APPENDIX ONE Degeneracy Degeneracy is a very complex topic but a very important one, especially when discussing the end stages of a star’s life. It is, however, a topic that sends quivers of apprehension down the back of most people. It has to do with quantum mechanics, and that in itself is usually enough for most people to move on, and not learn about it. That said, it is actually quite easy to understand, providing that the information given is basic and not peppered throughout with mathematics. This is the approach I shall take. In most stars, the gas of which they are made up will behave like an ideal gas, that is, one that has a simple relationship among its temperature, pressure, and density. To be specific, the pressure exerted by a gas is directly proportional to its temperature and density. We are all familiar with this. If a gas is compressed, it heats up; likewise, if it expands, it cools down. This also happens inside a star. As the temperature rises, the core regions expand and cool, and so it can be thought of as a safety valve. However, in order for certain reactions to take place inside a star, the core is compressed to very high limits, which allows very high temperatures to be achieved. These high temperatures are necessary in order for, say, helium nuclear reactions to take place. At such high temperatures, the atoms are ionized so that it becomes a soup of atomic nuclei and electrons. Inside stars, especially those whose density is approaching very high values, say, a white dwarf star or the core of a red giant, the electrons that make up the central regions of the star will resist any further compression and themselves set up a powerful pressure.1 This is termed degeneracy, so that in a low-mass red 191 192 Astrophysics is Easy giant star, for instance, the electrons are degenerate, and the core is supported by an electron-degenerate pressure. But a consequence of this degeneracy is that the behavior of the gas is not at all like an ideal gas. In a degenerate gas, the electron degenerate pressure is not affected by an increase in temperature, and in a red giant star, as the temperature increases, the pressure does not, and the core does not expand as it would if it were in an ideal gas. The temperature, therefore, continues to increase, and further nuclear reactions can take place. There comes a point, however, when the temperatures are so high that the electrons in the central core regions are no longer degenerate, and the gas behaves once again like an ideal gas. Neutrons can also become degenerate, but this occurs only in neutron stars. For a fuller and more rigorous description of degeneracy, I recommend the books mentioned in the latter appendices. Be warned, however, that mathematics is used liberally. Note 1. This is a consequence of the Pauli exclusion principle, which states that two electrons cannot occupy the same quantum state. Enough said, I think! APPENDIX TWO Books, Magazines, and Astronomical Organizations Books, Magazines, and Organizations There are many fine astronomy and astrophysics books in print, and to choose among them is a difficult task. Nevertheless, I have selected a few, which I believe are among the best on offer. I do not expect you to buy, or even read, them all, but it would be in your better interest to check at your local library to see if they have some of them. Star Atlases and Observing Guides Norton’s Star Atlas and Reference Handbook, 20th edn, Ian Ridpath (ed.), Prentice Hall, 2003 USA. Sky Atlas 2000.0, W. Tirion & R. Sinnott, Sky Publishing & Cambridge University Press, 1999, Massachusetts, USA. Millennium Star Atlas, R. Sinnott & M. Perryman, Sky Publishing, 2006, Massachusetts, USA Uranometria 2000.0, Vols.1&2,WilTirion (ed.), Willmann-Bell, 2001, Virginia, USA. 193 194 Astrophysics is Easy Observing Handbook and Catalogue of Deep-Sky Objects, C. Luginbuhl & B. Skiff, Cambridge University Press, 1990, Cambridge, UK. The Night Sky Observer’s Guide, Vols. I & II, G. Kepple & G. Sanner, Willman-Bell, 1999, Richmond, USA. Deep-Sky Companions: The Messier Objects, S. O’Meara, Cambridge University Press, 1999, Cambridge, UK. Deep-Sky Companions: The Caldwell Objects, S. O’Meara, Cambridge University Press, 2004, Cambridge, UK. Observing the Caldwell Objects, D. Ratledge, Springer-Verlag, 2000, London, UK. Burnham’s Celestial Handbook, R. Burnham, Dover Books, 1978, New York, USA. Star Clusters and How To Observe Them, M. Allison, Springer, 2006, New York, USA. Double & Multiple Stars and How To Observe Them, J. Mullaney, Springer, 2006, New York, USA. Nebulae and How To Observe Them, S. Coe, Springer, 2006, New York, USA. Galaxies and How To Observe Them, W. Steinicke & R. Jakiel, Springer, 2006, New York, USA. Astronomy and Astrophysics Books Astrophysical Techniques, 4th edn, C. Kitchin, Institute of Physics, 2003, Bristol, UK. Discovering the Cosmos, R. Bless, University Science Books, 1996, Sausilito, USA. The Cosmic Perspective, J. Bennett, M. Donahue, N. Schneider, M. Voit, Addison Wesley, 1999, Massachusetts, USA. Voyages Through The Universe, A. Fraknoi, D. Morrison, S. Wolff, Saunders College Publishing, 2000, Philadelphia, USA. Introductory Astronomy & Astrophysics, M. Zeilik, S. Gregory, E. Smith, Saunders College Publishing, 1999, Philadelphia, USA. Pathways To Astronomy, Schneider & Arny, McGraw-Hill, 2006, USA. An Introduction To The Sun & Stars, Green & Jones, Open University/Cambridge University Press, 2005, Cambridge, UK. An Introduction To Galaxies & Cosmology, Jones & Lambourne, Open University/ Cambridge University Press, 2005, Cambridge, UK. Introduction to Modern Astrophysics, 2nd edn, B. W. Carroll & D. A. Ostlie, Addison Wesley, 2006, USA. Stars, J. B. Kaler, Scientific American Library, 1998, New York, USA. Extreme Stars, J. B. Kaler, Cambridge University Press, 2001, Cambridge, UK. The Physics of Stars, 2nd edn, A. Phillips, Wiley, 1999, Chichester, UK. Stars, Nebulae and the Interstellar Medium, C. Kitchin, Adam Hilger, 1987, Bristol, UK. 100 Billion Stars, R. Kippenhahn, Princeton University Press, 1993, Princeton, USA. Stellar Evolution, A. Harpaz, A. K. Peters, Ltd, 1994, Massachusetts, USA. The Fullness of Space, G. Wynn-Williams, Cambridge University Press, 1992, Cambridge, UK. Astrophysics Of Gaseous Nebulae And Active Galactic Nuclei, 2nd edn, D. E. Osterbrock & G. J. Ferland, University Science Books, 2005, Sausilito, USA. The Dusty Universe, A. Evans, John Wiley, 1994, Chichester, UK. Galaxies and Galactic Structure, D. Elmegreen, Prentice Hall, 1998, USA. Books, Magazines, and Astronomical Organizations 195 Exploring Black Holes, E. Taylor & J. A. Wheeler, Princeton University Press, 2001, Princeton, USA. Magazines Astronomy Now,UK Sky & Telescope, USA New Scientist,UK Scientific American, USA Science, USA Nature,UK The first three magazines are aimed at a general audience and so are applicable to everyone, while the last three are aimed at the well-informed lay person. In addition, there are many research-level journals that can be found in university libraries and observatories. Organizations The Federation of Astronomical Societies, 10 Glan y Llyn, North Cornelly, Bridgend County Borough, CF33 4EF, Wales [http://www.fedastro.org.uk/] Society for Popular Astronomy, The SPA Secretary, 36 Fairway, Keyworth, Nottingham, NG12 5DU, UK [http://www.popastro.com/] The American Association of Amateur Astronomers, P.O. Box 7981, Dallas, TX 75209-0981 [http://www.astromax.com/] The Astronomical League [http://www.astroleague.org/] The British Astronomical Association, Burlington House, Piccadilly, London, W1V 9AG, UK [http://www.britastro.org/baa/] The Royal Astronomical Society, Burlington House, Piccadilly, London W1V 0NL [http://www.ras.org.uk/membership.htm] International Dark Sky Association [http://www.darksky.org/] Topic Index Absolute magnitude, 4, 10, 11, 35, 37, 117 CNO cycle, 154–155 Absorption lines, 23–27, 30, 39, 44, 102, 146 Color index, 17, 127 Active galactic nuclei, 177, 188 Color-magnitude diagram, 109 Active galaxies, 177–180 Convection, 59, 66, 67, 86, 87, 118, 124 AGN, 177–178, 188 Convection zone, 87 Alpha particles, 105, 142 Core, 87, 91 Apparent brightness, 3, 6, 7, 8, 10, 42, 43, 109 Core bounce, 142 Apparent magnitude, 4, 9–11, 14, 43, 117, 120 Core collapse, 142, 149, 150, 155 Arc-second, 1–3, 5, 6, 12, 14, 49 Core helium burning, 105, 107, 109, 118, 123 Astrometric binary, 92, 154 Core hydrogen burning, 98, 122, 124 Astronomical unit, 1, 95, 97, 140 Core rebound, 142 Asymptotic giant branch, 109, 122–123 Dark nebulæ, 53–55, 58, 62, 69, 72, 79, 113 Balmer lines, 26 Degeneracy, 105, 134, 138, 149–150, 155, Barnard objects, 58, 62 191–192 Barred spiral, 158, 170, 172, 187 Deuterium, 89, 90 B associations, 82 Disc, 71–72 Binary stars, 92–94, 96, 155 Distance modulus, 11 Bipolar outflow, 71 Doubly-ionized oxygen, 130 Black holes, 135, 147, 149–151, 156, 178, 179 Dredge-ups, 124 Blazers, 177, 189 BL Lacs, 177, 189 Dust grains, 53, 56, 58, 129, 144 Bok globules, 58 Dwarf elliptical, 159, 174, 186 Brightness ratio, 10 Bulge, 108, 155, 158–160, 162, 171 Eclipsing binary, 22, 95, 140 Elliptical galaxies, 154, 158–160, 172, 174, Carbon burning, 138–139, 146–147 176, 186 Chandrasekhar limit, 134–135, 137–138, 142, Emission lines, 23–25, 29, 70, 141, 146, 163, 180 146, 149 Emission line spectrum, 23 Circumstellar accretion disc, 71 Emission nebulæ, 47–49, 51, 56, 83, 153, 188 197 198 Topic Index Energy flux, 19 Jeans criteria, 59–60 Energy level, 23–26, 39, 44, 47–48, 61 Jeans length, 60–61 Event horizon, 150 Jeans