Abstract
We consider an expanding three-dimensional (3-D) piston as a driver of an MHD shock wave. It is assumed that the source-region surface accelerates over a certain time interval to achieve a particular maximum velocity. Such an expansion creates a large-amplitude wave in the ambient plasma. Owing to the nonlinear evolution of the wavefront, its profile steepens and after a certain time and distance a discontinuity forms, marking the onset of the shock formation. We investigate how the formation time and distance depend on the acceleration phase duration, the maximum expansion velocity (defining also acceleration), the Alfvén velocity (defining also Mach number), and the initial size of the piston. The model differs from the 1-D case, since in the 3-D evolution, a decrease of the wave amplitude with distance must be taken into account. We present basic results, focusing on the timing of the shock formation in the low- and high-plasma-beta environment. We find that the shock-formation time and the shock-formation distance are (1) approximately proportional to the acceleration phase duration; (2) shorter for a higher expansion velocity; (3) larger in a higher Alfvén speed environment; (4) only weakly dependent on the initial source size; (5) shorter for a stronger acceleration; and (6) shorter for a larger Alfvén Mach number of the source surface expansion. To create a shock causing a high-frequency type II burst and the Moreton wave, the source region expansion should, according to our results, achieve a velocity on the order of 1000 km s−1 within a few minutes, in a low Alfvén velocity environment.
Similar content being viewed by others
References
Cliver, E.W., Webb, D.F., Howard, R.A.: 1999, On the origin of solar metric type II bursts. Solar Phys. 187, 89 – 114.
Cliver, E.W., Nitta, N.V., Thompson, B.J., Zhang, J.: 2004, Coronal shocks of november 1997 revisited: The CME type II timing problem. Solar Phys. 225, 105 – 139. doi:10.1007/s11207-004-3258-1.
Karlický, M., Odstrčil, D.: 1994, The generation of MHD shock waves during the impulsive phase of the February 27, 1992 flare. Solar Phys. 155, 171 – 184.
Landau, L.D., Lifshitz, E.M.: 1987, Fluid Mechanics, Pergamon, Oxford.
Mann, G.: 1995, Simple magnetohydrodynamic waves. J. Plasma Phys. 53, 109 – 125.
Moreton, G.E., Ramsey, H.E.: 1960, Recent observations of dynamical phenomena associated with solar flares. Pub. Astron. Soc. Pac. 72, 357 – 358.
Nelson, G.J., Melrose, D.B.: 1985, Type II bursts. In: Solar Radiophysics: Studies of Emission from the Sun at Metre Wavelengths, 333 – 359.
Uchida, Y.: 1974, Behavior of the flare-produced coronal MHD wavefront and the occurrence of type II radio bursts. Solar Phys. 39, 431 – 449. http://www.springerlink.com/content/x55037j762342v51.
Veronig, A.M., Temmer, M., Vršnak, B., Thalmann, J.K.: 2006, Interaction of a Moreton/EIT wave and a coronal hole. Astrophys. J. 647, 1466 – 1471. doi:10.1086/505456.
Vršnak, B.: 2001, Solar flares and coronal shock waves. J. Geophys. Res. 106, 25291 – 25300. doi:10.1029/2000JA004009.
Vršnak, B., Lulić, S.: 2000, Formation of coronal MHD shock waves – I. The basic mechanism. Solar Phys. 196, 157 – 180.
Vršnak, B., Magdalenić, J., Zlobec, P.: 2004, Band-splitting of coronal and interplanetary type II bursts. III. Physical conditions in the upper corona and interplanetary space. Astron. Astrophys. 413, 753 – 763. doi:10.1051/0004-6361:20034060.
Vršnak, B., Ruždjak, V., Zlobec, P., Aurass, H.: 1995, Ignition of MHD shocks associated with solar flares. Solar Phys. 158, 331 – 351. http://www.springerlink.com/content/w43442359t000734.
Vršnak, B., Magdalenić, J., Aurass, H., Mann, G.: 2002, Band-splitting of coronal and interplanetary type II bursts. II. Coronal magnetic field and Alfvén velocity. Astron. Astrophys. 396, 673 – 682. doi:10.1051/0004-6361:20021413.
Warmuth, A., Mann, G.: 2005, A model of the Alfvén speed in the solar corona. Astron. Astrophys. 435, 1123 – 1135. doi:10.1051/0004-6361:20042169.
Warmuth, A., Vršnak, B., Aurass, H., Hanslmeier, A.: 2001, Evolution of two EIT/Hα Moreton waves. Astrophys. J. 560, L105 – L109. doi:10.1086/324055.
Warmuth, A., Vršnak, B., Magdalenić, J., Hanslmeier, A., Otruba, W.: 2004a, A multiwavelength study of solar flare waves. I. Observations and basic properties. Astron. Astrophys. 418, 1101 – 1115. doi:10.1051/0004-6361:20034332.
Warmuth, A., Vršnak, B., Magdalenić, J., Hanslmeier, A., Otruba, W.: 2004b, A multiwavelength study of solar flare waves. II. Perturbation characteristics and physical interpretation. Astron. Astrophys. 418, 1117 – 1129. doi:10.1051/0004-6361:20034333.
Wu, S.T., Zheng, H., Wang, S., Thompson, B.J., Plunkett, S.P., Zhao, X.P., Dryer, M.: 2001, Three-dimensional numerical simulation of MHD waves observed by the Extreme Ultraviolet Imaging Telescope. J. Geophys. Res. 106, 25089 – 25102. doi:10.1029/2000JA000447.
Author information
Authors and Affiliations
Corresponding author
Additional information
Radio Physics and the Flare-CME Relationship
Guest Editors: Karl-Ludwig Klein and Silja Pohjolainen
Rights and permissions
About this article
Cite this article
Žic, T., Vršnak, B., Temmer, M. et al. Cylindrical and Spherical Pistons as Drivers of MHD Shocks. Sol Phys 253, 237–247 (2008). https://doi.org/10.1007/s11207-008-9173-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11207-008-9173-0