  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 can
condense out of the hot ICM in global thermal balance when the background
$t_{\rm cool}/t_{\rm ff} \lesssim 10$. Recent observations suggest the presence
of cold gas even when the background profiles have somewhat large values of
${t_{\rm cool}/t_{\rm ff}}$. This partly motivates a better understanding of
additional factors such as large density perturbations that can enhance the
propensity for cooling and condensation even when the background ${t_{\rm
cool}/t_{\rm ff}}$ is high. Such large density contrasts can be seeded by
galaxy wakes or dense cosmological filaments. 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 in the condensation curve by varying
entropy stratification. Steeper (positive) entropy gradients shift the
condensation curve to higher amplitudes of perturbations (i.e., make
condensation difficult). 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.
