Well-motivated particle physics theories predict the existence of particles ( such as sterile neutrinos ) which acquire non-negligible thermal velocities in the early universe . These particles could behave as warm dark matter ( WDM ) and generate a small-scale cutoff in the linear density power spectrum which scales approximately inversely with the particle mass . If this mass is of order a keV , the cutoff occurs on the scale of dwarf galaxies . Thus , in WDM models the abundance of small galaxies , such as the satellites that orbit in the halo of the Milky Way , depends on the mass of the warm particle . The abundance also scales with the mass of the host galactic halo . We use the galform semi-analytic model of galaxy formation to calculate the properties of galaxies in universes in which the dark matter is warm . Using this method , we can compare the predicted satellite luminosity functions to the observed data for the Milky Way dwarf spheroidals , and determine a lower bound on the thermally produced WDM particle mass . This depends strongly on the value of the Milky Way halo mass and , to some extent , on the baryonic physics assumed ; we examine both of these dependencies . For our fiducial model we find that for a particle mass of 3.3 keV ( the 2 \sigma lower limit found by Viel et al . from a recent analysis of the Lyman- \alpha forest ) the Milky Way halo mass is required to be > 1.4 \times 10 ^ { 12 } \mathrm { M } _ { \odot } . For this same fiducial model , we also find that all WDM particle masses are ruled out ( at 95 % confidence ) if the halo of the Milky Way has a mass smaller than 1.1 \times 10 ^ { 12 } \mathrm { M } _ { \odot } , while if the mass of the Galactic halo is greater than 1.8 \times 10 ^ { 12 } \mathrm { M } _ { \odot } , only WDM particle masses larger than 2 keV are allowed .