Skip to main content

The Final Stages of Massive Star Evolution and Their Supernovae

  • Chapter
  • First Online:
Eta Carinae and the Supernova Impostors

Part of the book series: Astrophysics and Space Science Library ((ASSL,volume 384))

Abstract

In this chapter I discuss the final stages in the evolution of massive stars – stars that are massive enough to burn nuclear fuel all the way to iron group elements in their core. The core eventually collapses to form a neutron star or a black hole when electron captures and photo-disintegration reduce the pressure support to an extent that it no longer can hold up against gravity. The late burning stages of massive stars are a rich subject by themselves, and in them many of the heavy elements in the universe are first generated. The late evolution of massive stars strongly depends on their mass, and hence can be significantly effected by mass loss due to stellar winds and episodic mass loss events – a critical ingredient that we do not know as well as we would like. If the star loses all the hydrogen envelope, a Type I supernova results, if it does not, a Type II supernova is observed. Whether the star makes neutron star or a black hole, or a neutron star at first and a black hole later, and how fast they spin largely affects the energetics and asymmetry of the observed supernova explosion. Beyond photon-based astronomy, other than the sun, a supernova (SN 1987) has been the only object in the sky we ever observed in neutrinos, and supernovae may also be the first thing we will ever see in gravitational wave detectors like LIGO. I conclude this chapter reviewing the deaths of the most massive stars and of Population III stars.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E.B. Abdikamalov, C.D. Ott, L. Rezzolla, L. Dessart, H. Dimmelmeier, A. Marek, H.-T. Janka, Axisymmetric general relativistic simulations of the accretion-induced collapse of white dwarfs. Phys. Rev. D 81, 044012 (2010)

    Article  ADS  Google Scholar 

  2. T. Abel, G.L. Bryan, M.L. Norman, The formation of the first star in the universe. Science 295, 93–98 (2002)

    Article  ADS  Google Scholar 

  3. D. Arnett, D. Arnett, D. Arnett, Supernovae and Nucleosynthesis. An Investigation of the History of Matter, from the Big Bang to the Present. Princeton Series in Astrophysics (Princeton University Press, Princeton, 1996)

    Google Scholar 

  4. W.D. Arnett, J.N. Bahcall, R.P. Kirshner, S.E. Woosley, Supernova 1987A. ARA&A. 27, 629–700 (1989)

    Article  ADS  Google Scholar 

  5. I. Baraffe, A. Heger, S.E. Woosley, On the stability of very massive primordial stars. ApJ. 550, 890–896 (2001)

    Article  ADS  Google Scholar 

  6. E. Böhm-Vitense, Über die Wasserstoffkonvektionszone in Sternen verschiedener Effektivtemperaturen und Leuchtkräfte. Mit 5 Textabbildungen. ’Zeitsch. für Astron. 46, 108 (1958)

    Google Scholar 

  7. J.R. Bond, W.D. Arnett, B.J. Carr, The evolution and fate of very massive objects. ApJ. 280, 825–847 (1984)

    Article  ADS  Google Scholar 

  8. J. Braithwaite, H.C. Spruit, A fossil origin for the magnetic field in A stars and white dwarfs. Nature 431, 819–821 (2004)

    Article  ADS  Google Scholar 

  9. V. Bromm, P.S. Coppi, R.B. Larson, Forming the first stars in the universe: the fragmentation of primordial gas. ApJL. 527, L5–L8 (1999)

    Article  ADS  Google Scholar 

  10. V. Bromm, P.S. Coppi, R.B. Larson, The formation of the first stars. I. The primordial star-forming cloud. ApJ. 564, 23–51 (2002)

    Google Scholar 

  11. V. Bromm, A. Ferrara, P.S. Coppi, R.B. Larson, The fragmentation of pre-enriched primordial objects. MNRAS. 328, 969–976 (2001)

    Article  ADS  Google Scholar 

  12. V. Bromm, R.B. Larson, The first stars. ARA&A. 42, 79–118 (2004)

    Article  Google Scholar 

  13. E.M. Burbidge, G.R. Burbidge, W.A. Fowler, F. Hoyle, Synthesis of the elements in stars. Rev. Mod. Phys. 29, 547–650 (1957)

    Article  ADS  Google Scholar 

  14. R.G. Carlberg, An estimate of the mass of zero metal stars. MNRAS. 197, 1021–1029 (1981)

    ADS  Google Scholar 

  15. R. Cayrel, E. Depagne, M. Spite, V. Hill, F. Spite, P. François, B. Plez, T. Beers, F. Primas, J. Andersen, B. Barbuy, P. Bonifacio, P. Molaro, B. Nordström, First stars V – Abundance patterns from C to Zn and supernova yields in the early galaxy. A&A. 416, 1117–1138 (2004)

    Article  ADS  Google Scholar 

  16. N. Christlieb, B. Gustafsson, A.J. Korn, P.S. Barklem, T.C. Beers, M.S. Bessell, T. Karlsson, M. Mizuno-Wiedner, HE 0107-5240, a chemically ancient star. I. A detailed abundance analysis. ApJ. 603, 708–728 (2004)

    Google Scholar 

  17. D.D. Clayton, Principles of Stellar Evolution and Nucleosynthesis (McGraw-Hill, New York, 1968)

    Google Scholar 

  18. P.B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, J.W.T. Hessels, A twosolar-mass neutron star measured using Shapiro delay. Nature 467, 1081–1083 (2010)

    Article  ADS  Google Scholar 

  19. L. Dessart, A. Burrows, C.D. Ott, E. Livne, S.-C. Yoon, N. Langer, Multidimensional simulations of the accretion-induced collapse of white dwarfs to neutron stars. ApJ. 644, 1063–1084 (2006)

    Article  ADS  Google Scholar 

  20. M.F. El Eid, K.J. Fricke, W.W. Ober, Evolution of massive pregalactic stars. I – Hydrogen and helium burning. II – Nucleosynthesis in pair creation supernovae and pregalactic enrichment. A&A. 119, 54–68 (1983)

    Google Scholar 

  21. M.F. El Eid, L.-S. The, B.S. Meyer, Massive stars: input physics and stellar models. Space Sci. Rev. 147, 1–29 (2009)

    Article  ADS  Google Scholar 

  22. J.J. Eldridge, C.A. Tout, The progenitors of core-collapse supernovae. MNRAS. 353, 87–97 (2004)

    Google Scholar 

  23. C. Filloux, F. Durier, J.A.F. Pacheco, J. Silk, Evolution of supermassive black holes from cosmological simulations. Int. J. Mod. Phys. D 19, 1233–1240 (2010)

    Article  ADS  MATH  Google Scholar 

  24. A. Frebel, W. Aoki, N. Christlieb, H. Ando, M. Asplund, P.S. Barklem, T.C. Beers, K. Eriksson, C. Fechner, M.Y. Fujimoto, S. Honda, T. Kajino, T. Minezaki, K. Nomoto, J.E. Norris, S.G. Ryan, M. Takada-Hidai, S. Tsangarides, Y. Yoshii, Nucleosynthetic signatures of the first stars. Nature 434, 871–873 (2005)

    Article  ADS  Google Scholar 

  25. K. Freese, C. Ilie, D. Spolyar, M. Valluri, P. Bodenheimer, Supermassive dark stars: Detectable in JWST. ApJ. 716, 1397–1407 (2010)

    Article  ADS  Google Scholar 

  26. C.L. Fryer, Mass limits for black hole formation. ApJ. 522, 413–418 (1999)

    Article  ADS  Google Scholar 

  27. C.L. Fryer, S.E. Woosley, A. Heger, Pair-instability supernovae, gravity waves, and gamma-ray transients. ApJ. 550, 372–382 (2001)

    Article  ADS  Google Scholar 

  28. G.M. Fuller, S.E. Woosley, T.A. Weaver, The evolution of radiation-dominated stars. I – Nonrotating supermassive stars. ApJ. 307, 675–686 (1986)

    Google Scholar 

  29. W. Glatzel, M. Kiriakidis, The stability of massive main-sequence stars. MNRAS. 262, 85–92 (1993)

    ADS  Google Scholar 

  30. S.C.O. Glover, P.C. Clark, R.S. Klessen, V. Bromm, Fragmentation in turbulent primordial gas. ArXiv e-prints, arXiv:1007.2763 (2010)

    Google Scholar 

  31. A. Heger, N. Langer, Presupernova evolution of rotating massive stars. II. Evolution of the surface properties. ApJ. 544, 1016–1035 (2000)

    Google Scholar 

  32. A. Heger, S.E. Woosley, The nucleosynthetic signature of population III. ApJ. 567, 532–543 (2002)

    Article  ADS  Google Scholar 

  33. A. Heger, S.E. Woosley, Nucleosynthesis and evolution of massive metal-free stars. ArXiv e-prints, arXiv:0803.3161 (2008); ApJ. 724, 341–373 (2010)

    Google Scholar 

  34. A. Heger, N. Langer, S.E. Woosley, Presupernova evolution of rotating massive stars. I. Numerical method and evolution of the internal stellar structure. ApJ. 528, 368–396 (2000)

    Google Scholar 

  35. A. Heger, C.L. Fryer, S.E. Woosley, N. Langer, D.H. Hartmann, How massive single stars end their life. ApJ. 591, 288–300 (2003)

    Article  ADS  Google Scholar 

  36. A. Heger, S.E. Woosley, H.C. Spruit, Presupernova evolution of differentially rotating massive stars including magnetic fields. ApJ. 626, 350–363 (2005)

    Article  ADS  Google Scholar 

  37. R. Hirschi, G. Meynet, A. Maeder, Stellar evolution with rotation. XII. Pre-supernova models. A&A. 425, 649–670 (2004)

    MATH  Google Scholar 

  38. R. Hirschi, G. Meynet, A. Maeder, Stellar evolution with rotation. XIII. Predicted GRB rates at various Z. A&A. 443, 581–591 (2005)

    Google Scholar 

  39. L. Hüdepohl, B. Müller, H.-T. Janka, A. Marek, G.G. Raffelt, Neutrino signal of electron-capture supernovae from core collapse to cooling. PRL. 104, 251101 (2010)

    Article  ADS  Google Scholar 

  40. R.M. Humphreys, K. Davidson, N. Smith, Eta Carinae’s second eruption and the light curves of the Eta Carinae variables. PASP. 111 (1999)

    Google Scholar 

  41. F. Iocco, A. Bressan, E. Ripamonti, R. Schneider, A. Ferrara, P. Marigo, Dark matter annihilation effects on the first stars. MNRAS. 390, 1655–1669 (2008)

    ADS  Google Scholar 

  42. H.-T. Janka, Conditions for shock revival by neutrino heating in core-collapse supernovae. A&A. 368, 527–560 (2001)

    Article  ADS  Google Scholar 

  43. H.-T. Janka, K. Langanke, A. Marek, G. Martínez-Pinedo, B. Müller, Theory of core-collapse supernovae. PhR. 442, 38–74 (2007)

    Google Scholar 

  44. C.C. Joggerst, S.E. Woosley, A. Heger, Mixing in zero- and solar-metallicity supernovae. ApJ. 693, 1780–1802 (2009)

    Article  ADS  Google Scholar 

  45. G.C. Jordan IV, R.T. Fisher, D.M. Townsley, A.C. Calder, C. Graziani, S. Asida, D.Q. Lamb, J.W. Truran, Three-dimensional simulations of the deflagration phase of the gravitationally confined detonation model of Type Ia supernovae. ApJ. 681, 1448–1457 (2008)

    Article  ADS  Google Scholar 

  46. D. Kasen, L. Bildsten, Supernova light curves powered by young magnetars. ApJ. 717, 245–249 (2010)

    Article  ADS  Google Scholar 

  47. M. Kromer, S.A. Sim, M. Fink, F.K. Röpke, I.R. Seitenzahl, W. Hillebrandt, Double-detonation sub-chandrasekhar supernovae: Synthetic observables for minimum helium shell mass models. ApJ. 719 1067–1082 (2010)

    Article  ADS  Google Scholar 

  48. D.K. Lai, M. Bolte, J.A. Johnson, S. Lucatello, A. Heger, S.E. Woosley, Detailed abundances for 28 metal-poor stars: Stellar relics in the milkyway. ApJ. 681, 1524–1556 (2008)

    Article  ADS  Google Scholar 

  49. N. Langer, M.F. El Eid, K.J. Fricke, Evolution of massive stars with semiconvective diffusion. A&A. 145, 179–191 (1985)

    ADS  Google Scholar 

  50. N. Langer, K.J. Fricke, D. Sugimoto, Semiconvective diffusion and energy transport. A&A. 126, 207 (1983)

    Google Scholar 

  51. R.B. Larson, Early star formation and the evolution of the stellar initial mass function in galaxies. MNRAS 301, 569–581 (1998)

    Article  ADS  Google Scholar 

  52. A.I. MacFadyen, S.E. Woosley, Collapsars: Gamma-ray bursts and explosions in “failed supernovae”. ApJ. 524, 262–289 (1999)

    Article  ADS  Google Scholar 

  53. A. Maeder, G. Meynet, The evolution of rotating stars. ARA&A. 38, 143–190 (2000)

    Google Scholar 

  54. A. Maeder, G. Meynet, Stellar evolution with rotation and magnetic fields. II. General equations for the transport by Tayler-Spruit dynamo. A&A. 422, 225–237 (2004)

    Google Scholar 

  55. C. A. Meakin, T. Sukhbold, D. Arnett, Presupernova structure of massive stars. ArXive-prints, arXiv:1006.0513 (2010)

    Google Scholar 

  56. G. Meynet, A. Maeder, Stellar evolution with rotation. I. The computational method and the inhibiting effect of the μ-gradient. A&A. 321, 465–476 (1997)

    Google Scholar 

  57. F. Nakamura, M. Umemura, On the mass of population III stars. ApJ. 515, 239–248 (1999)

    Article  ADS  Google Scholar 

  58. K. Nomoto, Evolution of 8–10 solar mass stars toward electron capture supernovae. II – Collapse of an O + NE + MG core. ApJ. 322, 206–214 (1987)

    Google Scholar 

  59. K. Nomoto, M. Mashimoto, Presupernova evolution of massive stars. PhR. 163, 13–36 (1988)

    Google Scholar 

  60. W.W. Ober, M.F. El Eid, K.J. Fricke, Evolution of massive pregalactic stars – Part two – Nucleosynthesis in pair creation supernovae and pregalactic enrichment. A&A. 119, 61 (1983)

    ADS  Google Scholar 

  61. K. Omukai, R. Nishi, Formation of primordial protostars. ApJ. 508, 141–150 (1998)

    Google Scholar 

  62. B. W. O’Shea, C.F. McKee, A. Heger, T. Abel, First Stars III Conference Summary, in First Stars III eds. by B.W. O’Shea, A. Heger. AIP Conf. Series. vol. 990, (AIP, Melville, 2008), p. D13

    Google Scholar 

  63. S.P. Owocki, K.G. Gayley, N.J. Shaviv, A porosity-length formalism for photon-Tiring-limited mass loss from stars above the eddington limit. ApJ. 616, 525–541 (2004)

    Article  ADS  Google Scholar 

  64. P. Podsiadlowski, P.C. Joss, J.J.L. Hsu, Presupernova evolution in massive interacting binaries. ApJ. 391, 246–264 (1992)

    Article  ADS  Google Scholar 

  65. A.J.T. Poelarends, F. Herwig, N. Langer, A. Heger, The supernova channel of super-AGB stars. ApJ. 675, 614–625 (2008)

    Article  ADS  Google Scholar 

  66. L. Prandtl, Z. Angew. Math. Mech. 5, 136 (1925)

    MATH  Google Scholar 

  67. M.L. Pumo, M. Turatto, M.T. Botticella, A. Pastorello, S. Valenti, L. Zampieri, S. Benetti, E. Cappellaro, F. Patat, EC-SNe from super-asymptotic giant branch progenitors: theoretical models versus observations. ApJL. 705, L138–L142 (2009)

    Article  ADS  Google Scholar 

  68. M.J. Rees, Black hole models for active galactic nuclei. ARA&A. 22, 471–506 (1984)

    Article  ADS  Google Scholar 

  69. F.K. Röpke, W. Hillebrandt, W. Schmidt, J.C. Niemeyer, S.I. Blinnikov, P.A. Mazzali, A three-dimensional deflagration model for type Ia supernovae compared with observations. ApJ. 668, 1132–1139 (2007)

    Article  ADS  Google Scholar 

  70. A.J. Ruiter, K. Belczynski, S.A. Sim, W. Hillebrandt, M. Fink, M. Kromer, Type Ia supernovae and accretion induced collapse. ArXiv e-prints, arXiv:1009.3661 (2010)

    Google Scholar 

  71. S. Salviander, G.A. Shields, K. Gebhardt, E.W. Bonning, The black hole mass-galaxy bulge relationship for QSOs in the Sloan digital sky survey data release 3. ApJ. 662, 131–144 (2007)

    Article  ADS  Google Scholar 

  72. E. Scannapieco, P. Madau, S. Woosley, A. Heger, A. Ferrara, The detectability of pair-production supernovae at z  ≲ 6. ApJ. 633, 1031–1041 (2005)

    Article  ADS  Google Scholar 

  73. M. Schwarzschild, R. Härm, Evolution of very massive stars. ApJ. 128, 348 (1958)

    ADS  Google Scholar 

  74. M. Schwarzschild, R. Härm, On the maximum mass of stable stars. ApJ. 129, 637 (1959)

    Article  ADS  Google Scholar 

  75. J. Silk, The first stars. MNRAS. 205, 705–718 (1983)

    Google Scholar 

  76. S.J. Smartt, Progenitors of core-collapse supernovae. ARA&A. 47, 63–106 (2009)

    Google Scholar 

  77. H.C. Spruit, The rate of mixing in semiconvective zones. A&A. 253, 131–138 (1992)

    ADS  MATH  Google Scholar 

  78. H.C. Spruit, Differential rotation and magnetic fields in stellar interiors. A&A. 349, 189–202 (1999)

    ADS  Google Scholar 

  79. H.C. Spruit, Dynamo action by differential rotation in a stably stratified stellar interior. A&A. 381, 923–932 (2002)

    Article  ADS  Google Scholar 

  80. J.W. Truran Jr., A. Heger, Origin of the elements, in Meteorites, Comets and Planets: Treatise on Geochemistry, ed. by A.M. Davis, vol. 1 (Elsevier B. V, Amsterdam, 2005), p. 1

    Google Scholar 

  81. C. Tur, A. Heger, S.M. Austin, On the sensitivity of massive star nucleosynthesis and evolution to solar abundances and to uncertainties in helium-burning reaction rates. ApJ. 671, 821–827 (2007)

    Article  ADS  Google Scholar 

  82. M.J. Turk, T. Abel, B. O’Shea, The formation of population III binaries from cosmological initial conditions. Science 325, 601 (2009)

    Article  ADS  Google Scholar 

  83. A.J. van Marle, S.P. Owocki, N.J. Shaviv, Numerical simulations of continuum-driven winds of super-Eddington stars. MNRAS. 389, 1353–1359 (2008)

    Article  ADS  Google Scholar 

  84. H. Vogt, Die Beziehung zwischen den Massen und den absoluten Leuchtkräften der Sterne. Astron. Nachr. 226, 301 (1926)

    Article  ADS  MATH  Google Scholar 

  85. S. Wanajo, K. Nomoto, H.-T. Janka, F.S. Kitaura, B. Müller, Nucleosynthesis in electron capture supernovae of asymptotic giant branch stars. ApJ.695, 208–220 (2009)

    Google Scholar 

  86. T.A. Weaver, G.B. Zimmerman, S.E. Woosley, Presupernova evolution of massive stars. ApJ. 225, 1021–1029 (1978)

    Google Scholar 

  87. S.E. Woosley, Gamma-ray bursts from stellar mass accretion disks around black holes. ApJ. 405, 273–277 (1993)

    Article  ADS  Google Scholar 

  88. S.E. Woosley, Bright supernovae from magnetar birth. ApJL. 719, L204–L207 (2010)

    Google Scholar 

  89. S.E. Woosley, A. Heger, The progenitor stars of gamma-ray bursts. ApJ. 637, 914–921 (2006)

    Article  ADS  Google Scholar 

  90. S.E. Woosley, A. Heger, Nucleosynthesis and remnants in massive stars of solar metallicity. PhR. 442, 269–283 (2007)

    ADS  Google Scholar 

  91. S.E. Woosley, T.A. Weaver, The physics of supernova explosions. ARA&A. 24, 205–253 (1986)

    Article  Google Scholar 

  92. S.E. Woosley, T.A. Weaver, Sub-Chandrasekhar mass models for type IA supernovae. ApJ. 423, 371–379 (1994)

    Article  ADS  Google Scholar 

  93. S.E. Woosley, T.A. Weaver, The evolution and explosion of massive stars. II. Explosive hydrodynamics and nucleosynthesis. ApJS. 101, 181 (1995)

    Google Scholar 

  94. S.E. Woosley, R.G. Eastman, B.P. Schmidt, Gamma-ray bursts and type IC supernova SN 1998BW. ApJ. 516, 788–796 (1999)

    Article  ADS  Google Scholar 

  95. S.E. Woosley, A. Heger, T.A. Weaver, The evolution and explosion of massive stars. Rev. Mod. Phys. 74, 1015–1071 (2002)

    Article  ADS  Google Scholar 

  96. S.E. Woosley, S. Blinnikov, A. Heger, Pulsational pair instability as an explanation for the most luminous supernovae. Nature 450, 390–392 (2007)

    Article  ADS  Google Scholar 

  97. S.-C. Yoon, M. Cantiello, Evolution of massive stars with pulsation-driven superwinds during the red supergiant phase. ApJL. 717, L62–L65 (2010)

    Article  ADS  Google Scholar 

  98. S.-C. Yoon, N. Langer, Evolution of rapidly rotating metal-poor massive stars towards gamma-ray bursts. A&A. 443, 643–648 (2005)

    Article  ADS  Google Scholar 

  99. W. Zhang, S.E. Woosley, A. Heger, The propagation and eruption of relativistic jets from the stellar progenitors of gamma-ray bursts. ApJ. 608, 365–377 (2004)

    Article  ADS  Google Scholar 

  100. W. Zhang, S.E. Woosley, A. Heger, Fallback and black hole production in massive stars. ApJ. 679, 639–654 (2008)

    Article  ADS  Google Scholar 

  101. M. Zingale, A.S. Almgren, J.B. Bell, A. Nonaka, S.E. Woosley, Low mach number modeling of type IA supernovae. IV. White Dwarf convection. ApJ. 704, 196–210 (2009)

    Google Scholar 

Download references

Acknowledgements

I want to thank the editor, Roberta Humphreys, for her input, feedback, and patience with the completion of this article. Much of the scientific research on which this chapter is based has been done in collaboration with Stan Woosley, who I would like to thank for his continued support. Heger has been supported by the DOE Program for Scientific Discovery through Advanced Computing (SciDAC; DE-SC0002300/FC02-09ER41618), and by the US Department of Energy under grant DE-FG02-87ER40328. The early work on this chapter was carried out in part under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory and supported by Contract No. DE-AC52-06NA25396.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Heger .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Heger, A. (2012). The Final Stages of Massive Star Evolution and Their Supernovae. In: Davidson, K., Humphreys, R. (eds) Eta Carinae and the Supernova Impostors. Astrophysics and Space Science Library, vol 384. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-2275-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-2275-4_13

  • Published:

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4614-2274-7

  • Online ISBN: 978-1-4614-2275-4

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics