Formation of low-mass stars in elliptical galaxy cooling flows

Thermal X-ray emission from cooling flows in elliptical galaxies indicates that similar to 1 M(circle dot) of hot (T similar to 10(7) K) interstellar gas cools each year, accumulating similar to 10(10) Mo over a Hubble time. Paradoxically, optical and radio frequency emission from the cooled gas is lacking, indicating that less than similar to 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 hows 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(H II) similar to 10(4) K) by stellar ultraviolet radiation. The low filling factor of H II gas requires that the hot gas cools at similar to 10(6) cooling sites within several kpc of the galactic center. H II mass slowly increases at each site at similar to 10(-6) Mo yr-l until a neutral core develops. Neutral cores are heated (T(H) (I) similar to 15 K) and ionized (x similar to 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 similar to 2 M(circle dot). 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 less than or similar to 4.5 M(circle dot) 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 H beta 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 similar to 106 Mo 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 H beta 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, similar to 10(5) yr, is too short to permit dust formation and perhaps also gas phase formation of molecules.