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Register a new userThe Three-dimensional Evolution of Rising, Twisted Magnetic Flux Tubes in a Gravitationally Stratified Model Convection Zone
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We present three-dimensional numerical simulations of the rise and fragmentation of twisted, initially horizontal magnetic flux tubes which evolve into emerging Omega-loops. The flux tubes rise buoyantly through an adiabatically stratified plasma that represents the solar convection zone. The MHD equations are solved in the anelastic approximation, and the results are compared with studies of flux tube fragmentation in two dimensions. We find that if the initial amount of field line twist is below a critical value, the degree of fragmentation at the apex of a rising Omega-loop depends on its three-dimensional geometry: the greater the apex curvature of a given Omega-loop, the lesser the degree of fragmentation of the loop as it approaches the photosphere. Thus, the amount of initial twist necessary for the loop to retain its cohesion can be reduced substantially from the two-dimensional limit. The simulations also suggest that as a fragmented flux tube emerges through a relatively quiet portion of the solar disk, extended crescent-shaped magnetic features of opposite polarity should form and steadily recede from one another. These features eventually coalesce after the fragmented portion of the Omega-loop emerges through the photosphere.
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We present three-dimensional MHD simulations of buoyant magnetic flux tubes that rise through a stratified model convection zone in the presence of solar rotation. The equations of MHD are solved in the anelastic approximation, and the results are used to determine the effects of solar rotation on the dynamic evolution an Omega-loop. We find that the Coriolis force significantly suppresses the degree of fragmentation at the apex of the loop during its ascent toward the photosphere. If the initial axial field strength of the tube is reduced, then, in the absence of forces due to convective motions, the degree of apex fragmentation is also reduced. We show that the Coriolis force slows the rise of the tube, and induces a retrograde flow in both the magnetized and unmagnetized plasma of an emerging active region. Observationally, we predict that this flow will appear to originate at the leading polarity, and will terminate at the trailing polarity.
Magnetic flux tubes in the solar wind can be twisted as they are transported from the solar surface, where the tubes are twisted owing to photospheric motions. It is suggested that the twisted magnetic tubes can be detected as the variation of total (thermal+magnetic) pressure during their passage through observing satellite. We show that the total pressure of several observed twisted tubes resembles the theoretically expected profile. The twist of isolated magnetic tube may explain the observed abrupt changes of magnetic field direction at tube walls. We have also found some evidence that the flux tube walls can be associated with local heating of the plasma and elevated proton and electron temperatures. For the tubes aligned with the Parker spiral, the twist angle can be estimated from the change of magnetic field direction. Stability analysis of twisted tubes shows that the critical twist angle of the tube with a homogeneous twist is 70$^0$, but the angle can further decrease owing to the motion of the tube with regards to the solar wind stream. The tubes with a stronger twist are unstable to the kink instability, therefore they probably can not reach 1 AU.
(abridged) Context: The mechanisms that cause the formation of sunspots are still unclear. Aims: We study the self-organisation of initially uniform sub-equipartition magnetic fields by highly stratified turbulent convection. Methods: We perform simulations of magnetoconvection in Cartesian domains that are $8.5$-$24$ Mm deep and $34$-$96$ Mm wide. We impose either a vertical or a horizontal uniform magnetic field in a convection-driven turbulent flow. Results: We find that super-equipartition magnetic flux concentrations are formed near the surface with domain depths of $12.5$ and $24$ Mm. The size of the concentrations increases as the box size increases and the largest structures ($20$ Mm horizontally) are obtained in the 24 Mm deep models. The field strength in the concentrations is in the range of $3$-$5$ kG. The concentrations grow approximately linearly in time. The effective magnetic pressure measured in the simulations is positive near the surface and negative in the bulk of the convection zone. Its derivative with respect to the mean magnetic field, however, is positive in the majority of the domain, which is unfavourable for the negative effective magnetic pressure instability (NEMPI). Furthermore, we find that magnetic flux is concentrated in regions of converging flow corresponding to large-scale supergranulation convection pattern. Conclusions: The linear growth of large-scale flux concentrations implies that their dominant formation process is tangling of the large-scale field rather than an instability. One plausible mechanism explaining both the linear growth and the concentrate on of the flux in the regions of converging flow pattern is flux expulsion. Possible reasons for the absence of NEMPI are that the derivative of the effective magnetic pressure with respect to the mean magnetic field has an unfavourable sign and that there may not be sufficient scale separation.
We study how active-region-scale flux tubes rise buoyantly from the base of the convection zone to near the solar surface by embedding a thin flux tube model in a rotating spherical shell of solar-like turbulent convection. These toroidal flux tubes that we simulate range in magnetic field strength from 15 kG to 100 kG at initial latitudes of 1 degree to 40 degrees in both hemispheres. This article expands upon Weber, Fan, and Miesch (Astrophys. J., 741, 11, 2011) (Article 1) with the inclusion of tubes with magnetic flux of 10^20 Mx and 10^21 Mx, and more simulations of the previously investigated case of 10^22 Mx, sampling more convective flows than the previous article, greatly improving statistics. Observed properties of active regions are compared to properties of the simulated emerging flux tubes, including: the tilt of active regions in accordance with Joys Law as in Article 1, and in addition the scatter of tilt angles about the Joys Law trend, the most commonly occurring tilt angle, the rotation rate of the emerging loops with respect to the surrounding plasma, and the nature of the magnetic field at the flux tube apex. We discuss how these diagnostic properties constrain the initial field strength of the active region flux tubes at the bottom of the solar convection zone, and suggest that flux tubes of initial magnetic field strengths of geq 40 kG are good candidates for the progenitors of large (10^21 Mx to 10^22 Mx) solar active regions, which agrees with the results from Article 1 for flux tubes of 10^22 Mx. With the addition of more magnetic flux values and more simulations, we find that for all magnetic field strengths, the emerging tubes show a positive Joys Law trend, and that this trend does not show a statistically significant dependence on the magnetic flux.
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Juan Martinez-Sykora
, Viggo Hansteen
, Mats Carlsson (Institute ofn Theoretical Astrophysics
2007
3D numerical simulations of a horizontal magnetic flux tube emergence with different twist are carried out in a computational domain spanning the upper layers of the convection zone to the lower corona. We use the Oslo Staggered Code to solve the full MHD equations with non-grey and non-LTE radiative transfer and thermal conduction along the magnetic field lines. The emergence of the magnetic flux tube input at the bottom boundary into a weakly magnetized atmosphere is presented. The photospheric and chromospheric response is described with magnetograms, synthetic images and velocity field distributions. The emergence of a magnetic flux tube into such an atmosphere results in varied atmospheric responses. In the photosphere the granular size increases when the flux tube approaches from below. In the convective overshoot region some 200km above the photosphere adiabatic expansion produces cooling, darker regions with the structure of granulation cells. We also find collapsed granulation in the boundaries of the rising flux tube. Once the flux tube has crossed the photosphere, bright points related with concentrated magnetic field, vorticity, high vertical velocities and heating by compressed material are found at heights up to 500km above the photosphere. At greater heights in the magnetized chromosphere, the rising flux tube produces a cool, magnetized bubble that tends to expel the usual chromospheric oscillations. In addition the rising flux tube dramatically increases the chromospheric scale height, pushing the transition region and corona aside such that the chromosphere extends up to 6Mm above the photosphere. The emergence of magnetic flux tubes through the photosphere to the lower corona is a relatively slow process, taking of order 1 hour.
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