Formation of Low-Mass Stars in Elliptical Galaxy Cooling Flows

Thermal X-ray emission from cooling flows in elliptical galaxies indicates that ~1 M_solar of hot (T~10⁷ K) interstellar gas cools each year, accumulating ~10¹⁰ M_solar over a Hubble time. Paradoxically, optical and radio frequency emission from the cooled gas is lacking, indicating that less than ~10^-3 of the cooled gas remains. Many have speculated that the cooled gas has formed into relatively invisible low-mass stars, particularly in the context of massive cooling flows in galaxy clusters. We focus here on cooling flows in elliptical galaxies like NGC 4472 where the cooled gas is made visible in emission lines from H II regions ionized and heated (T_HII~10⁴ K) by stellar ultraviolet radiation. The low filling factor of H II gas requires that the hot gas cools at ~10⁶ cooling sites within several kpc of the galactic center. H II mass slowly increases at each site at ~10^-6 M_solar yr^-1 until a neutral core develops. Neutral cores are heated (T_HI~15 K) and ionized (x~10^-6) by thermal X-rays from the entire interstellar cooling flow. We show that the maximum mass of spherical H I cores that become gravitationally unstable is only ~2 M_solar. No star can exceed this mass, and fragmentation of collapsing cores produces stars of even lower mass. By this means we establish with some confidence that the hypothesis of low-mass star formation is indeed correct--the initial mass function is bottom heavy, but its stars may be optically luminous. Slightly more massive stars <~4.5 M_solar can form near the effective radius (r=8.57 kpc in NGC 4472) if sufficient masses of interstellar gas cool there, producing a luminous population of intermediate-mass stars perhaps with radial orbits that may contribute to the stellar Hβ index. The degree of ionization in gravitationally collapsing cores is sufficiently low to allow magnetic fields to disconnect by ambipolar diffusion. Low-mass star formation is very efficient, involving ~10⁶ M_solar of galactic cold gas at any time, in agreement with observed upper limits on cold gas mass. We discuss the cooling region surrounding a typical cooling site and show that the total X-ray absorption in cold and cooling gas is much less than that indicated by recent X-ray observations. Using a mass dropout scheme consistent with X-ray observations and dynamical mass-to-light ratios, we plot the global Hβ surface brightness profile in NGC 4472 and compare it with the smaller contribution from H II gas recently ejected from red giant stars. The lifetime of cooled gas at each cooling site, ~10⁵ yr, is too short to permit dust formation and perhaps also gas phase formation of molecules.