Chemical enrichment in cosmological, smoothed particle hydrodynamics
  simulations
  (Abridged) We present an implementation of stellar evolution and chemical
feedback for smoothed particle hydrodynamics (SPH) simulations. We consider the
timed release of individual elements by both massive (Type II supernovae and
stellar winds) and intermediate mass stars (Type Ia supernovae and asymptotic
giant branch stars). We illustrate the results of our method using a suite of
cosmological simulations that include new prescriptions for radiative cooling,
star formation, and galactic winds. Radiative cooling is implemented
element-by-element, in the presence of an ionizing radiation background, and we
track all 11 elements that contribute significantly to the radiative cooling.
We contrast two reasonable definitions of the metallicity of a resolution
element and find that while they agree for high metallicities, there are large
differences at low metallicities. We argue the discrepancy is indicative of the
lack of metal mixing caused by the fact that metals are stuck to particles. We
argue that since this is a (numerical) sampling problem, solving it using a
poorly constrained physical process such as diffusion could have undesired
consequences. We demonstrate that the two metallicity definitions result in
redshift z = 0 stellar masses that can differ by up to a factor of two, because
of the sensitivity of the cooling rates to the elemental abundances. We find
that by z = 0 most of the metals are locked up in stars. The gaseous metals are
distributed over a very wide range of gas densities and temperatures. The
shock-heated warm-hot intergalactic medium has a relatively high metallicity of
~ 10^-1 Z_sun that evolves only weakly and is therefore an important reservoir
of metals.
