New Constraints on the free-streaming of warm dark matter from intermediate and small scale Lyman-$\alpha$ forest data

Phys. Rev. D 96, 023522 (2017) 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 ($z=3 - 4.2$) and the high-resolution, high-redshift sample used in Viel et al. (2013) obtained with the HIRES/MIKE spectrographs ($z=4.2 - 5.4$). 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.