Biases on initial mass function determinations. III. Cluster masses
  derived from unresolved photometry
  It is currently common to use spatially unresolved multi-filter broad-band
photometry to determine the masses of individual stellar clusters (and hence
the cluster mass function, CMF). I analyze the stochastic effects introduced by
the sampling of the stellar initial mass function (SIMF) in the derivation of
the individual masses and the CMF and I establish that such effects are the
largest contributor to the observational uncertainties. An analytical solution,
valid in the limit where uncertainties are small, is provided to establish the
range of cluster masses over which the CMF slope can be obtained with a given
accuracy. The validity of the analytical solution is extended to higher mass
uncertainties using Monte Carlo simulations and the Gamma approximation. The
value of the Poisson mass is calculated for a large range of ages and a variety
of filters for solar-metallicity clusters measured with single-filter
photometry. A method that uses the code CHORIZOS is presented to simultaneously
derive masses, ages, and extinctions. The classical method of using unweighted
UBV photometry to simultaneously establish ages and extinctions of stellar
clusters is found to be unreliable for clusters older than approx. 30 Ma, even
for relatively large cluster masses. On the other hand, augmenting the filter
set to include longer-wavelength filters and using weights for each filter
increases the range of masses and ages that can be accurately measured with
unresolved photometry. Nevertheless, a relatively large range of masses and
ages is found to be dominated by SIMF sampling effects that render the observed
masses useless, even when using UBVRIJHK photometry. A revision of some
literature results affected by these effects is presented and possible
solutions for future observations and analyses are suggested.
