Ingredients for 21cm intensity mapping
  [Abridged] We study the abundance and clustering properties of HI at
redshifts $z\leqslant5$ using TNG100, a large state-of-the-art
magneto-hydrodynamic simulation of a 75 Mpc/h box size. We show that most of
the HI lies within dark matter halos and quantify the average HI mass hosted by
halos of mass M at redshift z. We find that only halos with circular velocities
larger than $\simeq$ 30 km/s contain HI. While the density profiles of HI
exhibit a large halo-to-halo scatter, the mean profiles are universal across
mass and redshift. The HI in low-mass halos is mostly located in the central
galaxy, while in massive halos is concentrated in the satellites. We show that
the HI and matter density probability distribution functions differ
significantly. Our results point out that for small halos the HI bulk velocity
goes in the same direction and has the same magnitude as the halo peculiar
velocity, while in large halos differences show up. We find that halo HI
velocity dispersion follows a power-law with halo mass. We find a complicated
HI bias, with HI becoming non-linear already at $k=0.3$ h/Mpc at $z\gtrsim3$.
Our simulation reproduces the DLAs bias value from observations. We find that
the clustering of HI can be accurately reproduced by perturbative methods. We
identify a new secondary bias, by showing that the clustering of halos depends
not only on mass but also on HI content. We compute the amplitude of the HI
shot-noise and find that it is small at all redshifts. We study the clustering
of HI in redshift-space, and show that linear theory can explain the ratio
between the monopoles in redshift- and real-space down to small scales at high
redshift. We find that the amplitude of the Fingers-of-God effect is larger for
HI than for matter. We point out that accurate 21 cm maps can be created from
N-body or approximate simulations rather than full hydrodynamic simulations.
