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Whitworth's (1981) Isothermal Free-Energy Surface
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Taken from the original version of this HyperText Book (H_Book):

November 18, 1994

Much of our present, basic understanding of the structure, stability, and dynamical evolution of individual stars, short-period binary star systems, and the gaseous disks that are associated with numerous types of stellar systems (including galaxies) is derived from an examination of the behavior of a specific set of coupled, partial differential equations. These equations — most of which also are heavily utilized in studies of continuum flows in terrestrial environments — are thought to govern the underlying physics of all macroscopic "fluid" systems in astronomy. Although relatively simple in form, they prove to be very rich in nature.

The literature on this subject is enormous, as serious discussions of the structure and dynamical properties of stars and galaxies date back more than a century. Although a reasonable attempt is made here to review this vast literature and to provide a bridge between discussions that traditionally have focused on stellar structure and those that have focused on galaxy disks, the primary purpose of this work is two-fold:

  • To document in an electronically accessible format many of the key physical principles that underlie modern discussions of the structure, stability, and dynamical evolution of astrophysical fluid systems;
  • To take advantage of the added dimensions offered by the hypertext medium — such as color, text/equation linkages, animation, VRML, and access to online computational algorithms — to effectively illustrate many of these physical principles.

January 24, 2010

In an effort to show the considerable overlap that exists between the discussions presented in this H_Book and the discussions that have appeared previously in the traditional print medium, we have constructed an appendix containing a set of key physical equations and, next to each equation, we have identified where this equation is introduced or discussed in each of six published texts. The texts that we have selected are:

  • [C67] Chandrasekhar, S. 1967 (originally, 1939), An Introduction to the Study of Stellar Structure (New York: Dover)
  • [LL75] Laundau, L. D. & Lifshitz, E. M. 1975 (originally, 1959), Fluid Mechanics (New York: Pergamon Press)
  • [ST83] Shapiro, S. L. & Teukolsky, S. A. 1983, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (New York: John Wiley & Sons); republished in 2004 by WILEY-VCH Verlag GmbH & Co. KGaA
  • [H87] Huang, K. 1987 (originally 1963), Statistical Mechanics (New York: John Wiley & Sons)
  • [BT87] Binney, J. & Tremaine, S. 1987, Galactic Dynamics (Princeton, NJ: Princeton University Press)
  • [KW94] Kippenhahn, R. & Weigert, A. 1994, Stellar Structure and Evolution (New York: Springer-Verlag)
  • [P00] Padmanabhan, T. 2000, Theoretical Astrophysics. Volume I: Astrophysical Processes (Cambridge: Cambridge University Press); and Padmanabhan, T. 2001, Theoretical Astrophysics. Volume II: Stars and Stellar Systems (Cambridge: Cambridge University Press)

The key equations that we have chosen to highlight are drawn from a wide assortment of sub-fields of physics that feed into and, indeed, are essential to our modern understanding of astrophysical systems, including: classical mechanics, fluid dynamics, thermodynamics & statistical mechanics, quantum mechanics, radiation transport, and relativity. Each time one of these equations appears in our discussion, it will be marked as a key equation so that, from the information contained in our key equations appendix, the reader can be guided to parallel discussions of related concepts as they have been presented in the above-identified, published texts.

It is important to note as well that virtually all of these key equations — and discussions of the physical concepts that underpin them — can also now be found in the pages of Wikipedia, or other online references. Where appropriate, links to these online discussions are also provided in the text of this H_Book so that readers can take advantage of this growing information resource.

Whitworth's (1981) Isothermal Free-Energy Surface

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