3.2. 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 of quasars. All are promising, but in each case the relevant physics remains somewhat uncertain.

The ⁵⁶Ni radioactivity method for determining H₀ using Type Ia SNe 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 for ⁵⁶Ni production. 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 SNe; the 1992 result h = 0.6 ± 0.1 (Schmidt, Kirschner, & Eastman 1992) was subsequently revised upward by the same authors to h = 0.73 ± 0.06 ± 0.07 (1994). 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). The history and more recent data have been reviewed by Birkinshaw (1999), who concludes that the available data give a Hubble parameter h 0.6 with a scatter of about 0.2. But since the available measurements are not independent, it does not follow that h = 0.6 ± 0.1; for example, there is a selection effect that biases low the h determined this way.

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 (first suggested by Refsdal 1964; reviewed in Williams & Schechter 1997). 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 (Kundic et al. 1997a, cf. Serra-Ricart et al. 1999 and references therein). Since t ² H₀^-1, this observation allows an estimate of the Hubble parameter. 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), and h = 0.62 ± 0.07 (Falco et al. 1997), where the error does not include systematic errors in the assumed form of the lensing mass distribution.

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. A simple model for the lensing galaxy and the nearby galaxies then leads to h = 0.42 ± 0.06 (Schechter et al. 1997), although higher values for h are obtained by more sophisticated analyses: 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.

Another quadruple-lens system, B1606+656, leads to h = 0.59 ± 0.08 ± 0.15, where the first error is the 95% C.L. statistical error, and the second is the estimated systematic uncertainty (Fassnacht et al. 1999). Time delays have also recently been determined for the Einstein ring system B0218+357, giving h = 0.69^+0.13_-0.19 (95% C.L.) (Biggs et al. 1999).

Mainly because of the systematic uncertainties in modelling the mass distribution in the lensing systems, the uncertainty in the h determination by gravitational lens time delays remains rather large. But it is reassuring that this completely independent method gives results consistent with the other determinations.