Constraints from Ly-$\alpha$ forests on non-thermal dark matter
  including resonantly-produced sterile neutrinos
  We use BOSS DR9 quasars to constrain 2 cases of dark matter models:
cold-plus-warm (C+WDM) where the warm component is a thermal relic, and sterile
neutrinos resonantly produced in the presence of a lepton asymmetry (RPSN). We
establish constraints on the relic mass m_x and its relative abundance
$F=\Omega_{wdm}/\Omega_{dm}$ using a suite of hydrodynamical simulations in 28
C+WDM configurations. We find that the 3 sigma bounds approximately follow F ~
$0.35 (keV/m_x)^{-1.37}$ from BOSS alone. We also establish constraints on
sterile neutrino mass and mixing angle by producing the non-linear flux power
spectrum of 8 RPSN models, where the input linear power spectrum is computed
directly from the particles distribution functions. We find values of lepton
asymmetries for which sterile neutrinos as light as 6.5 keV (resp. 3.5 keV) are
consistent with BOSS at the 2 sigma (resp. 3sigma) level. These limits tighten
by close to a factor of 2 for lepton asymmetries departing from those yielding
the coolest distribution functions.
  Our Ly-a forest bounds can be strengthened if we include higher-resolution
data from XQ-100, HIRES and MIKE. At these smaller scales, the flux power
spectrum exhibits a suppression that can be due to Doppler broadening, IGM
pressure smoothing or free-streaming of WDM particles. In the current work, we
show that if one extrapolates temperatures from lower redshifts via broken
power laws in T_0 and gamma, then our 3 sigma C+WDM bounds strengthen to F~
$0.20 (keV/m_x)^{-1.37}$, and the lightest RPSN consistent with our extended
data set have masses of 7.0 keV at the 3 sigma level. Using dedicated
hydrodynamical simulations, we show that a 7 keV sterile neutrino produced in a
lepton asymmetry $L = 8 \times 10^{-6}$ is consistent at 1.9 sigma (resp. 3.1
sigma) with BOSS (resp. BOSS + higher-resolution), for the thermal history
models tested in this work.
