  Most of the massive elliptical galaxies in the universe stopped forming stars
billions of years ago, even though plenty of hot gas remains available for star
formation. Here we present compelling evidence indicating that quenching of
star formation depends on both black-hole feedback and Type Ia supernova
heating. We analyze Chandra X-ray observations of ten massive ellipticals, five
with extended, potentially star-forming multiphase gas and five single-phase
ellipticals with no star formation. The ratio of cooling time to freefall time
at 1--10 kpc in the multiphase galaxies is tc/tff ~10, indicating that
precipitation-driven feedback limits cooling but does not eliminate
condensation. In the same region of the single-phase galaxies, the radial
profiles of gas entropy are consistent with a thermally stable (tc/tff > 20)
supernova-driven outflow that sweeps stellar ejecta out of the galaxy. However,
in one of those single-phase ellipticals (NGC 4261) we find tc/tff < 10 at <
300 pc. Notably, its jets are ~50 times more powerful than in the other nine
ellipticals, in agreement with models indicating that precipitation near the
black hole should switch its fueling mode from Bondi-like accretion to cold
chaotic accretion. We conclude by hypothesizing that particularly strong
black-hole outbursts can shut off star formation in massive elliptical galaxies
by boosting the entropy of the hot gas and flipping the system into the
supernova-sweeping state.
