A method for computing the periods of radial and non-radial modes of oscillations to determine the vibrational stability of differentially rotating polytropic gaseous spheres is presented and incorporated with averaging techniques of Kippenhahn and Thomas. The concepts of Roche-equipotential have also been used for obtaining the distorted structure of different stellar models. Numerical results based on this study are presented to explain the effect of differential rotation on the oscillations and stability of polytropic stars.
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A. K. Lal, A. Pathania, A. Bhalla, C. Mohan, J. Phys. A: Math. Theor. (IOP), 42, 485212, 2009.
C. Mohan, R. M. Saxena, Astrophys. Space Sci., 113, 155, 1985.
C. Mohan, R. M. Saxena, S. R. Agarwal, Astrophys. Space Sci., 178, 89, 1991.
C. Mohan, K. Singh, Astrophys. Space Sci., 77, 493, 1981.
P. Ledoux, Th. Walraven, Handbuch der Physik, Springer-Verlag Berlin, 51, 353–604, 1958.
M. J. Clement, Astrophys. J., 141, 210, 1965.
H. Saio, Astrophys. J., 244, 299, 1981.
S. Chandrasekhar, V. Ferrari, Proc. R. Soc. London A, 432, 247, 1991.
B. Dintrans, M. Rieutord, Astron. Astrophys., 354, 86, 2000.
F. Lignieres, M. Rieutord, D. Reese, Astron. Astrophys., 455, 607, 2006.
D. Reese, F. Lignieres, M. Rieutord, Astron. Astrophys., 455, 621, 2006.
C. C. Lovekin, R. G. Deupree, Astrophys. J., 679, 1499, 2008.
M. F. Woodard, Astrophys. J., 347, 1176, 1989.
W. A. Dziembowski, P. R. Goode, Astrophys. J., 394, 670, 1992.
V. A. Urpin, D. A. Shalybkov, H. C. Spruit, Astron. Astrophys., 306, 455, 1996.
C. Mohan, A. K. Lal, V. P. Singh, Indian J. Pure Appl. Math., 29, 199, 1998.
S. Karino, Y. Eriguchi, Astrophys. J., 592, 1119, 2003.
C. C. Lovekin, R. G. Deupree, M. J. Clement, Astrophys. J., 693, 677, 2009.
S. Saini, A. K. Lal, S. Kumar, Astrofizika, 57, 129, 2014.
R. Kippenhahn, H. C. Thomas, A simple method for the solution of stellar structure equation including rotation and tidal forces. Stellar rotation. ed. A. Slettebak, D. Reidel Publ. Co., Dordrecht, Holland, 1970.
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Published in Astrofizika, Vol. 58, No. 1, pp. 135–144 (February 2015).
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Kumar, S., Lal, A.K. & Saini, S. Vibrational Stability of Differentially Rotating Polytropic Stars. Astrophysics 58, 120–130 (2015). https://doi.org/10.1007/s10511-015-9370-0
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DOI: https://doi.org/10.1007/s10511-015-9370-0