Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On deviations from linear wave motion in inhomogeneous stars

Author: P. J. Melvin
Journal: Quart. Appl. Math. 35 (1977), 75-97
DOI: https://doi.org/10.1090/qam/99645
MathSciNet review: QAM99645
Full-text PDF

Abstract | References | Additional Information

Abstract: The hydrodynamic equations for the large-amplitude, adiabatic pulsations of a spherically symmetric, inhomogeneous star are solved by a method of approximation in which the form of the fluid velocity is specified a priori. The assumed velocity is a nonlinear function of the radius and contains two arbitrary functions of time. These two functions are determined by a pair of second-order, quasi-linear, ordinary differential equations, and an analytic, periodic solution to these equations is constructed. This solution corresponds to large amplitude, anharmonic, nonlinear pulsations of a star in which the fluid velocity is a travelling wave. A specific inhomogeneous star is studied to demonstrate the feasibility of numerically solving the pair of differential equations and of constructing the periodic solution.

References [Enhancements On Off] (What's this?)

  • [1] S. Rosseland, The pulsation theory of variable stars, Dover, New York, 1964, pp. 99-102
  • [2] G. C. McVittie, The non-adiabatic contraction of a gas sphere to a complete polytrope, Astr. J. 61 (1956), 451–462. MR 0087552
  • [3] M. J. Disney, D. McNally and A. E. Wright, Mon. Not. R. Astr. Soc. 140, 319 (1968)
  • [4] S. S. Lin, L. Mestel, and F. H. Shu, The gravitational collapse of a uniform spheroid, Astrophys. J. 142 (1965), 1431–1446. MR 0186378, https://doi.org/10.1086/148428
  • [5] M. Fujimoto, Astrophys. J. 152, 523 (1968)
  • [6] J. P. Cox and R. T. Giuli, Principles of stellar structure, Vol. II, Gordon and Breach, New York, 1968, p. 644 ff.
  • [7] Herbert Goldstein, Classical Mechanics, Addison-Wesley Press, Inc., Cambridge, Mass., 1951. MR 0043608
  • [8] J. M. A. Danby, Celestial mechanics, Macmillan, New York, 1963, p. 56 ff.
  • [9] G. W. Hill, On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Math. 8 (1886), no. 1, 1–36. MR 1554690, https://doi.org/10.1007/BF02417081
  • [10] N. W. McLachlan, Theory and application of Mathieu functions, Dover Publications, Inc., New York, 1964. MR 0174808
  • [11] P. J. Melvin, A homogeneous, nonadiabatic model of Delta Cephei, to appear in An international symposium on dynamical systems, ed. L. Cesari and A. R. Bednarek, Academic Press, New York, 1977
  • [12] T. J. Rudd and R. M. Rosenberg, A simple model for Cepheid variability, Astronom. and Astrophys. 6 (1970), 193–205. MR 0270718
  • [13] R. M. Rosenberg, Quart. Appl. Math. 22, 217 (1964)
  • [14] J. P. Cox, Rep. Prog. Phys. 37, 563 (1974)

Additional Information

DOI: https://doi.org/10.1090/qam/99645
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society