2.6: References and Supplemental Reading
- Page ID
- 141602
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. Chandrasekhar S.: An Introduction to the Study of Stellar Structure Dover, New York, 1957 p. 77.
For those who are interested in a further discussion of the integral theorems, some excellent articles are:
Chandrasekhar, S.: An Integral Theorem on the Equilibrium of a Star Ap. J. 87, 1938, pp. 535 - 552;
________________ The Opacity in the Interior of a Star Ap. J. 86, 1937, pp. 78 - 83;
________________ The Pressure in the Interior of a Star pp. 372 - 379;
________________ The Pressure in the Interior of a Star. astr. Soc. 96, 1936, pp. 644 - 647. Ap. J. 85, 1937, Mon. Not. R.
Milne, E.A.: The Pressure in the Interior of a Star Mon. Not. R. astr. Soc. 96, 1936, pp. 179 - 184.
For a complete discussion of polytropes and isothermal spheres see any of these:
Chandrasekhar S.: An Introduction to the Study of Stellar Structure Dover, New York, 1957, chap. 4, p. 84.
Eddington, A.S.: The Internal Constitution of the Stars Dover, New York, 1959, chap. 4, p. 79.
Cox, J. P., and Giuli, R. T.: Principles of Stellar Structure Gordon & Breach, New York, 1968, Chap. 12, p. 257.
An interesting example of the use of polytropes to explore the more complicated phenomenon of rotation can be found in
Limber, D. N., and Roberts, P.H. : On Highly Rotating Polytropes V, Ap. J. 141, 1965, pp.1439-1442.
Geroyannis, V.S., and Valvi, F. N. : Numerical Implementation of a Perturbation Theory Up to Third Order for Rotating Polytropic Stars: Parameters Under Differential Rotation, Ap.J. 312, 1987, pp. 219-226.
A brief but useful account of the physical nature of polytropes may be found in
Clayton, D. D.: Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill, New York, 1968, pp. 155-158.