Simultaneous dependence of the dark matter and gas clustering on the
  scale and environment
  In this work, we propose new statistical tools that are capable of
characterizing the simultaneous dependence of the matter clustering on the
scale and density environment, which are the environment-dependent wavelet
power spectrum (env-WPS) and environment-dependent wavelet cross-correlation
(env-WCC). We apply these statistics to the projected 2D dark matter and
baryonic gas density fields of the IllustrisTNG simulation at redshifts from
$z=3.0$ to $z=0.0$. Measurement of the env-WPSs indicates that the clustering
strengths of both the dark matter and gas increase with density. At all
redshifts, we observe that the env-WPS of the gas is suppressed on intermediate
and small scales, which is caused by baryonic processes. Furthermore, by
computing the environmental bias function, we find that this suppression varies
with the environment, scale and redshift. A noteworthy feature is that at
$z=0.0$, the bias value increases with density on scales $2\lesssim k \lesssim
10 \ h\mathrm{Mpc}^{-1}$, which is the reversal of that in earlier times. On
the other hand, the env-WCC also shows strong environmental dependence on
scales $k \gtrsim 2 \ h\mathrm{Mpc}^{-1}$ and is sensitive to the redshift. We
find that at $z=3.0$, the coherence of the dark matter and gas decreases with
density. At lower redshifts, the coherence in denser environments becomes much
higher than that in less dense environments. These results suggest that
baryonic processes have less effect on the matter clustering in high-density
environments at later times. Obviously, these statistics provide us rich
information and hence could improve our understanding of the matter clustering.
