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Calibration of Surface Brightness Fluctuations for Dwarf Galaxies in the Hyper Suprime-Cam $gi$ Filter System

Surface brightness fluctuation (SBF) magnitudes are a powerful standard candle to measure distances to semi-resolved galaxies in the local universe, a majority of which are dwarf galaxies that have often bluer colors than bright early-type galaxies. We present an empirical $i-$band SBF calibration in a blue regime, $0.2 \lesssim (g-i)_0 \lesssim 0.8$ in the Hyper Suprime-Cam (HSC) magnitude system. We measure SBF magnitudes for 12 nearby dwarf galaxies of various morphological types with archival HSC imaging data, and use their tip of the red giant branch (TRGB) distances to derive fluctuation - color relations. In order to subtract contributions of fluctuations due to young stellar populations, we use five different $g-$band magnitude masking thresholds, $M_{g,{\rm thres}} = -3.5, -4.0, -4.5, -5.0,$ and $-5.5$ mag. We find that the rms scatter of the linear fit to the relation is the smallest (rms = 0.16 mag) in the case of $M_{g,{\rm thres}} = -4.0$ mag, $\overline{M_i} = (-2.65\pm0.13)+ (1.28\pm0.24) \times (g-i)_0$. This scatter is much smaller than those in the previous studies (rms=0.26 mag), and is closer to the value for bright red galaxies (rms=0.12 mag). This calibration is consistent with predictions from metal-poor simple stellar population models.