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Planetary
Nebulae

by Paul Ruffle

This essay was originally published in the OU Physics Society's Fusion Newsletter Spring 2006.

It is based on the introduction to planetary nebulae in chapter 2 of my PhD thesis.

Planetary nebulae (PNe) consist of glowing shells of gas and plasma that have been ejected from low to medium mass stars at the end of their lives. The name originates from a supposed similarity in appearance to giant planets. About 1,500 PNe are known to exist in our galaxy, out of around 200 billion stars. They are generally less than 50 thousand years old, compared to typical stellar lifetimes of several billion years. This short lifetime compared to stellar lifetimes accounts for their rarity. They are found mostly near the plane of the Milky Way, with the greatest concentration in the galactic Bulge. A typical PN is roughly 3 pc across, and consists of tenuous gas, with a density of ∼103 cm-3. Young PNe can have higher densities, ∼106 cm-3, but as they age, expansion causes their density to decrease. The central stars of PNe are very hot, but their luminosity is very low, implying that they must be very small. Spectroscopic observations show that all PNe are expanding.

HST images of planetary nebulae

HST images of planetary nebulae taken by Bruce Balick and his collaborators (www.astro.washington.edu/balick/WFPC2).

PNe play a crucial role in the chemical evolution of galaxies. The early universe consisted almost entirely of hydrogen and helium, but successive generations of stars have created heavier elements via nucleosynthesis. When stars exhaust all their nuclear fuel they collapse to a small size, and for medium and low mass stars (< 8 Msun) PNe are the end stage of their evolution. The gases of PNe contain a large proportion of heavy elements (or metals), and as they evolve they return material such as carbon, nitrogen, oxygen and calcium to the interstellar medium (ISM). High mass stars (> 8 Msun) end their lives in a catastrophic supernova explosion, and either become neutron stars or black holes.

A typical star like our Sun spends most of its lifetime fusing hydrogen into helium in its core. The energy released prevents the star from collapsing under its own gravity, making the star stable. After ∼1010 years, the star runs out of hydrogen in its core, so fusion ceases to support the outer layers of the star. The core then contracts and heats up from ∼107 K to ∼108 K. This results in the outer layers of the star expanding and cooling because of the very high core temperature, and the star becomes a red giant. However, the core continues to contract and heat up, and when its temperature reaches 108 K, helium nuclei begin to fuse into carbon and oxygen, stopping further contraction of the core. The core then consists of inert carbon and oxygen, with a surrounding helium-burning shell. Helium fusion is extremely temperature sensitive, (r ∝ T40), so a 2 per cent increase in temperature more than doubles the reaction rate. This makes the star very unstable - a small rise in temperature releases a lot of additional energy, increasing the temperature further. This causes the helium-burning layer to rapidly expand and therefore cool, which reduces the reaction rate again. These pulsations build up and eventually become large enough to eject the star's atmosphere completely. Up to 90 per cent of the progenitor star's mass is lost to the newly formed nebula.

The core of the star is now exposed as more and more of the ejected atmosphere moves away from the star. Deeper and deeper layers of the core at higher and higher temperatures are exposed, and when the temperature reaches about 3 × 104 K, there are enough ultraviolet (UV) photons being emitted to heat the gas to the same temperature, ionising the ejected atmosphere and making it glow as a PN. The gas temperature is often seen to rise at increasing distances from the central star. This is because the more energetic a photon, the less likely it is to be absorbed, so less energetic photons tend to be absorbed in the inner regions of the nebula, while the higher energy photons tend to be absorbed in the outer regions.

The gases of a PN continue to move away from the central star at speeds of a few kilometres per second. As the gases expand, the central star cools, radiating away its residual energy. There are no further fusion reactions, because the remnant stellar core is not massive enough (∼0.6 Msun) to generate the temperatures required for carbon and oxygen to fuse. Eventually the core cools to the point that it does not give off enough UV radiation to ionise the increasingly distant gas cloud. The star becomes a white dwarf (∼0.01 Rsun), supported by the degeneracy pressure of its closely packed electrons (ρ = 107 - 1011 kg m-3), and the gas cloud continues to expand, and eventually merges into the ISM, enriching it with heavy elements such as carbon, nitrogen and oxygen, as well as organic molecules and refractory silicates and carbonaceous grains. The lifetime of a typical PN is ∼104 years from formation to recombination.

Hubble Space Telescope (HST) images reveal that many PNe have an extremely complex and varied morphology (see above). Generally speaking, PNe are symmetrical and about a fifth are roughly spherical, but a wide variety of shapes exist with some very complex forms seen. Approximately 10 per cent of PNe are strongly bipolar, and a small number are asymmetric. One is even rectangular. The reason for the huge variety of shapes is not yet fully understood, but interactions between stellar winds moving away from the star at different speeds is believed to give rise to most of the shapes that are observed. Other explanations include: gravitational interactions with companion stars if the central stars are double stars; or a star's planetary system disrupting the flow of material as the nebula forms. One recent study has found that several PNe contain strong magnetic fields, something which has long been hypothesised. Magnetic interactions with ionised gas could be responsible for shaping at least some PNe.

The outflow features of He2-104

The outflow features of He2-104 seen in the low intensity contours plotted by the author from images taken at the ESO 3.5m New Technology Telescope (NTT), La Silla Observatory, Chile.

As PNe are composed of extremely rarefied gas they show only a small number of emission lines. Some of the brightest of these are hydrogen, Hα, and doubly ionised oxygen, [OIII], at wavelengths of 6564Å and 5007Å respectively. These so-called forbidden lines can only be seen in very low density gases, because at such low densities, electrons can populate excited metastable energy levels in atoms and ions, which at higher densities would be rapidly de-excited by collisions.

PNe can be described as matter bounded or radiation bounded. In the former case, there is not enough matter in the PN to absorb all the UV photons, so the visible nebula is fully ionised. In the latter case, there are not enough UV photons to ionise all the surrounding gas, so an ionization front propagates outward into the circumstellar neutral envelope. As most of the gas in a typical PN is a plasma (i.e. ionised), magnetic fields can give rise to phenomena such as filamentation and plasma instabilities.

For most PNe distances are difficult to determine. For nearby PNe, it is possible to determine distances by measuring their expansion parallax: high resolution observations taken several years apart will show the expansion of the nebula perpendicular to the line of sight, while spectroscopic observations of the Doppler shift will reveal the velocity of expansion in the line of sight. Comparing the angular expansion with the derived velocity of expansion will reveal the distance to the nebula.

The angular diameter and flux of a PNe are much needed parameters when modelling the optical spectrum and evolution of the nebula and its central star. From these parameters the density and mass of the PNe can be calculated, as well as the extinction along the line of sight. PNe also provide an independent tracer of stellar populations and extinction in regions where visual tracers, such as hot luminous stars, are lacking.

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