© CAMBRIDGE UNIVERSITY PRESS 1999

1.3.2.3 Correcting for Virgocentric Infall

What about the HST Cepheid measurement of H₀, giving h = 0.80 ± 0.17 (Freedman et al. 1994), which received so much attention in the press? This calculated value is based on neither of the two methods (A) or (B) above, and it should not be regarded as being very reliable. Instead this result is obtained by assuming that M100 is at the core of the Virgo cluster, and dividing the sum of the recession velocity of Virgo, about 1100 km s^-1, plus the calculated ``infall velocity'' of the local group toward Virgo, about 300 km s<sup>-1</sup>, by the measured distance to M100 of 17.1 Mpc. (These recession and infall velocities are both a little on the high side, compared to other values one finds in the literature.) Adding the ``infall velocity'' is necessary in this method in order to correct the Virgo recession velocity to what it would be were it not for the gravitational attraction of Virgo for the Local Group of galaxies, but the problem with this is that the net motion of the Local Group with respect to Virgo is undoubtedly affected by much besides the Virgo cluster - e.g., the ``Great Attractor.'' For example, in our CHDM supercomputer simulations (which appear to be a rather realistic match to observations), galaxies and groups at about 20 Mpc from a Virgo-sized cluster often have net outflowing rather than infalling velocities. Note that if the net ``infall'' of M100 were smaller, or if M100 were in the foreground of the Virgo cluster (in which case the actual distance to Virgo would be larger than 17.1 Mpc), then the indicated H₀ would be smaller.

Freedman et al. (1994) gave an alternative argument that avoids the ``infall velocity'' uncertainty: the relative galaxy luminosities indicate that the Coma cluster is about six times farther away than the Virgo cluster, and peculiar motions of the Local Group and the Coma cluster are relatively small corrections to the much larger recession velocity of Coma; dividing the recession velocity of the Coma cluster by six times the distance to M100 again gives H₀ 80. However, this approach still assumes that M100 is in the core rather than the foreground of the Virgo cluster; and in deducing the relative distance of the Coma and Virgo clusters it assumes that the galaxy luminosity functions in each are comparable, which is uncertain in view of the very different environments. More general arguments by the same authors (Mould et al. 1995) lead them to conclude that h = 0.73 ± 0.11 regardless of where M100 lies in the Virgo cluster. But Tammann et al. (1996), using all the available HST Cepheid distances and their own complete sample of Virgo spirals, conclude that h 0.54.

To summarize, many observers, using mainly relative distance methods, favor a value h 0.6-0.8 although Sandage's group and some others continue to get h 0.5-0.6 and all of these values may need to be reduced by something like 10% if the full Hipparcos data set bears out the preliminary reports discussed above. Meanwhile the fundamental physics methods typically lead to h 0.4-0.7. Among fundamental physics approaches, there has been important recent progress in measuring h via time delays between different images of gravitationally lensed quasars, with the latest analyses of both of the systems with measured time delays giving h 0.6 ± 0.1.

The fact that the fundamental physics measurements giving lower values for h (via time delays in gravitationally lensed quasars and the Sunyaev-Zel'dovich effect) are mostly of more distant objects has suggested to some authors (Turner, Cen, & Ostriker 1992; Wu et al. 1995) that the local universe may actually be underdense and therefore be expanding faster than is typical. But in reasonable models where structure forms from Gaussian fluctuations via gravitational instability, it is extremely unlikely that a sufficiently large region has a density sufficiently smaller than average to make more than a rather small difference in the value of h measured locally (Suto, Suginohara, & Inagaki 1995; Shi & Turner 1997). Moreover, the small dispersion in the corrected maximum luminosity of distant Type Ia supernovae found by the LBL Supernova Cosmology Project (Kim et al. 1997) compared to nearby SNe Ia shows directly that the local and cosmological values of H₀ are approximately equal. The maximum deviation permitted is about 10%. Interestingly, preliminary results using 44 nearby Type Ia supernovae as yardsticks suggest that the actual deviation is about 5-7%, in the sense that in our local region of the universe, out to a radius of about 70 h^-1 Mpc (the distance of the Northern Great Wall), H₀ is this much larger than average (A. Dekel, private communication). The combined effect of this and the Hipparcos correction would, for example, reduce the ``mid-term'' value h ~ 0.73 from the HST Key Project on the Extragalactic Distance Scale, to h ~ 0.63.

There has been recent observational progress in both relative distance and fundamental physics methods, and it is likely that the Hubble parameter will be known reliably to 10% within a few years. Most recent measurements are consistent with h = 0.6 ± 0.1, corresponding to a range t₀ = 6.52 h^-1 Gyr = 9.3-13.0 Gyr for = 1 - in good agreement with the preliminary estimates of the ages of the oldest globular clusters based on the new data from the Hipparcos astrometric satellite.