Title: Constraining Reionization with the $z \sim 5-6$ Lyman-$α$ Forest Power Spectrum: the Outlook after Planck,
Abstract: The latest measurements of CMB electron scattering optical depth reported by
Planck significantly reduces the allowed space of HI reionization models,
pointing towards a later ending and/or less extended phase transition than
previously believed. Reionization impulsively heats the intergalactic medium
(IGM) to $\sim10^4$ K, and owing to long cooling and dynamical times in the
diffuse gas, comparable to the Hubble time, memory of reionization heating is
retained. Therefore, a late ending reionization has significant implications
for the structure of the $z\sim5-6$ Lyman-$\alpha$ (ly$\alpha$) forest. Using
state-of-the-art hydrodynamical simulations that allow us to vary the timing of
reionization and its associated heat injection, we argue that extant thermal
signatures from reionization can be detected via the ly$\alpha$ forest power
spectrum at $5< z<6$. This arises because the small-scale cutoff in the power
depends not only the the IGMs temperature at these epochs, but is also
particularly sensitive to the pressure smoothing scale set by the IGMs full
thermal history. Comparing our different reionization models with existing
measurements of the ly$\alpha$ forest flux power spectrum at $z=5.0-5.4$, we
find that models satisfying Planck's $\tau_e$ constraint, favor a moderate
amount of heat injection consistent with galaxies driving reionization, but
disfavoring quasar driven scenarios. We explore the impact of different
reionization histories and heating models on the shape of the power spectrum,
and find that they can produce similar effects, but argue that this degeneracy
can be broken with high enough quality data. We study the feasibility of
measuring the flux power spectrum at $z\simeq 6$ using mock quasar spectra and
conclude that a sample of $\sim10$ high-resolution spectra with attainable S/N
ratio will allow to discriminate between different reionization scenarios.