Constraints on the mass of warm dark matter particles and the shape of thelinear power spectrum from the Ly alpha 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; th is 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 coll isionless N-body simulations to follow the evolution of structure in warm d ark matter (WDM) models and analyze artificial Lya! forest spectra extracte d from them. By requiring that there be enough small-scale power in the lin ear power spectrum to reproduce the observed properties of the Ly alpha for est in quasar spectra, we derive a lower limit to the mass of the WDM parti cle of 750 eV. This limit is robust to reasonable uncertainties in our assu mption 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 m ore severely than a 750 eV WDM particle cannot produce the Ly alpha forest.