Cosmic microwave background constraint on residual annihilations of relic particles

Energy injected into the cosmic microwave background at redshifts $z\lesssim {10}^6$ will distort its spectrum permanently. In this paper we discuss the distortion caused by annihilations of relic particles. We use the observational bounds on deviations from a Planck spectrum to constrain a combination of annihilation cross section, mass, and abundance. For particles with an $(s-\mathrm{wave})$ annihilation cross section $〈\sigma |v|〉\equiv {\sigma }_0,$ the bound is ${f(m}_X/\mathrm{MeV}{)}^{-1}\left[\right({\sigma }_0/6\mathrm{}\times {10}^{-27}\hspace{0.5em}{\mathrm{cm}}^3{\mathrm{s}}^{-1}\left)\right({\Omega }_{X\overline{X}}{h}^2{)}^2]<0.2,$ where $m_X$ is the particle mass, ${\Omega }_{X\overline{X}}$ is the fraction of the critical density the particle and its antiparticle contribute if they survive to the present time, ${h=H}_0/100\mathrm{}\hspace{0.5em}\mathrm{km}{\mathrm{s}}^{-1}{\mathrm{Mpc}}^{-1},$ $H_0$ is the Hubble constant, and f is the fraction of the annihilation energy that interacts electromagnetically. We also compute the less stringent limits for p-wave annihilation. We update other bounds on residual annihilations and compare them to our CMB bound.