We investigate the relic abundance of asymmetric Dark Matter particles that
were in thermal equilibrium in the early universe. The standard analytic
calculation of the symmetric Dark Matter is generalized to the asymmetric case.
We calculate the asymmetry required to explain the observed Dark Matter relic
abundance as a function of the annihilation cross section. We show that
introducing an asymmetry always reduces the indirect detection signal from WIMP
annihilation, although it has a larger annihilation cross section than
symmetric Dark Matter. This opens new possibilities for the construction of
realistic models of MeV Dark Matter.Comment: 20 pages, 11 figures, Accepted by JCA