Abstract
We have studied the nature of the magnetohydrodynamic (MHD) kink waves in magnetically twisted flux tubes in the presence of plasma flow. To do this, the eigenfunctions of the kink oscillations have been determined using the dispersion relation and the boundary conditions of the tube. Then the components of the magnetic-tension force and the gradient of the pressure force have been obtained to determine the nature of the waves. For the waves with positive azimuthal wavenumber, the magnetic twist and plasma flow have opposite effects on the ratio of restoring forces and the wave has a mixed nature. However, for the waves with negative azimuthal wavenumber the magnetic twist and plasma flow strengthen the effects of each other in increasing the ratio of the magnetic-tension force to the gradient of the pressure force, and they make the nature of the wave more Alfvénic. In the presence of both plasma flow and magnetic twist, in the case of the waves with negative azimuthal wavenumber, for some specific values of the tube parameters, the magnetic-tension force becomes the dominant restoring force both in the radial and azimuthal directions, and the wave can be considered as an Alfvén wave in the internal region of the tube. However, in the case of the waves with positive azimuthal wavenumber, the nature of the wave remains mixed under all circumstances.
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References
Aschwanden, M.J.: 2005, Physics of the Solar Corona, Springer, Berlin.
Aschwanden, M.J., Fletcher, L., Schrijver, C.J., Alexander, D.: 1999, Coronal loop oscillations observed with the transition region and coronal explorer. Astrophys. J. 520, 880. DOI.
Bahari, K.: 2018, Spatial damping of kink MHD waves in the presence of magnetic twist and plasma flow. Astrophys. J. 864, 2. DOI.
Bahari, K., Khalvandi, M.R.: 2017, The effect of a twisted magnetic field on the nature of kink MHD waves. Solar Phys. 292, 192. DOI.
Brekke, P., Kjeldseth-Moe, O., Harrison, R.A.: 1997, High-velocity flows in an active region loop system observed with the Coronal Diagnostic Spectrometer (CDS) on SOHO. Solar Phys. 175, 511. DOI.
Carter, B.K., Erdélyi, R.: 2007, Sausage and kink oscillations in incompressible annular magnetic cylinders. Astron. Astrophys. 475, 323. DOI.
Carter, B.K., Erdélyi, R.: 2008, Kink oscillations in magnetic tubes with twisted annulus. Astron. Astrophys. 481, 239. DOI.
Erdélyi, R., Carter, B.K.: 2006, Wave propagation in incompressible MHD wave guides: the twisted magnetic annulus. Astron. Astrophys. 455, 361. DOI.
Goossens, M., Hollweg, J.V., Sakurai, T.: 1992, Resonant behaviour of MHD waves on magnetic flux tubes. Solar Phys. 138, 233. DOI.
Goossens, M., Terradas, J., Andries, J., Arregui, I., Ballester, J.L.: 2009, On the nature of kink MHD waves in magnetic flux tubes. Astron. Astrophys. 503, 213. DOI.
Innes, D.E., McKenzie, D.E., Wang, T.: 2003, Observations of \(1000~\text{km}\,\text{s}^{-1}\) Doppler shifts in \(10^{7}~\text{K}\) solar flare supra-arcade. Solar Phys. 217, 267. DOI.
Ionson, J.A.: 1978, Resonant absorption of Alfvénic surface waves and the heating of solar coronal loops. Astrophys. J. 226, 650I. DOI.
Joarder, P.S.: 2002, Hydromagnetic waves in solar wind flow-structures. Astron. Astrophys. 384, 1086. DOI.
Joarder, P.S., Narayanan, A.S.: 2000, Non-parallel propagation of hydromagnetic surface waves in the presence of steady shear-flows. Astron. Astrophys. 359, 1211.
Mikhalyaev, B.B., Solov’ev, A.A.: 2004, MHD waves in coronal loops with a shell. Astron. Lett. 30, 268. DOI.
Mikhalyaev, B.B., Solov’ev, A.A.: 2005, The oscillations of coronal loops including the shell. Solar Phys. 227, 249. DOI.
Nakariakov, V.M., Roberts, B.: 1995, Magnetosonic waves in structured atmospheres with steady flows I. Magnetic Slabs. Solar Phys. 159, 213. DOI.
Nakariakov, V.M., Ofman, L., DeLuca, E.E., Roberts, B.R., Davila, J.M.: 1999, TRACE observation of damped coronal loop oscillations: implications for coronal heating. Science 285, 862. DOI.
Narayanan, A.S.: 1991, Hydromagnetic surface waves in compressible moving cylindrical flux tubes. Plasma Phys. Control. Fusion 33, 333. DOI.
Ofman, L., Wang, T.J.: 2008, Hinode observations of transverse waves with flows in coronal loops. Astron. Astrophys. 482, L9. DOI.
Okamoto, T.J., Tsuneta, S., Berger, T.E., Ichimoto, K., Katsukawa, Y., Lites, B.W., et al.: 2007, Coronal transverse magnetohydrodynamic waves in a solar prominence. Science 318, 1577. DOI.
Ruderman, M.S.: 2010, The effect of flows on transverse oscillations of coronal loops. Solar Phys. 267, 377. DOI.
Ruderman, M.S., Erdélyi, R.: 2009, Transverse oscillations of coronal loops. Space Sci. Rev. 149, 199. DOI.
Soler, R., Terradas, J., Goossens, M.: 2011, Spatial damping of propagating kink waves due to resonant absorption: effect of background flow. Astrophys. J. 734, 80. DOI.
Somasundaram, K., Venkatraman, S., Sengottuvel, M.P.: 1999, Hydromagnetic surface waves along compressible cylindrical flux tubes with steady flows. Plasma Phys. Control. Fusion 41, 1421. DOI.
Terra-Homen, M., Erdélyi, R., Ballai, I.: 2003, Linear and nonlinear MHD wave propagation in steady-state magnetic cylinders. Solar Phys. 217, 199. DOI.
Terradas, J., Arregui, I., Verth, G., Goossens, M.: 2011, Seismology of transversely oscillating coronal loops with siphon flows. Astrophys. Lett. 729, L22. DOI.
Wentzel, D.G.: 1979, Hydromagnetic surface waves on cylindrical flux tubes. Astron. Astrophys. 76, 20w.
Winebarger, A.R., DeLuca, E.E., Golub, L.: 2001, Apparent flows above an active region observed with the transition region and coronal explorer. Astrophys. J. 553, L81.
Zirker, J.B., Engvold, O., Martin, S.F.: 1998, Counter-streaming gas flows in solar prominences as evidence for vertical magnetic fields. Nature 396, 440. DOI.
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This article belongs to the Topical Collection:
Magnetohydrodynamic (MHD) Waves and Oscillations in the Sun’s Corona and MHD Coronal Seismology
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Bahari, K. On the Nature of the Kink MHD Waves in Flowing and Twisted Coronal Flux Tubes. Sol Phys 296, 126 (2021). https://doi.org/10.1007/s11207-021-01872-8
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DOI: https://doi.org/10.1007/s11207-021-01872-8