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*,

while from a sample of 40 SNe Ia MB90 found

*M*_{B} = -18.36 ± 0.04 + 5 log *h*,

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*.

With *M*_{B}^{00} = - 19.6 ± 0.2
(Scetion 3.6), Equation 3 gives
*H*_{0} = 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 *H*_{0}, 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*_{B}^{00} = 11.92 ±
0.09 for six Virgo SNe Ia
(Table 2), we
have a Virgo distance modulus *µ*_{0} =
31.54 ± 0.31, a Virgo distance of
20.3 ± 2.9 Mpc, and a cosmic value of *H*_{0} = 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 *H*_{0} 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, *H*_{0}, but the value *H*_{t} at the
time of emission, which is a
function of *H*_{0} and *q*_{0}. The
determination of *q*_{0} from SNe Ia,
independent of *H*_{0}, will be discussed in
Section 4.4.

The prospects for firmly establishing the value of *H*_{0}
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.