Original article
Published 2010-06-09
Keywords
- Post-Newtonian approximation,
- galactic and stellar dynamics
How to Cite
Akímushkin, C., Ramos Caro, J., & González, G. A. (2010). Axially Symmetric Post-Newtonian Stellar Systems. Revista Integración, Temas De matemáticas, 28(1), 1–14. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/2056
Abstract
We introduce a method to obtain self-consistent, axially symmetricdisklike stellar models in the first post-Newtonian (1PN) approximation.By using in the field equations of the 1PN approximation a distributionfunction (DF) corresponding to a Newtonian model, two fundamental equationsdetermining the 1PN corrections are obtained. The rotation curves ofthe corrected models differs from the classical ones and the corrections areclearly appreciable with values of the mass and radius of a typical galaxy.On the other hand, the relativistic mass correction can be ignored for allmodels.
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References
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[2] González G. A., and Reina J. I., An infinite family of generalized Kalnajs discs, MNRAS, 371 (2006), 1873.
[3] González G. A., and Letelier P. S., Relativistic static thin disks with radial stress support, Class. Quantum Grav., 16 (1999), 479.
[4] González G. A. and Letelier P. S., Rotating relativistic thin disks, Phys. Rev., D 62 (2000), 064025.
[5] Hunter C., MNRAS, The structure and stability of self-gravitating disks, 126 (1963), 299.
[6] Hunter C., and Toomre A., Dynamics of the Bending of the Galaxy, ApJ, 155 (1969), 747.
[7] Jiang Z., Flattened Jaffe models for galaxies, MNRAS, 319 (2000), 1067.
[8] Jiang Z., and Moss D., Prolate Jaffe models for galaxies, MNRAS, 331 (2002), 117.
[9] Jiang Z. and Ossipkov L., Two-integral distribution functions for axisymmetric systems, MNRAS, 379 (2007), 1133.
[10] Kalnajs A. J., The equilibria and oscillations of a family of uniformly rotating stellar disks, ApJ, 175 (1972), 63.
[11] Kalnajs A. J., Dynamics of Flat Galaxies. III. Equilibrium models, ApJ, 205 (1976), 751.
[12] Lemos J. P. S., and Letelier P. S., Superposition of Morgan and Morgan disks with a Schwarzschild black hole, Class. Quantum Grav., 10 (1993), L75.
[13] Lemos J. P. S., and Letelier P. S., Exact general relativistic thin disks around black holes, Phys. Rev., D 49 (1994), 5135.
[14] Lemos J. P. S., and Letelier P. S., Two Families of exact general disks with acentral black hole, Int. J. Modern Phys. D 5 (1996), 53.
[15] Lynden-Bell D., Stellar dynamics: Exact solution of the self-gravitation equation, MNRAS, 123 (1962), 447.
[16] Mestel L., On the galactic law of rotation, MNRAS, 126 (1963), 553.
[17] Pedraza J. F., Ramos-Caro J., and González G. A., An infinite family of selfconsistent models for axisymmetric flat galaxies, MNRAS, 390 (2008), 1587.
[18] Rezania V., and Sobouti Y., Liouville’s equation in post Newtonian approximation I. Static solution, Astron. Astrophys., 354 (2000), 1110.
[19] Semerák O., and Zácek M., Gravitating discs around a Schwarzschild black hole: I, Class. Quantum Grav., 17 (2000), 1613.
[20] Semerák O., Thin disc around a rotating black hole, but with support in-between,Class. Quantum Grav., 19 (2002), 3829.
[21] Toomre A., On the distribution of matter within highly flattened galaxies, ApJ, 138 (1963), 385.
[22] Toomre A., On the gravitational stability of a disk of stars, ApJ, 139 (1964), 1217.
[23] Zácek M., and Semerák O., Gravitating discs around a Schwarzschild black hole: II, Czech. J. Phys., 52 (2002), 19.