Investigating the Non-linearity Effect on the Color-to-Metallicity Conversion of Globular Clusters

Metallicity distribution of globular clusters (GCs) provides an important clue for star formation history of their host galaxy. With an assumption that GCs are generally old, GC colors have been used as a proxy of GC metallicities. Bimodal GC color distributions observed in most large galaxies have, for decades, been interpreted as bimodal metallicity distributions, indicating the presence of two populations within a galaxy. However, the conventional view has been challenged by a new theory that non-linear GC color-metallicity relations (CMRs) can cause a bimodal color distribution even from a single-peaked metallicity distribution. Using the photometric and spectroscopic data of NGC 5128 GCs in combination with stellar population simulation models, we examine the effect of non-linearity in GC CMRs on the transformation of GC color distributions into metallicity distributions. Although, in some colors, offsets are present between observations and models in the CMRs, their overall shape agrees well for various colors. After the offsets are corrected, the observed spectroscopic metallicity distribution is well reproduced via modeled CMRs from various color distributions having different morphologies. On the other hand, the linearly converted metallicity distributions from GC colors show a significant discrepancy with the observed spectroscopic metallicity distribution. We discuss the implications of our results.