ABSTRACT

The X-ray Solar Physics Satellite Yohkoh has provided us with a number of new findings about the high temperature and high energy processes occurring in solar flares, in active regions, and in the background corona. According to these new findings, hot and dense corona above active regions seem to be maintained, at least in part, with the injections of already heated mass along the magnetic loops from the footpoint below. The outermost loops of the magnetic structures of these active regions are expanding away almost continuously in the case of “active” active regions. These give us quite a different and lively picture about the active region corona compared with a previous static picture with steady heating that we had based on the previous low cadence observations. New clues to the mechanism of flares, which were hidden thus-far in the yet fainter and relatively short stages before the start of flares, have been revealed by the wide-dynamic range, high cadence observations with the scientific instruments aboard Yohkoh. Those preflare signatures and their changes containing essential information about the mechanism of flares, now allow us to pursue truer understanding about the flare mechanism. The same merits of Yohkoh (wide-dynamic range and high-cadence observations) have shown us for the first time in its full form the highly dynamical behavior of the faint background corona, together with the influence of the changes in active regions sometimes exerting overwhelming effects on the surrounding corona.

FOREWORD

Broadly speaking, the inverse problem is the inverse of the forward problem. In the case of contemporary helioseismology, the forward problem is usually posed as that of determining the eigenfrequencies of free oscillation of a theoretical model of the sun. That problem is discussed by Christensen-Dalsgaard in this volume. I call inverting that problem the ‘main’ inverse problem. It is the one that I shall be discussing almost exclusively in this chapter. But also included in the forward problem must be the theoretical modelling of the oscillations as they really occur in the sun, forced, we believe, predominantly by the turbulence in the convection zone, and modulated by their nonlinear interactions with other modes of oscillation and by the perturbations they induce to the very convection that drives them, through variations in the turbulent fluxes of heat and momentum. The inverse of that problem is to derive from the fluid motion of the visible layers in the atmosphere of the sun, which I presume to be ‘observed’, estimates of the frequencies that the modes would have had had they not been disturbed by the other forms of motion. The outcome of that prior inversion provides the data for the main inverse problem.

This chapter is entitled: Testing solar models …. By ‘solar models’ is meant any theoretical description of the sun that we might have in mind.

INTRODUCTION

The present chapter addresses the forward problem, i.e., the relation between the structure of a solar model and the corresponding frequencies. As important, however, is the extent to which the frequencies reflect the physics and other assumptions underlying the model calculation. Thus in Section 2 I consider some aspects of solar model computation. In addition, the understanding of the diagnostic potential of the frequencies requires information about the properties of the oscillations, which is provided in Section 3. Section 4 investigates the relation between the properties of solar structure and the oscillations by considering several examples of modifications to the solar models and their effects on the frequencies, while Section 5 considers further analyses of the observed frequencies. Finally, the prospects of extending this type of work to other stars are addressed in Section 6.

A more detailed background on the theory of solar oscillations was given, for example, by Christensen-Dalsgaard & Berthomieu (1991), Gough (1993), and Christensen-Dalsgaard (1994). For other general presentations of the properties of solar and stellar oscillations see, e.g., Unno et al. (1989) and Gough & Toomre (1991).

A little history

The realization that observed frequencies of solar oscillation might provide information about the solar interior goes back at least two decades. Observations of fluctuations in the solar limb intensity (Hill & Stebbins 1975; Hill, Stebbins & Brown 1976), and the claimed detection of a Doppler velocity oscillation with a period close to 160 minutes (Brookes, Isaak & van der Raay 1976; Severny, Kotov & Tsap 1976) provided early indications that global solar oscillations might be detectable and led to the first comparisons of the reported frequencies with those of solar models (e.g. Scuflaire et al. 1975; Christensen-Dalsgaard & Gough 1976; Iben & Mahaffy 1976; Rouse 1977).

ANALYSIS TOOLS AND THE SOLAR NOISE BACKGROUND

When we observe solar oscillations, we are concerned with measuring perturbations on the Sun that are almost periodic in space and time. The periodic waves that interest us are, however, embedded in a background of broadband noise from convection and other solar processes, which tend to obscure and confuse the information we want. Also (and worse), the “almost-periodic” nature of the waves leads to problems in the interpretation of the time series that we measure. Much of the subject of observational helioseismology is thus concerned with ways to minimize these difficulties.

Fourier Transforms and Statistics

A common thread runs through all of the analysis tricks that one plays when looking at solar oscillations data, and indeed through many of the purely instrumental concerns as well: this thread is the Fourier transform. The reason for this commonality is, of course, that we are dealing with (almost) periodic phenomena – either the acoustic-gravity waves themselves, or the light waves that bring us news of them. Since many of the same notions will recur repeatedly, it is worth taking a little time (and boring the cognoscente) to review some of the most useful properties of Fourier transforms and power spectra. In what follows, I shall simply state results and indicate some of the more useful consequences. We shall see below that even when the Big Theorems of Fourier transforms do not apply, (as with Legendre transforms, for instance), analogous things happen, so that the Fourier example is a helpful guide to the kind of problems we may have.

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).