Introduction Unusually in physics, there is no pithy phrase that sums up the study of dynamics (the way in which forces produce motion), kinematics (the motion of matter), mechanics (the study of the forces and the motion they produce), and statics (the way forces combine to produce equilibrium). We will take the phrase dynamics and mechanics to encompass all the above, although it clearly does not!

To some extent this is because the equations governing the motion of matter include some of our oldest insights into the physical world and are consequentially steeped in tradition. One of the more delightful, or for some annoying, facets of this is the occasional use of arcane vocabulary in the description of motion. The epitome must be what Goldstein calls “the jabberwockian sounding statement” the polhode rolls without slipping on the herpolhode lying in the invariable plane, describing “Poinsot's construction” – a method of visualising the free motion of a spinning rigid body. Despite this, dynamics and mechanics, including fluid mechanics, is arguably the most practically applicable of all the branches of physics.

Moreover, and in common with electromagnetism, the study of dynamics and mechanics has spawned a good deal of mathematical apparatus that has found uses in other fields. Most notably, the ideas behind the generalised dynamics of Lagrange and Hamilton lie behind much of quantum mechanics.

Although PN are well known for their ring-shape appearance, they in fact have a diverse range of morphologies. Using photographs that he took at the Lick Observatory, Curtis (1918) was the first to arrange PN into different classes based on their appearances. The origin of such diverse shapes has remained a mystery for a long time. For example, the well known Ring Nebula (NGC 6720) has an elliptical ring appearance. The most obvious interpretation is that this represents a three-dimensional hollow shell projected onto the sky. However, the actual observed surface brightness of the “hole” in comparison to the shell is too low (∽1:20) to be consistent with this model (Minkowski and Osterbrock, 1960). The observed intensity distribution is in fact more compatible with an open-ended toroid viewed end on (Khromov and Kohoutek, 1968). Although this model gives a good approximation to the observed image, the origin of such a toroid is not explained. The physical origin of the different morphologies of PN and how they evolve to such forms therefore represents one of the greatest challenges in PN research.

Morphological classifications

Curtis (1918) classified his sample of 78 PN into helical, annular, disk (uniform and centrally bright), amorphous, and stellar. Subsequent classification schemes often use similar descriptive forms: stellar, disk, irregular, ring, anomalous (Perek & Kohoutek, 1967); elliptical, rings, bipolar, interlocking, peculiar, and doubtful (Greig, 1971; Westerlund and Henize, 1967); and round, elliptical, and butterfly (Balick, 1987).

Central stars of PN (CSPN) are difficult to study because of their faintness in the visible (due to their high temperature) and the contamination of their spectra by nebular emissions. Unlike stars on the main sequence (MS), for which there exists a unique relationship between mass and effective temperature, CSPN undergo considerable changes in temperature over their short lifetimes. Although their masses do not change significantly, their surface abundances do change as the result of nuclear burning and mass loss. Assuming that the stellar winds from the CSPN are driven by radiation pressure, the mass-loss rate is mainly a function of T* and surface gravity (log g). In this case, the spectral classification of central stars can in principle be determined by three parameters: effective temperature, surface abundance, and wind strength. In this chapter, we discuss these three parameters in turn.

Determination of the temperature of the central star

Zanstra temperature

Zanstra (1927) developed the method to derive the central star temperature by comparing the nebular recombination flux with the stellar continuum magnitude. This method is based on the assumption that the number of Lyman continuum photons absorbed in the nebula is equal to the total number of recombinations to all levels excluding the ground state. Harman and Seaton (1966) used the nebular Hβ flux to estimate the total number of Lyman continuum photons, and they derived T* by comparing the Hβ flux with the stellar V magnitude.

In the earlier chapters, we discussed the radiative and mechanical processes in PN. These processes all contribute toward the interstellar radiation field and the return of stellarprocessed material to the interstellar medium. The return of mass to the interstellar medium is not only important in providing material for the formation of next generation of stars, but also in seeding the interstellar medium with CNO products that provide the cooling agents necessary for the collapse of interstellar clouds and star formation. In order for the relative importance between PN and other contributors (e.g. Wolf-Rayet stars and supernovae) to be assessed, it is necessary to know the total PN population in the Galaxy.

The first estimate of the total population of PN in the Galaxy (6 × 104) was given by Shklovsky (1956b), using the distance scale that he developed. This determination is instrumental in establishing the evolutionary status of PN as a stage that is passed through by all low-mass stars (Abell and Goldreich, 1966). This number also gives us an insight into the star-formation history of the Galaxy, as the progenitor stars of the PN that we are observing today were born billions of years ago.

Formation rate of PN in the Galaxy

In principle, the derivation of the formation rate of PN (x) is straightforward once the local number density of PN is known.

Unlike stars which show a continuous spectrum, the optical spectrum of PN is dominated by emission lines. Line emission occurs when atoms or ions make a transition from one bound electronic state to another bound state at a lower energy. Such transitions, usually by means of spontaneous emission, are referred to as bound-bound (b-b) transitions. In the interior of stars, electrons in an atom are distributed over many energy levels because of the high particle and radiation densities. The bound electrons are excited either by free electrons colliding with the atom, or by the absorption of a photon. However, in the interstellar medium, both the particle and radiation densities are low, and the population distribution of the bound electrons can be far from the thermodynamical equilibrium condition given by the Boltzmann equation [Eq. (2.23)].

The typical energy separations between the electronic states of atoms are of the order of 1 eV, corresponding to photons in the visible or UV parts of the spectrum. The only available visible or UV background in the interstellar medium is from diluted starlight, which is generally not strong enough for excitation by stimulated absorption to be significant. Therefore the only way that a bound electron can be found in an excited state is by collisional excitation from a lower state, or as a consequence of recombination between a free electron and a proton.

Traditional theories of PN ejection appeal to a variety of sudden ejection mechanisms including dynamical instabilities induced by recombination (Roxburgh, 1967; Lucy, 1967), pulsational instabilities (Kutter and Sparks, 1974; Wood, 1974; Tuchman et al., 1979), envelope relaxation oscillations due to thermal instability in the core (Smith and Rose, 1972), radiation pressure (Faulkner, 1970; Finzi and Wolf, 1971), or thermal pulses (Härm and Schwarzschild, 1975; Trimble and Sackman, 1978). The pulsation models represent an extension of the theory of Mira pulsation and predict that finite amplitude pulsation in the fundamental mode is not possible, leading to subsequent relaxation oscillations and PN ejection (Wood, 1981). The thermal-pulse theories rely on the luminosity peak just after the helium flash, which could lead to greater pulsational instability as the result of an enlarged stellar radius. Although these sudden-ejection models are intuitively appealing, none of them is quantitatively successful in ejecting the right amount of mass.

The difficulties of the sudden-ejection models should have been apparent given Paczyński's results. Paczyński's models have shown that the central star will remain at low effective temperatures if the envelope mass is higher than ∼10–3M⊙. It is impossible for any instability mechanism to be so precise in leaving behind just the right amount of mass. For example, if the sudden ejection removes 0.199 M⊙ instead of 0.2 M⊙, the star will stay on the red side of the H-R diagram long after the (never-ionized) nebula is completely dissipated.

We now recognize that a planetary nebula is a dynamical system whose nebular evolution is closely coupled to the evolution of the central star. The existence of a planetary nebula depends on the nebular and central star components evolving in step with each other. A complete description of the PN phenomenon therefore requires the following elements:

1. Evolution model of the central star [L*(t) and T*(t)]. Other than the question of whether central stars of PN are predominately hydrogen or helium burning, one major uncertainty is the extent of mass loss in the post-AGB phase. Since the evolution time from the end of AGB to the beginning of photoionization is critical for the existence of PN, a better estimate on the mass-loss rate during the post-AGB phase is needed.

2. Winds from central stars of PN [睅(t) and v(t)]. Whereas mass loss during the post-AGB phase affects the transition time to PN, mass loss during the PN phase has crucial effects on the dynamics of the nebula. Not only does the wind from the central star compress and accelerate the nebular shell, it also shapes the morphology of the nebula. On the observational side, the line profiles can be used to measure the terminal velocity and the mass-loss rate. Since the winds are likely to be driven by radiation pressure on resonance lines, theoretical estimates on 睅 can also be made.

3. […]

Stars on the main sequence (MS) obey a well-defined luminosity-spectral type relationship. The method of “spectroscopic parallax” assumes that a star of a certain spectral type will have a certain intrinsic luminosity, and by comparing with its visual magnitude, it is possible to derive its distance. However, the central stars of many PN cannot be observed, and even in the case where a visual magnitude is available, their high temperatures imply that large bolometric corrections are required. Whereas stars on the MS remain stationary in the same position on the H-R diagram, CSPN undergo large changes in temperature and luminosity over their lifetime. As a result, any derivations of distances from stellar properties are necessarily model dependent.

Except for a few cases of nearby PN where trigonometric parallaxes are possible, or in cases where there is a MS binary companion, most of the distances to PN have to be estimated from their nebular properties. By making certain assumptions on the nebular structure, distances can be derived by measurements of fluxes, angular sizes, electron densities, and so on. These methods are collectively called statistical distances.

A well-determined distance scale for PN is necessary for the investigation of the space density, galactic distribution, total number of PN, and the birth rate of PN in the Galaxy (see Chapter 18). Unfortunately, after many years of efforts, distances to PN remain controversial.

The first planetary nebula was observed by Charles Messier in 1764 and was given the number 27 in his catalog of nebulous objects. The final version of the Messier catalog of 1784 included four planetary nebulae (PN) together with other nonstarlike objects such as galaxies and star clusters. The name planetary nebulae was given by William Herschel, who found that their appearances resembled the greenish disk of a planet. With better telescope resolution, nebulae that are made up of stars (e.g., galaxies) were separated from those made up of gaseous material. PN were further distinguished from other galactic diffuse nebulae by that fact that PN have definite structures and are often associated with a central star. This distinction became even clearer with spectroscopy. The first spectrum of a PN (NGC 6543) was taken by William Huggins on August 29, 1864. The spectra of PN are dominated by emission lines, and not a continuous spectrum as in the case of stars. The first emission line identified was a Balmer line of hydrogen (Hβ), although stronger unidentified lines could be seen in the spectrum. Since the spectra of PN are entirely different from those of stars, their luminosity cannot be due to reflected starlight.

The idea that PN derive their energy from a nearby star was first considered by Herschel (1791). However, no further progress was made for another century.

In this book, we have addressed three aspects of PN research: radiation mechanisms, evolution, and applications. We have discussed the various physical mechanisms that are responsible for the emission of radiation from PN, and how different techniques (imaging, photometry and spectroscopy) in the radio, submillmeter, infrared, optical, ultraviolet, and X-ray can be used to probe the physical conditions in different parts of the nebulae. The wealth of data obtained through multi-wavelength observations have served as laboratories for the testing of radiation theories as well as for atomic and molecular physics. The discoveries of new phenomena such as forbidden lines and unidentified infrared features have stimulated the laboratory spectroscopy of atomic and molecular species.

The central stars of PN are hot and luminous objects. Although most of the starlight is in the form of high-energy UV photons, the nebulae are able to intercept these photons and downgrade them to visible wavelengths. Through photoionization, the radiative energy of the star is transferred to the kinetic energy pool of the gaseous nebula, which then emits low-energy line and continuum photons through the processes of recombination and collisional excitation. As the result, PN become bright visible objects and can be detected at large (cosmological) distances. For nearby PN, it is possible to obtain very high-quality spectra which allow for the accurate determination of chemical abundances and kinematic structure of the nebulae.

This book reflects the extraordinary amount of progress made in planetary nebulae research in the last thirty years. Before 1970, observations of planetary nebulae were limited to the visible region, and the oretical understanding focused on the physical processes in the ionized region. As the result of observations across the electromagnetic spectrum, we now have a much better appreciation of the richness of the planetary nebulae phenomenon. All states of matter (ionized, atomic, molecular, and solid state) are present in planetary nebulae, emitting radiation via a variety of mechanisms. More importantly, we have achieved a much better understanding of the origin and evolution of planetary nebulae (hence the title of the book).

When I was first approached by the Cambridge University Press about the possibility of writing a book on planetary nebulae, I as initially hesitant given the heavy teaching and administrative duties that I have at the University. In the end, I am glad to have done it because it offered me relief from writing reports and doing budgets as well as the opportunity to organize my own thoughts on the subject. The task of writing was made easier because of the availability of software tools: the manuscript was written in CUP LATEX, the calculations performed using MATHCAD, and many of the figures prepared using AXUM.

The infrared spectrum of PN was expected to be dominated by forbidden-line emissions from the ionized gas, and the discovery of strong infrared excess in NGC 7027 was totally unpredicted (Gillett et al, 1967). A photometric survey by Cohen and Barlow (1974, 1980) using the 1.5-m telescope at Mt. Lemmon showed that many PN display strong infrared emission from dust. Far infrared photometry observations from the Kuiper Airborne Observatory (KAO) by Telesco and Harper (1977) found the dust in NGC 7027 to be cool, with a color temperature of ∽100 K. Further KAO observations by Moseley (1980) confirmed the presence of cool dust in 13 PN.

The discovery of cool dust in PN and the observations of circumstellar dust envelopes in AGB stars (Section 10.4.1) suggest that they share the same origin (Kwok, 1982). If PN descend from mass-losing AGB stars, then the remnants of the AGB dust envelope must still be present in PN. The dispersal of the dust envelope since the end of the AGB implies a gradual decrease of the dust temperature, and the shifting of the peak of the dust continuum from mid-infrared to the far-infrared. According to the Wien's law, a blackbody of 100 K will peak at 30μm, beyond the longest infrared window observable from the ground. Since the flux decreases exponentially on the short wavelength side of the Planck function, dust emission from PN is difficult to detect from the ground.

Stars are classified as low, intermediate, or high mass according to the nuclear reactions they undergo. Low-mass stars are defined as those that develop electron-degenerate He cores on the red giant branch (RGB). If the He core grows to ∽0.45 M⊙, the star will undergo a core He flash until degeneracy is removed and quiescent He burning begins. Intermediate-mass stars can initiate core He burning under nondegenerate conditions and develop an electron-degenerate carbon-oxygen (C-O) core after core He exhaustion. At the completion of core He burning, low-mass stars also develop an electron-degenerate C-O core, and their subsequent evolution is similar to that of intermediate-mass stars. This is the beginning of the asymptotic giant branch. Stars that are massive enough can undergo He-shell flashes (also called thermal pulses) on the AGB. The AGB is terminated by either (a) complete removal of the hydrogen envelope by mass loss; or (b) ignition of carbon in the degenerate core. Massive stars are defined as those that develop a nondegenerate C-O core and therefore can ignite carbon nonviolently. They are able to go through a series of nuclear burnings (C, O, Ne, etc.), leading to the construction of the iron core followed by core collapse and supernova explosion.

The end products of evolution for low-, intermediate-, and high-mass stars are very different.