Abstract
The free oscillations of coronal loops with a constant density and a variable magnetic field changing according to parabolic laws are investigated. Using our developed method, we derive the wave equations with constant coefficients that describe the kink oscillations of symmetric and asymmetric magnetic flux tubes. For such models, we obtain analytical expressions for the oscillation spectra and amplitudes as well as the magnitudes and directions of the displacements of the extrema of the fundamental and first modes relative to their values for homogeneous tubes. For the first mode of an asymmetric loop, we have determined the dependence of the coordinate displacement for the internal node on the ratios of the magnetic field strengths in its asymmetric parts and the ratio of the amplitudes at the extremum points.
Similar content being viewed by others
References
J. Andries, T. van Doorsselaere, B. Roberts, et al., Space Sci. Rev. 149, 3 (2009).
M. J. Aschwanden, Physics of the Solar Corona. An Introduction with Problems and Solutions (Springer, Berlin, 2005), p. 909.
M. J. Aschwanden, L. Fletcher, C. J. Schrijver, et al., Astrophys. J. 520, 880 (1999).
T. van Doorsselaere, E. Verwichte, and J. Terradas, Space Sci. Rev. 149, 299 (2009).
T. van Doorsselaere, V. Nakariakov, and E. Verwichte, Astron. Astrophys. 473, 959 (2007).
M. V. Dymova and M. S. Ruderman, Astron. Astrophys. 457, 1059 (2006).
I. de Moortel and V. M. Nakariakov, Phil. Trans. R. Soc. A 370, 3193 (2012).
V. Nakariakov, L. Ofman, E. E. DeLuca, et al., Science 285, 862 (1999).
T. J. Okamoto, S. Tsuneta, T. E. Berge, et al., Science 318, 1577 (2007).
E. O’Shea, A. K. Srivastava, J. G. Doyle, et al., Astron. Astrophys. 473, 13 (2007).
N. S. Petrukhin, E. N. Pelinovsky, and E. K. Batsyna, JETP Lett. 93, 564 (2011).
N. S. Petrukhin, E. N. Pelinovsky, and T. G. Talipova, Izv., Atmos. Ocean. Phys. 48, 169 (2012a).
N. S. Petrukhin, E. N. Pelinovsky, and E. K. Batsyna, Astron. Lett. 38, 388 (2012b).
N. S. Petrukhin, E. N. Pelinovsky, and E. K. Batsyna, Geomagn. Aeron. 52, 814 (2012c).
B. de Pontieu, S. W. McIntosh, M. Carlsson, et al., Science 318, 1574 (2007).
M. Ruderman, S. G. Verth, and R. Erdelyi, Astrophys. J. 686, 684 (2008).
M. S. Ruderman and R. Erdelyi, Space Sci. Rev. 149, 199 (2009).
M. S. Ruderman, E. Pelinovsky, N. S. Petrukhin, et al., Solar Phys. 286, 417 (2013).
H. C. Spruit, Astron. Astrophys. 98, 155 (1981).
A. V. Stepanov, V. V. Zaitsev, and V. M. Nakaryakov, Phys. Usp. 55, 929 (2012).
T. G. Talipova, E. N. Pelinovsky, and N. S. Petrukhin, Oceanology 49, 622 (2009).
G. Verth, Astron. Nachr. 328, 764 (2007).
G. Verth and R. Erdelyi, Astron. Astrophys. 486, 1015 (2008).
E. Verwichte, V. M. Nakariakov, L. Ofman, et al., Solar Phys. 223, 77 (2004).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.S. Petrukhin, 2014, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2014, Vol. 40, No. 6, pp. 416–425.
Rights and permissions
About this article
Cite this article
Petrukhin, N.S. Kink oscillations of asymmetric coronal loops. Astron. Lett. 40, 372–381 (2014). https://doi.org/10.1134/S1063773714060073
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063773714060073