Annu. Rev. Astron. Astrophys. 1998. 36: 17-55 Copyright © 1998 by Annual Reviews. All rights reserved

3.2. Matching the Calibrators to the Hubble Flow

The ways that have been used to obtain H₀ by comparing the local Cepheid-calibrated SNe Ia to Hubble-flow SNe Ia are considered here more or less in order of increasing complexity.

The intent of the HST SN Ia Consortium all along has been to simply treat SNe Ia as nearly standard candles. In their most recent paper, Saha et al (1997) assigned mean values for M_B and M_V of the calibrators to the mean values of 56 non-red (B - V < 0.2) Hubble-flow SN Ia to obtain H₀ = 58⁺⁷_-8, where extinction of the non-red Hubble-flow SN Ia is neglected. Saha et al emphasized that for H₀ higher than 65, nearly all of the Hubble-flow SNe Ia would be intrinsically dimmer than nearly all of the Cepheid-calibrated SNe Ia (Figure 9), in spite of the observational bias in favor of discovering the most luminous of the Hubble-flow SNe Ia. The larger the SN Ia absolute-magnitude dispersion actually is (cf van den Bergh 1996), the stronger an argument this is for a low value of H₀ because the effect of the bias increases with the size of the dispersion. For an insightful discussion of the effects of selection bias on distance determinations, see Teerikorpi (1997) in this series.

Figure 9. Absolute magnitude is plotted against distance modulus for Cepheid-calibrated SNe Ia (diamonds) and other non-red SNe Ia after 1985 (circles). The absolute magnitudes of the latter are shown for three values of H0. From Saha et al (1997).

Others have used Saha et al's Cepheid distances, together with slightly different adopted apparent magnitudes of the SN Ia calibrators and in some cases using only subsets of the calibrators, to make their own estimates of H₀. For example, the local calibrators are in blue galaxies, and since SNe Ia in blue galaxies tend to be more luminous than those in red galaxies, it would seem to be appropriate to match the calibrators only to Hubble-flow SNe Ia in blue galaxies. Branch et al (1996b) obtained H₀ = 57 ± 4 in this way, and Saha et al (1997) showed that this hardly affects their result for H₀. If a Cepheid distance to NGC 1316 can be obtained, it will provide a valuable calibration of two SNe Ia in an early-type red galaxy.

Another way to match the calibrators to Hubble-flow SNe Ia is to use the supernova B - V color to standardize the absolute magnitudes. The correlation between absolute magnitude and B - V will be anything but perfect because even if a one-to-one intrinsic relation existed, it wouldn't be exactly like the relation produced by extinction. Nevertheless this approach has the attractive feature that it requires no extinction estimates for the calibrators or the Hubble-flow events. In this way, Branch et al (1996a), using several subsets of calibrators (none of which included SN 1895B because there is no estimate of its V magnitude) and several subsets of Hubble-flow SNe Ia, obtained values of H₀ ranging from 54 ± 5 to 60 ± 6.

The standardization method for absolute magnitudes that has received the most attention so far is the use of light-curve decline rates or shapes. Hamuy et al (1996b) matched the calibrators to their non-red Hubble-flow SNe Ia using their linear relations between absolute magnitude and m₁₅ and obtained H₀ = 63 ± 3.4 (internal) ± 2.9 (external). The requirement of an accurate value of m₁₅ restricted the number of calibrators to four: SNe 1937C, 1972E, 1981B, and 1990N; extinction of the non-red Hubble-flow SNe Ia was neglected. Schaefer (1996b) considered the apparent magnitudes of the calibrators in the U, B, V, and H bands (where possible) and obtained H₀ = 55 ± 3. Kim et al (1997) matched the calibrators to five of Perlmutter et al's (1997c) high-redshift SNe Ia with the two samples adjusted to a common mean value of m₁₅ and obtained estimates of H₀ that depend slightly on the values of _m and (see their Figure 3). For example, for _m = 1 and = 0, their result for H₀ was 59 ± 3, whereas for _m = 0.3 and = 0, it was 62 ± 4. Tripp (1997) matched the calibrators to a combination of the Calán-Tololo and high-redshift samples, all adjusted to a common mean m₁₅, and obtained H₀ = 60 ± 5. When Tripp (1998) allowed absolute magnitude to depend linearly on both B - V and m₁₅, he obtained H₀ = 60 ± 6. Freedman et al (1997) assumed that a Cepheid-based distance to the spiral galaxy NGC 1365 gives the distance to the Fornax cluster and to the early-type galaxies NGC 1380, the parent of SN 1992A, and NGC 1316, the parent of SN 1980N; by applying a magnitude-decline relation to these two events together with some of the other calibrators, they obtained H₀ = 67 ± 8. But assigning the distance of NGC 1365 to the early-type parent galaxies of SNe 1992A and 1980N is highly controversial (Freedman 1997, Saha et al 1997, Sandage & Tammann 1997, Tammann & Federspiel 1997).

Riess et al (1996a) used their MLCS technique with three calibrators, SNe 1972E, 1981B, and 1990N, to calibrate the absolute distances to their sample of 20 Hubble-flow SNe Ia and obtained H₀ = 64 ± 3 (statistical) ± 6 (total error). In this approach, individual extinctions of the Hubble-flow events are derived rather than assumed or neglected.