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The Topic of Degeneracy Is a Very Important One, Especially in the Later Part of a Star's Life

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The Topic of Degeneracy Is a Very Important One, Especially in the Later Part of a Star's Life The topic of degeneracy is a very important one, especially in the later part of a star's life. It is, however, a topic that sends quivers of apprehension down the backs 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 a star is made up will behave like an ideal gas; i.e., one that has a simple relationship between 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. 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 tempera­ tures are necessary in order for, say, helium nuclear reactions to take place. At such high temperatures, the atoms are ionised so that they become a soup of atomic nuclei and electrons. Inside stars, especially those where the density is approach­ ing 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.' This is termed degeneracy, so that in a low­ mass red giant star, for instance, the electrons are degenerate, and the core is supported by an electron degenerate pressure. I This is a consequence of the Pauli exclusion principle, which state s that two electrons cannot occupy the same quantum state. Enough said I think! Observer's Guide to Stellar Evolution But a consequence of this degeneracy is that the behaviour 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, then I recommend some of the books mentioned in the latter appendices. Be warned, however, that mathematics is used liberally. There are many fine astronomy and astrophysics books in print, and to choose amongst them is a difficult task. Nevertheless, I have selected a few which I believe are amongst the best on offer. I do not expect you to buy, or even read them all, but it would be in your better interests to check at your local library to see if they have some of them. Norton's Star Atlas and Reference Handbook, I. Ridpath (ed.), Longmans, 1999, Harlow, UK. Sky Atlas 2000.0, W. Tirion and R. Sinnott, Sky Publishing and Cambridge University Press, 1999, Massachusetts, USA. Millennium Star Atlas, R. Sinnott and M. Perryman, Sky Publishing, 1999, Massachusetts, USA. Uranometria 2000.0: Volumes 1 and 2, Wil Tirion (ed.), Willmann-Bell; Virginia, 2001, USA. Observing Handbook and Catalogue of Deep-Sky Objects, C. Luginbuhl and B. Skiff, Cambridge University Press, 1990, USA. The Night Sky Observer's Guide: Vols. I and II, G. Kepple and G. Sanner, Willman-Bell, 1999, Richmond, USA. Deep-Sky Companions: The Messier Objects, S. O'Meara, Cambridge University Press, 1999, 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 . 18 Observer's Guide to Stellar Evolution Astrophysical Techniques, C. Kitchin, Institute of Physics, 1998, Bristol, UK. Discovering the Cosmos, R. Bless, University Science Books, 1996, Sausolito, USA. The Cosmic Perspective, J. Bennett, M. Donahue, N. Schneider and M. Voit, Addison Wesley, 1999, Massachusetts, USA. Voyages Through The Universe, A. Fraknoi, D. Morrison and S. Wolff, Saunders College Publishing, 2000, Philadelphia, USA. Introductory Astronomy and Astrophysics, M. Zeilik, S. Gregory and E. Smith, Saunders College Publishing, 1999, Philadelphia, USA. Stars, J. B. Kaler, Scientific American Library, 1998,New York, USA. Extreme Stars, J.B. Kaler, Cambridge University Press, 2001, UK. The Physics of Stars, 2nd Edition, A. Phillips, Wiley, 1999, Chichester, UK. Stars, Nebulae and the Interstellar Medium, C. Kitchin, Adam Hilger, 1987, Bristol, UK. 100Billion Stars, R. Kippenhahn, Princeton University Press, 1993, Princeton, USA. Stellar Evolution, A. Harpaz, A.K. Peters Ltd, 1994, Massa­ chusetts, USA. The Fullness of Space, G. Wynn-Williams, Cambridge University Press, 1992, UK. The Dusty Universe, A. Evans, John Wiley, Chichester, 1994, UK. Exploring Black Holes, E. Taylor and J.A. Wheeler, Princeton University Press, 2001, Princeton, USA. Ma azines Astronomy Now, UK Sky and 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, 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. Books, Magazines and Organizations 1 The Federation of Astronomical Societies, 10 Glan y Llyn, North Cornelly, Bridgend County Borough , CF33 4EF, Wales. [http://www.fedastro .demon.co.uk!] Society for Popular Astronomy, The SPA Secretary, 36 Fairway, Keyworth, Nottingham NGI2 5DU, UK. [http :// www.popastro .com!] The American Association of Amateur Astronomers, P.O. Box 7981 , Dallas, TX 75209- 0981. [http ://www.corvus.com] The Astronomical League. [http ://www.astroleague.org/] The British Astronomical Association, Burlington House, Piccadilly, London, WIV 9AG, UK. [http ://www.ast.cam.ac. uk/ -ebaa/] The Royal Astronomical Society, Burlington House, Picca­ dilly, London, WIV ONL, UK. [http://www.ras.org.uk/ membership.htm] Campaign for Dark Skies, 38 The Vineries, Colehill, Wim­ borne, Dorset, BH21 2PX, UK. [http://www.dark-skies. freeserve.co.uk!] The following is a quick reference guide to the Greek letters, used in the Bayer classification system. Each entry shows the uppercase letter, the lowercase letter, and the pronunciation. A C( Alpha N v Nu B f3 Beta N ~ Xi r y Gam ma 0 0 Omicro n 6- 8 Delta n IT Pi E E Epsi lon P p Rho Z t: Zeta ~ a Sigma H /1 Eta T r Tau (~) e Theta y v Ups ilon I Iot a <P ¢ Phi K K Kappa X Chi , X A A Lambda \jJ 1j; Psi M II Mu Q w Omega 21 NGC 1850. The double cluster NGC 1850, found in one of our neighbouring galaxies, the Large Magellanic Cloud, is on eye<atching object. It is a young , " qlobulcr-like" star cluster - a type of object unknown in our own Milky Way Galaxy. Moreover, NGC 1850 is surrounded by a filigree pattern of diffuse gas, which scientists believe was created by the explosion of massive stars. NGC 1850, imaged here with the NASA Hubble Space Telescope, is an unusual double cluster that lies in the bar of the Large Magellanic Cloud, a satellite ga laxy of our own Milky Way. After the 30 Doradus complex , NGC 1850 is the brightest star cluster in the Large Magellanic Cloud . It is representative of a special class of objects - young, globular~ike star clusters - that have no counterpart in our galaxy. The two components of the cluster ore both relatively young and consist of a main , globular-like cluster in the centre and an even younger, smaller cluster, seen below and to the right, compased of extremely hot, blue stars and , fainter red T-Tauri stars. The main cluster is about 50 million yea rs old ; the smaller cluster is only 4 million years old . Imagescourtesy 01: NASA, ESA, and Martino Romoniello (European Southern Observatory, Gerrnony] . Acknowledgments: Martino Romaniello. Rich~rd Hook.BobFosbury and the Hubble European Space AgencyInlormation Centre. 2 22 Observer's Guide to Stellar Evolution Colour Photographs 2 Barnard 68 (above). At a distance of only 4 10 Iight-yeors, Barnard 68 is one of the neorest dark clouds. Itssize is about 12,500 AU 1= 2 million million km; 1 Astronom ical Unit [AU] =15 0 million km), or just about the same as the so-celled " O ort Cloud " of long-period comets that surrounds the solar system. The temperature of Barnard 68 is 16 Kelvin (-257 q and the pressure at its boundary is 0.0025 nPa, or about 10 times higher than in the interstellar medi um (but still 40,000 million million times less than the atmosphe ric pressure at the Earth's surface !). The total mass of the cloud is about twice that of the Sun. Image courtesy 01the Europeon Southern Observotory. .... Star Forming Region: 30 Doradus (opposite). NASA's Hubble Space Telescope has snapped a panoramic portrait of a vast, sculpted landscape of gas and dust where thousands of stars are being born . This fertile star-forming region, called the 30 Doradus Nebula, has a sparkling stellar centrep iece: the most spectacular cluster of massive stars in our cosmic neighbourhood of about 25 ga laxies.
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