2.3.6. The Distance to the Virgo Cluster

Within the limitations discussed above, each of these 5 distance indicators has been used to determine the distance to the Virgo Cluster. The Virgo cluster is the nearest cluster of galaxies and contains about 200 members which are brighter than M33. The core of the Virgo cluster is dominated by the very bright elliptical galaxy M87. This is shown in Figure 2-21. As will be discussed in Chapter 3, knowing the distance to Virgo does not automatically allow for a determination of H₀ but it is one of the last steps to be taken. However, a good distance to the Virgo cluster might be quite useful in establishing the calibration for SN Ia or BCM based indicators, which can be applied over much larger distances.

Figure 2-21: Photograph of the central part of the Virgo cluster defined by the two bright ellipticals M84 and M87 which are near the right hand side. This image was constructed from Palomar Digital Sky Survey by the author.

The TF distance: There are approximately 30 spiral galaxies that are contained in the nominal 6 degree angular diameter region of the sky that defines the Virgo cluster and which have favorable inclinations. The main limitation is the depth of the sample along the line of sight. If this depth is 5 Mpc ( ± 2.5 Mpc from the center), then this will introduce 0.4 mag of range in the TF relation (see Fukugita et al. 1993). There is also the possibility that the spiral population of Virgo is actually in the form of a shell of galaxies currently falling into the core. In either case, the front-to-back distance of the spiral sample does seem to be appreciable. There have been many estimates of the distance to Virgo from the TF relation. The most complete sample is that of Pierce and Tully (1988) who derive (m - M) = 30.88 ± 0.20 where the error bar is dominated by the depth of the sample and the zeropoint is set by their adopted distances to M31 and M33. A comprehensive recent treatment by Yasuda et al. (1996) uses two samples of galaxies for calibration. The first sample uses Cepheid distances for M31, M33, M81, NGC 300, NGC 2403, NGC 3109 (an irregular galaxy and hence a questionable calibrator), and NGC 3368 to yield a calibrating Blue band TF relation which has a scatter of 0.29 mag. This sample is combined with distance estimates of 13 galaxies in nearby groups to yield a TF relation for Virgo spirals which also has a scatter of 0.29 mag. This indicates that the larger sample has not improved the precision of the calibrating relationship but has just made the statistical determination of the zeropoint more reliable. The analysis of Yasuda et al. (1996) clearly shows that Virgo has a high degree of substructure as well as depth along the line of sight. From a study of 43 spiral galaxies, they derive a mean Virgo distance of (m - M) = 31.18 ± 0.40.

The PNLF distance: Jacoby et al. (1990) apply this method to six Elliptical/S0 galaxies in the core of the Virgo cluster to derive (m - M) = 30.84 ± 0.05. The extremely small dispersion reflects the lack of depth in this sample and the fact that the uncertainty in the distance of M31 is not included. A more realistic error bar is closer to 0.10 mag for this sample, which is still rather good.

Surface brightness fluctuation distance: Tonry et al. (1990) measured V and I-band fluctuations of 10 E and S0 galaxies to derive (m - M) = 30.86 ± 0.13. The new Tonry et al. (1996) calibration of the method coupled with augmentations to the Virgo sample of galaxies has increased this distance to (m - M) = 31.03 ± 0.06.

Supernovae Ia distance: Sandage and Tammann (1993) used a sample of 10 SN Ias which have occurred in Virgo cluster galaxies from 1919-1990. Six of these host galaxies are Elliptical and the other four are spirals. They derive a mean value of < M_v > = 12.16 ± 0.14. If only the Cepheid distance to IC 4182 is used as the zeropoint, the Virgo cluster modulus is (m - M) = 31.89 ± 0.21. Using both the IC 4182 and NGC 5253 zeropoints reduces this estimate by 0.2 mags to (m - M) = 31.70 ± 0.21. These distance estimates are significantly larger than those obtained by the previously discussed methods. There are, however, a number of possible problems with this estimate including:

There is evidence of a correlation between the maximum SN Ia luminosity and B - V color (see Hamuy et al. 1995). As shown in Tammann and Sandage (1995), SN 1937C and SN 1972E are marginally bluer than the Supernova observed in Virgo cluster galaxies.

The most recent SN Ia to occur in Virgo was 1994D in the host galaxy NGC 4526 (see Richmond et al. 1995). If (m - M) = 31.7 for Virgo, then the photometry of SN 1994D shows it to be significantly under-luminous.

Seven of the 10 SN Ia used in Sandage and Tammann (1993) occurred in 1961 or before and thus only have photographic photometry.

The host galaxies to the Virgo SN Ia are all luminous ellipticals and spirals yet the two calibrating galaxies, NGC 5253 and IC 4182, are low mass, amorphous, irregular galaxies. According to von Hippel et al. (1997) there is a small dependence of SN Ia luminosity on galaxy type.

The Cepheid distance to M100, in Virgo, host of 3 SN Ia over the last 100 years, is (m - M) = 31.16 (see below). M100 is not used in the Virgo Cluster SN sample of Sandage and Tammann.

GCLF distance: Based on observations of the statistically determined GCLF of Virgo ellipticals, Harris et al. (1991) determine (m - M) = 31.47 ± 0.25. Sandage and Tammann (1995) use that same dataset, but apply a different Galactic GCLF zeropoint to derive (m - M) = 31.64 ± 0.25. They arrive at this distance estimate without any discussion of the kind of population sampling biases they previously used to discount the TF and PNLF distances. Such sampling biases, of course, are most severe in the case of the GCLF precisely because the GCLF itself is a statistical determination. Interestingly, Nielsen et al. (1997) derive a distance of (m - M) = 31.05 ± 0.07 to the elliptical galaxy NGC 4478 using luminosity fluctuations as measured with HST. These observations also permitted the identification of the GCS of NGC 4478 from which a GCLF distance of (m - M) = 31.25 ± 0.2 was derived. This is rather inconsistent with the earlier results for the GCLF distance to Virgo.