© CAMBRIDGE UNIVERSITY PRESS 1999

1.3.2.2 Fundamental Physics Approaches

The fundamental physics approaches involve either Type Ia or Type II supernovae, the Sunyaev-Zel'dovich (S-Z) effect, or gravitational lensing. All are promising, but in each case the relevant physics remains somewhat uncertain.

The ⁵⁶Ni radioactivity method for determining H₀ using Type Ia SN avoids the uncertainties of the distance ladder by calculating the absolute luminosity of Type Ia supernovae from first principles using plausible but as yet unproved physical models. The first result obtained was that h = 0.61 ± 0.10 (Arnet, Branch, & Wheeler 1985; Branch 1992); however, another study (Leibundgut & Pinto 1992; cf. Vaughn et al. 1995) found that uncertainties in extinction (i.e., light absorption) toward each supernova increases the range of allowed h. Demanding that the ⁵⁶Ni radioactivity method agree with an expanding photosphere approach leads to h = 0.60^+0.14_-0.11 (Nugent et al. 1995). The expanding photosphere method compares the expansion rate of the SN envelope measured by redshift with its size increase inferred from its temperature and magnitude. This approach was first applied to Type II SN; the 1992 result h = 0.6 ± 0.1 (Schmidt, Kirschner, & Eastman 1992) was subsequently revised upward by the same authors (1994) to h = 0.73 ± 0.06 ± 0.07. However, there are various complications with the physics of the expanding envelope (Ruiz-Lapuente et al. 1995; Eastman, Schmidt, & Kirshner 1996).

The S-Z effect is the Compton scattering of microwave background photons from the hot electrons in a foreground galaxy cluster. This can be used to measure H₀ since properties of the cluster gas measured via the S-Z effect and from X-ray observations have different dependences on H₀. The result from the first cluster for which sufficiently detailed data was available, A665 (at z = 0.182), was h = (0.4-0.5) ± 0.12 (Birkinshaw, Hughes, & Arnoud 1991); combining this with data on A2218 (z = 0.171) raised this somewhat to h = 0.55 ± 0.17 (Birkinshaw & Hughes 1994). Early results from the ASCA X-ray satellite gave h = 0.47 ± 0.17 for A665 and h = 0.41^+0.15_-0.12 for CL0016+16 (z = 0.545) (Yamashita 1994). A few S-Z results have been obtained using millimeter-wave observations (Wilbanks 1994), and this method may allow more such measurements soon. New results for A2218 and A1413 (z = 0.14) using the Ryle radio telescope and ROSAT X-ray data gave h = 0.38^+0.17_-0.12 and h = 0.47^+0.18_-0.12, respectively (Lasenby 1996). New results from the OVRO 5.5m telescope for the four X-ray brightest clusters give h = 0.54 ± 0.14 (Myers et al. 1997). Corrections for the near-relativistic electron motions (Rephaeli 1995) and for lensing by the cluster (Loeb & Refregier 1997) may raise these estimates for H₀ a little, but it seems clear that the S-Z results favor a smaller value than many optical astronomers obtain. However, since the S-Z measurement of H₀ is affected by the isothermality of the clusters (Roettiger et al. 1997) and the unknown orientation of the cluster ellipticity with respect to the line of sight, and the errors in the derived values remain rather large, this lower S-Z H₀ can only become convincing with more detailed observations and analyses of a significant number of additional clusters. Perhaps this will be possible within the next several years.

Several quasars have been observed to have multiple images separated by a few arc seconds; this phenomenon is interpreted as arising from gravitational lensing of the source quasar by a galaxy along the line of sight. In the first such system discovered, QSO 0957+561 (z = 1.41), the time delay t between arrival at the earth of variations in the quasar's luminosity in the two images has been measured to be, e.g., 409 ± 23 days (Pelt et al. 1994), although other authors found a value of 540 ± 12 days (Press, Rybicki, & Hewitt 1992). The shorter t has now been confirmed by the observation of a sharp drop in Image A of about 0.1 mag in late December 1994 (Kundic et al. 1995) followed by a similar drop in Image B about 405-420 days later (Kundic et al. 1997a). Since t ² H₀^-1, this observation allows an estimate of the Hubble parameter, with the early results h = 0.50 ± 0.17 (Rhee 1991), or h = 0.63 ± 0.21 (h = 0.42 ± 0.14) including (neglecting) dark matter in the lensing galaxy (Roberts et al. 1991), with additional uncertainties associated with possible microlensing and unknown matter distribution in the lensing galaxy and the cluster in which this is the first-ranked galaxy. Deep images allowed mapping of the gravitational potential of the cluster (at z = 0.36) using weak gravitational lensing, which led to the conclusion that h 0.70 (1.1 yr / t) (Dahle, Maddox, & Lilje 1994; Rhee et al. 1996, Fischer et al. 1997). Detailed study of the lensed QSO images (which include a jet) constrains the lensing and implies h = 0.85(1 - )(1.1 yr / t) < 0.85, where the upper limit follows because the convergence due to the cluster > 0, or alternatively h = 0.85(/322 km s^-1)² (1.1 yr / t) without uncertainty concerning the cluster if the one-dimensional velocity dispersion in the core of the giant elliptical galaxy responsible for the lensing can be measured (Grogin & Narayan 1996). The latest results for h from 0957+561, using all available data, are h = 0.64 ± 0.13 (95% C.L.) (Kundic et al. 1997a), h = 0.62 ± 0.07 (Falco et al. 1997, where the error does not include systematic errors in the assumed form of the mass distribution in the lens; uncertainties can also be reduced with new HST images of the system, allowing improved accuracy in the lens galaxy position).

The first quadruple-image quasar system discovered was PG1115+080. Using a recent series of observations (Schechter et al. 1997), the time delay between images B and C has been determined to be about 24 ± 3 days, or 25^+3.3_-3.8 days by an alternative analysis (BarKana 1997). A simple model for the lensing galaxy and the nearby galaxies then leads to h = 0.42 ± 0.06 (Schechter et al. 1997) or h = 0.41 ± 0.12 (95% C.L.) (BarKana, private communication), although higher values for h are obtained by a more sophisticated analysis: h = 0.60 ± 0.17 (Keeton & Kochanek 1996), h = 0.52 ± 0.14 (Kundic et al. 1997b). The results depend on how the lensing galaxy and those in the compact group of which it is a part are modelled. Such models need to be constrained by new HST observations, especially of the light profile in the lensing galaxy, and spectroscopy to better determine the velocity dispersion of the lensing galaxy and of the group.

Although the most recent time-delay results for h from both lensed quasar systems are remarkably close, the uncertainty in the h determination by this method remains rather large. But it is reassuring that this completely independent method gives results consistent with the other determinations. The time-delay method is promising (Blandford & Kundic 1996), and when these systems are better understood and/or delays are reliably measured in several other multiple-image quasar systems, such as B1422+231 (Hammer, Rigaut, & Angonin-Willaime 1995, Hjorth et al. 1996), or radio Einstein-ring systems, such as PKS 1830-211 (van Ommen et al. 1995) or B0218+357 (Corbett et al. 1996), that should lead to a more precise and reliable value for H₀.