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The observed Lyman-$\alpha$ flux power spectrum (FPS) is suppressed on scalesbelow $\sim~ 30~{\rm km~s}^{-1}$. This cutoff could be due to the hightemperature, $T_0$, and pressure, $p_0$, of the absorbing gas or,alternatively, it could reflect the free streaming of dark matter particles inthe early universe. We perform a set of very high resolution cosmologicalhydrodynamic simulations in which we vary $T_0$, $p_0$ and the amplitude of thedark matter free streaming, and compare the FPS of mock spectra to the data. Weshow that the location of the dark matter free-streaming cutoff scalesdifferently with redshift than the cutoff produced by thermal effects and ismore pronounced at higher redshift. We, therefore, focus on a comparison to theobserved FPS at $z>5$. We demonstrate that the FPS cutoff can be fit assumingcold dark matter, but it can be equally well fit assuming that the dark matterconsists of $\sim 7$ keV sterile neutrinos in which case the cutoff is dueprimarily to the dark matter free streaming.

The Lyman-$\alpha$ forest as a diagnostic of the nature of the dark matter