New Constraints on Warm Dark Matter from the Lyman-$\alpha$ Forest Power Spectrum

The forest of Lyman-$\alpha$ absorption lines detected in the spectra of distant quasars encodes information on the nature and properties of dark matter and the thermodynamics of diffuse baryonic material. Its main observable -- the 1D flux power spectrum (FPS) -- should exhibit a suppression on small scales and an enhancement on large scales in warm dark matter (WDM) cosmologies compared to standard $\Lambda$CDM. Here, we present an unprecedented suite of 1080 high-resolution cosmological hydrodynamical simulations run with the Graphics Processing Unit-accelerated code Cholla to study the evolution of the Lyman-$\alpha$ forest under a wide range of physically-motivated gas thermal histories along with different free-streaming lengths of WDM thermal relics in the early Universe. A statistical comparison of synthetic data with the forest FPS measured down to the smallest velocity scales ever probed at redshifts $4.0\lesssim z\lesssim 5.2$ (Boera et al. 2019) yields a lower limit $m_{\rm WDM}>3.1$ keV (95 percent CL) for the WDM particle mass and constrains the amplitude and spectrum of the photoheating and photoionizing background produced by star-forming galaxies and active galactic nuclei at these redshifts. Interestingly, our Bayesian inference analysis appears to weakly favor WDM models with a peak likelihood value at the thermal relic mass of $m_{\rm WDM}=4.5$ keV. We find that the suppression of the FPS from free-streaming saturates at $k\gtrsim 0.1\,\mathrm{s}\,\mathrm{km}^{-1}$ because of peculiar velocity smearing, and this saturated suppression combined with a slightly lower gas temperature provides a moderately better fit to the observed small-scale FPS for WDM cosmologies.