Introduction

Before embarking on the full theory of N = 1 supergravity in the following chapters, it is necessary to review some of what is known about quantum cosmology based on general relativity, possibly coupled to spin-0 or spin-1/2 (non-supersymmetric) matter. The ideas presented in this chapter, based to a considerable extent but not exclusively on Hamiltonian methods, will recur throughout the book. Perhaps the main underlying idea is that there is an analogy between the classical dynamics of a point particle with position x and that of a three-geometry hij(x). The theory of point-particle dynamics, when written in parametrized form [Kuchař 1981] and cast into Hamiltonian form, and the theory of general relativity, again in Hamiltonian form, bear a strong resemblance. In the Hamiltonian form of general relativity, hij(x) can be taken to be the ‘coordinate’ variable, corresponding to x in particle dynamics. In section 2.2, for parametrized particle dynamics, it is shown following [Kuchař 1981] how a constraint arises classically in the Hamiltonian theory, which, when quantized, gives the appropriate Schrödinger or wave equation for the quantum wave function ψ(x, t). As described in subsequent sections, the quantization of the analogous constraint in general relativity gives the Wheeler–DeWitt equation [DeWitt 1967, Wheeler 1968], a second-order functional differential equation for the wave function Ψ[hij(x)], which contains all the information in quantum gravity, if only one could solve and interpret it.

The Hamiltonian form of general relativity is derived from the Einstein–Hilbert Lagrangian in section 2.3.

The application of canonical methods to gravity has a long history [De-Witt 1967]. In [Dirac 1950] a general Hamiltonian approach was presented, which allowed for the presence of constraints in a theory, due to the momenta not being independent functions of the velocities. In particular, this occurs in general relativity, because of the underlying coordinate invariance of gravity. The general approach above was applied to general relativity in [Dirac 1958a,b, 1959] and further described in [Dirac 1965]. It was seen that there are four constraints, usually written ℋi(i = 1,2,3) and ℋ⊥, associated with the freedom to make coordinate transformations in the spatial and normal directions relative to a hypersurface t = const. in the Hamiltonian decomposition. Classically, these four constraints must vanish for allowed initial data. In the quantum theory, as will be seen in chapter 2, these constraints become operators on physically allowed states Ψ, which must obey ℋiΨ = 0, ℋ⊥Ψ = 0. Here, in the simplest representation, Ψ is a functional of the spatial metric hij(x). It was shown in [Higgs 1958, 1959] that the constraints ℋiΨ = 0 precisely describe the invariance of the wave function under spatial coordinate transformations. The Hamiltonian formulation of gravity was also studied by [Arnowitt et al. 1962], who provided the standard definition of the mass or energy M of a spacetime, as measured at spatial infinity.

Supernova and supernova remnant research are two of the most active fields of modern astronomy. SN 1987A has given us a chance to observe a supernova explosion and its aftermath in unprecedented detail, a process that continues to unfold today. Meanwhile, thanks to major advances in optical, radio, and X-ray astronomy, we have gained unprecedented views of the populations and spectrum evolution of supernovae of all kinds. These results have spurred a renaissance in theoretical studies of supernovae. Likewise, samples of well-observed supernovae are becoming large enough that we are closing fast on the goal of using supernovae to determine the cosmic distance scale.

Studies of supernovae and supernova remnants are inextricably linked and we are learning fast about the connections. We now recognize that mass loss from the supernova progenitor star can determine the structure of the circumstellar medium with which the supernova ejecta interact. An outstanding example is the ring around SN1987A. There are many supernovae in which much of the early optical, radio and X-ray emission are due to interaction of the ejecta with circumstellar matter rather than radioactivity within the supernova itself. Just in time for this colloquium, nature provided a particularly spectacular example of such an interacting supernova with SN1993J in M81, one of the brightest supernovae of this century. Moreover, the X-ray spectra of supernova remnants provide a powerful new tool to measure supernova nucleosynthesis yields.

Observational selection effects and the lack of accurate distances for most Galactic SNRs pose problems for studies of the distribution of SNRs in the Galaxy. However, by comparing the observed Galactic longitude distribution of high surface brightness SNRs with that expected from simple models – which avoids some of the problems with selection effects and the lack of distances – a Gaussian scale length of ≈ 7 kpc in Galactocentric radius is obtained for SNRs.

Introduction

The distribution of SNRs in the Galaxy is of interest for many astrophysical studies, particularly in relation to their energy input into the ISM and for comparison with the distributions of possible progenitor populations. Such studies are, however, not straightforward. First, current catalogues of SNRs miss objects due to observational selection effects. Second, there are no reliable distance estimates available for most identified remnants. Here I use a sample of 182 Galactic SNRs from a recently revised catalogue (this proceedings), all but one of which have observed radio flux densities and angular sizes, to derive the distribution of SNRs in the Galaxy by comparing the observed distribution of bright remnants with Galactic longitude with that expected from simple models.

The Problems

The Selection Effects

Although, as discussed by Aschenbach (this proceedings), many new SNRs may soon be identified from the ROSAT X-ray survey, the identification of SNRs in existing catalogues has, generally, been made at radio wavelengths.

Explosion calculations of SN 1987A generate pictures of Rayleigh-Taylor fingers of radioactive 56Ni (56Ni → 56Co → 56Fe) which are boosted to velocities of several thousand km s−1. From the KAO observations of the mid-IR iron lines, a picture of the iron in the ejecta emerges which is consistent with the ‘frothy iron fingers’ having expanded to fill about 50% of the metal-rich volume of the ejecta (vm ≤ 2500 km s−1). The ratio of the nickel line intensities I([Ni I]7.5µm)/I([Ni II]6.6µm) yields a high ionization fraction of xNi 0.9 in the volume associated with the iron-group elements at day 415, before dust condenses in the ejecta.

From the KAO observations of the dust's thermal emission (2 µm − 100 µm), it is deduced that when the grains condense their infrared radiation is trapped, their apparent opacity is gray, and they have a surface area filling factor of about 50%. The dust emission from SN 1987A is featureless: no 9.7 µm silicate feature, nor PAH features, nor dust emission features of any kind are seen at any time. The total dust opacity increases with time even though the surface area filling factor and the dust/gas ratio remain constant. This suggests that the dust forms along coherent structures which can maintain their radial line-of-sight opacities, i.e., along fat ringers. The coincidence of the filling factor of the dust and the filling factor of the iron strongly suggests that the dust condenses within the iron, and therefore the dust is iron-rich.

Recent observations of the galactic supernova remnants the Crab Nebula, SN 1006, Cas A, and the Cygnus Loop are reviewed. New studies of the Crab Nebula suggest its progenitor may have had appreciable mass loss in the form of a circumstellar disk resulting in both a bipolar expansion and formation of the synchrotron ‘bays’. Unusually high proper motion knots near to and possibly directed away from the pulsar also have been reported. In the Cas A remnant, a NE jet of ejecta appears to be a plume of mantle material with expansion velocities up to 12000 km s−1 or nearly twice that seen in the main ejecta shell. HST observations of the sdOB star located behind SN 1006 indicate symmetrically expanding Fe II ejecta out to 8100 km s−1. Lastly, deep images of the Cygnus Loop reveal emission structures similar to those seen in 2D & 3D shocked cloud simulations.

Optical research on the properties of galactic supernova remnants (SNRs) continues to yield important new results. Though only a small fraction of the radio catalogued 170+ galactic SNRs are optically detectable, optical measurements permit one to investigate such SNR properties as chemical abundances relative to hydrogen, expansion velocities, gas densities and temperatures, and ejecta filament morphologies and distribution. With the advent of the International Ultraviolet Explorer (IUE) in 1978 and now the Hubble Space Telescope (HST), UV observations on the brighter and less reddened optical SNRs are possible, substantially adding to our knowledge.

Radio observations have shown that some supernovae are powerful radio emitters which increase rapidly in brightness to radio luminosities which are hundreds to thousands of times greater than even the brightest known supernova remnant, Cas A. They then fade over a period of weeks, months, or years. This radio emission has been found to provide important information about the nature of the progenitor stars, their mass loss rates, and the circumstellar material surrounding them. RSN observations may also offer the possibility of extragalactic distance measurements and the presence of radio emission appears to be indicator of strong x-ray emission and late time optical emission.

Introduction

Detailed studies of radio emission from supernovae have now been carried out for over a decade with SN1979C providing the first example of a radio supernova (RSN) which could be detected and monitored in detail over a lengthy time span. The monitoring of the radio emission from SN1979C is still continuing. Additionally, in the intervening 13 years a number of other SNe have been detected at radio wavelengths and these are listed in Table 1. This list is complete at the present time. However, it is limited to objects which show most or all of the RSN properties which are listed in Section 5, and in practice includes only “young” SNe occurring since the first radio detection of an SN, SN1970G, by Gottesman et al. (1972).

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 postcollapse model of the 1.31 M⊙ iron core of a 15 M⊙ 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.

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(Ho/75)2 supernovae (SNe) per century per 1010 LB(⊙). 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.

Extragalactic Supernova Rates

The first estimate of extragalactic supernova rates was made by Zwicky (1938), who introduced the idea that “control time” was a critical factor needed to determine the supernova frequency.

The quality of observational data on Type Ia 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 Ia supernovae, focusing the discussion on our observations of SN1992A in the S0 galaxy NGC 1380 in the Fornax cluster as a reference to other Type Ia events. We now have strong evidence that Type Ia 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-O white dwarf at the Chandrasekhar mass.

Introduction

A stellar explosion is an unlikely physical environment to produce a homogeneous energy flux, given the fantastic brightness of a supernova at maximum light which can reach 10% of the luminosity of the whole galaxy for a period of a few weeks. Yet it is the brightness of the event that makes the use of supernovae as “standard candles” so attractive, since they can be readily observed to cosmologically interesting distances.

Core collapse in very massive stars can lead to a cerntral black hole that swallows the rest of the star and in less massive stars to a central neutron star and explosion. There is probably an intermediate mass range that gives an explosion and a central black hole; supernova remnants with no observable central object are candidates. The association of pulsars with Type II supernovae gives an estimate of the pulsar power to be expected in a supernova, but the uncertainty in the initial pulsar periods gives a wide range in possible powers. The relativistic wind bubble model for the Crab Nebula has steadily developed and there are now predictions regarding particle acceleration in the optical wisps. The bubble model with expansion into supernova gas can also be applied to other young pulsar nebulae.

Introduction

The study of compact objects in supernova remnants has long been troubled by the lack of evidence for such objects. For many years, the Crab and Vela pulsars were the only compact objects observed in remnants. More recently, the number of pulsar/remnant associations has increased to 9 or 10 (Kaspi et al. 1992; Kulkarni et al. 1993). In other cases, the presence of a pulsar is inferred from a centrally condensed, flat radio spectrum nebula thought to be created by a pulsar. The study of these objects, as well as more detailed study of the Crab Nebula, has led to a general theoretical picture, although many basic uncertainties remain.

Existing evidence of photometric and spectroscopic diversity among Type Ia 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 M⊙ of 56Ni synthesized in the explosions is derived from the nebular spectra of a sample of SNe Ia. For SN 1991bg, however, a 56Ni mass of ∼ 0.1 M⊙ 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.

Introduction

Type Ia supernovae (SNIa) are attributed to the thermonuclear explosion of C+O white dwarfs. Explosive ignition would be the outcome of accretion of matter from a close companion in a binary system and it would completely burn the star, leaving no bound remnant. In most models, explosive C burning starts at the center of the WD as a result of the increase in density and temperature induced by quasistatic mass growth.

The oldest historical supernova (SN), recorded by ancient Chinese in 14th Century B.C. on pieces of tortoise shells or bones, is identified with the aid of modern space γ-ray observations. Hard X-rays with energy up to 20 keV were observed from IC 443 by the X-ray satellite Ginga. We infer from these observations the age of IC 443 is ∼ 1000 – 1400 yrs. The result supports the hypothesis that IC 443 is the remnant of the historical SN 837 that occurred during the Tang Dynasty.

The association between the supernova remnant (SNR) CTB 80 and SN 1408 has been hotly debated for about ten years and is briefly reviewed and discussed here. A new picture is presented to explain this association.

High energy emission from historical SNRs can persist in a multiphase interstellar medium (ISM). As a result, the study of the relationship between SNRs and ancient guest stars has gained new vitality.

The First Supernova Observed by Mankind

SN 1987A, the first supernova observed by the naked eye in nearly 400 years, stimulates a high tide in supernova research. It also tempts us to ask: what is the earliest supernova recorded by mankind? Recently, we have discussed this topic in a few articles (Wang 1987 a,b; Xu, Wang & Qu 1992). The earliest supernova recorded by mankind is the great new star that occurred in 14th century B.C. recorded by the ancient Chinese on a piece of Tortoise shell or bone in Yin-Shang Dynasty (Fig. 1).