Nonlinear Color--Metallicity Relations of Globular Clusters. VI. On Calcium II Triplet Based Metallicities of Globular Clusters in Early-type Galaxies

The metallicity distribution function of globular clusters (GCs) in galaxies is a key to understanding galactic formation and evolution. The calcium II triplet (CaT) index has recently become a popular metal abundance indicator thanks to its sensitivity to GC metallicity. Here we revisit and assess the reliability of CaT as a metallicity indicator using our new stellar population synthesis simulations based on empirical, high-resolution fluxes. The model shows that the CaT strength of old ($>$ 10 Gyr) GCs is proportional to ${\rm [Fe/H]}$ below $-0.5$. In the modest metal-rich regime, however, CaT does not increase anymore with ${\rm [Fe/H]}$ due to the little contribution from coolest red giant stars to the CaT absorption. The nonlinear nature of the color--$CaT$ relation is confirmed by the observations of GCs in nearby early-type galaxies. This indicates that the CaT should be used carefully when deriving metallicities of metal-rich stellar populations. Our results offer an explanation for the observed sharp difference between the color and $CaT$ distributions of GCs in the same galaxies. We take this as an analogy to the view that metallicity--color and metallicity--Lick index nonlinearity of GCs is primarily responsible for their observed "bimodal" distributions of colors and absorption indices.