Dark-matter annihilation J-factor ($J={\int }_{\Delta \Omega }d\Omega \int {\rho }_{\chi }^{2}dl$)

The line-of-sight, solid-angle integral of squared dark-matter density used for annihilation fluxes with a position-independent rate coefficient. It separates an astrophysical density model from particle yields and annihilation rates. A decay signal instead scales with a single power of density. Substructure or spatially varying velocity-dependent rates can prevent a simple smooth-density factorization.