Baryons in the CosmicWeb of IllustrisTNG - I: Gas in Knots, Filaments,
  Sheets and Voids
  We analyze the IllustrisTNG simulations to study the mass, volume fraction
and phase distribution of gaseous baryons embedded in the knots, filaments,
sheets and voids of the Cosmic Web from redshift $z=8$ to redshift $z=0$. We
find that filaments host more star-forming gas than knots, and that filaments
also have a higher relative mass fraction of gas in this phase than knots. We
also show that the cool, diffuse Intergalactic Medium (IGM; $T<10^5 \, {\rm
K}$, $ n_{\rm H}<10^{-4}(1+z) \, {\rm cm^{-3}}$) and the Warm-Hot Intergalactic
Medium (WHIM; $ 10^5 \, {\rm K} <T<10^7 \, {\rm K}$, $ n_{\rm H}
<10^{-4}(1+z)\, {\rm cm^{-3}}$) constitute $\sim 39\%$ and $\sim 46\%$ of the
baryons at redshift $z=0$, respectively. Our results indicate that the WHIM may
constitute the largest reservoir of {\it missing} baryons at redshift $z=0$.
Using our Cosmic Web classification, we predict the WHIM to be the dominant
baryon mass contribution in filaments and knots at redshift $z=0$, but not in
sheets and voids where the cool, diffuse IGM dominates. We also characterise
the evolution of WHIM and IGM from redshift $z=4$ to redshift $z=0$, and find
that the mass fraction of WHIM in filaments and knots evolves only by a factor
$\sim 2$ from redshift $z=0$ to $z=1$, but declines faster at higher redshift.
The WHIM only occupies $4-11\%$ of the volume at redshift $0\leq z \leq 1$. We
predict the existence of a significant number of currently undetected OVII and
NeIX absorption systems in cosmic filaments which could be detected by future
X-ray telescopes like Athena.
