Formation of Low‐Mass Stars in Elliptical Galaxy Cooling Flows

X-ray emission from hot (T = 10^7 K) interstellar gas in massive ellipticalgalaxies indicates that 10^{10} M_sun has cooled over a Hubble time, butoptical and radio evidence for this cold gas is lacking. We provide detailedtheoretical support for the hypothesis that this gas has formed into lowluminosity stars. Within several kpc of the galactic center, interstellar gasfirst cools to T = 10^4 K where it is heated by stellar UV and emits theobserved diffuse optical line emission. This cooling occurs at a large number(10^6) of isolated sites. After less than a solar mass of gas has accumulated(10^{-6} M_sun/yr) at a typical cooling site, a neutral (HI or H_2) coredevelops in the HII cloud where gas temperatures drop to T = 15 K and theionization level (from thermal X-rays) is very low (x = 10^{-6}). We show thatthe maximum mass of cores that become gravitationally unstable is only about 2M_sun. No star can exceed this mass. Fragmentation of collapsing cores producesa population of low mass stars with a bottom-heavy IMF and radial orbits.Gravitational collapse and ambipolar diffusion are rapid. The total mass ofstar-forming (dust-free) HI or H_2 cores in a typical bright elliptical is only10^6 M_sun, below current observational thresholds.Comment: 23 pages in AASTEX LaTeX with 8 figures; accepted by Astrophysical Journa