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  1. Abstract

    Massive elliptical galaxies harbor large amounts of hot gas (T≳ 106K) in their interstellar medium (ISM) but are typically quiescent in star formation. The jets of active galactic nuclei (AGNs) and Type Ia supernovae (SNe Ia) inject energy into the ISM, which offsets its radiative losses and keeps it hot. SNe Ia deposit their energy locally within the galaxy compared to the larger few ×10 kiloparsec-scale AGN jets. In this study, we perform high-resolution (5123) hydrodynamic simulations of a local (1 kpc3) density-stratified patch of the ISM of massive galaxies. We include radiative cooling and shell-averaged volume heating, as well as randomly exploding SN Ia. We study the effect of different fractions of supernova (SN) heating (with respect to the net cooling rate), different initial ISM density/entropy (which controls the growth timettiof the thermal instability), and different degrees of stratification (which affect the freefall timetff). We find that SNe Ia drive predominantly compressive turbulence in the ISM with a velocity dispersion ofσvup to 40 km s−1and logarithmic density dispersion ofσs∼ 0.2–0.4. These fluctuations trigger multiphase condensation in regions of the ISM, wheremin(tti)/tff0.6exp(6σs), in agreement with theoretical expectations that large density fluctuations efficiently trigger multiphase gas formation. Since the SN Ia rate is not self-adjusting, when the net cooling drops below the net heating rate, SNe Ia 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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    Gas in the central regions of cool-core clusters and other massive haloes has a short cooling time (≲1 Gyr). Theoretical models predict that this gas is susceptible to multiphase condensation, in which cold gas is expected to condense out of the hot phase if the ratio of the thermal instability growth time-scale (tti) to the free-fall time (tff) is tti/tff ≲ 10. The turbulent mixing time tmix is another important time-scale: if tmix is short enough, the fluctuations are mixed before they can cool. In this study, we perform high-resolution (5122 × 768–10242 × 1536 resolution elements) hydrodynamic simulations of turbulence in a stratified medium, including radiative cooling of the gas. We explore the parameter space of tti/tff and tti/tmix relevant to galaxy and cluster haloes. We also study the effect of the steepness of the entropy profile, the strength of turbulent forcing and the nature of turbulent forcing (natural mixture versus compressive modes) on multiphase gas condensation. We find that larger values of tti/tff or tti/tmix generally imply stability against multiphase gas condensation, whereas larger density fluctuations (e.g. due to compressible turbulence) promote multiphase gas condensation. We propose a new criterion min (tti/min (tmix, tff)) ≲ c2 × exp (c1σs) for when the halo becomes multiphase, where σs denotes the amplitude of logarithmic density fluctuations and c1 ≃ 6, c2 ≃ 1.8 from an empirical fit to our results.

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