Cosmic microwave background constraint on residual annihilations of relic particles

Energy injected into the cosmic microwave background at redshifts z less than or similar to 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-wave) annihilation cross section (sigma \v \ > equivalent to sigma (0)), the bound is f(m(X)/MeV)(-1)[(sigma (0)/06 x 10(-27) cm(3) s(-1))(Omega (X(X) over bar)h(2))(2)] < 0.2, where m(X) is the particle mass, Omega(X(X) over bar), is the fraction of the critical density the particle and its antiparticle contribute if they survive to the present time, h = H-0/100 km s(-1) 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.