1.67834699001666 * r_exp_pc. This profile is a projected exponential with a Bessel-K0 three-dimensional deprojection, not a pure three-dimensional exponential. Plummer and Sersic still accept re_pc directly.

Sersic deprojection domains

density_3d() selects the deprojection explicitly. The lgm selection uses the Lima Neto–Gerbal–Márquez approximation for \(0.5\le n\le10\); its normalization is lgm_norm_3d, independently of auto. The VM20 approximation is restricted to \(0.5\le n\le10\) and \(10^{-3}\le r/r_e\le10^3\); VM20bis uses \(0.5\le n\le3.4\) and \(10^{-4}\le r/r_e\le10^3\). The default auto route selects VM20bis inside its domain, the SP04 approximation for \(3.4<n\le10\) over that radius range, and numerical Abel integration outside these domains. Explicit approximation VM20/VM20bis methods reject unsupported values instead of extrapolating them silently. See that method’s API entry for the quadrature controls of numerical.

Anisotropy families

The spherical implementations include ConstantAnisotropyModel, OsipkovMerrittModel and BaesAnisotropyModel; consult their API entries for parameters and supported kernels. The theory page defines spherical and cylindrical anisotropy. For JAX BaesEta2AnisotropyModel, solver="auto" uses Abel integration. Select solver="kernel" to activate its specialized Appell-F1 kernel, controlled by n_kernel. The eta=2 specialization alone does not change solver selection. The restriction \(\beta<1\) alone does not establish the existence of a nonnegative distribution function.

Halo cutoff conventions

Spherical NFW and Zhao mass_density_3d methods return zero for r > r_t_pc in both NumPy/SciPy and JAX; the boundary is included. Their enclosed mass is constant outside the same cutoff. r_t_pc=np.inf gives an untruncated halo at finite radii. Zhao uses alpha, beta, gamma for transition, outer and inner slopes in both geometries.

The spheroidal AxisymmetricZhaoModel applies this convention to m = sqrt(R**2 + z**2/Q**2). Its enclosed mass is inside that ellipsoid. For annihilation factors, use the factor guide to select the finite cone or an explicitly named approximation.