  The optical color distributions of globular clusters (GCs) in most large
elliptical galaxies are bimodal. Based on the assumed linear relationship
between GC colors and their metallicities, the bimodality has been taken as
evidence of two GC subsystems with different metallicities in each galaxy and
led to a number of theories in the context of galaxy formation. More recent
observations and modeling of GCs, however, suggest that the color-metallicity
relations (CMRs) are inflected, and thus colors likely trace metallicities in a
nonlinear manner. The nonlinearity could produce bimodal color distributions
from a broad underlying metallicity spread, even if it is unimodal. Despite the
far-reaching implications, whether CMRs are nonlinear and whether the
nonlinearity indeed causes the color bimodality are still open questions. Given
that the spectroscopic refinement of CMRs is still very challenging, we here
propose a new photometric technique to probe the possible nonlinear nature of
CMRs. In essence, a color distribution of GCs is a "projected" distribution of
their metallicities. Since the form of CMRs hinges on which color is used, the
shape of color distributions varies depending significantly on the colors.
Among other optical colors, the u-band related colors (e.g., u - g and u - z)
are theoretically predicted to exhibit significantly less inflected CMRs than
other preferred CMRs (e.g., for g - z). As a case study, we performed the
HST/WFPC2 archival u-band photometry for the M87 (NGC 4486) GC system with
confirmed color bimodality. We show that the u-band color distributions are
significantly different from that of g - z, and consistent with our model
predictions. With more u-band measurements, this method will support or rule
out the nonlinear-CMR scenario for the origin of GC color bimodality with high
confidence. [Abridged]
