Extragalactic supernova rates are reviewed. The main uncertainties in calculated rates are due to (1) the influence of the (still poorly known) luminosity function of supernova of a given type on “control times”, to (2) uncertain corrections for possible inclination - dependent bias in supernova discovery probabilities, and (3) interstellar absorption. The total supernova rate in late-type galaxies is found to be ∼ 2(H0/75)2 supernovae (SNe) per century per 1010LB(ʘ) This is consistent with the rate of 3 SNe per century that is derived from the historical data on Galactic supernovae. It is, however, a source of some concern that none of the three Galactic SNe expected to have occurred during the last century was actually observed!

The expansion velocities of SNe Ia are found to correlate strongly with parent galaxy Hubble type. This relation is in the sense that low expansion velocities are only observed for those SNe Ia that occur in early-type galaxies. This suggests that V(exp) correlates with the ages of SNe Ia progenitors. It is speculated that the progenitors of a few SNe Ia with high V(exp) values in E and S0 galaxies were formed during recent starbursts.

SNe Ia rates appear to be enhanced in post-starburst galaxies. It is suggested that supernova rates might be quite high in the recently discovered population of faint blue galaxies at intermediate redshifts.

Although emerging from a range of progenitor stars and the product of different explosion mechanisms the light curves of the various supernova types are shaped mainly by radioactive power. Core-collapse supernovae have in addition early peaks from shock breakout with a subsequent cooling phase and massive extended stars a recombination (plateau) phase. Variations occur mostly due to differences of the progenitor stars. While there appears to be a fair understanding of the light curves of SNell, new wrinkles are emerging for SNela. The photometry of SNe lb and SNe Ic remains unsatisfactory.

Knowledge of the size and age of the Universe depends on understanding supernovae. The direct geometric measurement of the circumstellar ring of SN 1987A using IUE spectra and HST images provides an independent test of the Cepheid distance scale to the Large Magellanic Cloud. Understanding the details of the mass distribution in the circumstellar matter is important to improving the precision of this distance. Type la supernovae have a narrow distribution in absolute magnitude, and new Cepheid distances to IC 4182 (the site of SN 1937C) and to NGC 5253 (the site of SN 1972E) obtained with HST by Sandage and his collaborators allow that absolute magnitude to be calibrated. Comparison with more distant SNIa gives H0 = 56 ± 8 km s-1 Mpc-1. Recent work in supernova spectroscopy and photometry shows that the apparent homogeneity of SNIa is not quite what it seems, and a deeper understanding of these variations is needed to use the SNIa to best advantage. The Expanding Photosphere Method (EPM) allows direct measurement to each Type II supernova that has adequate photometry and spectroscopy. There are now 18 such objects. The sample of EPM distances from 4.5 Mpc to 180 Mpc indicates H0 = 73±6 (statistical) ±7 (systematic) km s-1 Mpc-1. Better understanding of supernova atmospheres can reduce the systematic error in this approach, which is completely independent of all other astronomical distances.

In order to study the question whether the appearance of SNIa should be uniform from theoretical point of view, we present light curves (LC) for a broad variety of models using our elaborated LC scheme, including implicit LTE-radiation transport, expansion opacities, MC-γ transport, etc. For more details see Khokhlov (1991), Höflich et al. (1992), Höflich et al. (1993), Khokhlov et al. (1993), and Müller et al. (1993).

We consider a set of 19 SNIa explosion models, which encompass all currently discussed explosion scenarios. The set consists of three deflagration models (DF1, DF1MIX, W7 o), two detonation models (DET1, DET2 *), two delayed detonation models (N21, N32 •), detonations in low density white dwarfs (CO095, CO10, CO11 *), six pulsating delayed detonation models (PDD3, PDD5-9 Δ) and three tamped detonation models (DET2ENV2, DET2ENV4, DET2ENV6 Δ). We also included the widely-used deflagration model W7 of Nomoto et al. (1984)

We give an update of current research on the use of nebular spectra of SNe la as distance indicators. Results of the application of the method to a group of SNe la are reported. We describe the status of the research including theoretical and observational requirements of the method. Our results point toward a shorter distance scale than methods based on the “standard candle” hypothesis for Type la SNe.

The quality of observational data on Type la supernovae has improved remarkably in the last few years, due mainly to monitoring programs with CCD-equipped detectors on small aperture telescopes at observatories across the world, and at the space observatories. I will review the recent observational characteristics of Type la supernovae, focusing the discussion on our observations of SN1992A in the SO galaxy NGC 1380 in the Fornax cluster as a reference to other Type la events. We now have strong evidence that Type la events are not a homogeneous class, but vary in both color and brightness at maximum light, vary in rise time and decline from maximum, and have spectral characteristics at maximum light that are correlated with these photometric parameters. Insofar as the SBF, PNLF, and infrared Tully-Fisher distance scales are correct, the observed (uvoir) bolometric light curves also indicate that these supernovae are less luminous than expected from the models of the explosion of a C-0 white dwarf at the Chandrasekhar mass.

We summarize various explosion models of Type la supernovae and their nucleosynthesis features for both Chandrasekhar and sub-Chandrasekhar mass white dwarf models. These models provide different predictions of the photometric and spectroscopic variations among Type la supernovae, which are compared with observations. Some attempts to model the peculiar SNe 1991T and 1991bg are shown.

Existing evidence of photometric and spectroscopic diversity among Type la supernovae is compared with the predictions from physical modeling of the explosions. Concerning light curves, changes in the central ignition density of massive (M ≃ Mch) C+O white dwarfs alone do not give appreciable variation. Spectroscopic diversity has been found in the nebular phase, the underluminous SN 1991bg providing an extreme case. A range of 0.4-0.8 Mʘ of 56Ni synthesized in the explosions is derived from the nebular spectra of a sample of SNe la. For SN 1991bg, however, a 56Ni mass of ∼ 0.1 Mʘ only is obtained. That leads us to explore models based on the detonation of low-mass WDs for this SN. Additionally, a nebular spectrum of SN 1991bg shows narrow Hα emission at the position of the SN. If this emission is confirmed against background contamination from the galaxy, it would be first evidence of a nondegenerate, H-rich companion in a SNIa.

The status for the identification of specific astronomical objects as SNIa progenitors is reviewed. Single or double degenerate progenitors? Chandrasekhar or sub-Chandrasekhar mass exploders? These are the two main questions still to be answered concerning the progenitors of Type la supernovae. Although all four combinations may be represented in nature, searches for double degenerates seem to indicate that such systems provide a minor channel for the production of SNIa’s. The more promising candidates appear to be symbiotic stars, consisting of a single degenerate star and a sub-Chandrasekhar mass star.

The convective deflagration mechanism in white dwarfs became widely used to explain Type la Supernovae (SNIa) due the success of a single model, namely model W7 of Nomoto et al. (1984). Problems concerning the deflagration model were discussed by Sutherland & Wheeler (1984), Nomoto et al. (1984), Woosley & Weaver (1986), Woosley (1990), Khokhlov (1991a) and others. The main question however is still: does the deflagration model have any hydrodynamical basis, or, could the assumed Rayleigh Taylor instability accelerate the flame to the required speed?

Several multidimensional computations of hydrodynamics related to supernovae have been completed, and are summarized here. More detail may be found in Arnett 1994a,b, Arnett & Livne 1994a,b, and Livne & Arnett 1993. The hydro code PROMETHEUS is based upon an implementation of the piecewise-parabolic method (PPM) of Colella & Woodward 1984, as described in Fryxell et al. 1991. A detailed comparison of PPM with other schemes is given in Woodward & Colella 1984. The method constructs the physics of the flow between grid points by a nonlinear solution of the equations of continuity of mass, momentum and energy (the Riemann problem) rather than the usual mathematical approach of a Taylor expansion about the grid points. This gives it better resolution per grid point, which is highly desirable for multidimensional problems. Although the effort required per grid point is greater, the number of such points is less (often much less) for a given level of accuracy. Because the computational load per grid point is greater, more realistic physics (reactions, radiation, gravity, etc.) may be added before affecting the runtime significantly. Thus PPM is well suited for multidimensional problems with significant physics beyond the bare hydrodynamics.

In this paper, I summarize two new developments in the theory of core-collapse supernovae. The first is the recent establishment of an analytic context for understanding neutrino-driven explosions. Converting the supernova problem into an eigenvalue problem, Burrows & Goshy (1993) have derived a critical condition on neutrino luminosity and mass accretion rate through a stalled bounce shock for instability and explosion. The second development is the recent calculation of Burrows & Pryxell (1993) of the boost in the neutrino luminosities by the Rayleigh-Taylor-like overturn of the shocked mantle of a protoneutron star. This boost may turn duds into explosions and may be the missing ingredient of supernova theory.

Hydrodynamical simulations of type-II supernovae in one and two dimensions are performed for the revival phase of the delayed shock by neutrino energy deposition. Starting with a post-collapse model of the 1.31 Mʘ iron core of a 15 Mʘ star immediately after the stagnation of the prompt shock about 10 ms after core bounce, the models are followed for several hundred milliseconds with varied neutrino fluxes from the neutrino sphere. The variation of the neutrino luminosities is motivated by the considerable increase of the neutrino emission due to convective processes inside and close to the neutrino sphere (see Janka 1993), which are driven by negative gradients of entropy and electron concentration left behind by the prompt shock (Burrows & Fryxell 1992, Janka & Müller 1992). The size of this luminosity increase remains to be quantitatively analyzed yet and may require multi-dimensional neutrino transport. However, in the presented simulations the region below the neutrino sphere is cut out and replaced by an inner boundary condition, so that the convective zone is only partially included and the neutrino flows are treated as a freely changeable energy source.

For small neutrino luminosities the energy transfer to the matter is insufficient to revive the stalled shock. However, there is a sharp transition to successful explosions, when the neutrino luminosities lie above some ‘threshold value’. Once the shock is driven out and the density and temperature of the matter between neutrino sphere and shock start to decrease during the expansion, suitable conditions for further neutrino energy deposition are maintained, and an explosion results. With the neutrino energy deposition the entropy per nucleon in the region between neutrino sphere and shock grows, and convective overturn will set in. Multi-dimensional simulations show that due to the large pressure scale height a large-scale pattern of up-flows and down-flows with velocities close to the local speed of sound develops. Consequently, cold, postshock material is advected down into the neutrino heating layer close to the neutrino sphere and hot material is transported outwards, thus reducing energy losses by re-emission of neutrinos and increasing the pressure behind the shock. Therefore these convective processes are found to be a very important aid to the delayed supernova explosion. In fact, two-dimensional models explode even in cases where spherically symmetrical computations fail.

We discuss a new scenario for the production of SNII explosion and present the results of numerical modelling studies of SNe II light curves which are being done in our group.

We calculate a nonlinear growth of the Rayleigh-Taylor instability in the exploding red supergiant stars with a two-dimensional hydrodynamical code, and examine how the extent of mixing depends on the progenitor's core mass and the envelope mass. The results are compared with the observations of type II-P supernovae and the recent type Il-b supernova 1993J.

We review critical physics affecting the observational characteristics of those supernovae that occur in massive stars. Particular emphasis is given to 1) how mass loss, either to a binary companion or by a radiatively driven wind, affects the type and light curve of the supernova, and 2) the interaction of the outgoing supernova shock with regions of increasing pr3 in the stellar mantle. One conclusion is that Type II-L supernovae may occur in mass exchanging binaries very similar to the one that produced SN 1993J, but with slightly larger initial separations and residual hydrogen envelopes (∼1 Mʘ and radius ∼ several AU). The shock interaction, on the other hand, has important implications for the formation of black holes in explosions that are, near peak light, observationally indistinguishable from ordinary Type II-p and lb supernovae.

We review the fundamental classification scheme and statistical analysis of supernovae, emphasizing recently introduced subtypes, SN1987K, and SN1993J. Type Ib/Ic and Type II supernovae are of interest for starburst galaxies. We discuss possible progenitors of SNIb and SN Ic, and the possibility that they may be Wolf-Rayet stars.