Two months after the discovery of comet Shoemaker-Levy 9 came the astonishing announcement that the comet would impact Jupiter in July 1994. Computing the orbital motion of this remarkable comet presented several unusual challenges. We review the pre-impact orbit computations and impact predictions for SL9, from the preliminary orbit solutions shortly after discovery to the final set of predictions before the impacts. The final set of predicted impact times were systematically early by an average of 7 minutes, probably due to systematic errors in the reference star catalogs used in the reduction of the fragments' astrometric positions. The actual impact times were inferred from the times of observed phenomena for 16 of the impacts. Orbit solutions for the fragments were refined by using the actual impact times as additional data, and by estimating and removing measurement biases from the astrometric observations. The final orbit solutions for 21 fragments are tabulated, along with final estimates of the impact times and locations. The pre-breakup orbital history of the comet was investigated statistically, via a Monte Carlo analysis. The progenitor nucleus of SL9 was most likely captured by Jupiter around 1929 ± 9 years. Prior to capture, the comet was in a low-eccentricity, low-inclination heliocentric orbit entirely inside Jupiter's orbit, or, less likely, entirely outside. The ensemble of possible pre-capture orbits is consistent with a group of Jupiter family comets known as the quasi-Hildas.

The breakup of Comet Shoemaker-Levy 9 is discussed both in the context of splitting as a cometary phenomenon, comparing this object with other split comets, and as an event with its own idiosyncrasies. The physical appearance of the comet is described, features diagnostic of the nature of tidal splitting are identified, and the implications for modelling the event are spelled out. Among the emphasized issues is the problem of secondary fragmentation, which documents the comet's continuing disintegration during 1992–94 and implies that in July 1992 the parent object split tidally near Jupiter into 10–12, not 21, major fragments. Also addressed are the controversies involving models of a strengthless agglomerate versus a discrete cohesive mass and estimates for the sizes of the progenitor and its fragments.

Introduction

Splitting is a relatively common phenomenon among comets, even though its detection is observationally difficult because companions are almost invariably very diffuse objects with considerable short-term brightness variations. Comet Shoemaker-Levy 9's behavior was generally less erratic than that of an average split comet, which may have in part been due to a major role of large-sized dust. The breakup products that contributed most significantly to the comet's total brightness are referred to below as components, or, because of their diffuse appearance, as condensations, both common terms of cometary phenomenology. The terms nuclei and fragments are instead reserved for genuine solid bodies of substantial dimensions (≳ 1 km across) that were “hidden” in the condensations.

A new analytical model that is calibrated against numerical simulations performed with the CTH shock physics code provides a useful description of the entry of Periodic Comet Shoemaker-Levy 9 into the Jovian atmosphere. Mass loss due to radiative heating of fragments larger than 100 m in diameter is insignificant because of energy conservation during the ablative process. Nevertheless, radiative ablation is a major contributor to atmospheric energy deposition at high altitude and plays an important role in early-time fireball evolution. The analytical model provides the initial conditions from which fireball and plume evolution can be calculated using CTH. The results from these simulations suggest that if the tops of the plumes originated from a specific level of the Jovian atmosphere then maximum plume heights are independent of fragment size provided the fragments penetrated at least 30 km below this level. If the tops of the plumes originated from the visible cloud tops, then fragment masses greater than 4 × 1012 g, corresponding to 200 m diameter fully dense water ice, are required to explain the observations. If the plumes originated from the NH4SH layer then masses greater than 3 × 1013 g (400 m water ice) are required. The lateral extent and mass of the observable plume are functions of fragment size and contribute to the lateral extent and albedo of the debris patterns after re-impact with the atmosphere.

The SL9 impacts are known by their plumes. Several of these were imaged by HST towering 3000 km above Jupiter's limb. The heat released when they fell produced the famous infrared main events. The reentry shocks must have been significantly hotter than the observed color temperature would imply, which indicates that the shocks were radiatively cooled, and that most of the energy released on reentry was radiated. This allows us to use the infrared luminosities of the main event to estimate the energy of the impacts; we find that the R impact released some 0.3 − 1 × 1027 ergs. Shock chemistry generates a suite of molecules not usually seen on Jupiter. The chemistry reflects a wide range of different shock temperatures, pressures, and gas compositions. The primary product, apart from H2, is CO, the yield of which depends only weakly on the comet's composition, and so can be used to weigh the comet. Abundant water and S2 are consistent with a somewhat oxidized gas (presumably the comet itself), but the absence of SO2 and CO2 shows that conditions were neither too oxidizing nor the shocks too hot. Meanwhile, production of CS, CS2, and HCN appears to require a source in dry jovian air; i.e., the airbursts occurred above the jovian water table. Tidal disruption calculations and models of the infrared light curves agree on an average fragment diameter of about half a kilometer.

Images of Jupiter taken by the Hubble Space Telescope (HST) reveal two concentric circular rings surrounding five of the impact sites from comet Shoemaker-Levy 9 (SL9). The rings are visible 1.0 to 2.5 hours after the impacts. The outer ring expands at a constant rate of 450 ms−1. The inner ring expands at about half that speed. The rings appear to be waves. Other features (diffuse rings and crescent) further out appear to be debris thrown out by the impact. Sound waves (p-modes), internal gravity waves (g-modes), surface gravity waves (f-modes), and rotational waves (r-modes) all are excited by the impacts. Most of these waves do not match the slow speed, relatively large amplitude, and narrow width of the observed rings. Ingersoll and Kanamori have argued that internal gravity waves trapped in a stable layer within the putative water cloud are the only waves that can match the observations. If they are correct, and if moist convection in the water cloud is producing the stable layer, then the O/H ratio on Jupiter is roughly ten times that on the Sun.

Introduction

Much of what we know about the interior of the Earth has come from the study of seismic waves—a branch of seismology. Recently, much has been learned about the interior of the Sun from helioseismology. Now, the SL9 impacts give us an opportunity to do jovian seismology. The waves probe Jupiter's atmosphere to depths that cannot be reached by remote-sensing instruments.

One-dimensional photochemical models are used to provide an assessment of the chemical composition of the Shoemaker-Levy 9 impact sites soon after the impacts, and over time, as the impact-derived molecular species evolve due to photochemical processes. Photochemical model predictions are compared with the observed temporal variation of the impact-derived molecules in order to place constraints on the initial composition at the impact sites and on the amount of aerosol debris deposited in the stratosphere. The time variation of NH3, HCN, OCS, and H2S in the photochemical models roughly parallels that of the observations. S2 persists too long in the photochemical models, suggesting that some of the estimated chemical rates constants and/or initial conditions (e.g., the assumed altitude distribution or abundance of S2) are incorrect. Models predict that CS and CO persist for months or years in the jovian stratosphere. Observations indicate that the model results with regard to CS are qualitatively correct (although the measured CS abundance demonstrates the need for a larger assumed initial abundance of CS in the models), but that CO appears to be more stable in the models than is indicated by observations. The reason for this discrepancy is unknown. We use model-data comparisons to learn more about the unique photochemical processes occurring after the impacts.

The Hubble Space Telescope Wide Field Planetary Camera 2 imaging data provide the highest spatial resolution of individual Shoemaker-Levy 9 impact sites. Analysis of images obtained with the F410M filter yielded horizontal translation rates of tropospheric cloud structures and the east-west components have been interpreted as zonal winds which vary with latitude. When the tropospheric zonal winds between −60° and −30°, which were derived from the SL9 images, are compared with Voyager data there are no discernible changes in the magnitude or latitudinal positions of wind minima and maxima. This result provides additional evidence of the long-term stability of the zonal winds. Changes in individual sites during a two week period in July 1994 have been mapped. Their evolution is consistent with zonal winds decreasing with height and it provides evidence that local circulation associated with isolated weather systems perturbs the lower stratosphere.

Introduction

On July 16, 1994 at 21h30–51m the first multicolor images revealed the site of the A fragment impact of Comet P/Shoemaker-Levy 9 (SL9) as it rotated into view about 1.5 hours after it formed. The lack of color dependence and the resulting orientation and morphology of the ejecta blanket had not been anticipated. The blowout region was located more to the east than expected and dark rings and crescent-shaped structures centered on the impact site were observed, but the most obvious aspect of site A was the dark core (see the chapter by Hammel).

Earth-based observations at near- and mid-infrared wavelengths were obtained for at least 15 of the SL9 impacts, ranging from the spectacular G, K and L events to the barely-detected N and V impacts. Although there were a few exceptions, most of the IR lightcurves fit a common pattern of one or two relatively faint precursor flashes, followed several minutes later by the main infrared event as the explosively-ejected plume crashed down onto the jovian atmosphere. Correlations with the impact times recorded by the Galileo spacecraft and plumes imaged by the Hubble Space Telescope lead to an interpretation of the twin precursors in terms of (i) the entry of the bolide into the upper atmosphere, and (ii) the re-appearance of the rising fireball above Jupiter's limb. Positive correlations are observed between the peak IR flux observed during the splashback phase and both pre-impact size estimates for the individual SL9 fragments and the scale of the resulting ejecta deposits. None of the fragments observed to have moved off the main train of the comet by May 1994 produced a significant impact signature. Earth-based fireball temperature estimates are on the order of 750 K, 30–60 sec after impact. For the larger impacts, the unexpectedly protracted fireball emission at 2.3 μm remains unexplained. A wide range of temperatures has been inferred for the splashback phase, where shocks are expected to have heated the re-entering plume material at least briefly to several thousand K, and further modelling is required to reconcile these data.

This review attempts to give a coherent explanation of the main observations of the entry Comet Shoemaker-Levy 9 and the aftermath of the resulting explosions by using models of the tidal breakup of the comet, the entry of individual fragments into the jovian atmosphere, and the resulting fireballs and plumes. A critical review shows that the models appear reasonably well understood. The biggest theoretical uncertainties currently concern how to best tie models of the entry to models of the resulting fireballs. The key unknown before the impact was the size and kinetic energy of the comet fragments. The evidence now available includes the behavior of the chain of fragments, the luminosity of the observed visible fireballs and later infrared emission, the chemistry of the spots, and the lack of seismic waves or perturbations at the water cloud pressure level. These observations point to the fragments having diameters under a kilometer, densities of order 0.5 g cm−3, and kinetic energies of order 1027 erg.

Introduction

In this review and in the review by Zahnle (this volume; hereafter “the plume review”), we make the argument that the fragments of Comet Shoemaker-Levy 9 that hit Jupiter were quite small, with diameters of under a kilometer and densities of order 0.5 g cm−3. The largest fragments probably had kinetic energies of order 1027 ergs.

In a cosmic sense, the collision of the ninth periodic comet discovered by the team of Carolyn and Gene Shoemaker and David Levy with the planet Jupiter was unremarkable. The history of the solar system, indeed its very genesis, has been marked by countless such events. The cratered surfaces of planetary bodies are a testament to this ubiquitous phenomenon; even the Earth's ephemeral surface records the continued action of this elemental process in impact craters and in the fossil record.

In human terms, on the other hand, the impact of Comet Shoemaker-Levy 9's 20-odd fragments into Jupiter was an unprecedented event of global significance. After a year of planning and preparation, the largest astronomical armada in history focussed on the planet Jupiter in July 1994. News of each successively more astonishing image or spectrum was broadcast with almost instantaneous speed over the world's increasingly sophisticated computer communications network. Astronomers were, for a time, to be found on daily newscasts and the front pages of newspapers. For a week in July, the world looked up from its normal preoccupations long enough to notice, and to ponder, the awesome beauty of the natural world and the surprising unpredictability of the universe.

Still one more perspective on this event remains. What has science gained from the terabytes of images, lightcurves and spectra obtained over the entire range of the electromagnetic spectrum?

This paper reviews spectroscopic measurements relevant to the chemical modifications of Jupiter's atmosphere induced by the Shoemaker-Levy 9 impacts. Such observations have been successful at all wavelength ranges from the UV to the centimeter. At the date this paper is written, newly detected or enhanced molecular species resulting from the impacts include H2O, CO, S2, CS2, CS, OCS, NH3, HCN and C2H4. There is also a tentative detection of enhanced PH3 and a controversial detection of H2S. All new and enhanced species were detected in Jupiter's stratosphere. With the exception of NH3 (and perhaps H2S and PH3), apparently present down to the 10–50 mbar level, the minor species are seen at pressures lower than 1 mbar or less, consistent with a formation during the plume splashback at 1–100 microbar. NH3 may result from upwelling associated with vertical mixing generated by the impacts. The main oxygen species is apparently CO, with a total mass of a few 1014 g for the largest impacts, consistent with that available in 400–700 m radius fragments. The observed O/S ratio is reasonably consistent with cometary abundances, but the O/N ratio (inferred from CO/HCN) is much larger, suggesting that another N species was formed but remained undetected, presumably N2. The time evolution of NH3, S2, CS2 shows evidence for photochemical activity taking place during and after the impact week.

What did the break-up of comet Shoemaker-Levy 9 (SL9) and its subsequent impact on Jupiter teach us about the nature and constitution of this comet? The break-up of the comet apparently triggered activity of the fragments. Although a dust coma was continuously present around the fragments that orbited Jupiter, spectroscopic observations did not reveal any sign of gas. The impact itself was so energetic that most molecules of the impactor were dissociated and that any chemical memory was lost. Ultraviolet and visible spectroscopy of the impact sites revealed emission lines from several atoms, giving potential information on elemental abundances. However, the fact that both neutral and ionized atoms are emitting, and that both fundamental and inter-system lines are present, suggest that the medium is out-of-equilibrium and that emitting mechanisms other than simple resonance fluorescence are at work. Ultraviolet, infrared, and radio spectroscopy revealed lines of several molecular species, in emission and/or absorption, that are not normally present in Jupiter's upper atmosphere. In the visible, dark spots due to aerosols developed at the impact sites. It is not clear at the present time which part of this material is coming from preserved impactor material, from the recombination of the dissociated impactor material, from reactions between the impactor's and Jupiter's material, or from material coming from the lower layers of Jupiter's atmosphere. Realistic modelling of the impacts and of the following chemical reactions will be necessary to address all these issues.

In this chapter we present the arguments which establish that the Schwarzschild metric describes the only static, asymptotically flat vacuum spacetime with regular (not necessarily connected) event horizon (Israel 1967, Müller zum Hagen et al. 1973, Robinson 1977, Bunting and Masood–ul–Alam 1987). We then discuss the generalization of this result to the situation with electric fields; that is, we demonstrate the uniqueness of the 2–parameter Reissner–Nordström solution amongst all asymptotically flat, static electrovac black hole configurations with nondegenerate horizon (Israel 1968, Müller zum Hagen et al. 1974, Simon 1985, Ruback 1988, Masood–ul–Alam 1992). Taking magnetic fields into account as well, we finally establish the uniqueness of the 3–parameter Reissner–Nordström metric. We conclude this chapter with a brief discussion of the Papapetrou-Majumdar metric, representing a static configuration with M = |Q| and an arbitrary number of extreme black holes (Papapetrou 1945, Majumdar 1947). This metric is not covered by the static uniqueness theorems, since the latter apply exclusively to electrovac solutions which are subject to the inequality M > |Q|.

Throughout this chapter the domain of outer communications is assumed to be static. In the vacuum or the electrovac case staticity is, as we have argued in the previous chapter, a consequence of the symmetry conditions for the matter fields.

Our main objective in this chapter concerns the “modern” approach to the static uniqueness theorem, which is based on conformal transformations and the positive energy theorem. We shall, however, start this chapter with some comments on the traditional line of reasoning, which is due to Israel, Müller zum Hagen, Robinson and others.

In this chapter we consider self–gravitating electromagnetic fields which are invariant under the action of one or more Killing fields. As an application, we present the derivation of the Kerr–Newman metric in the last section.

In the first section we introduce the electric and magnetic 1–forms, E = –iKF and B = iK * F, which can be defined in terms of the electromagnetic field tensor (2–form) F and a Killing field K. We also express the stress–energy tensor in terms of K, E and B. We then focus on the case where spacetime admits two Killing fields, k and m, say, and establish some algebraic identities between their associated electric and magnetic 1–forms.

The invariance conditions for electromagnetic fields are introduced in the second section. The homogeneous Maxwell equations imply the existence of a complex potential, Λ, which can be as-sociated with E and B if the Killing field K acts as a symmetry transformation on F. In terms of Λ, the remaining Maxwell equations reduce to one complex equation for ΔΛ, involving the twist, ω, and the norm, N, of the Killing field. In the Abelian case, to which we restrict our attention in this chapter, the presence of gauge freedom does not require a modified invariance concept for F. In contrast, the symmetry conditions must be reexamined if one deals with arbitrary gauge groups (see, e.g., Forgács and Manton 1980, Harnad et al. 1980, Jackiw and Manton 1980, Brodbeck and Straumann 1993, 1994, Heusler and Straumann 1993b).

In this chapter we present the uniqueness theorem for the Kerr–Newman metric. The latter describes the only asymptotically flat, stationary and axisymmetric electrovac black hole solution with regular event horizon. The proof of this fact involves the following steps: First, one has to establish circularity of the domain of outer communications as a consequence of the symmetry properties of the electromagnetic field. The Einstein–Maxwell equations are then reduced to a 2–dimensional elliptic boundary–value problem for the complex Ernst potentials E and Λ. One then takes advantage of the symmetries of the Ernst equations to derive a divergence identity for the difference of two solutions. Since the boundary and regularity conditions are completely parametrized in terms of the total mass, angular momentum and charge, Stokes' theorem finally yields the desired result.

The chapter is organized as follows: The first section gives a short outline of the reasoning. In the second section we parametrize the Ernst potentials in terms of the hermitian matrix Φ, describing the nonlinear sigma model on the symmetric space G/H = SU(1, 2)/S(U(1) × U(2)) (or G/H = SU(1, 1)/U(1) in the vacuum case). We then establish the variational equation for Φ and derive an identity for the difference of two solutions to this equation. Evaluating the expressions in a circular spacetime, we obtain the Mazur identity (Mazur 1982) in the third section. This identity - or a related identity found by Bunting in 1983 - must be considered the key to the uniqueness theorems for rotating black holes.