The magnetic versus the gravitational field in a homogeneous, incompressible, pulsating sphere of infinite conductivity.

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view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The magnetic versus the gravitational field in a homogeneous, incompressible, pulsating sphere of infinite conductivity. Sen, Hari K. Abstract In the present paper, we have considered the meridional oscillations of Ferraro's model 1 of a homogeneous, incompressible spherical star of infinite conductivity in a central, monopole magnetic field, taking into account gravitational forces.2 This has led us to a modification of one of the boundary conditions used by Schwarzschild,3 Ferraro and Memory,1 for the purely magnetic oscillations, viz., that the pressure variation at the undisturbed surface of the star will not vanish but will be equal to the amount of matter supported after the oscillatory distortion. This pressure variation is of the same order as the radial amplitude of the oscillation and was correctly obtained by Miss Gjellestad4 in a paper in which she considered the gravitational oscillations of the Schwarzschild model. To estimate the comparative roles of the magnetic and the gravitational fields, we have considered, in particular, two limiting cases, viz., of small and large magnetic fields. For small fields we have used a perturbation method in which the non-dimensional constant 82 = H82/4irpX2a2 appears as a parameter; a is the radial distance from the center of an internal point in the star, H8 is the surface value of the permanent magnetic field, and 2ir/X is the periodic time of the harmonic vibrations of the star. For Babcock's star ~ (HD 125248), 82 ~ I0-~. To the first order in 82 we find that oscillations with the gravitational period only are possible and that it is necessary to postulate the existence of surface currents. For very large magnetic fields (82 oc) we find imaginary values for X, indicating either a building up or damping of the oscillation. Physically, the action of the magnetic field would be to damp rather than build up oscillations, and therefore we conclude that in our idealized case of infinite magnetic field the sphere has no (finite) period of oscillation. Ferraro S series solutions are poorly convergent for intermediate and large values of the variable. We have therefore used asymptotic series expansions of the solutions for intermediate magnetic fields and find again that no oscillations can exist except gravitational ones with surface currents. We conclude that no meridional oscillations are possible for the Ferraro model of a homogeneous, incompressible, spherical star of infinite conductivity in a central, monopole magnetic field, except the gravitational ones with surface currents. Miss Gjellestad4 reached a similar conclusion for Schwarzschild's model. The result seems to be independent of the model and may very well be true for any initial distribution of density and magnetic field. Further, it is hard to believe that non-meridional oscillations would occur in the absence of meridional ones. An investigation will be worth while on whether the negative result obtained in this paper is due to the assumption of infinite conductivity that inhibits any motion across the lines of magnetic force. Treatment of a reasonably simple model of finite conductivity and derivation of the asymptotic behavior of the model when the conductivity increases without limit will provide a most useful check. I.Ferraro and Memory, M. N. 112, 361, 1952. 2.Cf. Cowling, M. N. 112, 527, 1952. 3.Ann. Astroph. 12, 148, 1949. 4.Ann. Astroph. 15, 276, 1952. 5.Ap. J. "4, 1, 1951. National Bureau of Standards, Washington, D. C. Publication: The Astronomical Journal Pub Date: 1953 DOI: 10.1086/106904 Bibcode: 1953AJ.....58Q.227S full text sources ADS |