  Using a novel suite of cosmological simulations zooming in on a Mpc-scale
intergalactic sheet or "pancake" at z~3-5, we conduct an in-depth study of the
thermal properties and HI content of the warm-hot intergalactic medium (WHIM)
at those redshifts. The simulations span nearly three orders of magnitude in
gas-cell mass, from ~(7.7x10^6-1.5x10^4)Msun, one of the highest resolution
simulations of such a large patch of the inter-galactic medium (IGM) to date.
At z~5, a strong accretion shock develops around the main pancake following a
collision between two smaller sheets. Gas in the post-shock region proceeds to
cool rapidly, triggering thermal instabilities and the formation of a
multiphase medium. We find neither the mass, nor the morphology, nor the
distribution of HI in the WHIM to be converged at our highest resolution.
Interestingly, the lack of convergence is more severe for the less dense, more
metal-poor, intra-pancake medium (IPM) in between filaments and far from any
star-forming galaxies. As the resolution increases, the IPM develops a
shattered structure, with ~kpc scale clouds containing most of the HI. From our
lowest to highest resolution, the covering fraction of metal-poor
(Z<10^{-3}Zsun) Lyman-limit systems (NHI>10^{17.2}/cm^2) in the IPM at z~4
increases from (3-15)%, while that of Damped Lyman-alpha Absorbers
(NHI>10^{20}/cm^2) with similar metallicity increases threefold, from
(0.2-0.6)%, with no sign of convergence. We find that a necessary condition for
the formation of a multiphase, shattered structure is resolving the cooling
length, lcool=cs*tcool, at T~10^5K. If this scale is unresolved, gas "piles up"
at these temperatures and cooling to lower temperatures becomes very
inefficient. We conclude that state-of-the-art cosmological simulations are
still unable to resolve the multi-phase structure of the low-density IGM, with
potentially far-reaching implications.
