jfactor_spherical_aperture

jeanspy.model.ZhaoModel.jfactor_spherical_aperture

Class and construction: ZhaoModel.

ZhaoModel.jfactor_spherical_aperture(dist_pc, roi_deg=0.5)

Calculate the small-angle spherical-aperture approximation.

Let R_max = dist_pc * sin(roi_deg). This method integrates the spherical luminosity only out to min(R_max, r_t_pc).

If R_max >= r_t_pc, the aperture contains the entire truncated halo and this reduces to Ullio & Valli (2016), Eq. (B.10), with the halo boundary mathcal R = r_t_pc. If R_max < r_t_pc, this is instead a spherical-aperture approximation: projected contributions from shells with R_max < r < r_t_pc are omitted. Use jfactor_cone() for the full finite-ROI geometry of Eqs. (B.8)–(B.9).

Notes

Inputs and units. dist_pc is observer distance in pc; roi_deg is cone half-angle in degrees. Distance, aperture and the stored r_t_pc must all be scalars; array geometry raises ValueError.

Returns and shape. A scalar J in GeV^2 cm^-5.

Validity. Small-aperture spherical approximation; outer shells projected into the cone are omitted. Require a positive finite halo cutoff and a convergent inner cusp. Small-angle variants enforce the configured small_angle_limit_deg bound.