Optical Surface Brightness Fluctuations of shell galaxies towards 100 Mpc

We measure F814W Surface Brightness Fluctuations (SBF) for a sample of distant shell galaxies with radial velocities ranging from 4000 to 8000 km/s. The distance at galaxies is then evaluated by using the SBF method. For this purpose, theoretical SBF magnitudes for the ACS@HST filters are computed for single burst stellar populations covering a wide range of ages (t=1.5-14 Gyr) and metallicities (Z=0.008-0.04). Using these stellar population models we provide the first $\bar{M}_{F814W}$ versus $(F475W-F814W)_0$ calibration and we extend the previous I-band versus $(B-I)_0$ color relation to colors $(B-I)_{0}\leq 2.0$ mag. Coupling our SBF measurements with the theoretical calibration we derive distances with a statistical uncertainty of $\sim 8%$, and systematic error of $\sim 6 %$. The procedure developed to analyze data ensures that the indetermination due to possible unmasked residual shells is well below $\sim 12 %$. The results suggest that \emph{optical} SBFs can be measured at $d \geq 100 Mpc$ with ACS@HST imaging. SBF-based distances coupled with recession velocities corrected for peculiar motion, allow us obtain $H_{0} = 76 \pm 6$ (statistical) $\pm 5$ (systematic) km/s/Mpc.