10.4 Calibration

There are no elliptical galaxies near enough to the Milky Way to be used for absolute calibration. M32 has both too low a central dispersion ( < 100 km s^-1) and too high a surface brightness (I_B < 19.5) to be a candidate. Furthermore, because the D_n- method carries a relatively large uncertainty for distances to individual galaxies, a large number of calibrators would be required to reduce the zero-point uncertainty to 10%.

Three attempts have been made to tie the D_n- distances to other scales. Dressler (1987) argued on the basis of samples in the Virgo and Coma clusters that the D_n- relation for the bulges of S0s and early type spirals is identical to that for ellipticals. To minimize the effects of disk contamination and dust he used diameter measurements based on a mean enclosed blue surface brightness of 19.75 and calibrated his relation using CCD frames of M31 and M81 and photoelectric photometry from the literature. Using bulge velocity dispersions of = 150 km s^-1 for M31 (McElroy 1983) and = 166 km s^-1 for M81 (Whitmore et al. 1985), and distance moduli of 24.2 for M31 and 27.5 for M81, he estimated the distance to Virgo as 21.3 and 18.3 Mpc from these two galaxies respectively.

Pierce (1989) calibrated the luminosity-surface brightness-velocity dispersion relation (Djorgovski and Davis 1987) in the Leo I Group by assuming a distance of 10.0 ± 1.0 Mpc based on the planetary nebula luminosity function (Ciardullo et al. 1989). (This distance estimate is in excellent agreement with the distances derived from the globular cluster luminosity function [10.7 Mpc; Harris 1990], the Tully-Fisher relation [10.5 Mpc; Bottinelli et al. 1985], and the surface brightness fluctuation method [9.3 Mpc; Tonry 1991].) This calibration gave a distance of 14.1 ± 1.6 Mpc to Virgo and 13.5 ± 2.2 Mpc to Fornax. If the same Leo distance is used to calibrate the D_n- relation and the model of LFBDDTW, the distances to Virgo and Fornax become 15.5 ± 2.2 Mpc and 16.6 ± 2.2 Mpc, respectively. The values for Virgo are in good agreement, and, although the Fornax numbers differ by 20%, they fall within the mutual error estimates. Note, however, that two estimates are not completely independent, since Pierce utilized the velocity dispersion measurements from Whitmore et al. (1985) and the 7S.

More recently Tonry (1991) has used a new calibration of the the surface brightness fluctuation method (SBF) to determine the distances of four groups or clusters (Leo, Virgo, Fornax and Eridanus) with respect to that of M31 and M32 which he took to be 0.77 Mpc. He then compared these distances to those derived from the Planetary Nebula Luminosity Function (PNLF), Infrared Fisher Tully (IRTF) and D_n- methods. The agreement between the SBF and the PNLF method (on a galaxy-by-galaxy basis) was found to be excellent, consistent with the error estimates. Surprisingly the agreement between SBF and IRTF (on a group-by-group basis) was better than would be expected on the basis of the error estimates (but see Sec. 11). The agreement with the D_n- method was found to have greater scatter as would be expected from the larger uncertainty of the D_n- method but with the additional anomaly that the distance estimate to Eridanus derived from the D_n- method is greater (by three standard deviations) than from either the IRTF or SBF methods. This difference is difficult to explain other than by noting the small number of galaxies (five) available for the comparison. Note, however, that is Sec. 11, we show that overall D_n- compares to other distance indicators as expected from the error estimates.