Verdini, A. and Grappin, R. and Velli, M. (2012) Coronal heating in coupled photosphere-chromosphere-coronal systems: turbulence and leakage. Astronomy and Astrophysics, 538 . Art. No. A70. ISSN 0004-6361 http://resolver.caltech.edu/CaltechAUTHORS:20120404-100910641
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Context. Coronal loops act as resonant cavities for low-frequency fluctuations that are transmitted from the deeper layers of the solar atmosphere. These fluctuations are amplified in the corona and lead to the development of turbulence that in turn is able to dissipate the accumulated energy, thus heating the corona. However, trapping is not perfect, because some energy leaks down to the chromosphere on a long timescale, limiting the turbulent heating. Aims. We consider the combined effects of turbulence and energy leakage from the corona to the photosphere in determining the turbulent energy level and associated heating rate in models of coronal loops, which include the chromosphere and transition region. Methods. We use a piece-wise constant model for the Alfvén speed in loops and a reduced MHD-shell model to describe the interplay between turbulent dynamics in the direction perpendicular to the mean field and propagation along the field. Turbulence is sustained by incoming fluctuations that are equivalent, in the line-tied case, to forcing by the photospheric shear flows. While varying the turbulence strength, we systematically compare the average coronal energy level and dissipation in three models with increasing complexity: the classical closed model, the open corona, and the open corona including chromosphere (or three-layer model), with the last two models allowing energy leakage. Results. We find that (i) leakage always plays a role. Even for strong turbulence, the dissipation time never becomes much lower than the leakage time, at least in the three-layer model; therefore, both the energy and the dissipation levels are systematically lower than in the line-tied model; (ii) in all models, the energy level is close to the resonant prediction, i.e., assuming an effective turbulent correlation time longer than the Alfvén coronal crossing time; (iii) the heating rate is close to the value given by the ratio of photospheric energy divided by the Alfvén crossing time; (iv) the coronal spectral range is divided in two: an inertial range with 5/3 spectral slope, and a large-scale peak where nonlinear couplings are inhibited by trapped resonant modes; (v) in the realistic three-layer model, the two-component spectrum leads to a global decrease in damping equal to Kolmogorov damping reduced by a factor u_(rms)/V_a^c where V_a^c is the coronal Alfvén speed.
|Additional Information:||© 2012 ESO. Received 7 September 2011. Accepted 16 November 2011. Published online 03 February 2012. We benefited from useful discussions with G. Belmont. A.V. acknowledges support from the Belgian Federal Science Policy Office through the ESA-PRODEX program. The research described in this paper was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.|
|Subject Keywords:||methods: numerical; Sun: corona; magnetohydrodynamics (MHD); turbulence; Sun: transition region; waves|
|Official Citation:||Coronal heating in coupled photosphere-chromosphere-coronal systems: turbulence and leakage A70 A. Verdini, R. Grappin and M. Velli Published online: 3 February 2012 DOI: http://dx.doi.org/10.1051/0004-6361/201118046|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||04 Apr 2012 17:41|
|Last Modified:||26 Dec 2012 15:02|
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