From light to mass: accessing the initial and present-day Galactic
  globular cluster mass functions
  The initial and present-day mass functions (ICMF and PDMF, respectively) of
the Galactic globular clusters (GCs) are constructed based on their observed
luminosities, the stellar evolution and dynamical mass-loss processes, and the
mass-to-light ratio (MLR). Under these conditions, a Schechter-like ICMF is
evolved for approximately a Hubble time and converted into the luminosity
function (LF), which requires finding the values of 5 free parameters: the mean
GC age (\tA), the dissolution timescale of a $10^5 \ms$ cluster ($\tau_5$), the
exponential truncation mass (\mc) and 2 MLR parametrising constants. This is
achieved by minimising the residuals between the evolved and observed LFs, with
the minimum residuals and realistic parameters obtained with MLRs that increase
with luminosity (or mass). The optimum PMDFs indicate a total stellar mass of
$\sim4\times10^7$ \ms\ still bound to GCs, representing $\sim15%$ of the mass
in clusters at the beginning of the gas-free evolution. The corresponding ICMFs
resemble the scale-free MFs of young clusters and molecular clouds observed in
the local Universe, while the PDMFs follow closely a lognormal distribution
with a turnover at $\mto\sim7\times10^4$\,\ms. For most of the GC mass range,
we find an MLR lower than usually adopted, which explains the somewhat low
\mto. Our results confirm that the MLR increases with cluster mass (or
luminosity), and suggest that GCs and young clusters share a common origin in
terms of physical processes related to formation.
