The hydrodynamic response of small-scale structure to reionization drives large IGM temperature fluctuations that persist to z = 4

The thermal history and structure of the intergalactic medium (IGM) at $z \geq 4$ is an important boundary condition for reionization, and a key input for studies using the Ly$\alpha$ forest to constrain the masses of alternative dark matter candidates. Most such inferences rely on simulations that lack the spatial resolution to fully resolve the hydrodynamic response of IGM filaments and minihalos to HI reionization heating. In this letter, we use high-resolution hydrodynamic+radiative transfer simulations to study how these affect the IGM thermal structure. We find that the adiabatic heating and cooling driven by the expansion of initially cold gas filaments and minihalos sources significant small-scale temperature fluctuations. These likely persist in much of the IGM until $z \leq 4$. Capturing this effect requires resolving the clumping scale of cold, pre-ionized gas, demanding spatial resolutions of $\leq 2$ $h^{-1}$kpc. Pre-heating of the IGM by X-Rays can slightly reduce the effect. Our preliminary estimate of the effect on the Ly$\alpha$ forest finds that, at $\log(k /[{\rm km^{-1} s}]) = -1.0$, the Ly$\alpha$ forest flux power (at fixed mean flux) can increase $\approx 10\%$ going from $8$ and $2$ $h^{-1}$kpc resolution at $z = 4-5$ for gas ionized at $z < 7$. These findings motivate more careful analyses of how the effects studied here affect the Ly$\alpha$ forest.