Planetary Nebulae

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Planetary Nebulae

In astronomy, high-density, localized conglomerates of interstellar dust or gaseous clouds are referred to as nebulae. The word nebular is from the Latin word for cloud because before the invention of the telescope all celestial objects that appeared to have a diffuse (or cloudy) appearance were referred to as nebulae. These nebulae, both dark and luminous, are equally important since the chemical analyses of these objects contribute significantly to the study of cosmic abundances. Bright or incandescent nebulae, just as dark nebulae, are not self-luminous.

It is the star or stars imbedded in these nebulae that produce the luminous objects and are responsible for the atomic processes that may take place. Nebulae may be divided into four groups: dark, reflection, diffuse, and planetary, with the latter three representing the luminous objects.

The study of bright-line spectra of gaseous nebulae, namely diffuse and planetary, is important because it contributes in no small way to the determination of cosmic abundances. It has been suggested that these objects can be studied with greater ease since all portions of a nebula are observable, and even though departures from thermodynamic equilibrium

are significant, the processes seem to be well understood and can be treated theoretically.

A disadvantage in using gaseous nebulae is that many of them possess a filamentary structure that is due to non-uniform density and temperature, from point-to-point. In instances where stratification occurs, the temperature and excitation level will be different for the inner and outer parts of the nebula. Also, an element maybeobservedinoneortwostagesofionizationand yet may exist in several unobserved stages of ionization.

In the study of nebulae there are four fundamental quantities that are needed at the outset: distance, mass, electron temperature, and density. Of these, the distance parameter is probably the most important one because without it the real dimensions of the nebula cannot be determined from the apparent ones. To determine the mass it is necessary to know the density, and this can be determined, in some cases, from forbidden line data.

For diffuse nebulae, the distances are found from the stars with which they are associated, and the most commonly used methods are statistical parallaxes and moving clusters. However, none of these methods apply for planetary nebulae because they are too far away for a direct trigonometric measurement; they are not members of moving clusters; and statistical parallaxes are inapplicable since they do not appear to move randomly. Instead, the approach is to obtain parallaxes of the individual objects, or by special methods in which the mass of the nebular shell is assumed constant, or the absolute magnitude of nebula is assumed constant.

From the bright-line spectra of gaseous nebulae the abundances of the elements and ions can be determined, the contribution to the elements and ions can be determined, and the contribution to the cosmic abundances can be assessed. The mechanisms of excitation (ionization) and recombination that operate is well understood, so that from these spectra reliable results can be expected. Physically, the electron from the ionized atom, for example hydrogen), moves about freely for approximately ten years, and during that period it will collide with other electrons, thereby altering its energy. In addition, periodically it will excite ions to the metastable levels. Since the electron undergoes so many energy exchanges with other electrons, the velocity distribution turns out to be Maxwellian so that the gas kinetic temperature, and specifically the electron temperature, is of physical significance. It must be noted, also, that an atom in the nebula is subjected to dilute or attenuated temperature radiation from a star that subtends a very small angle. The energy distribution or quality of this radiation corresponds to temperatures ranging from 36,000 to 180,000°F (20,000 to

100,000°C). However, the density of this radiation is attenuated by a factor of 10¹⁴.

The mechanisms that are operating in gaseous nebulae are as follows:

Primary mechanism

In general terms, an atom or ion may be ionized by very energetic photons, a process referred to as photo-ionization. Photons of the far-ultraviolet region have sufficient energy to ionize an atom that is in the ground state. After being photo-ionized from the ground level, the ion recaptures an electron in any one of its various excited levels. After this recombination, as it is called, the electron cascades down to the lower levels, emitting photons of different frequencies (Figure 1). The origin of the permitted lines of hydrogen (H) and helium (He) are explained in this manner. This also applies to the ionic permitted lines of (C), nitrogen (N), oxygen (O), sulfur (S), and neon (Ne) observed in the ordinary optical region. These lines are weaker, however, than those of hydrogen (H) and

helium (He), and this is due to their much lower abundance in the nebula.

Collisional excitation mechanism

The excitation of atoms and ions to metastable levels by electron collision is followed by cascading to lower levels that, in the process, emit the so-called forbidden quanta. The transition probabilities of spectral lines are quite few by comparison to the allowed transition. The allowed transitions are electric dipole radiations, whereas forbidden transitions correspond to magnetic-dipole and/or electric-quadruple radiations. There are three types of transitions that are the result of collisional excitation: nebular, auroral, and transauroral (Figure 2). all the upward transitions are due to collisional excitation only; however, the downward transitions can be one of two types, i.e., superelastic collisions, or radiation of forbidden lines. The level density and atomic constants determine which of the latter transitions is likely to take place in depopulating the level. In addition, the forbidden spectra are observed only for ions whose metastable levels lie a few electron volts above the ground state. Collisionally excited lines are observed in low lying levels of the spectra of CIII, CIV, NIII, NIV, NV, SIIII, etc., in the far ultraviolet.

The study of forbidden lines is one of the major areas of investigation in gaseous nebulae since they dominate the spectra of most gaseous nebulae.

Bowen’s fluorescent mechanism

In the spectra of many high excitation planetary nebula, certain permitted lines of OIII and NIII appear, and these are sometimes quite intense. Bowen observed that the OIII lines could be produced by atoms cascading from the 2p3d³P₂ level. Bowen noticed that there was a frequency coincidence between the resonant Ly transition of the HeII and the transition from the 2p²3P₂ to the 2p3d³P₂ level of OIII, i.e., 303.78Å Ly of HeII and the 3033.693Å and 303.799Å of OIII (Figure 3). bowen further observed an equally surprising similarity, namely that the final transition of the OIII, i.e., 2p3s³PÅ-2p³P₂ emitting a photon of 374.436Å, coincides with the resonance line 374.442Å of the 2p²P_3/2-3d²D_3/2 of NIII, which also produces in this ion a similar fluorescent cycle. Detailed investigations and analyses showed that the Bowen fluorescent mechanism was fundamentally correct both qualitatively and quantitatively. It has applications to high excitation gaseous nebulae, quasars, and stellar envelopes.

Continuous spectra mechanism

In addition to emitting discrete line radiation, the bright-line spectra of a nebula emits a characteristic continuum. The physical mechanisms that are involved in the production of a nebular continuum are as follows: (a) Recombinations of electrons on discrete levels of hydrogen and to a lesser degree of helium, i.e., because of its lower abundance helium gives only a minor contribution. (b) Free-free transitions wherein kinetic energy is lost in the electrostatic field of the ions. The thermal radiation from these free-free transitions is observed particularly in the radio-frequency region since these transitions become more important at lower frequencies. (c) The 2-photon emission is produced by hydrogen atoms cascading from the 2s level to the ground level (Figure 4). the two-photon emission in hydrogen can be expressed as ν₁ + ν₂ = ν_Ly between the series limits. The recombination spectra decrease as the rate of e^-hν/kT (where h is Planck’s constant, ν is the light frequency, k is Boltzmann’s constant, and T is the nebula temperature) and it has a maximum approximately halfway between the origin and the Ly. Besides the above, there

KEY TERMS

Absolute magnitude— The apparent brightness of a star, measured in units of magnitudes, at a fixed distance of 10 parsecs.

Apparent magnitude or brightness— The brightness of a star, measured in units of magnitudes, in the visual part of the electromagnetic spectrum, the region to which human eyes are most sensitive.

Balmer lines— Emission or absorption lines in the spectrum of hydrogen that arise from transitions between the second- (or first-excited) and higher-energy states of the hydrogen atom.

Dark nebula— A cloud of interstellar dust that obscures the light of more distant stars and appears as an opaque curtain—for example, the Horsehead nebula.

Diffuse nebula— A reflection or emission nebula produced by interstellar matter.

Excitation— The process of imparting to an atom or an ion an amount of energy greater than that it has in its normal state, raising an electron to a higher energy level.

Forbidden lines— Spectral lines that are not usually observed under laboratory conditions because they result from atomic transitions that are of low probability.

Free-free transition— An atomic transition in which the energy associated with an atom or ion and a passing electron changes during the encounter, but without capture of the electron by the atom or ion.

Ionization— The production of atoms or molecules that have lost or gained electrons, and therefore have gained a net electric charge.

Nebula— A relatively dense dust cloud in interstellar space that is illuminated by imbedded starlight.

Planetary nebula— A shell of gas ejected from, and expanding about, a certain kind of extremely hot star that is nearing the end of its life.

Recombination— The reverse of excitation or ionization.

Statistical parallax— A method for determining the distance to a class of similar objects assumed to have the same random motion with respect to the Sun.

Temperature (effective)— The temperature of a blackbody that would radiate the same total amount of energy that a star does.

are other possibilities for contributions to the nebular continuum, namely, electron scattering, fluorescence, and H- emissions. However, the contributions from these do not appear to be especially significant.

The most important feature that is observed in the continuum is the jump, referred to as the Balmer Jump, at the limit of the Balmer series that is produced by the recombination of electron and ions in the n = 2 level of hydrogen. A smaller jump has also been observed at the Paschen limit. The spectral quantities, as well as angular diameter, surface brightness, relative brightness of the principal emission lines, and at times the brightness of the central star are, by and large, readily measurable. Due to this fact, significant contribution can be made to the cosmic abundances as well as to galactic structure.