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

4.2 The Hubble Constant

From the Hubble diagram for their sample of 35 SNe Ia, Tammann & Leibundgut (1990) inferred

M_B = -18.13 ± 0.09 + 5 log h, 1.

while from a sample of 40 SNe Ia MB90 found

M_B = -18.36 ± 0.04 + 5 log h, 2.

where h is the Hubble constant in units of 100 km s^-1 Mpc^-1. The difference is primarily due to the fact that Tammann & Leibundgut did not apply any corrections for parent-galaxy extinction while MB90 did apply a simple inclination dependent correction procedure to the apparently faint SNe Ia in disk galaxies. For nine SNe Ia in elliptical galaxies MB90 found

M_B = -18.33 ± 0.11 + 5 log h. 3.

With M_B⁰⁰ = - 19.6 ± 0.2 (Scetion 3.6), Equation 3 gives H₀ = 56 ± 6 km s^-1 Mpc^-1. This result does not depend on parent-galaxy extinction, but it does depend on the absolute-magnitude calibration, and because the nine SNe Ia are in galaxies having a median recessional velocity of only about 4000 km s^-1 the result is not guaranteed to be free of local streaming motions.

SNe Ia also can be used to obtain a solution for the cosmic (> 4000 km s^-1) value of H₀, however, through the Virgo cluster. The cosmic velocity of the cluster, i.e. the velocity freed of all local effects, can be inferred from much more distant clusters whose distance relative to the Virgo cluster is known (Sandage & Tammann 1990). It can be shown that the distant clusters with a median velocity of 6400 km s^-1 do not partake of the local microwave dipole motion and that they therefore constitute, to a good approximation, a Machian frame (Jerjen & Tammann 1992). Within this cosmic frame the Virgo recession velocity becomes 1182 ± 19 km s^-1. Now excluding (to avoid circularity) the Virgo-cluster calibration of SNe Ia in Section 3.6, we have M_B = -19.6 ± 0.3. With m_B⁰⁰ = 11.92 ± 0.09 for six Virgo SNe Ia (Table 2), we have a Virgo distance modulus µ₀ = 31.54 ± 0.31, a Virgo distance of 20.3 ± 2.9 Mpc, and a cosmic value of H₀ = 58 ± 8 km s^-1 Mpc^-1. This result for the Virgo distance is independently supported by globular clusters, novae, the D_n - and Tully-Fisher relations, and the requirement that our Galaxy and M31 not be oversized. These methods give a Virgo distance modulus of 31.64 ± 0.09 (Tammann 1991b) which, if taken at face value, suggest that 1. the low extinction of SNe Ia adopted in Section 2.5 cannot be increased without increasing the difference between the Virgo distances from SNe Ia and from other evidence, and 2. the formal difference of -0.10 ± 0.32 between the Virgo moduli from SNe Ia and from external evidence represents an external error to the SN Ia luminosity calibration of M = - 19.6 adopted in Section 3.6. The agreement within the errors between H₀ at ~ 4000 km s^-1 and its cosmic value is very satisfactory, and is consistent with the linearity of the expansion over a wide range of scales (Sandage 1992).

It should perhaps be noted that the determination of distances at large redshift would not yield the present value of the expansion rate, H₀, but the value H_t at the time of emission, which is a function of H₀ and q₀. The determination of q₀ from SNe Ia, independent of H₀, will be discussed in Section 4.4.

The prospects for firmly establishing the value of H₀ from SNe Ia are excellent. The historical Galactic supernovae may never be more than an interesting consistency check, but the calibration via IC 4182 and eventually the Virgo cluster can be checked by means of cepheids. Advances in both observation and modeling of SNe Ia will allow the thermal emission and radioactivity methods to fuse into one complete physical picture that will demand a particular maximum luminosity for each event. The accuracy may then be limited primarily by uncertainties associated with departures from spherical symmetry.