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The interest in supernovae has risen dramatically with their application to cosmological problems. Their unique capabilities as distance indicators on the cosmic scale have pushed them into the limelight of cosmology. These objects, however, are interesting and exciting in their own right. Supernova physics relates some of the most complicated physical processes from the explosion mechanisms to nucleosynthesis, radiation transport, and shock physics as well as some of the most intriguing astrophysics ranging from star formation and stellar evolution to cosmic metal enrichment, evolution of galaxies, and the scale and fate of the universe. Their brightness makes them ideal stellar tracers at large distances and look back times. Solving some of the supernova specific problems will hence give us clues on a much larger scale.

Stellar explosions have been observed for many centuries. Nonetheless, supernovae are extremely rare and only six of them have been observed over the last millennium in our own Galaxy (Clark & Stevenson 1977, Murdin & Murdin 1985, van den Bergh & Tammann 1991). The number of extragalactic supernova detections has grown continuously. Originally only searched by a few limited experiments (e.g. Zwicky 1965) with about a dozen SNe detected each year, the topic has taken a big turn with SN 1987A and the emergence of deep coordinated searches for distant supernovae in the last decade. There are now nearly 200 SNe detected each year (cf. IAU Central Bureau for Astronomical Telegrams 1, Asiago Supernova Catalog 2 (Barbon et al. 1999), Sternberg Astronomical Institute Supernova Catalog 3 (Bartunov & Tsvetkov 1997)). This plethora of objects has revealed an increasing number of peculiar, i.e. not easily classified, supernovae. On the other hand, it has allowed us to conduct detailed studies of specific supernova classes and find the commonalities as well as the individuality among supernovae. The surge of data has further provided many new constraints for the models.

It has become increasingly clear that two main classes of supernovae (Type Ia vs. Type II and Type Ib/c) with physically completely different backgrounds exist. Originally an observational separation according to spectral features (Minkowski 1941, 1964, Harkness & Wheeler 1990, Filippenko 1997a) the classification scheme has proven to identify physically distinct objects. On the other hand, the classification system has not turned out to be sufficient. Several objects defy a clear classification and have forced extensions to the system. There is, however, a move to a more physical description of individual objects. Especially bright, well-observed, events have increased our understanding of the explosions.

Type Ia Supernovae (SNe Ia) are now almost universally accepted as thermonuclear explosions in low-mass stars (Trimble 1982, 1983, Woosley & Weaver 1986). All other known supernova explosions are thought to be due to the core collapse in massive stars.

There are many reviews on (Type Ia) Supernovae available. The most comprehensive books are Petschek (1990), Wheeler, Piran, & Weinberg (1990), Woosley (1991), McCray & Wang (1996), Bludman et al. (1997), Ruiz-Lapuente et al. (1997), Niemeyer & Truran (1999), and Livio et al. (2000). Excellent reviews were given by Trimble (1982, 1983) and Woosley & Weaver (1986). More recent monographs on Type Ia in general are Wheeler et al. (1995) and Filippenko (1997b). Possible progenitor systems (Branch et al. 1995, Renzini 1996, Livio 1999), supernova classifications (Filippenko 1997a), supernova rates (van den Bergh & Tammann 1991), the Hubble constant from SNe Ia (Branch 1998) and the status of explosion models (Hillebrandt & Niemeyer 2000) are covered in more specific reviews.

1.1. Classification

Supernovae are classified by their spectrum near maximum light (see Filippenko 1997a for a review on supernova classifications). The Type Ia Supernovae are characterized by the complete absence of hydrogen and helium lines and a distinct, strong absorption line near 6100Å, which comes from a doublet of singly ionized silicon with lambda lambda6347Å and 6371Å. Hydrogen or helium lines never appear in the spectra of SNe Ia at any phase of the evolution. Significant variations have been observed within this scheme, but in general SNe Ia can safely be distinguished from any other supernovae (Filippenko 1997a). Great care has to be taken to separate the SN Ia from SNe Ib/c which can display a similar spectrum at early phases.

Secondary classification criteria are the late-phase spectrum dominated by forbidden iron and cobalt lines, light curve shape, color evolution, and host galaxy morphology. None of these is sufficient by itself, but may provide additional evidence for a classification.

1.2. Astrophysical importance

Since SNe Ia are possibly the main producer of iron in the universe, they provide a clock for the metal enrichment of matter. The relative long progenitor life times, as compared to massive stars which become core-collapse supernovae, provides a convenient feature in the relative metal abundances of alpha -elements and iron-group elements (Renzini 1999).

The heating of the interstellar medium, in particular for elliptical galaxies, depends on the SN Ia rates and their energy input (Ciotti et al. 1991).

As explosions of white dwarfs SNe Ia are placed at the end of one of the major stellar evolution channels. Although only a few white dwarfs really explode as SNe Ia, they still can provide important information on the binary fraction of stars and the evolution of binary systems both in our Galaxy (e.g. Iben & Tutukov 1994, 1999) and as a function of look back time (Yungelson & Livio 1998, Ruiz-Lapuente & Canal 1998).

Supernovae also play an important feedback role during the early galaxy evolution and might be responsible for substantial loss of material from galaxies (e.g. Wyse & Silk 1985, Burkert & Ruiz-Lapuente 1997, Ferrara & Tolstoy 2000) and the regulation of the star formation process. The contribution of SNe Ia as opposed to core-collapse supernovae from massive stars is, however, unclear.

1.3. Type Ia Supernovae and Cosmology

Recent years have seen SNe Ia taking center stage in observational cosmology. As the momentarily best distance indicator beyond the Virgo cluster, they provide the main route to the current expansion rate (Branch 1998) and the deceleration of the universe (Riess et al. 1998a, Perlmutter et al. 1999). Almost all Hubble constant determinations are now involving SNe Ia in one form or another. Two large HST programs have adopted SNe Ia as their prime distance indicator beyond the reach of Cepheid stars (Saha et al. 1999, Gibson et al. 2000, Mould et al. 2000). Although other secondary distance indicators are still discussed, in most approaches they enter the analyses with lower weight (Mould et al. 2000). It is also gratifying to see that a general convergence of the value of H0 to within the respective error bars between 60 and 70 km s-1 Mpc-1 has been reached.

The claim, based on SNe Ia, for an accelerated universe (Riess et al. 1998a, Perlmutter et al. 1999) has triggered an enthralling debate in cosmology. It will be an important next step to verify that supernova evolution is not mimicking a signal which has been interpreted as a cosmological constant. Other explanations of the supernova result apart from a cosmological constant and based on decaying particle fields have been proposed as well (for a recent review see Kamionkowski & Kosowsky 1999).

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