NumCosmoHaloCatalogMemberGenerator

Populates a host NcHaloCatalog with member galaxies through a NcGalaxyHOD.

A standalone, reusable object that consumes an existing host catalog (halos or clusters) and, for each host, draws its central and satellite galaxies from a halo occupation distribution. The members are placed in 3D within the host and projected back to sky coordinates and redshift, and returned as a linked NcHaloCatalog of kind NC_HALO_CATALOG_KIND_MEMBER.

The host catalog must provide the columns produced by NcHaloCatalogGenerator with positions and radius enabled:

• ra, dec: host sky position (degrees);
• z_true: host redshift;
• lnM_true: host natural-log mass (fed to the HOD);
• r_Delta: host spherical-overdensity radius (Mpc).

For each host the central galaxy sits at the host position; satellites are placed uniformly in volume within r_Delta ($R = r_\Delta\,U^{1/3}$), isotropically in direction ($\cos\theta$ uniform, $\phi$ uniform). The displacement is decomposed about the line of sight: the radial part $R\cos\theta$ becomes a Hubble-flow redshift offset $\delta z = H(z)\, R\cos\theta / c$, and the transverse part $R\sin\theta$ becomes an angular separation $R\sin\theta / d_A(z)$ applied to the host position with the spherical law of cosines. (Two inconsistencies of the reference Python prototype are not reproduced: it used $c$ in m/s while $H$ is in km/s/Mpc, and it used the full $R$ instead of $R\sin\theta$ for the transverse separation; here $c$ is in km/s and the projection uses $R\sin\theta$.)

The generated member catalog has columns galaxy_id (id), parent_id (linking back to the host id, or the host row index when the host has no id column), is_central, ra, dec and z.