This website can be used to calculate the relic density of dark
matter, and the annihilation cross section in the local halo and in
the limit of low velocity, for a simple example model with Sommerfeld
enhancement and two nearly degenerate dark matter states (detailed in
[1]). It can also be used to estimate the relic fraction of dark
matter in the excited state, x_e, prior to decay (however, see the
caveats below). The output Y is defined conventionally as the DM number density divided by the entropy density. x_e is the fraction of particles remaining in the excited state after DM-DM self-scattering decouples. The "boost factor" is defined as < sigma v > / 3 x 10^(-26) cm^3/s (it is not the same as the Sommerfeld enhancement factor S). The "local" annihilation section is computed assuming a Maxwell-Boltzmann distribution with sigma=150 km/s. Decays from the excited state to the ground state are turned off in this application to speed computation time; this choice has no effect on the relic density, but the relic excitation fraction calculated here is only relevant if the decay lifetime is longer than the age of the universe. In the computation of the "boost factors" it is assumed that all the DM is in the ground state. The approximation used for the DM-DM inelastic self-scattering cross section is based on a simple modification to the elastic self-scattering cross section that has not been tested in detail; this does not affect the relic density, but results for the relic excitation fraction should only be taken as order-of-magnitude estimates. If the input parameters lie in a region of parameter space where the approximation employed for the Sommerfeld enhancement is thought to be unreliable, a warning message will appear. If this message does not appear the accuracy of the approximation should be 5-10% or better. For some parameters, especially for very large alpha, an error message will appear indicating a failure of the ODE solver.
References: [1] D. P. Finkbeiner, L. Goodenough, T. R. Slatyer, M. Vogelsberger and N. Weiner, "Consistent Scenarios for Cosmic-Ray Excesses from Sommerfeld-Enhanced Dark Matter Annihilation". [2] T. R. Slatyer, "The Sommerfeld enhancement for dark matter with an excited state", arXiv:0910.5713. |