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Revista mexicana de física
Print version ISSN 0035-001X
Rev. mex. fis. vol.53 suppl.2 México Feb. 2007
Aspects of cosmic magnetism
T. Zannias
Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Apartado Postal 282, 58040 Morelia, Mich, MÉXICO email: zannias@ginette.ifm.umich.mx
Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005
Abstract
In this paper, after a brief review of the current observational evidences regarding the phenomenon of cosmic magnetism, we discuss the problems associated with the generation of electromagnetic fields by conducting fluid flows. In particular, we examine the electromagnetic field generated by a conducting fluid flow in the socalled magnetohydrodynamical (MHD) regime in the nonrelativistic and general relativistic limit. Our efforts are directed at the status of Cowlings theorem for the two limits. We show that electromagnetic fields generated by conducting fluids in an arbitrary spacetime (M, g) are influenced by the conducting and kinematical variables defining the fluid flow, but also influenced by the curvature and topology of the underlying spacetime. For the particular case of spatially homogeneous and isotropic backgrounds or stationaryaxially symmetric circular spacetimes, we show that the dynamical equations describing electromagnetics fields generated by particular conducting flows reduce to a form structurally similar to the nonrelativistic limit. Despite this siplification, the issue whether axially symmetric conducting fluid flows can maintain an axisymmetric magnetic field against Ohmic dissipation is still open.
Keywords: Magnetohydrodynamics; compact objects; gravitation.
Resumen
En este artículo damos una breve revisión de las evidencias observacionales relacionadas con el fenómeno del magnetismo cósmico. Se discute el problema asociado con la generación de un campo magnético por el flujo de un fluido conductor en el regimen magnetohidrodinámico en el caso no relativista y en relatividad general. El esfuerzo se enfoca en establecer la validez del teorema de Cowling para los dos limites. Los campos electromagnéticos generados por fluidos conductores en un espacio tiempo arbitrario (M, g) son influenciados por las variables de conducción y variables cinemáticas que definen el flujo del fluido, asi como por la curvatura y topología de del espacio tiempo. Para el caso particular de un fondo homogeneo e isotrópico o espacios tiempo estacionarios con simetria axial y circular, se muestra que las ecuaciones dinámicas que describen los campos electromagnéticos generados por flujos conductores se reducen a una forma estructuralmente similar al limite no relativista. Aun asi, queda abierta la cuestión de si flujos de fluidos conductores axial simétricos pueden mantener un campo magnético axialsimétrico a pesar de la disipación ohmica.
Descriptores: Magnetohidrodinámica; objeto compactos; gravitación.
PACS: 04.20q; 95.30; 95.30.Sf
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Acknowledgments
It is a pleasure to thank U. Nucamendi and in particularl Joaquin Delgado Estevez for many discussions on some of the technical aspects raised in the relativistic treatment. This research was partially supported by a grant from Coordinacion Científica UMSNH.
References
1. H.W. Babcock, Astrophys J. 105 (1947) 109. [ Links ]
2. W.A. Hiltner, Science 109 (1949) 165; [ Links ]Nature 163 (1949) 283. [ Links ]
3. J.S. Hall W., Science 109 (1949) 166. [ Links ]
4. L.J. Davis and J.L. Greenstein, Astrophys J. 114 (1951) 206. [ Links ]
5. E. Fermi, Phys. Rev. 75 (1949) 1169. [ Links ]
6. H. Alfven, Arkiv. Mat. F. Ast. B 29 (1943) 2. [ Links ]
7. H.W. Babcock and H.D. Babcock: In the Sun (ed Kuiper, Univ of Chi. Press, 1955). [ Links ]
8. A. Hewish et al., Nature 217 (1968) 709. [ Links ]
9. A.G. Lyne and F.G. Smith, Nature 218 (1968) 214. [ Links ]
10. R. Beck et al., Annual Rew of Astron and Astroph. 34 (1996) 155. [ Links ]
11. L. Widrow, Rev. Mod. Phys 74 (2002) 775. [ Links ]
12. M. Giovannini, Astroph/0312614. [ Links ]
13. J.D. Jakson, Classical Electrodynamics, 2a Ed (1975). [ Links ]
14. H.K. Moffat, Magnetic field generation in electrically conducting fluids (C.U.P, 1978). [ Links ]
15. Ya. B. Zeldovich, A.A. Ruzmaikin, and A.D. Sokolof, Magnetic field in astrophysics (Gordon and Breach (1983)). [ Links ]
16. T.G. Cowling, MNRAS, 94 39 (1934); [ Links ] See also: T.G. Cowling, Magnetohydrodynamics (Inters. 1957). [ Links ]
17. M. Steenbeck, F. Krause, and KH Radler, Z. Naturforschang 21a (1966) 369. [ Links ]
18. F. Krause and KH Radler, MeanField Magnetohydrodynamics and Dynamo Theory (AkademieVerl., Berlin, and Pergamon Press, Oxford, 1980). [ Links ]
19. KH Radler in: 2nd Guanajuato Meeting in Astrophysics (Eds. D. Page anf G. Hirsch Astr. y Astpoh. Ser. 2002). [ Links ]
20. U. Geppert, D. Page, and T. Zannias, Phys Rev D 61 (2000) 123004; [ Links ] D. Page U. Geppert, and T. Zannias, Astron. and Astoph. 360 (2000) 1052; [ Links ] KH Radler et al., Phys. Rev. D 6 (2001) 083008. [ Links ]
21. R.D. Blandford et al., MRSA 204 (1983) 1025. [ Links ]
22. Ch. Thomson and R.C. Duncan, Astrop. J 408 (1993) 194. [ Links ]
23. R. Beck et al., Annu. Rev. Astron. Astroph. 94 (1996) 155. [ Links ]
24. P.L. Biermann and C.F. Galeana, Astroph/ 0302168. [ Links ]
25. M. Turner and L. Widrow, Phys. Rev. 37 (1988) 2743; [ Links ] B. Ratra, Astrop. J. L1 (1992) 391; [ Links ] E. Calzeta et al., Phys. Rev. D 57 (1998) 7139. [ Links ]
26. C. Hogan, Phys. Rev. Lett. 91 (1983) 1488; [ Links ] B. Cheng and A.V. Olinto, Phys Rev. D 50 (1994) 2421; [ Links ] G. Sigl, A.V. Olinto, and G. Jedeanzik, Phys. Rev. D 55 (1997) 4582; [ Links ] G. Baym et al. Phys. Rev. D 53 (1996) 662. [ Links ]
27. R.M. Wald General Relativity (Chicago. Univ. Press., 1984). [ Links ]
28. J. EstevezDelgado and T. Zannias, On Local and Global Properties of Magnetic Fields On Cosmological Settings (submitted). [ Links ]