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

4.4 The Deceleration Parameter

For the greatest problem of observational cosmology during the coming decades - the determination of the deceleration parameter, q₀, - SNe Ia will play an important and perhaps decisive role. The route to q₀ has been mapped out by Sandage (1961). At that time he proposed first-ranked cluster galaxies as standard candles. They have the advantage of extremely high luminosity but they suffer from luminosity and dynamical evolution. SNe Ia are about 3.7 mag fainter in V than first-ranked cluster galaxies (at z = 0), but they are expected to be much less subject to evolutionary effects. They also offer the important advantages of being point sources, thus greatly facilitating the photometry, and of being very good standard candles with little luminosity scatter at maximum.

A strategy to determine q₀ from SNe Ia as standard candles has been outlined by Tammann (1979). Including a K-correction, Leibundgut (1990) has calculated m_V for SNe Ia as a function of z for the cases q₀ = 0 and q₀ = 1/2. At redshifts of z = 0.3 and 0.5 the SNe Ia will be brighter in a critical universe than in an empty one by 0.2 and 0.3 mag, respectively. Even if the intrinsic scatter of SNe Ia is as large as 0.25 mag, ten SNe Ia at z = 0.3 (and m_V 21.4) would distinguish the two cases at the 3.2 level (cf Burns et al 1990). At z = 0.5 the distinction between the two cases would be even easier, but here the SNe Ia would be fainter by about 1.7 mag. This is because the K-correction in the V band is negative for z = 0.3 but then increases rapidly with increasing z. Thus, if q₀ is to be determined at higher redshifts, SNe Ia should be observed redwards of the V band.

A determination of q₀, or a combination of q₀ and if the cosmological constant is permitted to be nonzero (Sandage & Tammann 1984), by means of SNe Ia appears to be feasible. In any case, among the methods proposed so far, SNe Ia offer the best hope.