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
21 NGC 1850. The double cluster NGC 1850, found in one of our neighbouring galaxies, the Large Magellanic Cloud, is on eye
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. The mosaic picture shows that ultraviolet rad iat ion and high-speed material unleashed by the stars in the cluster, ca lled R136 [the large blue blob below centre), are weaving a tapestry of creotion and destruction, triggering the collapse of loo ming ga s and dust clouds and for ming pillor-like structures that are incuba tors for nascent star s. Imoges courtesy 01: NASA, N. Walborn andJ.Maiz·Apell6niz (SpaceTelescope Science lnstitute, Baltimore, MDI, R. BarbO (La Plato Observotcry, La Plaia, Arqent inc ]. 226 Observer's Guide to Stellar Evolution Colour Photographs 22
HH 34 (above). This is an image of the young ob ject Herbig-Hero 34 (HH·341, now in the protostar stage of evolution. It is based on CCD frames ob tained w ith the FORS2 instrument in imaging mode, on November 2 and 6, 1999 . This obj ect has a remarkable, very comp licated appearance that includes two oppos ite jets that ram into the surrounding interstellar matter. This structure is produced by a mcchine-qun-like blast of " bullets" of dense gas ejected from the star at high velocities (approaching 250 km/sec). This seems to ind icate that the star experiences episodic " outbursts" when large chunks of material fall onto it from a surrounding disk. HH-34 is located at a distance of approx. 1,500 light·years, near the famous O rio n Nebula, one of the most productive star birth regions. Note also the enigma tic " waterfall" to the upper left, a feature that is still unexplained . Imagecourtesy of the European Southern Observatory.
CHl (opposite) . This imoge disploys a sky area near the Chamaeleon I comp lex of br ight nebulae and hot stars in the constellation of the same name, close to the southern celestial pole . Image courtesyof the European Southern Observotory. 2 Obsehrer'5 Guide to Stellar Evolution
N70. N70 is a " Super Bubble" in the large Magellanic Claud (LMC). a satellite galaxy to the M ilky Way system , located in the southern sky at a distance of about 160,000 light-years. This photo is based on CCD frames obtained with the FORS2 instrument in imaging mode in the morning of November 5, 1999 . N 70 is a luminous bubble of interstellar gas, measuring about 300 light-years in diame ter. It was created by winds from hot, massive stars and supernova explosions and the interior is filled wi th tenuous, hot expand ing gas. An object like N70 provides astronomers with on excellent oppo rtunity to explore the connection between the lifecycles of stars and the evolution of galaxies. Very massive stars profoundly affect their environment. They stir and mix the interstellar clouds of gas and dust, and they leave their mark in the compositions and locations of future generations of stars and star systems. Imag e courtesy 01 the European Southern Observatory. Colour Photographs
Crab Nebula. This is the well-known Crab Nebula (also known as " M essier 1" j. as observed w ith the FORS2 instrument in imaging mode on the morning of November 10 , 19 99. It is the remnant of 0 supernova exp losion at a distance of about 6,000 light-year s, ob served almost 1000 years ago, in the year 1054. It conta ins a neutro n star near its centre that spins 30 times per second around its ax is (see below) . The green light is predominantly produced by hydrog en emission from material ejected by the star that exp loded. The bl ue light is predom inantly emitted by very high-energy ("relativistic") electron s that spira l in a larg e-scale mag netic Field (so-called synch rotron emission] , It is believed that these electrons ar e continuously accelera ted and ejected by the rapidly spinning neutron star at the centre of the nebula and wh ich is the remnant core of the exploded star . This pulsar has been identified w ith the lower-rig ht of the two close stars near the geometric centre of the nebula, immedi ately left of the small arc-like feature. Image courtesyof the European Southern Observatory. Object Index
This list referen ces the main en try of the objec t in the book. It may actua lly be ment ioned in othe r sections.
Achern ar /8 Barn ard 87, 65-7 80 Caldwell 56 /89 Acrux 30 Barn ard 103 80 Caldwe ll 58 /06 Aleyo ne 48 Barn ard 110- 1 80 Caldwell 59 /87 Aldeba ran 18 Barnard 142- 3 80 Caldwe ll 63 /88 Alderamin 49 Barn ard 145 8 1 Caldwe ll 64 /0 7 Algeiba 5/ Barn ard 228 79 Caldwell 76 /08 Algenib 47 Barn ar d 343 8 1 Canopus 50 Alhe na 48 Barn ard 352 81 Capella /8 Almach 51 Barn ard's Loop 207 Cas tor 48 " Aqu arii 50 Barnard's Sta r 6 Cat's Eye Nebula /87 " Canis Majoris 6 Becrux /8 CE Ta ur i 200
(i Canis Minoris 6 Beehive /0 7 Cha mae leo n I 226 " Carinae 50 Bellat rix 30 Cocoon Nebula 75 (i Cephei 49 Ii And ro me dae 52 Collinder 33 / /0 a Cygni 49 Ii Aqua rii 50 Collinder 69 II / u Eridani /8 Ii Ceti 5 / Collinde r 81 1Il u Gem inoru m 48 Ii Cruc is /8 Cra b Nebula 207, 229 u Leonis 30 Ii Gem inorum 18 Crescent Neb ula 75 ir Op hiuchi 49 Ii Leoni s 49 Cygnus-C arina Arm Il6 " Pera si 47 Ii Libra e 30 " Aquilae /9 Ii Leo Minor is 51 o Aurigae 18 Ii Pegasi 52 8 Cephei /63 u Bootis /8 Ii Virgi nis 50 8 Leoni s 49 o Centauri 6 Ii Canis Majoris 47 Deneb 49 u Cruc is 30 Ii Centaur i 18 Denebola 49 u Erid ani /8 Ii Ori on is /8 Dou ble Cluster I/O u Herculis 36 Betelgeuse /8 Duck Neb ula 74 u Lyrae / 9 Blinking Planet ary /87 Dumbbell Nebula /88 u Orionis 18 Blue Flash Nebula 188
(1 Pisces Austrini 7 Blue Snowball 188 u Scorpii / 9 Bubble Neb ula 76 Eagle Nebula 74 o Ta uri / 8 Electra 48 " Ursae Minor is 163 En if 5/ " Sco rpii 52 Caldwell 4 83 ') Aquilae 163 u Ursae Minoris 50 Caldwell 6 187 E Cygni 51 u Virginis 18 Cald well 11 76 E Eridani 7 ,,' Herculi s 53 Caldwell 13 /09 E Pega si 51 ,,' l.ibrae 50 Caldwell 14 / /0 E Sagitta rii 48 ,, ' Herculis 49 Caldwell IS 187 Eskimo Nebula 139 Alpha Per sei Strea m 1/ 7 Caldwell 19 75 'I Canis Majoris 48 Altair /9 Caldwell 20 75 '} Persei 36 Aludra 48 Caldwell 22 /88 q Tauri 48 Anta res 19 Caldwell 27 75 Arctu ru s 18 Caldwell 31 84 Caldwell 33 206 IS Monocerotis 47 Caldwell 34 206 Flaming Star Nebula 84 b Velo ru m 50 Caldwell 39 /86 Formalhaut 19 Barnard 33 8 / Caldwell 41 II / 40 Erida ni B / 96 Barnard 59, 65- 7 80 Caldwell 46 76 FU Orionis 98 Barnard 68, 225 Caldwell 49 76 Barnard 78 80 Caldwell 54 /07 Barna rd 86 80 Caldwell 55 188 Gacru x 52
23 3 Observer's Guide to Stellar Evolution y' Andromedae 51 Messier 11 109 Perseus Spiral Arm 109 y Cassiopeiae 47 Messier 12 152 Pipe Nebula 80 y Herculis 49 Messier 13 151 PK206-40.1 189 y Geminorum 48 Messier 14 153 Plaskett' s Star 47 y' Velorum 201 Messier 15 153 Pleiades 110 y' Leonis 51 Messier 16 74 Polaris 50 yA Crucis 52 Messier 17 74 Pollux 18 y Orionis 30 Messier 19 152 Praesepe 107 y Pegasi 47 Messier 20 74 Procyon 6 Garnet Star 31 Messier 22 152 Procyon f3 196 Ghost of Iupiter 187 Messier 24 108 Proxima Centauri 6 Gienah 51 Messier 25 109 y,1Aurigae 36 Gliese 229B 95 Messier 27 188 Great Cygnus Loop 206 Messier 29 109 Great Rift 81 Messier 37 111 R Aquarii 138 Great Sagittarius Star Cloud 80 Messier 38 111 R Cassiopeiae 138 Gum 4 74 Messier 41 106 R Corona Borealis 177 GX And 7 Messier 42 96 R Leonis 138 Messier 44 107 R Leporis 31 Messier 45 110 R Sci I 177 Hadar 18 Messier 48 107 Ras Algethi 51 HD 93129A 47 Messier 53 150 Ras Alhague 49 Helix Nebula 158 Messier 54 153 Regulus 30 Herbig Haro 34 227 Messier 57 187 Rigel Kentaurus 19 Hercules Cluster 151 Messier 67 107 Rigel 18 Herschel 16 188 Messier 68 150 Ring Nebula 187 Herschel 53 189 Messier 76 189 Rosette Molecular Complex 76 Herschel's Garnet Star 31 Messier 80 151 Rosette Nebula 76 Hind's Crimson Star 31 Messier 92 153 RR Lyrae 166 Hind's Variable Nebula 77 Messier 97 187 RS Cygni 138 Horsehead Nebula 81 Messier 107 151 RT Aurigae 163 Hubble's Variable Nebula 76 Mira 53 RV Arietis 166 Hyades 111 Mirfak 50 RW Arietis 166 Hyades Stream 116 Mirach 52 RY Draconis 176 f1 Cephei 31 RY Sagittarii 177 f1 Gemino rum 200 IC 405 84 Murzim 47 IC 410 84 S Apodis 177 IC 417 84 S Cephei 177 IC 1396 75 NGC 604 76 Sadal Melik 50 IC 2118 206 NGC 1333 83 Sadal Suud 50 IC 5067-70 75 NGC 1435 84 Sagitai 48 Ink Spot 80 NGC 1554-55 77 Sagittarius- Carina Spiral Arm 108 NGC 1850 223 Saturn Nebula 188 NGC 1973-75- 77 84 Scheat 52 KQ Puppis 36 NGC 2024 76 Scorpius-Centaurus Association 19 Piscium 138 116 Norma Spiral Arm 108 Sharpless 2 - 276 207 La Superba 176 North America Nebula 75 Sharpless 2-264 111 Lacille 7 Northern Coalsack 81 Sirius A 6 Lagoon Nebula 74 N70 228 Sirius B 195 Large Magellanic Cloud 118 v' Bootis 52 Sirius Supercluster 116 Little Dumbbell Nebula 189 v Draconis 48 61 Cygni A 7 Lynds 906 81 v' Draconis 48 Small Sagittarius Star Cloud 108 Lynds Dark Nebula 80 ,; Canis Majoris 51 Spica 18 SU Cassiopeiae 164 Sun 30 Maia 48 Omega Nebula 74 SU Tauri 177 Melotte 20 117 o Ceti 53 Merope 30 0 ' Eradini 196 Messier I 207 Orion Association 116 T Lyr 176 Messier 2 153 Orion Nebula 96 T Monoceroti s 164 Messier 3 150 Owl Nebula 187 T Vulpeculae 164 Messier 4 151 Oyster Nebula 189 Taurus Dark Cloud Complex 110 Messier 5 151 Tempel's Nebula 84 Messier 7 108 e Apodis 53 Messier 8 74 Parrot Nebula 80 oOrionis C 47 Messier 9 152 Pease-I 153 30 Doradus 224 Messier 10 152 Pelican Nebula 75 Triffid Nebula 74 Object Index 33
Trumpler 24 108 V Pav 176 Witch Head Nebula 206 T-Taur i 98 V467 Sagittar i 166 2 Monoc erotis 49 Van Maanen's Star 196 Vega 19 X Cnc 176 Veil Nebula 206 U Aquilae 164 VV Cephei 36 U Cam 177 VV Tauri 98 Y Ophiuchi 164 Ursa Major Moving Strea m 116 UV Ceti 7 Zeta Persei Association 116 W Ori 177 f Scorpii 52 V Aql 176 W Sagittae 164 Zubenelgenubi 50 V Hydrae 176 Wild Duck Cluster J09 Zubeneschamali 30 Subject Index
This list references the main entry of the topic in the book. It may actually be mentioned in other sections.
Absolute magnitude 17 Fluorescence 71 Nebulae 70 Absorption lines 40 Flux 12 Neon burning 197 Apparent brightness 12 Neutrino 127 Apparent magnitude 14 Neutron star 211 Arcsecond 1 Galactic clusters 100 Neutronization 203 Astronomical unit 2 Galactic plane 149 Neutrons 127 Asymptotic Giant Branch 179 Gamma rays 127 Nuclear Burning 197 Giant molecular clouds 101 Nuclear fusion 88 Globular cluster s 146 Nucleon 201 B associations 115 Gravitational equilibrium 88 Balmer Lines 44 Ground state 44 Barnard objects 86 OB associations 115 Bipolar outflow 99 Opacity 125 Black holes 214 Halo Population 6 Oxygen 142 Bok globules 87 Helium 127 Brightn ess Ratio 15 Helium burning 141 Helium capture 197 Parsec 2 Helium Flash 143 Period-Luminosity Carbon burning 197 Helium -shell flash 183 relationship 159 Chandrasekhar Limit 191 Herbig- Haro object s 99 Photometry 13 Circumstellar accretion disc 99 Hertzsprung-Russell Diagram 59 Photosphere 122 CNO cycle 172 HI! regions 72 Planetary Nebulae 183 Colour index 29 Horizontal branch 147 Plasma 123 Colour-magnitude diagram 147 Horizontal branch stars 147 Plerion 213 Convection 92 Hydrog en 127 Population I 160 Convection zone 123 Hydrogen burning 62 Population II 160 Core bounce 203 Hydrogen burning shell 135 Positron 127 Core collaps e 203 Hydrostatic equilibrium 88 Proper motion 6 Core helium-burning 127 Proto -galaxy clouds 147 Core hydrogen burning 130 Proton-proton chain 125 Instability strip 156 Protons 126 Interstellar extinction 83 Proto-Stars 86 Protostellar disk 99 Dark Nebulee 78 Interstellar Medium 70 Degenerac y 191 Invers e square law 12 Pulsars 212 Deuterium 126 Ionisation 71 Distanc e modulus 13 Isotope 126 Doubly-ionized oxygen 72 Radiation zone 123 Dredge-Ups 172 Radiative transfer 92 Random walk 128 Dust grain s 78 Lithium 97 Red-giant branch 170 Luminosity 12 Reflection Nebulae 81 Luminosity Distance formula 13 Roche Lobe 210 Emission line spectrum 41 Lyman alpha 72 Emission lines 40 Emission Nebulze 70 Second dredge-up 173 Energy flux 34 Main Sequence 62 Second red-giant phase 171 Energy level 40 Main -sequence lifetim e 130 Shapley-Sawyer Concentration Evolutionary track 88 Main-s equence star 62 Class 150 Mass loss 97 Shell helium burning 171 Mass-Luminosity Relationship 93 Shell hydrogen burning 135 First dredge-up 172 Molecular clouds 85 Shock waves 204
3 Observer's Guide to Stellar Evolution
Silicon burning 198 Lifetime 130 Supernova 201 Small molecular cloud s 101 Long period variable 162 Type II 209 Solar lumino sity 124 Mass 65 Type I 209 Spectra of Stars 39 Nearest 4 Supernova remn ant. 205 Spectral type 43 Pulsating variable 154 Surface temper ature 26 Stars RR Lyrae variable 162 Ae stars 98 Red giant 136 AGB star 179 Subdwarf 45 T Associations 115 Be stars 98 Subgiant 45 Thermal pulse 173 Biggest 36 Supergiant 199 Third dredge-up 173 Brightest 18 T Tauri 97 Transitions 41 Blue stragglers 107 Type 43 Triple (J( process 142 Brown dwarfs 95 Early 43 Trumpler Classification 105 Carbon 173 Late 43 Turnoff point 149 Cepheids 158 intermediate 43 Type I 160 Wolf-Rayet 201 Vorontsoz-Vellyaminov Classifica Type II 160 White dwarf 190 tion System 186 Clusters 100 Zero-age-main-sequence 130 Open 100 Star Format ion Triggers 117 Galactic 100 Stefan-Boltzmann law 33 Wien Law 26 Globular 146 Stellar association s 114 Constituents 38 Stellar Classification 43 X-ray binary pulsar 212 Dwarf 45 Stellar Parallax 1 X-ray bur sters 212 High-mass 197 Stellar stream 116 Infrared 173 Stellar Wind 173 Giants 62 Sun 122 Zams 130