Investigating the Low-Mass End of the Initial Mass Function in Stellar Clusters

Despite decades of investigation, we do not yet know whether the stellar initial mass function (IMF) is the same across all environments. Dynamical measurements of the V-band mass-to-light ratios (Upsilon) of stellar clusters span a range from the "expected" values consistent with a Kroupa-like IMF to values larger than those consistent with a Salpeter IMF. Large values of Upsilon may be due to an excess of low-mass stars, known as a bottom-heavy IMF, but dynamical mass measurements do not provide information about the source of the mass. With one exception, the high Upsilon clusters are younger than the low Upsilon clusters, raising concerns about the role of systematic errors in the model-based corrections applied to account for the evolution of stellar populations when comparing clusters of different ages and metallicities. We use several methods to address these issues. First, we count resolved stars in NGC 6535, the single old cluster that initially appeared to have unusually high Upsilon. Surprisingly, we find a deficit of low-mass stars in this cluster, exacerbating the discrepancy between the dynamical measurement and its known stellar content. With no old, high Upsilon clusters remaining, age-related errors become an even larger concern. Problems that might exist in the stellar evolution models used to compare the V-band luminosities of clusters would not affect all photometric bands equally. We therefore measure Upsilon in multiple bands from ultraviolet to infrared. We compare predicted colors and Upsilons from two different stellar population models to our cluster observations. The observed colors are reproduced well by the models and the trend in Upsilon with age is indistinguishable between UV, V, and IR bands. We conclude that the models are accurately calculating the luminosities and that any variation in Upsilon arises from real or artificial variations in the proportion of mass in these clusters rather than in a corresponding variation in their luminosities. Finally, we use the spectral fitting program alf to fit detailed stellar population models to spectra of eight stellar clusters. These models are sensitive to light from stars of different masses, making it possible to measure the abundance of very low-mass stars and to compare the result to dynamical mass measurements. Our preliminary study suggests that the spectra for the clusters under consideration are generally consistent with a Kroupa-like IMF and possibly slightly inconsistent with the dynamical results. We also find that contamination from interstellar absorption, which is not a large concern for the application of alf to galaxies due to their redshifts, may affect the results for clusters in our own Galaxy and satellite galaxies. In conclusion, we have found no evidence of systematic errors in the determination of the varying dynamical values of Upsilon and a marginal indication that the observed variation is not due to variations in the low-mass end of the stellar mass function. Given our confirmation of the value of comparing dynamical and spectral determinations of Upsilon, we believe that the latter can now be confirmed or refuted using more spectral fitting of younger clusters