Beyond profiles: Using log-normal distributions to model the multiphase circumgalactic medium

Recent observations and simulations reveal that the circumgalactic medium (CGM) surrounding galaxies is multiphase, with the gas temperatures spanning a wide range at most radii -- $\sim 10^4 {\rm~K}$ to the virial temperature ($\sim 10^6$ K for Milky Way). Traditional CGM models using simple density profiles are inadequate in describing such a multiphase atmosphere. Alternatively, a model based on probability distribution functions (PDFs) with parameters motivated by relevant physical processes can better match multi-wavelength observations. In this work, we use log-normal distributions, commonly seen in the simulations of the multiphase interstellar and circumgalactic media, to quantify the volume fraction of different phases. We generalize the isothermal background model by Faerman et al. 2017 to include more general CGM profiles. We extend the existing probabilistic models from 1D-PDFs in temperature to 2D-PDFs in density-temperature phase space and constrain its parameters using a Milky Way-like {\tt Illustris TNG50-1} halo. We generate various synthetic observables such as column densities of different ions, UV/X-ray spectra, dispersion, and emission measures. X-ray and radio (Fast Radio Burst) observations constrain the hot gas properties. However, interpreting cold/warm phase diagnostics is not straightforward since these phases are clumpy/patchy, with inherent variability in intercepting these clouds along arbitrary lines of sight. We provide a tabulated comparison of model predictions to observations, and plan to expand this into a comprehensive compilation of models and data. Our modeling provides a simple, analytic framework that is useful to describe important aspects of the multiphase CGM.