2. THE HUBBLE CONSTANT

The global value of H₀ has long been uncertain by a factor of two. Before 1980 the dispute was basically between two schools: Sandage and collaborators had insisted on H₀ = 50 (Sandage & Tammann 1982); de Vaucouleurs and collaborators preferred a high value H₀ = 90-100 (de Vaucouleurs 1981). Conspicuous progress was brought by the discovery of an empirical but tight relationship between galaxy's luminosity and rotation velocity, known as the Tully-Fisher relation (Tully & Fisher 1977). The use of the Tully-Fisher relation has largely reduced subjective elements in the distance work, and H₀ = 80-90 has been derived from a straightforward reading of the Tully-Fisher relation. Representative of this work are the papers of Aaronson et al. (1986) and Pierce & Tully (1988). A doubt was whether the result was marred with the Malmquist bias - whether the sample selects preferentially bright galaxies, and hence the result was biased towards a shorter distance (Kraan-Korteweg, Cameron & Tammann 1988; Sandage 1993a). A related dispute was over the distance to the Virgo cluster, whether it is 16 Mpc or 22 Mpc: the different results depending on which sample one used.

The next momentous advancement was seen in 1989-1990 when a few qualified distance indicators were discovered. One of them is a technique using planetary nebula luminosity function (PNLF), the shape of which looked universal (Jacoby et al. 1990a). Another important technique is the use of surface brightness fluctuations (SBF), utilizing the fact that the images of distant galaxies show a smoother light distribution; while surface brightness does not depend on the distance, pixel-to-pixel fluctuations in a CCD camera decreases as d_L^-1 (Tonry & Schneider 1988). They proposed that this smoothness can be a distance indicator if the stellar population is uniform. What was important is that the two completely independent methods predicted distances to individual galaxies in excellent agreement with each other (Ciardullo, Jacoby & Tonry 1993). The PNLF/SBF distance also agreed with the value from the Tully-Fisher relation, with a somewhat larger scatter. These new techniques, when calibrated with the distance to M31, yielded a value around H₀ = 80 and the Virgo distance of 15 Mpc (For a review of the methods, see Jacoby et al. 1992).

Around the same time the use of Type Ia supernovae (SNeIa) became popular (Tammann & Leibundgut 1990; Leibundgut & Pinto 1992; Branch & Miller 1993). The principle is that the maximum brightness of SNIa is nearly constant, which can be used as an absolute standard candle. Arnett, Branch and Wheeler proposed that the maximum brightness is reliably calculable using models which are constrained from observations of released kinetic energy (Arnett, Branch & Wheeler 1985; Branch 1992). This led to H₀ = 50-55, in agreement with the calibration based on the first Cepheid measurement of the nearest SNIa host galaxy using the pre-refurbished Hubble Space Telescope (HST) (Sandage et al. 1992). In the early nineties the discrepancy was dichotomous as whether H₀ = 80 or 50. (see Fukugita, Hogan & Peebles 1993 for the status at that time; see also van den Bergh 1989, 1994).

The next major advancement was brought with the refurbishment mission of HST, which enabled one to resolve Cepheids in galaxies as distant as 20 Mpc (1994). This secured the distance to the Virgo cluster and tightened the calibrations of the extragalactic distance indicators, resulting in H₀ = (70-75) ± 10, 10% lower than the `high value'. Another important contribution was the discovery that the maximum brightness of SNeIa varies from supernova to supernova, and that it correlates with the decline rate of brightness (Pskovskii 1984; Phillips 1993; Riess, Press & Kirshner 1995; Hamuy et al. 1996a). This correction, combined with the direct calibration of the maximum brightness of several SNeIa with HST Cepheid observations, raised the `low value' of H₀ to 65⁺⁵_-10, appreciably higher than 55. This seemed to resolve the long-standing controversy.

All methods mentioned above use distance ladders and take the distance to Large Magellanic Clouds (LMC) to be 50 kpc (m - M = 18.5) as the zero point. Before 1997 few doubts were cast on the distance to LMC (TABLE 1 shows a summary of the distance to LMC known as of 1997). With the exception of RR Lyr, the distance converged to m - M = 18.5 ± 0.1, i.e., within 5% error, and the discrepency of the RR Lyr distance was blamed on its larger calibration error. It had been believed that the Hipparcos mission (ESA 1997) would secure the distance within MW and tighten the distance to LMC. To our surprise, the work using the Hipparcos catalogue revealed the contrary; the distance to LMC was more uncertain than we had thought, introducing new difficulties into the determination of H₀. In this connection, the age of the Universe turned out to be more uncertain than it was believed.

During the nineties, efforts have also been conducted to determine the Hubble constant without resorting to astronomical ladders. They are called `physical methods'. The advantage of the ladder is that the error of each ladder can be documented relatively easily, while the disadvantage is that these errors accumulate. Physical methods are free from the accumulation of errors, but on the other hand it is not easy to document the systematic errors. Therefore, the central problem is how to minimise the model dependence and document realistic systematic errors. Nearly ten years of effort has brought results that can be compared with the distances from ladders. The physical methods include the expansion photosphere model (EPM) for type II SNe (Schmidt, Kirshner & Eastman 1992) and gravitational lensing time delay (Refsdal 1964). Use of SNeIa maximum brightness was once taken to be a physical method (Branch 1992), but then `degraded' to be a ladder, which however significantly enhanced its accuracy.