  Intensity mapping experiments are beginning to measure the spatial
distribution of neutral atomic hydrogen (HI) to constrain cosmological
parameters and the large-scale distribution of matter. However, models of the
behaviour of HI as a tracer of matter is complicated by galaxy evolution. In
this work, we examine the clustering of HI in relation to galaxy colour,
stellar mass, and HI mass in IllustrisTNG at $z$ = 0, 0.5, and 1. We compare
the HI-red and HI-blue galaxy cross-power spectra, finding that HI-red has an
amplitude 1.5 times higher than HI-blue at large scales. The cross-power
spectra intersect at $\approx 3$ Mpc in real space and $\approx 10$ Mpc in
redshift space, consistent with $z \approx 0$ observations. We show that HI
clustering increases with galaxy HI mass and depends weakly on detection limits
in the range $M_{\mathrm{HI}} \leq 10^8 M_\odot$. We also find that blue
galaxies in the greatest stellar mass bin cluster more than blue galaxies in
other stellar mass bins. Red galaxies in the greatest stellar mass bin,
however, cluster the weakest amongst red galaxies. These trends arise due to
central-satellite compositions. Centrals correlate less with HI for increasing
stellar mass, whereas satellites correlate more, irrespective of colour.
Despite the clustering relationships with stellar mass, we find that the
cross-power spectra are largely insensitive to detection limits in HI and
galaxy surveys. Counter-intuitively, all auto and cross-power spectra for red
and blue galaxies and HI decrease with time at all scales in IllustrisTNG. We
demonstrate that processes associated with quenching contribute to this trend.
The complex interplay between HI and galaxies underscores the importance of
understanding baryonic effects when interpreting the large-scale clustering of
HI, blue, and red galaxies at $z \leq 1$.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics