Revisiting Ca II Activity Indices in FGK Stars: Systematic Biases in Infrared Triplet Measurements

Synthetic-template subtraction is widely used to measure chromospheric activity in large spectroscopic surveys. However, many solar-like FGK stars show systematically negative Ca II infrared triplet (IRT) residual indices, implying that the observed line cores are deeper than those predicted by parameter-matched templates. We investigate this effect using solar-like stars from LAMOST DR9, MaStar, and XSL DR3, measuring activity indices (R+) for both the Ca II H&K and IRT lines in a uniform framework. We find that observational effects, including atmospheric-parameter offsets, treatment of the instrumental line-spread function, and propagated measurement uncertainties, contribute to scatter but do not explain the systematic negative bias in R+_IRT. The results instead suggest that the negative bias most likely arises because photospheric templates underestimate the depth of the IRT cores, likely owing to missing chromospheric structure and, to a lesser extent, NLTE effects. An empirical increase in the adopted microturbulent velocity deepens the synthetic IRT cores and partially mitigates the negative offset. In addition, R+ values derived from different synthesis configurations show systematic offsets but generally preserve strong linear correlations, indicating that they can be cross-calibrated. These results clarify the origin of negative Ca II IRT residual indices and help interpret template-dependent systematics in chromospheric activity measurements based on synthetic-template subtraction.