Supernovae, as extremely luminous (MB ~ -19.5) point sources, offer an attractive route to extragalactic distances. In this review the emphasis will be on supernovae of Type Ia (SNe Ia). Type II supernovae have a wide range in peak absolute magnitude and can not be treated as standard candles. Distances to individual SNe II can be estimated by means of the expanding photosphere (Baade-Wesselink) and the expanding radiosphere methods, but only elementary applications based on simplifying assumptions have been made to SNe II beyond the Local Group (Kirshner and Kwan 1974, Branch et al. 1981, Bartel 1991). For applications of the method to SN 1987A in the Large Magellanic Cloud, based on detailed calculations, see Chilikuri and Wagoner (1988), Eastman and Kirshner (1989), Schmutz et al. (1990), and Höflich (1991). Supernovae of Type Ib, Type Ic, or Type II-L may turn out to be good standard candles but the present samples are small and all three subtypes have the disadvantage of being less luminous than Type Ia.
Supernovae of Type Ia lack hydrogen lines and helium lines in their optical spectra; during the first month after maximum light they do have a strong absorption feature produced by the red doublet (6347, 6371 Å) of singly ionized silicon. For a review of the spectral classification of supernovae see Harkness and Wheeler (1990). For the purposes of this review, we adopt the model that Type Ia supernovae are the result of the nuclear detonation of a white dwarf which is at or near the Chandrasekhar mass limit (see Sec. 6.2). Since such stars are present in the old stellar populations of all galaxies (but see Foss et al. 1991), there is good reason to believe that Type Ia supernovae behave as standard candles.
Numerous analyses of unrestricted samples of SNe Ia, involving various assumptions about relative distances and interstellar extinction, have produced values of the dispersion in peak Mpg or MB that are generally consistent with the early results of Kowal (1968), who determined = 0.6 mag. Smaller dispersions of 0.3-0.5 mag have been obtained by restricting the SN Ia samples to those beyond the Local Supercluster (Branch and Bettis 1978), in elliptical galaxies (Branch and Bettis 1978, Tammann 1978, Cadonau et al. 1985), in the Virgo cluster (Tammann 1978, 1988, Capaccioli et al. 1990), and in the Coma cluster (Barbon 1978, Capaccioli et al. 1990). The restriction to remote samples lowers the dispersion by a combination of two effects: (1) the avoidance of the problem of uncertain relative distances for the nearby galaxies, and (2) the tendency to select against SNe Ia that are observationally subluminous (whether they are intrinsically subluminous or are highly extinguished).
Several attempts have been made to divide SNe Ia (actually SNe I, prior to the recognition of SN Ib and SN Ic as separate subtypes in the 1980s) into photometric subclasses that may have different luminosities. Barbon et al. (1973) split SNe I into those having ``fast'' and ``slow'' light curves and saw some evidence that the fast events might be more luminous than the slow ones, but Barbon et al. (1975) found no significant brightness difference. Rust (1974) classified SNe I according to the rate of light-curve decline and found a correlation with brightness (see also de Vaucouleurs and Pence 1976). Pskovskii (1977, 1984) classified SNe I according to the immediate post-peak decay rate and found a similar correlation (see also Branch 1981, 1982).
The most recent studies, based on larger supernova samples and incorporating models for the retarded expansion of the local supercluster (Virgocentric flow) point to a low intrinsic dispersion in the peak brightness of SNe Ia that leaves little room for correlations with the light-curve decay rate. Leibundgut and Tammann (1990) review the data on SNe Ia in the Virgo cluster and find that when the sample is restricted to six SNe Ia for which photoelectric B photometry is available, the dispersion in MB is only 0.18 mag, even with no extinction corrections; a larger dispersion of 0.41 mag in Mpg for seven Virgo SNe Ia is attributed to the poorer quality of the photographic photometry, but could be due, in part, to the intrinsic depth of the cluster. Leibundgut and Tammann conclude that the intrinsic scatter among Virgo SNe Ia could be vanishingly small. Tammann and Leibundgut (1990) find an observational dispersion of 0.53 mag in MB for 35 SNe Ia that occurred in non-Virgo galaxies having recession velocities greater than 1000 km s-1 after correction according to Kraan-Korteweg's (1986) model of the retarded expansion of the local supercluster. An allowance for errors in the distances reduces the dispersion in MB to 0.32 mag. Tammann and Leibundgut argue that errors in peak apparent magnitudes and the neglect of parent-galaxy extinction are responsible for a scatter of at least 0.2 mag, and conclude that the intrinsic SN Ia dispersion is 0.25 mag.
Miller and Branch (1990) take SN Ia apparent magnitudes (B or mpg) from the Asiago Supernova Catalogue (Barbon et al. 1989) and galaxy distances from the Nearby Galaxies Catalog (Tully 1988a) and find = 0.70 mag for an unrestricted sample of 45 SNe Ia. For a sample of nine SNe Ia in elliptical galaxies the dispersion reduces to 0.32 mag. The dispersion in the unrestricted sample is strongly affected by six observationally subluminous SNe Ia, all of which turn out to have appeared in inclined disk galaxies (S or S0 galaxies having i > 50). This suggests that the observationally subluminous SNe Ia are intrinsically normal but highly extinguished, as argued previously by Tammann (1982) on the basis of supernova colors. Miller and Branch find that by adopting a simple single-parameter thin-disk model for the extinction layer in the parent galaxies the dispersion for SNe Ia in disk and elliptical galaxies can be reduced to 0.27 mag. The SNe Ia absolute magnitudes, both before and after the parent-galaxy extinction procedure is applied, fail to correlate with Pskovskii's light-curve decline rates. Miller and Branch (1992) calculate the SN Ia dispersion not only on the basis of a Virgocentric flow model but also for a Great Attractor model (Burstein 1990) and an IRAS cluster model (Rowan-Robinson et al. 1990); for all three models the dispersion is about 0.3 mag.
The implication of the recent work cited above is that the intrinsic dispersion among SNe Ia is too small to be measured by the available data. Other evidence that supports or at least is consistent with a small ( 0.5 mag) dispersion can be cited.
(1) Hamuy et al. (1991) present definitive photometry of two SNe Ia in the same galaxy, 1980N and 1981D in NGC 1316 (Fornax A), and find that the maximum-light magnitudes were the same to within 0.1 mag.
(2) SNe Ia show a small dispersion among the almost extinction-free infrared absolute magnitudes (Elias et al. 1981, 1985, Leibundgut 1988).
Direct or indirect evidence for a larger dispersion, on the other hand, is weak.
(1) Not only has the evidence for a correlation between brightness and light-curve speed deteriorated, but even the question of whether there is a significant range in the shapes of the light curves of ordinary SNe Ia is disputed (Younger and van den Bergh 1985; Cadonau et al. 1985; Leibundgut 1988; Filippenko 1989). Three relatively recent SNe Ia, SN 1986G (Frogel et al. 1987, Phillips et al. 1987, Leibundgut 1988, Christiani et al. 1992), SN 1991T (Filippenko et al. 1992a, Ruiz-Lapuente et al. 1992, Phillips et al. 1992, Jeffery et al. 1992), and SN 1991bg (Filippenko et al. 1992b) do appear to have had somewhat peculiar light curves, but all three definitely had peculiar spectra. Owing to uncertainties in extinction and distances, it is not clear that the absolute magnitudes of SNe 1986G and 1991T were unusual, but SN 1991bg occurred in the Virgo cluster and was subluminous by 3 magnitudes in the B band. SN 1991bg demonstrates that spectroscopically peculiar SNe Ia must not be included in ``standard-candle'' samples.
(2) An intrinsic dispersion in a spectroscopic property - the blueshift of the red Si II absorption feature at and shortly after maximum light - has been demonstrated (Branch et al. 1988). This establishes that there are real differences (or asymmetries) in the outermost ejected layers of SNe Ia, but these could prove to be compatible with a uniform peak luminosity.
In summary, current evidence favors a small intrinsic dispersion for ordinary SNe Ia that may be 0.3 mag. Most SNe Ia that are observationally subluminous tend to be red and in inclined disk galaxies, and probably just suffer high interstellar extinction. The peculiar, intrinsically subluminous SN 1991bg also was red. If observationally faint events enter into samples of remote SNe Ia, in spite of the selection against them, they can be recognized by their colors, and, in the case of those that are intrinsically abnormal, by their spectra. There is not yet any solid evidence for anomalously bright SNe Ia.
From the Hubble diagram for their sample of 35 SNe Ia Tammann and Leibundgut (1990) infer
where h is the Hubble constant in units of 100 km s-1
Mpc-1. From a sample of 40 SNe Ia Miller and Branch (1990) find
The difference is primarily due to the fact that Tammann and
Leibundgut do not apply any corrections for parent-galaxy extinction, while
Miller and Branch do apply an inclination-dependent correction to those SNe Ia
in spirals that appear to be subluminous. Perhaps the most accurate available
estimate for the intrinsic absolute magnitude is that obtained by Miller and
Branch for nine SNe Ia in ellipticals:
To find the value of the Hubble constant from SNe Ia we need to make
a velocity-independent determination of the intrinsic absolute magnitude of at
least one SN Ia, for insertion into equation (10).
where h is the Hubble constant in units of 100 km s-1 Mpc-1. From a sample of 40 SNe Ia Miller and Branch (1990) find
The difference is primarily due to the fact that Tammann and Leibundgut do not apply any corrections for parent-galaxy extinction, while Miller and Branch do apply an inclination-dependent correction to those SNe Ia in spirals that appear to be subluminous. Perhaps the most accurate available estimate for the intrinsic absolute magnitude is that obtained by Miller and Branch for nine SNe Ia in ellipticals:
To find the value of the Hubble constant from SNe Ia we need to make a velocity-independent determination of the intrinsic absolute magnitude of at least one SN Ia, for insertion into equation (10).