Nonlinear Color-Metallicity Relations of Globular Clusters. XI. Nonlinearity Effect Revealed by NGC 5128 (Centaurus A) and NGC 4594 (Sombrero) Galaxies

Metallicity distributions (MDs) of globular clusters (GCs) provide crucial clues for the assembly and star formation history of their host galaxies. GC colors, when GCs are old, have been used as a proxy of GC metallicities. Bimodal GC color distributions (CDs) observed in most early-type galaxies have been interpreted as bimodal MDs for decades, suggesting the presence of merely two GC subpopulations within single galaxies. However, the conventional view has been challenged by a new theory that nonlinear metallicity-to-color conversion can cause bimodal CDs from unimodal MDs. The unimodal MDs seem natural given that MDs involved many thousand protogalaxies. The new theory has been tested and corroborated by various observational and theoretical studies. Here we examine the nonlinear nature of GC color-metallicity relations (CMRs) using photometric and spectroscopic GC data of NGC 5128 (Centaurus A) and NGC 4594 (Sombrero), in comparison with stellar population simulations. We find that, with a slight offset in color, the overall shapes of observed and modeled CMRs agree well for all available colors. Diverse color-depending morphologies of GC CDs of the two galaxies are well reproduced based on their observed spectroscopic MDs via our CMR models. The results corroborate the nonlinear CMR interpretation of the GC color bimodality, shedding further light on theories of galaxy formation.