11.3 Virgo - A Case Study
The Virgo Cluster has historically played a central role in the determination of the extragalactic distance scale. This is because Virgo is the nearest cluster with a full complement of morphological types so that many different methods of distance determination may be applied. Furthermore, it is sufficiently rich that unusual events occur frequently (e.g., supernovae, novae), it is at high galactic latitude so that foreground extinction is not a serious matter, and it is at low declination so that it may be studied from both northern and southern hemispheres. In addition, Virgo is sufficiently distant that most of its recessional velocity derives from the Hubble expansion, and is therefore valuable as a cosmological probe.
We summarize in Table 4 the uncertainties (internal, external, and total) in distance to an individual Virgo galaxy that these 7 methods can achieve. (Cepheids are included for completeness, but are restricted to Local Group distances.) Internal errors are taken from the individual sections of this review; external errors are dominated by the uncertainty in the zero-point calibrations. Because most of the methods have common systematic errors (e.g., the Cepheid distance to M31), averaging the distances does not reduce the overall uncertainty.
| Method |  internal (mags) | external
(mags) | Total a (mags) |
| Cepheids GCLF Novae SN Ia Tully-Fisher b PNLF SBF Dn-
c
| 0.10 0.30 0.33 0.20 0.25 0.10 0.10 0.45 | 0.13 0.27 0.22 0.50 0.13 0.13 0.13 0.21 | 0.16 0.40 0.40 0.53 0.28 0.16 0.16 0.50 |
| a Total
uncertainty is defined as sqrt(2int + 2ext)
| |||
| b Assumes I or H luminosities; Buncertainties will be larger due to extinction correction errors. | |||
| c External error is the zero-point uncertainty based on the two Leo I elliptical calibrators. | |||
In Table 5, we present a summary of the results
from the seven methods when applied to the Virgo Cluster and assuming
E (B - V) = 0.02, which is typical of Virgo galaxies
(Burstein and
Heiles 1984).
The errors in the averages presented in the last rows are rms errors;
they have not been reduced by 
N statistics because of the systematic errors in common.
Note that the total range in distances has an extent (defined as
Dmax / Dmin - 1) of only ~ 37%, not
the sometimes quoted
``factor of 2'' (i.e., an extent of 100%). Furthermore, the values
exhibit an rms dispersion about the mean of ~ 12%,
and all values are contained within a spread of ± 1.6 times this
dispersion. One element of added confusion is that each method includes
a different sample of galaxies and intrinsic depth plays a role approaching
the level of the dispersion. Methods basing their distances on a few galaxies
(GCLF, PNLF, Novae, SN Ia) are particularly susceptible to skewed results
by including a single near or distant member. In summary,
the deviations among the techniques are nearly equal to the accuracies
of the techniques. There are no discrepancies of statistical
significance.
| Method | (m - M)Virgo - (m - M)M31 | Distance (Mpc) a |
| GCLF Novae SN Ia Tully-Fisher PNLF SBF b Dn- unweighted average weighted average | 6.94 ± 0.40 7.19 ± 0.40 7.00 ± 0.50 6.57 ± 0.20 6.50 ± 0.15 6.44 ± 0.12 6.70 ± 0.29 6.79 ± 0.26 6.59 ± 0.22 | 18.8 ± 3.8 21.1 ± 3.9 19.4 ± 5.0 15.8 ± 1.5 15.4 ± 1.1 15.9 ± 0.9 16.8 ± 2.4 17.6 ± 2.2 16.0 ± 1.7 |
| a Assumes M31 distance of 770 Mpc | ||
| b Virgo Distance is an average of grouped galaxies rather than a simple average as for other methods. | ||