Biases on Initial Mass Function Determinations. Iii. Cluster Masses Derived From Unresolved Photometry

Abstract

It is currently common to use spatially unresolved multifilter broadband 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 ≈ 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.

Wide-fieldHST/ACS images of M81: the population of compact star clusters

“…The scatter on the redder side can be understood in terms of interstellar reddening. On the other hand, the blueward shift of the distribution with respect to the colour expected for the 10–300 Myr SSP could be due to the stochastic sampling of the stellar IMF that affects the colours of low‐mass clusters (Cerviño & Luridiana 2004; Maiz‐Apellaniz 2009). Hence, the presence of many clusters bluer than B − I <0.5 mag suggests that majority of the clusters has mass of <10 4 M.…”

Super star clusters in Haro 11: properties of a very young starburst and evidence for a near-infrared flux excess

“…(2) Uneven IMF sampling in less massive clusters can also affect the expected NIR flux. Studies of the evolution of the stellar isochrones (Maíz Apellániz 2009, among many others) have shown that red supergiants (RSGs) dominate the SC light in red and near‐IR wavelengths as early as 6 Myr. Z01 models are constructed by integrating the contribution to the cluster's light from all the stars populating a well‐sampled IMF, normalized with respect to the mass of the cluster.…”

The star cluster – field star connection in nearby spiral galaxies

“…However, standard SSP models assume a continuously populated stellar initial mass function (SIMF), while clusters consist of a finite number of stars. For unresolved clusters, the random sampling of the SIMF can strongly affect integrated properties such as cluster colors, magnitudes, and parameters (ages, masses) derived from them (Cerviño & Luridiana 2006;Maíz Apellániz 2009;Popescu & Hanson 2010a,b). A promising attempt to take the stochastic color fluctuations into account when deriving ages and masses has been made by Fouesneau & Lançon (2010), based on a Bayesian approach.…”