Instability of Thermally Conducting Self-Gravitating Systems

ABSTRACT

The gravitational instability of a thermally conducting self-gravitating system permeated by a uniform and oblique magnetic field has been analyzed in the framework of Tsallis’ nonextensive theory for possible mod-ifications in the Jeans’ instability criterion. It is concluded that the instability criterion is indeed modified into one that depends explicitly on the nonextensive parameter. The influence of thermal conductivity on the system stability is also examined.

The gravitational instability of a thermally conducting self-gravitating system permeated by a uniform and oblique magnetic field has been analyzed in the framework of Tsallis’ nonextensive theory for possible mod-ifications in the Jeans’ instability criterion. It is concluded that the instability criterion is indeed modified into one that depends explicitly on the nonextensive parameter. The influence of thermal conductivity on the system stability is also examined.

Cite this paper

nullS. Shaikh and A. Khan, "Instability of Thermally Conducting Self-Gravitating Systems,"*Journal of Modern Physics*, Vol. 1 No. 1, 2010, pp. 77-82. doi: 10.4236/jmp.2010.110010.

nullS. Shaikh and A. Khan, "Instability of Thermally Conducting Self-Gravitating Systems,"

References

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[2] S. Chandrasekhar, “Hydrodynamics & Hydromagnetic Stability,” Clarendron Press, Oxford, 1961.

[3] P. D. Ariel, “The Character of Equilibrium of an Inviscid Infinitely Conducting Fluid of Variable Density in the Presence of a Horizontal Magnetic Field with Hall-Ur-rent,” Journal of Plasma Physics, Vol. 4, 1970, pp. 523-530.

[4] G. Bhowmik, “Rayleigh Taylor Instability of a Viscous Hall Plasma with Magnetic Field,” Journal of Plasma Physics, Vol. 7, 1972, pp. 117-132.

[5] A. Ali and P. K. Bhatia, “Magnetic Resistivity and Hall Currents Effects on the Stability of a Self-Gravitating Plasma of Varying Density in Variable Magnetic Field,” Astrophysics and Space Science, Vol. 201, 1993, pp. 15-27.

[6] M. K. Vyas and R. K. Chhajlani, “Gravitational Instabil-ity of a thermally-conducting Plasma Flowing through a Porous Medium in the Presence of Suspended Particles,” Astrophysics and Space Science, Vol. 149, 1988, pp. 323-342.

[7] R. C. Sharma and T. Chand, “Gravitational Instability for Some Astrophysical Systems,” Astrophysics and Space Science, Vol. 183, 1991, pp. 215-224.

[8] A. Khan and P. K. Bhatia, “Stability of Two Superposed Viscoelastic Fluid in a Horizontal Magnetic Field,” In-dian Journal of Pure and Applied Mathematics, Vol. 32, 2001, pp. 98-108.

[9] S. S. Kumar, “On Gravitational Instability, III,” Publica-tions of the Astronomical Society of Japan, Vol. 13, 1961, pp. 121-124.

[10] R. H. Chhajlani and D. S. Vaghela, “Magnetogravitational Stability of Self-Gravitating Plasma with Thermal Conduc-tion and Finite Larmor Radius through Porous Medium,” Astrophysics and Space Science, Vol. 134, 1987, pp. 301- 315.

[11] V. Mehta and P. K. Bhatia, “Gravitational Instability of a Rotating Viscous Thermally Conducting plasma,” Con-tributions to Plasma Physics, Vol. 29, 1989, pp. 617-626.

[12] T. Padmanabhan, “Statistical Mechanics of Gravitating Systems,” Physics Reports, Vol. 188, 1990, pp. 285-362.

[13] A. Taruya and M. Sakagami, “Thermodynamic Properties of Stellar Polytrope,” Physica A, Vol. 318, 2003, pp. 387-413.

[14] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,” Journal of Statistical Physics, Vol. 52, 1988, pp. 479-487.

[15] R. Silva, J. A. Alcaniz and J. A. S. Lima, “Constraining Nonextensive Statistics with Plasma Oscillation Data,” Physica A, Vol. 356, 2005, pp. 509-516.

[16] S. Shaikh, A. Khan and P. K. Bhatia, “Jeans’ Gravita-tional Instability of a Thermally Conducting, Unbounded, Partially Ionized Plasma,” Zeitschrift für Naturforschung, Vol. 61, 2006, pp. 275-280.

[17] V. Munoz, “A Nonextensive Statistics Approach for Langmuir Waves in Relativistic Plasmas,” Nonlinear Processes in Geophysics, Vol. 13, 2006, pp. 237-241.

[18] F. Valentini, “Nonlinear Landau Damping in Nonex-ten-sive Statistics,” Physics of Plasmas, Vol. 12, 2005, pp. 1-7.

[19] M. P. Leubner, “Nonextensive Theory of Dark Matter and Gas Density Profiles,” The Astrophysical Journal, Vol. 632, 2005, pp. L1-L4.

[20] J. A. S. Lima, R. Silva and J. Santos, “Jeans’ Gravita-tional Instability and Nonextensive Kinetic Theory,” As-tronomy and Astrophysics, Vol. 396, 2002, pp. 309-313.

[21] J. L. Du, “Jeans’ Criterion and Nonextensive Velocity Distribution Function in Kinetic Theory,” Physics Letters A, Vol. 320, 2004, pp. 347-351.

[22] J. L. Du, “Nonextensivity in Nonequilibrium Plasma Systems with Coulombian Long-Range Interactions,” Physics Letters A, Vol. 329, 2004, pp. 262-267.

[23] J. L. Du, “What Does the Nonextensive Parameter Stand for in Self-Gravitating Systems?” Astrophysics and Space Science, Vol. 305, 2006, pp. 247-251.

[24] J. L. Du, “Nonextensivity and the Power-Law Distribu-tions for the Systems with Self-Gravitating Long-Range Interactions,” Astrophysics and Space Science, Vol. 312, 2007, pp. 47-55.

[25] A. Plastino and A. R. Plastino, “Stellar Polytropes and Tsallis’ Entropy,” Physics Letters A, Vol. 174, 1993, pp. 384-386.

[26] S. Abe, “Thermodynamic Limit of a Classical gas in Nonextensive Statistical Mechanics: Negative Specific Heat and Polytropism,” Physics Letters A, Vol. 263, 1999, pp. 424-429.

[27] R. Silva and J. S. Alcaniz, “Negative Heat Capacity and Non-Extensive Kinetic Theory,” Physics Letters A, Vol. 313, 2003, pp. 393-396.

[28] J. M. Liu, J. S. D. Groot, J. P. Matte, T. W. Johnston and R. P. Drake, “Measurements of Inverse Bremsstrahlung Absorption and Non-Maxwellian Electron Velocity Dis-tributions,” Physical Review Letters, Vol. 72, 1994, pp. 2717-2720.

[29] E. G. D. Cohen, “Statistics and Dynamics,” Physica A, Vol. 305, 2002, pp. 19-26.

[30] S. Shaikh, A. Khan and P. K. Bhatia, “Stability of Ther-mally Conducting Plasma in a Variable Magnetic Field,” Astrophysics and Space Science, Vol. 312, 2007, pp. 35-40.

[31] S. Shaikh, A. Khan and P. K. Bhatia, “Thermally Con-ducting Partially Ionized Plasma in a Variable Magnetic Field,” Contributions to Plasma Physics, Vol. 47, No. 3, 2007, pp. 147-156.

[32] S. Shaikh, A. Khan and P. K. Bhatia, “Jeans’ Gravita-tional Instability of a Thermally Conducting Plasma,” Physics Letters A, Vol. 372, 2008, pp. 1451-1457.

[1] J. H. Jeans, “The Stability of Spherical Nebulae,” Phi-losophical Transactions of the Royal Society of London, A 199, 1902, pp. 1-53.

[2] S. Chandrasekhar, “Hydrodynamics & Hydromagnetic Stability,” Clarendron Press, Oxford, 1961.

[3] P. D. Ariel, “The Character of Equilibrium of an Inviscid Infinitely Conducting Fluid of Variable Density in the Presence of a Horizontal Magnetic Field with Hall-Ur-rent,” Journal of Plasma Physics, Vol. 4, 1970, pp. 523-530.

[4] G. Bhowmik, “Rayleigh Taylor Instability of a Viscous Hall Plasma with Magnetic Field,” Journal of Plasma Physics, Vol. 7, 1972, pp. 117-132.

[5] A. Ali and P. K. Bhatia, “Magnetic Resistivity and Hall Currents Effects on the Stability of a Self-Gravitating Plasma of Varying Density in Variable Magnetic Field,” Astrophysics and Space Science, Vol. 201, 1993, pp. 15-27.

[6] M. K. Vyas and R. K. Chhajlani, “Gravitational Instabil-ity of a thermally-conducting Plasma Flowing through a Porous Medium in the Presence of Suspended Particles,” Astrophysics and Space Science, Vol. 149, 1988, pp. 323-342.

[7] R. C. Sharma and T. Chand, “Gravitational Instability for Some Astrophysical Systems,” Astrophysics and Space Science, Vol. 183, 1991, pp. 215-224.

[8] A. Khan and P. K. Bhatia, “Stability of Two Superposed Viscoelastic Fluid in a Horizontal Magnetic Field,” In-dian Journal of Pure and Applied Mathematics, Vol. 32, 2001, pp. 98-108.

[9] S. S. Kumar, “On Gravitational Instability, III,” Publica-tions of the Astronomical Society of Japan, Vol. 13, 1961, pp. 121-124.

[10] R. H. Chhajlani and D. S. Vaghela, “Magnetogravitational Stability of Self-Gravitating Plasma with Thermal Conduc-tion and Finite Larmor Radius through Porous Medium,” Astrophysics and Space Science, Vol. 134, 1987, pp. 301- 315.

[11] V. Mehta and P. K. Bhatia, “Gravitational Instability of a Rotating Viscous Thermally Conducting plasma,” Con-tributions to Plasma Physics, Vol. 29, 1989, pp. 617-626.

[12] T. Padmanabhan, “Statistical Mechanics of Gravitating Systems,” Physics Reports, Vol. 188, 1990, pp. 285-362.

[13] A. Taruya and M. Sakagami, “Thermodynamic Properties of Stellar Polytrope,” Physica A, Vol. 318, 2003, pp. 387-413.

[14] C. Tsallis, “Possible Generalization of Boltzmann-Gibbs Statistics,” Journal of Statistical Physics, Vol. 52, 1988, pp. 479-487.

[15] R. Silva, J. A. Alcaniz and J. A. S. Lima, “Constraining Nonextensive Statistics with Plasma Oscillation Data,” Physica A, Vol. 356, 2005, pp. 509-516.

[16] S. Shaikh, A. Khan and P. K. Bhatia, “Jeans’ Gravita-tional Instability of a Thermally Conducting, Unbounded, Partially Ionized Plasma,” Zeitschrift für Naturforschung, Vol. 61, 2006, pp. 275-280.

[17] V. Munoz, “A Nonextensive Statistics Approach for Langmuir Waves in Relativistic Plasmas,” Nonlinear Processes in Geophysics, Vol. 13, 2006, pp. 237-241.

[18] F. Valentini, “Nonlinear Landau Damping in Nonex-ten-sive Statistics,” Physics of Plasmas, Vol. 12, 2005, pp. 1-7.

[19] M. P. Leubner, “Nonextensive Theory of Dark Matter and Gas Density Profiles,” The Astrophysical Journal, Vol. 632, 2005, pp. L1-L4.

[20] J. A. S. Lima, R. Silva and J. Santos, “Jeans’ Gravita-tional Instability and Nonextensive Kinetic Theory,” As-tronomy and Astrophysics, Vol. 396, 2002, pp. 309-313.

[21] J. L. Du, “Jeans’ Criterion and Nonextensive Velocity Distribution Function in Kinetic Theory,” Physics Letters A, Vol. 320, 2004, pp. 347-351.

[22] J. L. Du, “Nonextensivity in Nonequilibrium Plasma Systems with Coulombian Long-Range Interactions,” Physics Letters A, Vol. 329, 2004, pp. 262-267.

[23] J. L. Du, “What Does the Nonextensive Parameter Stand for in Self-Gravitating Systems?” Astrophysics and Space Science, Vol. 305, 2006, pp. 247-251.

[24] J. L. Du, “Nonextensivity and the Power-Law Distribu-tions for the Systems with Self-Gravitating Long-Range Interactions,” Astrophysics and Space Science, Vol. 312, 2007, pp. 47-55.

[25] A. Plastino and A. R. Plastino, “Stellar Polytropes and Tsallis’ Entropy,” Physics Letters A, Vol. 174, 1993, pp. 384-386.

[26] S. Abe, “Thermodynamic Limit of a Classical gas in Nonextensive Statistical Mechanics: Negative Specific Heat and Polytropism,” Physics Letters A, Vol. 263, 1999, pp. 424-429.

[27] R. Silva and J. S. Alcaniz, “Negative Heat Capacity and Non-Extensive Kinetic Theory,” Physics Letters A, Vol. 313, 2003, pp. 393-396.

[28] J. M. Liu, J. S. D. Groot, J. P. Matte, T. W. Johnston and R. P. Drake, “Measurements of Inverse Bremsstrahlung Absorption and Non-Maxwellian Electron Velocity Dis-tributions,” Physical Review Letters, Vol. 72, 1994, pp. 2717-2720.

[29] E. G. D. Cohen, “Statistics and Dynamics,” Physica A, Vol. 305, 2002, pp. 19-26.

[30] S. Shaikh, A. Khan and P. K. Bhatia, “Stability of Ther-mally Conducting Plasma in a Variable Magnetic Field,” Astrophysics and Space Science, Vol. 312, 2007, pp. 35-40.

[31] S. Shaikh, A. Khan and P. K. Bhatia, “Thermally Con-ducting Partially Ionized Plasma in a Variable Magnetic Field,” Contributions to Plasma Physics, Vol. 47, No. 3, 2007, pp. 147-156.

[32] S. Shaikh, A. Khan and P. K. Bhatia, “Jeans’ Gravita-tional Instability of a Thermally Conducting Plasma,” Physics Letters A, Vol. 372, 2008, pp. 1451-1457.