@article{KliemToeroekThompson2012,
  author    = {Kliem, Bernhard and T{\"o}r{\"o}k, Tibor and Thompson, William T.},
  title     = {A parametric study of erupting flux rope rotation modeling the "Cartwheel CME" on 9 April 2008},
  series = {Solar physics : a journal for solar and solar-stellar research and the study of solar terrestrial physics},
  volume    = {281},
  journal   = {Solar physics : a journal for solar and solar-stellar research and the study of solar terrestrial physics},
  number    = {1},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0038-0938},
  doi       = {10.1007/s11207-012-9990-z},
  pages     = {137 -- 166},
  year      = {2012},
  abstract  = {The rotation of erupting filaments in the solar corona is addressed through a parametric simulation study of unstable, rotating flux ropes in bipolar force-free initial equilibrium. The Lorentz force due to the external shear-field component and the relaxation of tension in the twisted field are the major contributors to the rotation in this model, while reconnection with the ambient field is of minor importance, due to the field's simple structure. In the low-beta corona, the rotation is not guided by the changing orientation of the vertical field component's polarity inversion line with height. The model yields strong initial rotations which saturate in the corona and differ qualitatively from the profile of rotation vs. height obtained in a recent simulation of an eruption without preexisting flux rope. Both major mechanisms writhe the flux rope axis, converting part of the initial twist helicity, and produce rotation profiles which, to a large part, are very similar within a range of shear-twist combinations. A difference lies in the tendency of twist-driven rotation to saturate at lower heights than shear-driven rotation. For parameters characteristic of the source regions of erupting filaments and coronal mass ejections, the shear field is found to be the dominant origin of rotations in the corona and to be required if the rotation reaches angles of order 90 degrees and higher; it dominates even if the twist exceeds the threshold of the helical kink instability. The contributions by shear and twist to the total rotation can be disentangled in the analysis of observations if the rotation and rise profiles are simultaneously compared with model calculations. The resulting twist estimate allows one to judge whether the helical kink instability occurred. This is demonstrated for the erupting prominence in the "Cartwheel CME" on 9 April 2008, which has shown a rotation of a parts per thousand aEuro parts per thousand 115(a similar to) up to a height of 1.5 R (aS (TM)) above the photosphere. Out of a range of initial equilibria which include strongly kink-unstable (twist I broken vertical bar=5 pi), weakly kink-unstable (I broken vertical bar=3.5 pi), and kink-stable (I broken vertical bar=2.5 pi) configurations, only the evolution of the weakly kink-unstable flux rope matches the observations in their entirety.},
  language  = {en}
}
@phdthesis{Sule2007,
  author    = {Sule, Aniket},
  title     = {Formation and stability of the solar tachocline in MHD simulations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14612},
  school      = {Universit{\"a}t Potsdam},
  year      = {2007},
  abstract  = {The solar tachocline is a thin transition layer between the solar radiative zone rotating uniformly and the solar convection zone, which has a mainly latitudinal differential rotation profile. This layer has a thickness of less than \$0.05R_{\sun}\$ and is subject to extreme radial as well as latitudinal shears. Helioseismological estimates put this layer at roughly \$0.7R_{\sun}\$. The tachocline mostly resides in the sub-adiabatic, non-turbulent radiative interior, except for a small overlap with the convection zone on the top. Many proposed dynamo mechanisms involve strong toroidal magnetic fields in this transition region. The exact mechanisms behind the formation of such a thin layer is still disputed. A very plausible mechanism is the one involving a weak, relic poloidal magnetic field trapped inside the radiative zone, which is responsible for expelling differential rotation outwards. This was first proposed by \citet{RK97}. The present work develops this idea with numerical simulations including additional effects like meridional circulation. It is shown that a relic field of 1~Gauss or smaller would be sufficient to explain the observed thickness of the tachocline. The stability of the solar tachocline is addressed as the next part of the problem. It is shown that the tachocline is stable up to a differential rotation of 52\\% in the absence of magnetic fields. This is a new finding as compared to the earlier two dimensional models which estimated the solar differential rotation (about 28\\%) to be marginally stable or even unstable. The changed stability limit is attributed to the changed stability criterion of the 3-dimensional model which also involves radial gradients of the angular velocity. In the presence of toroidal magnetic field belts, the lowest non-axisymmetric mode is shown to be the most unstable one for the radiative part of the tachocline. It is estimated that the tachocline would become unstable for toroidal fields exceeding about 100~Gauss. With both formation and stability questions satisfactorily addressed, this work presents the most comprehensive analysis of the physical processes in the solar tachocline to date.},
  language  = {en}
}