  High resolution N-body simulations of cold dark matter (CDM) models predict
that galaxies and clusters have cuspy halos with excessive substructure.
Observations reveal smooth halos with central density cores. One possible
resolution of this conflict is that the dark matter is warm (WDM); this will
suppress the power spectrum on small scales. The Lyman-alpha forest is a
powerful probe of the linear power spectrum on these scales. We use
collisionless N-body simulations to follow the evolution of structure in WDM
models, and analyze artificial Lyman-alpha forest spectra extracted from them.
By requiring that there is enough small-scale power in the linear power
spectrum to reproduce the observed properties of the Lyman-alpha forest in
quasar spectra, we derive a lower limit to the mass of the WDM particle of 750
eV. This limit is robust to reasonable uncertainties in our assumption about
the temperature of the mean density gas (T0) at z=3. We argue that any model
that suppresses the CDM linear theory power spectrum more severely than a 750
eV WDM particle cannot produce the Lyman-alpha forest.
