Decaying dark matter and the deficit of dwarf haloes

The hierarchical clustering inherent in Lambda cold dark matter cosmology seems to produce many of the observed characteristics of large-scale structure. But some glaring problems still remain, including the overprediction (by a factor of 10) of the number of dwarf galaxies within the virialized population of the local group. Several secondary effects have already been proposed to resolve this problem. It is still not clear, however, whether the principal solution rests with astrophysical processes, such as early feedback from supernovae, or possibly with as yet undetermined properties of the dark matter itself. In this paper, we carry out a detailed calculation of the dwarf halo evolution incorporating the effects of a hypothesized dark matter decay, D -> D'+l, where D is the unstable particle, D' is the more massive daughter particle and l is the other, lighter (or possibly massless) daughter particle. This process preferentially heats the smaller haloes, expanding them during their evolution and reducing their present-day circular velocity. We find that this mechanism can account very well for the factor of 4 deficit in the observed number of systems with velocity 10-20 km s(-1) compared to those predicted by the numerical simulations, if Delta m/m(D') similar to 5-7 x 10(-5), where Delta m is the mass difference between the initial and final states. The corresponding lifetime tau cannot be longer than similar to 30 Gyr, but may be as short as just a few Gyr.