Nonlinear Color-Metallicity Relations of Globular Clusters. IX.
  Different Radial Number Density Profiles between Blue and Red Clusters
  The optical colors of globular clusters (GCs) in most large early-type
galaxies are bimodal. Blue and red GCs show a sharp difference in the radial
profile of their surface number density in the sense that red GCs are more
centrally concentrated than blue GCs. An instant interpretation is that there
exist two distinct GC subsystems having different radial distributions. This
view, however, was challenged by a scenario in which, due to the nonlinear
nature of the GC metallicity-to-color transformation for old ($\gtrsim$10 Gyr)
GCs, a broad unimodal metallicity spread can exhibit a bimodal color
distribution. Here we show, by simulating the radial trends in the GC color
distributions of the four nearby giant elliptical galaxies (M87, M49, M60, and
NGC 1399), that the difference in the radial profile between blue and red GCs
stems naturally from the metallicity-to-color nonlinearity plus the well-known
radial metallicity gradient of GC systems. The model suggests no or little
radial variation in GC age even out to $\sim$20${R}_{\rm eff}$. Our results
provide a simpler solution to the distinct radial profiles of blue and red GCs
that does not necessarily invoke the presence of two GC subsystems and further
fortify the nonlinearity scenario for the GC color bimodality phenomenon.
