Tracing Multiphase Structure in the Circumgalactic Medium: Insights from Magnetohydrodynamic Turbulence Simulations

The circumgalactic medium (CGM) is the diffuse gas surrounding a galaxy's halo, and it plays a vital role in the galactic baryon cycle. However, its mass distribution across the virial phase and the cooler, denser atomic phase, remains uncertain. To investigate this, we perform high-resolution magnetohydrodynamic simulations of 0.125--8 kpc-scale representative patches of the CGM, with parameters informed by quasar absorption line observations. Our simulations resolve the cooling length (the minimum across all temperatures of $c_s t_{\rm cool}$, where $c_s$ is the sound speed and $t_{\rm cool}$ is the cooling time in isobaric conditions), allowing us to track the evolution of cold gas more accurately. We find that low-density CGM gas ($3\times10^{-4}$ cm$^{-3}$) cannot sustain cold gas below $10^4$ K for long, due to a large value of the ratio between the cooling to mixing time ($t_{\rm cool}/t_{\rm mix}$). In contrast, higher-density environments ($3\times10^{-3}~{\rm cm}^{-3}$) reach a turbulent multiphase steady state, with up to $50\%$ of the mass in the cold phase, occupying only about $1\%$ of the volume. To connect with large-volume cosmological simulations and small ${\rm pc}$-scale idealized simulations, we explore different box sizes (0.125--8 kpc) and identify a key scaling relation: simulations with similar $t_{\rm cool}/t_{\rm mix}$ exhibit comparable cold gas mass fractions and lifetimes. Importantly, we find that simply sub-sampling (reducing box-size) a small region from a large-volume simulation while maintaining a constant turbulent energy density injection rate from larger to smaller scales artificially shortens $t_\mathrm{mix}$, leading to inaccurate predictions for cold gas survival. This means that cold gas at small $\lesssim 10$ kpc scales arises in relatively dense, quiescent regions of the CGM rather than the turbulent ones undergoing cascade from large scales.