Massive elliptical galaxies harbor large amounts of hot gas (T≳106 K) in their interstellar medium (ISM) but are typically quiescent in star formation. Active-galactic nuclei (AGNs) jets and Type Ia supernovae (SNIa) inject energy into the ISM which offsets its radiative losses and keeps it hot. SNIa deposit their energy locally within the galaxy compared to the larger few×10 kpc-scale AGN jets. In this study, we perform high-resolution (5123) hydrodynamic simulations of a local (1 kpc3) density-stratified patch of massive galaxies' ISM. We include radiative cooling and shell-averaged volume heating, as well as randomly exploding SNIa. We study the effect of different fractions of supernova heating (with respect to the net cooling rate), different initial ISM density/entropy (which controls the thermal-instability growth time tti) and different degrees of stratification (which affects the free-fall time tff). We find that the SNIa drive predominantly compressive turbulence in the ISM with a velocity dispersion σv up to 40 kms−1 and logarithmic density dispersion σs∼0.2--0.4. These fluctuations trigger multiphase condensation in regions of the ISM where min(tti)/tff≲0.6exp(6σs), in agreement with theoretical expectations that large density fluctuations efficiently trigger multiphase gas formation. Since the SNIa rate is not self-adjusting, when the net cooling drops below the net heating rate the SNIa drive a hot wind which sweeps out most of the mass in our local model. Global simulations are required to assess the ultimate fate of this gas.
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