Annu. Rev. Astron. Astrophys. 1992. 30: 359-89 Copyright © 1992 by Annual Reviews. All rights reserved

4.3 Testing the Nature of the Redshift

The extragalactic redshift generally is assumed to be caused by a universal expansion, but direct tests are few in number and difficult to execute. Hubble (1953) himself kept open the possibility that the universe does not expand. Two tests are known, one of which is best performed with SNe Ia.

1. The Tolman test. In an expanding universe, surface brightness varies as (1 + z)^-4 (Tolman 1930, 1934; Kristian & Sachs 1966). This holds for galaxies, provided that surface brightness within a metric diameter is used. Sandage & Perelmuter (1991) recently have applied the test using surface photometry and Petrosian diameters (Petrosian 1976) for the several brightest galaxies in 56 nearby clusters and groups of galaxies. After the application of reduction procedures to remove observational biases, the data appear to support the reality of the expansion, but Sandage & Perelmuter give reasons to view this result with caution.

2. The time dilation test. In an expanding universe the observed rate of a distant clock is slowed down by a factor of (1 + z). The standard light curves of SNe Ia therefore are broadened by this factor (Wilson 1939, Rust 1974, de Vaucouleurs & Pence 1976). This provides, at least in principle, a very simple test for the nature of the redshifts of SNe Ia and their parent galaxies. At a redshift z = 0.3, for instance, the inflection point of the B light curve at t_B = 44 days should be delayed by 13 days.

A practical complication is the wavelength dependence of the standard light curves. It has been proposed, therefore, to measure the light curve of the supernova at the rest wavelength of the B band in the frame of the parent galaxy (Tammann 1979). An alternative solution is to use a K-correction to predict the shape of the standard light curve in, for instance, the V band, at a redshift z. Because of the pronounced color evolution of SNe Ia (Figure 4) the K-correction is strongly variable, resulting in a deformation of the light curve, Using information on the SN Ia spectral energy distribution at various phases, Leibundgut (1990) has calculated the expected standard light curves in the V band for discrete values of z.

Heroic search efforts have so far provided one supernova that may be suitable for the test: SN 1988U at z = 0.28 (Hansen et al 1989, Norgaard-Nielsen et al 1989). The somewhat fragmentary V photometry of SN 1988U (not certain to be of Type Ia) indicates an initial decline rate of 0.10 mag per day, which is nearer to the rate of 0.12 mag per day that is predicted when the (1 + z) factor is included than to the rate of 0.15 mag per day predicted for a stationary universe (Leibundgut 1991b).

A few confirmed SNe Ia with good photometry at z 0.3 should provide a definitive test of the time dilation in the near future.