Multiphase gas in the circumgalactic medium: relative role of $t_{\rm cool}/t_{\rm ff}$ and density fluctuations

We perform a suite of simulations with realistic gravity and thermal balance in shells to quantify the role of the ratio of cooling time to the free-fall time ($t_{\rm cool}/t_{\rm ff}$) and the amplitude of density perturbations ($\delta \rho/\rho$) in the production of multiphase gas in the circumgalactic medium (CGM). Previous idealized simulations, focussing on small amplitude perturbations in the intracluster medium (ICM), found that cold gas condenses out of the hot ICM in global thermal balance when the background $t_{\rm cool}/t_{\rm ff} \lesssim 10$. Sources such as galaxy wakes and dense cosmological filaments can seed large density contrast in the medium and give rise to cold gas in halos with $(t_{\rm cool}/t_{\rm ff}) > 10$, consistent with the recent observations. From our simulations, we introduce a condensation curve in the $(\delta \rho/\rho)$ - min$(t_{\rm cool}/t_{\rm ff})$ space, that defines the threshold for condensation of multiphase gas in the CGM. We show that this condensation curve corresponds to ${(t_{\rm cool}/t_{\rm ff})}_{\rm blob} \lesssim 10$ applied to the overdense blob instead of the background for which $t_{\rm cool}/t_{\rm ff}$ can be higher. We also study the modification of the condensation curve under different conditions like entropy stratification, jet injection and the introduction of buoyantly rising bubbles. Steeper (positive) entropy gradients and bubbles shift the condensation curve to higher amplitudes of perturbations (i.e., make condensation difficult) while gentle outflows shift it to lower amplitudes of perturbations, making condensation easier. A constant entropy core, applicable to the CGM in smaller halos, shows condensation over a larger range of radii as compared to the steeper entropy profiles in the ICM.