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(475)-z(850)) color and z(850)-band surface brightness fluctuations (SBFs) measurements for 43 early-type galaxies in the Fornax cluster imaged with the Hubble Space Telescope Advanced Camera for Surveys. These are combined with our earlier measurements for Virgo cluster galaxies to derive a revised, nonlinear calibration of the z(850)-band SBF absolute magnitude (M) over bar (z) as a function of (g(475)-z(850)) color, valid for the AB color range 0.8 < (g(475)-z(850)) < 1.6. In all, we tabulate recalibrated SBF distances for 134 galaxies in Virgo, Fornax, the Virgo W' group, and NGC 4697 in the Virgo Southern Extension. The calibration procedure yields a highly precise relative distance modulus for Fornax with respect to Virgo of Delta(m - M)(FV) = 0.42 +/- 0.03 mag, or a distance ratio d(F) / d(V) = 1.214 +/- 0.017. The resulting Fornax distance modulus is (m - M)(For) = 31.51 +/- 0.03 +/- 0.15 mag, corresponding to d(F) = 20.0 +/- 0.3 +/- 1.4 Mpc, where the second set of error bars reflects the total systematic uncertainty from our assumed Virgo distance of 16.5 Mpc. The rms distance scatter for the early-type Fornax cluster galaxies is sigma(d) = 0.49(-0.15)(+0.11) Mpc, or a total line-of-sight depth of 2.0(-0.6)(+0.4) Mpc, consistent with its compact appearance on the sky. This translates to a depth scatter smaller than the intrinsic, or "cosmic," scatter sigma(cos) in the SBF calibration, unlike the case for the larger Virgo cluster. As a result, we are able to place the first tight constraints on the value of sigma(cos). We find sigma(cos) = 0.06 +/- 0.01 mag, with a firm upper limit of scos < 0.08 mag, for the subsample of galaxies with (g(475)-z(850)) > 1.02, but it is about twice as large for bluer galaxies. We also present an alternative SBF calibration based on the " fluctuation count" parameter (N) over bar = (m) over bar - m(tot), a proxy for galaxy mass. This gives a consistent relative distance but with larger intrinsic scatter, and we adopt the result from the calibration on (g(475)-z(850)) because of its basis in stellar population properties alone. 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.