Astronomy and Astrophysics – Astrophysics
Scientific paper
May 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...160..148h&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 160, no. 1, May 1986, p. 148-156.
Astronomy and Astrophysics
Astrophysics
12
Polytropic Processes, Stellar Models, Stellar Structure, Bessel Functions, Gravitational Fields, Hyperspaces
Scientific paper
The general solution is presented in terms of Bessel functions for the polytrope of index n = 1, and a straightforward method to obtain the Schuster-Emden integral in N-dimensional space. The intimate connection between polytropic sheets, isothermal cylinders and the Schuster-Emden integral in N-dimensional space, (N not less than 3), is found from Emden's equation. A compilation of all exact analytic solutions of the Lane-Emden equation so far found is presented. The behavior of Lane-Emden functions is studied numerically for the imaginary sequence, and an exact seven-digit tabulation for the boundary values of polytropic sheets, cylinders and spheres is provided for the polytropic indexes of principal interest. Finally, an improved determination of the Seidov-Kuzakhmedov (1978) minimum mass occurring for spherical polytropes at polytropic index n of about 4.823 is quoted.
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