Simultaneous Dependence of Matter Clustering on Scale and Environment

In this work, we propose new statistical tools that are capable of characterizing the simultaneous dependence of dark matter and gas clustering on the scale and the density environment, and these are the environment-dependent wavelet power spectrum (env-WPS), the environment-dependent bias function (env-bias), and the environment-dependent wavelet cross-correlation function (env-WCC). These statistics are applied to the dark matter and baryonic gas density fields of the \texttt{TNG100-1} simulation at redshifts of $z=3.0$-$0.0$, and to \texttt{Illustris-1} and \texttt{SIMBA} at $z=0$. The measurements of the env-WPSs suggest that the clustering strengths of both the dark matter and the gas increase with increasing density, while that of a Gaussian field shows no density dependence. By measuring the env-bias and env-WCC, we find that they vary significantly with the environment, scale, and redshift. A noteworthy feature is that at $z=0.0$, the gas is less biased in denser environments of $\Delta \gtrsim 10$ around $3 \ h\mathrm{Mpc}^{-1}$, due to the gas reaccretion caused by the decreased AGN feedback strength at lower redshifts. We also find that the gas correlates more tightly with the dark matter in both the most dense and underdense environments than in other environments at all epochs. Even at $z=0$, the env-WCC is greater than $0.9$ in $\Delta \gtrsim 200$ and $\Delta \lesssim 0.1$ at scales of $k \lesssim 10 \ h\mathrm{Mpc}^{-1}$. In summary, our results support the local density environment having a non-negligible impact on the deviations between dark matter and gas distributions up to large scales.