Characterizing the Pressure Smoothing Scale of the Intergalactic Medium

The thermal state of the intergalactic medium (IGM) at z < 6 constrains the nature and timing of cosmic reionization events, but its inference from the Ly-alpha forest is degenerate with the 3-D structure of the IGM on ~100 kpc scales, where, analogous to the classical Jeans argument, the pressure of the T~$10^4$ K gas supports it against gravity. We simulate the IGM using smoothed particle hydrodynamics, and find that, at z < 6, the gas density power spectrum does not exhibit the expected Jeans filtering cutoff, because dense gas in collapsed halos dominates the small-scale power masking pressure smoothing effects. We introduce a new statistic, the real-space Ly-alpha flux, $F_\mathrm{real}$, which naturally suppresses dense gas, and is thus robust against the poorly understood physics of galaxy formation, revealing pressure smoothing in the diffuse IGM. The $F_\mathrm{real}$ power spectrum is accurately described by a simple fitting function with cutoff at $\lambda_F$, allowing us to rigorously quantify the filtering scale for the first time: we find $\lambda_F$ = 79 kpc (comoving) at z=3 for our fiducial thermal model. This statistic has the added advantage that it directly relates to observations of correlated Ly-alpha forest absorption in close quasar pairs, recently proposed as a method to measure the filtering scale. Our results enable one to quantify the filtering scale in simulations, and ask meaningful questions about its dependence on reionization and thermal history. Accordingly, the standard description of the IGM in terms of the amplitude $T_0$ and slope $\gamma$ of the temperature-density relation $T = T_0\Delta^{\gamma-1}$ should be augmented with a third filtering scale parameter $\lambda_F$.