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The ACS Fornax Cluster Survey. V. Measurement and Recalibration of Surface Brightness Fluctuations and a Precise Value of the Fornax--Virgo Relative Distance

We present g-z color and z-band surface brightness fluctuations (SBF) measurements for 43 early-type galaxies in the Fornax cluster imaged with HST/ACS. These are combined with measurements for Virgo cluster galaxies to derive a revised, nonlinear calibration of the z-band SBF absolute magnitude as a function of g-z. In all, we tabulate recalibrated SBF distances for 134 galaxies in Virgo, Fornax, the Virgo W' group, and NGC4697 in the Virgo Southern Extension. The calibration procedure yields a precise relative distance modulus for Fornax with respect to Virgo of 0.42+/-0.03 mag, or a distance ratio 1.214 +/- 0.017. The resulting Fornax distance modulus is 31.51 +/-0.03 +/-0.15 mag, 20.0 +/-0.3 +/-1.4 Mpc, where the second set of error bars reflects systematic uncertainty from our assumed Virgo distance of 16.5 Mpc. The rms distance scatter for the early-type Fornax galaxies is 0.49^{+0.11}_{-0.15} Mpc, consistent with its compact appearance on the sky. This translates to a depth scatter smaller than the intrinsic, or "cosmic", scatter sigma_cosmic in the SBF calibration, unlike in Virgo. As a result, we are able to place the first tight constraints on the value of sigma_cosmic, finding 0.06 +/- 0.01 mag, with a firm upper limit of sigma_cosmic<0.08 mag, at least for galaxies with g-z>1.02. We also present an alternative SBF calibration based on the `fluctuation count' parameter Nbar, a proxy for galaxy mass, which gives a consistent relative distance. Finally, we find no evidence for systematic trends of the galaxy distances with position or velocity (e.g., no current infall); the Fornax cluster appears both compact and well virialized.[abridged]