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Manuscript Title: Calculation of the equilibrium structure and oscillations of polytropic stars pervaded by toroidal magnetic fields.
Authors: M.J. Miketinac
Program title: TOROID
Catalogue identifier: AAAE_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 7(1974)410
Programming language: Fortran.
Computer: UNIVAC 1106.
Operating system: EXEC 8.
Program overlaid: yes
RAM: 43K words
Word size: 36
Keywords: Astrophysics, Polytropic star, Equilibrium Configuration, Toroidal magnetic field, Frequency of oscillation.
Classification: 1.7.

Nature of problem:
This program solves the structure equations determining the equilibrium configurations of a self-gravitating, axisymmetric, perfectly conducting polytrope with the polytropic index n(>=1)in the presence of a toroidal magnetic field. Parameters, such as mass, volume, radius etc. , characterizing an equilibrium configuration are calculated. In addition, frequencies of the characteristic modes of oscillation are determined using Chandrasekhar's virial tensor method and assuming that the ratio of the specific heats, gamma, is equal to 5/3.

Solution method:
The structure problem is mathematically a boundary-value problem for a second-order, non-linear, two-dimensional partial differential equation. This problem is solved numerically by following Stoeckly's method improved by Miketinac and Barton, who used it to calculate post- newtonian corrections to the equilibrium configurations of rotating polytropes.

The mathematical method adopted in developing the program works only for poloytropes whose polytropic index is greater than or equal to one. However, in addition to calculating equilibrium configurations of polytropes pervaded by toroidal magnetic fields, the program, with minor modifications, could also be used for calculating equilibrium configurations of (uniformly or non-uniformly) rotating polytropes or rotating polytropes pervaded by toroidal magnetic fields or (rotating) polytropes containing toroidal magnetic fields of the type other than the one considered. The ratio of the specific heats, gamma, can be any number.

Running time:
The time required for the test run is 2 min and 54 s on a UNIVAC 1106 computer, of which 5.16 s is taken in compiling.