Abstract
We present new measurements of the free-streaming of warm dark matter (WDM)
from Lyman-$\alpha$ flux-power spectra. We use data from the medium resolution,
intermediate redshift XQ-100 sample observed with the X-shooter spectrograph
and the high-resolution, high-redshift sample used in Viel et al. (2013)
obtained with the HIRES/MIKE spectrographs. Based on further improved modelling
of the dependence of the Lyman-$\alpha$ flux-power spectrum on the
free-streaming of dark matter, cosmological parameters, as well as the thermal
history of the intergalactic medium (IGM) with hydrodynamical simulations, we
obtain the following limits, expressed as the equivalent mass of thermal relic
WDM particles. The XQ-100 flux power spectrum alone gives a lower limit of 1.4
keV, the re-analysis of the HIRES/MIKE sample gives 4.1 keV while the combined
analysis gives our best and significantly strengthened lower limit of 5.3 keV
(all 2$\sigma$ C.L.). The further improvement in the joint analysis is partly
due to the fact that the two data sets have different degeneracies between
astrophysical and cosmological parameters that are broken when the data sets
are combined, and more importantly on chosen priors on the thermal evolution.
These results all assume that the temperature evolution of the IGM can be
modelled as a power law in redshift. Allowing for a non-smooth evolution of the
temperature of the IGM with sudden temperature changes of up to 5000K reduces
the lower limit for the combined analysis to 3.5 keV. A WDM with smaller
thermal relic masses would require, however, a sudden temperature jump of
5000\,K or more in the narrow redshift interval $z=4.6-4.8$, in disagreement
with observations of the thermal history based on high-resolution resolution
Lyman-$\alpha$ forest data and expectations for photo-heating and cooling in
the low density IGM at these redshifts.
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