Constraints on the mass of warm dark matter particles and the shape of the linear power spectrum from the Lyα forest

High-resolution N-body simulations of cold dark matter (CDM) models predict that galaxies and clusters have cuspy halos with considerable substructure. Observations reveal smooth halos with central density cores. One possible resolution of the substructure problem is that the dark matter is warm; this will suppress the power spectrum on small scales. The Ly 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 warm dark matter (WDM) models and analyze artificial Lya! forest spectra extracted from them. By requiring that there be enough small-scale power in the linear power spectrum to reproduce the observed properties of the Ly 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 gas at mean density (T-0) 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 Ly alpha forest.