On The Birth Masses of the Ancient Globular Clusters
  All globular clusters (GCs) studied to date show evidence for internal
variation in their light element abundances. These variations have been
interpreted as evidence for multiple star formation episodes within GCs, with
secondary episodes fueled, at least in part, by the ejecta of AGB stars from a
first generation of stars. A major puzzle emerging from this otherwise
plausible scenario is that the fraction of stars associated with the second
episode of star formation is observed to be much larger than expected for a
standard IMF. The present work investigates this tension by modeling the
observed anti-correlation between [Na/Fe] and [O/Fe] for 20 Galactic GCs. If
the abundance pattern of the retained AGB ejecta does not depend on GC mass at
fixed [Fe/H], then a strong correlation is found between the fraction of
current GC stellar mass comprised of pure AGB ejecta, f_p, and GC mass. This
fraction varies from 0.20 at low masses (10^4.5 Msun) to 0.45 at high masses
(10^6.5 Msun). The fraction of mass associated with pure AGB ejecta is directly
related to the total mass of the cluster at birth; the ratio between the
initial and present mass in stars can therefore be derived. Assuming a star
formation efficiency of 50%, the observed Na-O anti-correlations imply that GCs
were at least 10-20 times more massive at birth. These factors are lower limits
because any mass-loss mechanism that removes first and second generation stars
equally will leave f_p unchanged. The mass-dependence of f_p probably arises
because lower mass GCs are unable to retain all of the AGB ejecta from the
first stellar generation. Recent observations of elemental abundances in
intermediate-age LMC clusters are re-interpreted and shown to be consistent
with this basic scenario. A convincing explanation of these trends is currently
lacking.
