Magnetic buoyancy

In plasma physics, magnetic buoyancy is an upward force exerted on magnetic flux tubes that are immersed in electrically conducting fluids and are under the influence of a gravitational force. It acts on magnetic flux tubes in stellar convection zones where it plays an important role in the formation of sunspots and starspots.^[1] It was first proposed by Eugene Parker in 1955.

Magnetic flux tubes

For a magnetic flux tube in hydrostatic equilibrium with the surrounding medium, the tube's interior magnetic pressure ${\displaystyle p_{m}}$  and fluid pressure ${\displaystyle p_{i}}$  must be balanced by the fluid pressure ${\displaystyle p_{e}}$  of the exterior medium, that is,

${\displaystyle p_{e}=p_{i}+p_{m}.}$ 

The magnetic pressure is always positive, so ${\displaystyle p_{e}>p_{i}.}$  As such, assuming that the temperature of the plasma within the flux tube is the same as the temperature of the surrounding plasma, the density of the flux tube must be lower than the density of the surrounding medium. Under the influence of a gravitational force, the tube will rise.^[2][3]

Instability

The magnetic buoyancy instability is a plasma instability that can arise from small perturbations in systems where magnetic buoyancy is present. The magnetic buoyancy instability in a system with magnetic field ${\displaystyle \mathbf {B} }$  and perturbation wavevector ${\displaystyle \mathbf {k} }$ , has three modes: the interchange instability where the perturbation wavevector is perpendicular to the magnetic field direction ${\displaystyle \left(\mathbf {k} \perp \mathbf {B} \right)}$ ; the undular instability, sometimes referred to as the Parker instability or magnetic Rayleigh–Taylor instability, where the perturbation wavevector is parallel to the magnetic field direction ${\displaystyle \left(\mathbf {k} \parallel \mathbf {B} \right)}$ ; and the mixed instability, sometimes referred to as the quasi-interchange instability, a combination of the interchange and undular instabilities.^[3][4][5][6]

Parker instability in astrophysics

In astrophysics, the Parker instability is a magnetohydrodynamic instability in a gas layer where a horizontal magnetic field supports gas against gravity, causing it to become buoyant and rise.^[7] This buoyancy, driven by magnetic fields and cosmic ray pressure, leads to the formation of magnetic loops, gas outflow, and can influence star formation^[8] and the structure of the interstellar medium.^[9][10] It is a fundamental process affecting galactic dynamics and is modified by factors like rotation, cooling, and the degree of cosmic ray isotropy. It is sometimes called magnetic buoyancy.^[7] Parker instability is a Rayleigh-Taylor-like instability.^[11]

It was first studied by Eugene Parker in 1966.^{[12][13][14][15][16]}

Parker instability is associated with molecular cloud formation, and can be triggered in the arms of spiral galaxies.^[17]

Further reading

• Shu, F. H. (1974). "The Parker Instability in Differentially-rotating Disks". Astronomy and Astrophysics. 33: 55. Bibcode:1974A&A....33...55S.
• Nelson, A. H. (1985). "Cosmic rays and the Parker instability". Monthly Notices of the Royal Astronomical Society. 215 (2): 161–170. doi:10.1093/mnras/215.2.161.
• Kim, J.; Ryu, D.; Hong, S. S.; Lee, S. M.; Franco, J. (2005). "The Parker Instability". How does the Galaxy Work?. Astrophysics and Space Science Library. Vol. 315. pp. 315–322. doi:10.1007/1-4020-2620-X_65. ISBN 1-4020-2619-6.

References

1. Guerrero, G.; Käpylä, P. J. (September 2011). "Dynamo action and magnetic buoyancy in convection simulations with vertical shear". Astronomy & Astrophysics. 533: A40. arXiv:1102.3598. Bibcode:2011A&A...533A..40G. doi:10.1051/0004-6361/201116749. S2CID 118582079.
2. Parker, Eugene N. (March 1955). "The Formation of Sunspots from the Solar Toroidal Field". The Astrophysical Journal. 121: 491. Bibcode:1955ApJ...121..491P. doi:10.1086/146010.
3. Acheson, D. J. (May 1979). "Instability by magnetic buoyancy". Solar Physics. 62 (1): 23–50. Bibcode:1979SoPh...62...23A. doi:10.1007/BF00150129. S2CID 121629539.
4. Matsumoto, R.; Tajima, T.; Shibata, K.; Kaisig, M. (September 1993). "Three-dimensional magnetohydrodynamics of the emerging magnetic flux in the solar atmosphere". The Astrophysical Journal. 414: 357. Bibcode:1993ApJ...414..357M. doi:10.1086/173082.
5. Gilman, Peter A. (24 January 2018). "Magnetic Buoyancy and Rotational Instabilities in the Tachocline". The Astrophysical Journal. 853 (1): 65. Bibcode:2018ApJ...853...65G. doi:10.3847/1538-4357/aaa4f4. S2CID 126268222.
6. Kim, J.; Ryu, D.; Hong, S. S.; Lee, S. M.; Franco, J. (2005). "The Parker Instability". How Does the Galaxy Work?. Astrophysics and Space Science Library. 315: 315–322. doi:10.1007/1-4020-2620-X_65. ISBN 1-4020-2619-6.
7. "An Etymological Dictionary of Astronomy and Astrophysics - English-French-Persian".
8. Tharakkal, Devika; Shukurov, Anvar; Gent, Frederick A.; Sarson, Graeme R.; Snodin, Andrew (2023). "Steady states of the Parker instability: The effects of rotation". Monthly Notices of the Royal Astronomical Society. 525 (2): 2972–2984. doi:10.1093/mnras/stad2475.
9. Heintz, Evan; Bustard, Chad; Zweibel, Ellen G. (2020). "The Role of the Parker Instability in Structuring the Interstellar Medium". The Astrophysical Journal. 891 (2): 157. arXiv:1910.03588. Bibcode:2020ApJ...891..157H. doi:10.3847/1538-4357/ab7453.
10. Lee, Sang Min; Hong, S. S. (2011). "Parker Instability in a Self-Gravitating Magnetized Gas Disk. III. Nonlinear Development of the Parker Instability". The Astrophysical Journal. 734 (2): 101. Bibcode:2011ApJ...734..101L. doi:10.1088/0004-637X/734/2/101.
11. Rodrigues, L. F. S.; Sarson, G. R.; Shukurov, A.; Bushby, P. J.; Fletcher, A. (2016). "The Parker Instability in Disk Galaxies". The Astrophysical Journal. 816 (1): 2. arXiv:1510.06318. Bibcode:2016ApJ...816....2R. doi:10.3847/0004-637X/816/1/2.
12. Parker, E. N. (1966). "The Dynamical State of the Interstellar Gas and Field". The Astrophysical Journal. 145: 811. Bibcode:1966ApJ...145..811P. doi:10.1086/148828.
13. Parker, E.N. (1967). "The dynamical state of the interstellar gas and field. II. Non-linear growth of clouds and forces in three dimensions". Astrophysical Journal. 149.
14. Parker, E.N. (1967). "The Dynamical State of the Interstellar Gas and Field. III. Turbulence and Enhanced Diffusion". Astrophysical Journal. 149.
15. Lerche, I.; Parker, E.N. (1968). "The Dynamical State of the Interstellar Gas and Field. VI. Instability and Enhanced Diffusion in a Twisted Field". Astrophysical Journal. 154.
16. Parker, E.N. (1969). "Galactic effects of the cosmic-ray gas". Space Science Reviews. 9 (5): 651. Bibcode:1969SSRv....9..651P. doi:10.1007/BF00174032.
17. Basu, Shantanu; Mouschovias, Telemachos Ch.; Paleologou, Efthimios V. (1997). "Dynamical Effects of the Parker Instability in the Interstellar Medium". The Astrophysical Journal. 480 (1): L55 – L58. Bibcode:1997ApJ...480L..55B. doi:10.1086/310620.