Neutron stars for undergraduates

American Journal of Physics

Volumn 72, Issue 7, 2004, Pages 892-905

  Silbar, Richard R ^a   Reddy, Sanjay ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042770793     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1703544     Document Type: Article

References (33)

1. A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, and R. A. Collins, "Observation of a rapidly pulsating radio source," Nature (London) 217, 709-713 (1968).
2. It is widely believed that neutron stars were proposed by Lev Landau in 1932, very soon after the neutron was discovered (although we are not aware of any documented evidence for this belief). In 1934 Fritz Zwicky and Walter Baade speculated that they might be formed in Type II supernova explosions, which is now generally accepted as true.
3. An online catalog of pulsars can be found at 〈http:/pulsar. princeton.edu〉
4. 4 An intermediate-level online tutorial on the physics of pulsars can be found at 〈http://www.jb.man.ac.uk/research/pulsar〉. This tutorial follows the book by Andrew G. Lyne and Francis Graham-Smith, Pulsar Astronomy, 2nd ed. (Cambridge University Press, Cambridge, MA, 1998).
5. R. C. Tolman, ''Static solutions of Einstein's field equations for spheres of fluid," Phys. Rev. 55, 364-373 (1939): J. R. Oppenheimer and G. M. Volkov, "On massive neutron cores," ibid. 55, 374-381 (1939).
6. R. C. Tolman, ''Static solutions of Einstein's field equations for spheres of fluid," Phys. Rev. 55, 364-373 (1939): J. R. Oppenheimer and G. M. Volkov, "On massive neutron cores," ibid. 55, 374-381 (1939).
7. Steven Weinberg, Gravitation and Cosmology (Wiley, New York. 1972), Chap. 11.
8. M. Prakash, "Equation of state," in The Nuclear Equation of State, edited by A. Ausari and L. Satpathy (World Scientific, Singapore, 1996).
9. See, for example, M. A. Preston, Physics of the Nucleus (Addison-Wesley, Reading, MA, 1962), Sec. 9-3. A more recent, fuller discussion of nuclear compressibility is given by J. P. Blaizot, "Nuclear compressibilities, " Phys. Rep. 64, 171 (1980).
10. See, for example, M. A. Preston, Physics of the Nucleus (Addison-Wesley, Reading, MA, 1962), Sec. 9-3. A more recent, fuller discussion of nuclear compressibility is given by J. P. Blaizot, "Nuclear compressibilities, " Phys. Rep. 64, 171 (1980).
11. If you are a mentor for such a student, you may want to see some of the Mathematica and MathCad files we developed. Send email to the first author convincing him that you are such a mentor, and he will direct you to a web site from which they can be downloaded. The idea behind this misdirection is that students will learn more by doing the programming themselves.
12. R. Balian and J.-P. Blaizot, "Stars and statistical physics: A teaching experience," Am. J. Phys. 67, 1189-1206 (1999).
13. S. L. Shapiro and S. A. Teukolsky, Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects (Wiley-Interscience, New York, 1983).
14. We apologize to readers who are enthusiasts about SI units, but the first author was raised on CGS units. Also, much of today's astrophysical literature still uses CGS units. Besides, we strongly believe that by the time physics students are at this level, they should be comfortable in switching from one system of units to another.
15. A discussion of how to solve these equations (using conventional programming languages) is given in S. Koonin, Computational Physics (Benjamin-Cummings, New York, 1986).
16. For more details on white dwarfs, NASA provides a useful web page at 〈http://imagine.gsfc.nasa.gov/docs/science/knowl1/dwarfs.html〉
17. This maximum mass of 1.4M⊙ is usually referred to as the Chandrasekhar limit. See S. Chandrasekhar's 1983 Nobel Prize lecture, 〈http://www.nobel.se/physics/laureates/1983/〉. For more detail see his treatise, An Introduction to the Study of Stellar Structure (Dover, New York, 1939).
18. See, for example, C. Kittel and H. Kroemer, Thermal Physics (W. H. Freeman, San Francisco, CA, 1980). This result is from their modern physics course that students should review if they do not remember it.
19. Mathematica is product of Wolfram Research, 〈http://www.wolfram. com〉, and its use is described by S. Wolfram, in The Mathematica Book, 4th ed. (Cambridge University Press, Cambridge, 1999). Whenever we use the phrase "using Mathematica," we really mean using whatever package one has available or is familiar with, be it Maple, MathCad, or whatever. We did almost all of the numerical/symbolic work that we describe in this paper in Mathematica, but some of its notebooks were duplicated in MathCad.
20. Enough of these explicit flags! Most of the equations from here on present challenges for the student to work through.
21. For the Newtonian case, a polytropic equation of state also allows for a somewhat more analytic solution in terms of Lane-Emden functions. See Ref. 6, Sec. 11.3, or C. Flynn, Lectures on Stellar Physics, 〈http://www.astro.utu. fi/~cflynn/Stars/〉, especially Lectures 4 and 5.
22. 0, the astute student will not be lulled into thinking that this factor has anything to do with a Coulomb potential or the dielectric constant of the vacuum.
23. Note that the right-hand side of Eq. (23) is negative (for positive p̄), so p̄(r) must fall monotonically from p̄(0).
24. F. However, this is where the pure neutron approximation itself is least accurate. The surface of a neutron star is likely made of elements like iron. A fictional account of what life might be like on such a surface can be found in Robert Forward, Dragon's Egg, first published in 1981 by Del Rey Publishing and republished in 2000.
25. See Ref. 6, Sec. 11.2.
26. Because it is almost noninteraeting with nuclear matter, a neutrino tends to escape from the neutron star. This escape is the major cooling mechanism as the neutron star is being formed in a supernova explosion. George Gamow named this mechanism the URCA process, the name of a Brazilian casino where people lost a lot of money.
27. 0 so as to rewrite this equation in CGS units?
28. See, for example, J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (Wiley, New York, 1952), Chap. 6, Sec. 2.
29. -1.
30. People interested in RHIC physics might want to, however. (RHIC stands for Relativistic Heavy Ion Collider, an accelerator at the Brookhaven National Laboratory which is studying reactions like Au nuclei striking each other at center of mass energies around 200 GeV/nucleon.)
31. See, for example, Hugh Young, University Physics, 8th ed. (Addison-Wesley, Reading MA, 1992), Sec. 19-5.
32. See, for example, P. J. E. Peebles and Bharat Ratra, "The cosmological constant and dark energy," Rev. Mod. Phys. 75, 559-606 (2003).
33. W. Y. Pauchy Hwang (private communication).