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 M̄_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 Δ(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 σ_d = 0.49^+0.11 _-0.15 Mpc, or a total line-of-sight depth of 2.0^+0.4 _-0.6 Mpc, consistent with its compact appearance on the sky. This translates to a depth scatter smaller than the intrinsic, or "cosmic," scatter σ_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 σ_cos. We find σ_cos = 0.06 0.01 mag, with a firm upper limit of σ_cos < 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 N̄, m̄-m_tota 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.