  The luminosities of the centers of nearby elliptical galaxies are very low
compared to models of thin disc accretion to their black holes at the Bondi
rate, typically a few hundredths to a few tenths of a solar mass per year. This
has motivated models of inefficiently-radiated accretion that invoke weak
electron-ion thermal coupling, and/or inhibited accretion rates due to
convection or outflows. Here we point out that even if such processes are
operating, a significant fraction of the accreting gas is prevented from
reaching the central black hole because it condenses into stars in a
gravitationally unstable disc. Star formation occurs inside the Bondi radius
(typically ~100pc in giant ellipticals), but still relatively far from the
black hole in terms of Schwarzschild radii. Star formation depletes and heats
the gas disc, eventually leading to a marginally stable, but much reduced,
accretion flow to the black hole. We predict the presence of cold (~100K),
dusty gas discs, containing clustered H-alpha emission and occasional type II
supernovae, both resulting from the presence of massive stars. Star formation
accounts for several features of the M87 system: a thin disc, traced by H-alpha
emission, is observed on scales of about 100pc, with features reminiscent of
spiral arms and dust lanes; the star formation rate inferred from the intensity
of H-alpha emission is consistent with the Bondi accretion rate of the system.
Star formation may therefore help suppress accretion onto the central engines
of massive ellipticals. We also discuss some implications for the fueling of
the Galactic center and quasars.
