  The filamentary network of intergalactic medium (IGM) gas that gives origin
to the Lyman-alpha forest in the spectra of distant quasars encodes information
on the physics of structure formation and the early thermodynamics of diffuse
baryonic material. Here, we use a massive suite of more than 400
high-resolution cosmological hydrodynamical simulations run with the Graphics
Processing Unit-accelerated code Cholla to study the IGM at high spatial
resolution maintained over the entire computational volume. The simulations
capture a wide range of possible thermal histories of intergalactic gas by
varying the amplitude and timing of the photoheating and photoionizing
background produced by star-forming galaxies and active galactic nuclei. A
statistical comparison of synthetic spectra with the observed 1D flux power
spectra of hydrogen in 14 redshift bins over the full range 2.2 <= z <= 5.0 and
with the Lyman-alpha opacity of helium in 5 redshift bins over the range 2.4 <
z < 2.9 tightly constrains the photoionization and photoheating history of the
IGM. By leveraging the constraining power of the available Lyman-alpha forest
data to break model degeneracies, we find that the IGM experienced two main
reheating events from the non-equilibrium ionization of hydrogen and helium
over 1.2 Gyr of cosmic time. For our best-fit model, hydrogen reionization
completes by z~6.0 with a first IGM temperature peak T_0 ~ 1.3x10^4 K, and is
followed by the reionization of HeII that completes by z~3.0 and yields a
second temperature peak of T_0 ~ 1.4x10^4 K. We discuss how our results can be
used to obtain information on the timing and the sources of hydrogen and helium
reionization.
