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The use of supernovae as distance indicators has grown dramatically in the last few years. Supernovae have been applied to the Hubble Constant problem, to measurement of the cosmological parameters Omega0 and Lambda, and even, in a preliminary way, to constraining bulk peculiar motions. There is every reason to believe that in the next decade supernovae will become still more important as distance indicators. It is certain that many more will be discovered, especially at high redshift.

Supernovae come in two main varieties. Type Ia supernovae (SNe Ia) are thought to result from the nuclear detonation of a white dwarf star that has been overloaded by mass transferred from an evolved (Population II) companion. (Recall that a white dwarf cannot have a masss above the Chandrasekhar limit, 1.4 Msmsun When mass transfer causes the white dwarf to surpass this limit, it explodes.) Type II supernovae result from the imploding cores of high-mass, young (Population I) stars that have exhausted their nuclear fuel. (1) Of the two, it is the Type Ias that have received the most attention lately. Type IIs have shown somewhat less promise as distance indicators. They are considerably fainter (~ 2 mag), and thus are detected less often in magnitude limited surveys (although their intrinsic frequency of occurrence is in fact greater than that of Type 1as). The discussion to follow will be restricted to Type Ias.

Because SNe Ias result (in all likelihood) from detonating white dwarfs, and because the latter tend to have very similar masses, SNe Ias tend to have very similar luminosities. That is, they are very nearly standard candles, so comparison of their apparent and abolute magnitudes yields a distance. Recent work suggests that Type Ia SNe are not quite standard candles, in that their peak luminosities correlate with the shape of their light curves (Phillips 1993; Hamuy et al. 1995; Riess et al. 1995a, b; Perlmutter et al. 1997). Basically, broad light curves correspond to brighter, and narrow light curves to fainter, supernovae. When this effect is accounted for, the scatter in SNe Ia predicted peak magnitudes might be as small as 0.1 mag, as found by Riess et al. (1995b). Hamuy et al. (1995) and Perlmutter et al. (1997) find that the scatter drops from ltapprox 0.3 mag mag when SNe Ia are treated as standard candles to 0.17 mag when the light curve shape is taken into account. The precise scatter of SNe Ias remains a subject for further study.

The wealth of new SNe data that has become available in recent years is due to the advent of large-scale, systematic search techniques. To understand this, it may be worth stating the obvious. It is not possible to pick an arbitrary galaxy and get a supernova distance for it because most galaxies, at a given time, do not have a supernova in them. Thus, it is necessary to search many galaxies at random and somehow identify the small fraction (~ 10-4) in which a supernova is going off at any given time. Methods for doing this have been pioneered by Perlmutter and collaborators (Goobar & Perlmutter 1995; Perlmutter et al. 1995, 1996, 1997). Deep images are taken of the same region of the sky 2-3 weeks apart. Stellar objects which appear in the second image but not in the first are candidate supernovae to be confirmed by spectroscopy. By means of such an approach, of order 30 high-redshift (z = 0.35-0.65) are now known. Related approaches for finding moderate- (Adams et al. 1995; Hamuy et al. 1995) and high- (Schmidt et al. 1995) redshift supernovae have been developed by other groups as well.

Figure 6. Hubble diagrams using SNe Ia. The upper panel shows the observed peak apparent magnitudes; in the lower panel the magnitudes are corrected for the light curve width effect (see main text for details). The inset in the lower panel shows the redshifts of 16 additional SNe Ias recently discovered but not yet analyzed by the Perlmutter group.

Search techniques such as those of the Perlmutter group survey many faint galaxies in limited regions of the sky, and are not very good at finding low-redshift (z ltapprox 0.03) supernovae. Thus, they are not particularly relevant to peculiar velocity studies (but see below). However, precisely because they detect intermediate to high redshift supernovae, such techniques will be useful for measuring H0 (with supernovae found at z ltapprox 0.2, where cosmological effects are relatively unimportant), and are among the best existing methods for determining the cosmological parameters Omega0 and Lambda (with supernovae at z gtapprox 0.3, which probe spatial curvature.) To see how this works, one can plot Hubble diagrams for recently discovered supernovae both at moderate and high redshift. This is done in Figure 6, which has been adapted from the 1996 San Antonio AAS meeting contribution by the Perlmutter group. The low redshift data (log (cz) < 4.5) are from Hamuy et al. (1995), and the high redshift data are from Perlmutter et al. (1996).

Figure 6 contains several important features. First, the observed peak apparent magnitudes are plotted versus log redshift in the top panel. To the degree SNe Ias are standard candles, one expects these apparent magnitudes to go as const. + 5 log (cz), the straight line plotted through the points at low redshift. Correcting the SNe Ia magnitudes for the light curve widths (i.e., going from the top to the bottom panel) significantly improves the agreement with this low-redshift prediction. This is the main reason that the light curve width correction is thought to greatly reduce the SNe Ia scatter. Whether or not the correction is made, however, the data provide unequivocal proof of the linearity of the Hubble law at low (z appeq 0.1) redshift. Second, one expects that that at higher redshifts the mB - log (cz) relation will depart from linearity because of spacetime curvature. The departure from linearity is, to first order in z, a function only of the deceleration parameter q0 - or equivalently, if the universe has vanishing cosmological constant Lambda (see below), by the density parameter Omega0, which in that case is exactly twice q0. Figure 6 assumes Lambda ident 0 and thus labels the curves by Omega0. There is a hint in the behavior of the light-curve-shape corrected magnitudes that this departure from linearity has been detected, and in particular that Omega0 appeq 1 is a better fit to the data than Omega0 appeq 0 (Perlmutter et al. 1996).

Neither q0 nor Omega0 alone fully characterizes the departure from a linear Hubble diagram. More generally, the behavior of the Hubble diagram at high redshift depends on the cosmological parameters Omega0 and OmegaLambda ident Lambda / 3H02. Perlmutter et al. (1997) suggest that the SNe Ia data should be interpreted for now in the context of two cosmological paradigms: a Lambda = 0 universe, and a spatially flat (Omega0 + OmegaLambda = 1) universe. (2) Perlmutter et al. (1997) carried out a statistical analysis of the 7 high-redshift (0.354 leq z leq 0.458) supernovae discovered in their survey, and the 9 lower redshift SNe Ias found by the Hamuy group, that are shown in Figure 6. They find that Omega0 = 0.96+.56-.50 if a Lambda = 0 universe is assumed. If the universe is flat, Omega0 = 0.98+.28-.24, with corresonding limits on OmegaLambda = 1 - Omega0. The constraints are stronger in the flat universe case because of the strong effect of a cosmological constant on the apparent magnitudes of high-redshift standard candles. These results are, potentially, highly significant for cosmology. Low-density, spatially flat models have become popular lately because they make the universe older (for a given H0 and Omega0), provide a better fit to large-scale structure data than Omega0 = 1 models, and yet remain consistent with the attractive idea that the early universe underwent inflation. Currently favored versions of such models have OmegaLambda appeq 0.6-0.7 (Ostriker & Steinhardt 1995). The SNe Ia results of Perlmutter et al. (1997), which strongly disfavor such a large OmegaLambda, will be difficult to reconcile with low-density flat models.

The analysis just described did not require absolute calibration of SNe Ias. Indeed, Perlmutter et al. (1997) use a formalism similar to that used in peculiar velocity studies, in which distances are measured in km s-1, and absolute magnitudes are, correspondingly, defined only up to an arbitrary constant. The SNe Ia data can be used to determine H0, however, only to the degree that the true absolute magnitudes (preferably corrected for light curve width) of such objects are known. This requires either theoretical calibration or empirical calibration in galaxies with Cepheid distances. Both of these approaches pose difficulties. A range of models of exploding white dwarfs predict peak absolute magnitudes for SNe Ias of MV appeq -19.5 with small scatter, but significantly lower luminosities can result if some of the key inputs to the models (especially the mass of the 56Ni ejectae) are varied (Höflich et al. 1995). This suggests that the absolute magnitudes of SNe Ias cannot yet be predicted theoretically, and that an empirical calibration using Cepheid distances will do better. However, because local galaxies with Cepheid distances are scarce, and SNe Ias are rare, there are still few reliable local calibrators for SNe Ias. It has been necessary to analyze historical as well as modern SNe Ia data (Saha et al. 1995; Sandage et al. 1996) in Cepheid galaxies in order to increase the number of calibrators. This approach encounters the problem of relating modern CCD photometry with photometric methods from decades past. Pending the detection and analysis of SNe Ias in a larger number of local galaxies with Cepheid distances, one should view estimates of H0 inferred from supernovae as preliminary.

Being rare events, SNe Ias are unlikely to provide a detailed map of the local peculiar velocity field. However, because of their small scatter (see above), a few well-observed SNe Ias distributed on the sky may lead to useful constraints on amplitude and scale of large-scale bulk flows. A first attempt at this was carried out by Riess et al. (1995b), who used 13 SNe Ias with peak magnitudes corrected by light curve widths to place limits on the bulk flow within ~ 7000 km s. They found the data to be consistent with at most a small (ltapprox 400 km s) bulk streaming, and to be inconsistent with the large bulk flow found by Lauer & Postman (1994) using an independent method (cf. Section 7). However, one must be cautious in interpreting such results because small-scale power in the velocity field can obscure large-scale motion (Watkins & Feldman 1995). Constraints on bulk flows using SNe Ias are likely to improve in the coming years.

1 It is inconvenient that Type I supernovae occur in Type II stellar populations, while Type II supernovae occur in Type I populations. Inconvenient nomenclature is, of course, nothing new in astronomy - and must be tolerated as usual. Back

2 With a large sample of SNe Ias that spans a large redshift range, it may be possible to constrain Omega0 and OmegaLambda separately, without assuming either a flat universe or a vanishing cosmological constant (Goobar & Perlmutter 1995). Back.

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