Free Access
Issue
A&A
Volume 532, August 2011
Article Number A112
Number of page(s) 11
Section The Sun
DOI https://doi.org/10.1051/0004-6361/201116708
Published online 03 August 2011

Online material

Appendix A: Temporal evolution of the plasma ejection

thumbnail Fig. A.1

Side view of the 3D computational box showing the synthesized emission in O vi and Mg x (top row), the normalized currents and the current fluctuations (bottom row; see Eqs. (A.1) and (A.2) and Appendix A for details). Each panel covers 50 Mm in the horizontal and 30 Mm in the vertical direction. This snapshot shows the ejection at t = 47 min, i.e., at the same time as the middle row of Fig. 1 and as Fig. 9. The arrow points at the location of the high energy input that causes the ejection. A movie showing the temporal evolution over 1 h is available in the online edition. The movie is also available at http://www.mps.mpg.de/data/outgoing/peter/papers/plasma-ejection/blob.mpg (6 MB).

Open with DEXTER

The temporal evolution of the plasma ejection is best displayed by a movie showing the emission as well as the heating rate integrated through the computational box. To mimic the situation at the limb, a horizontal line of sight is chosen, e.g., the y-direction. The trajectory of the ejection is tilted by approximately 20° with respect to the x-direction (cf. Fig. 8), thus, these projections nicely show the ejection flying through the corona.

The intensities I(x,z;t) = ∫yε(x,y,z;t)   dy, are displayed in the top row of Fig. A.1, where ε is the emissivity at a given grid point x,y,z and time t. To avoid Moiré patterns when displaying the images, the values for density and temperature were interpolated on a grid with higher spatial resolution before the emissivities were calculated using CHIANTI (see also Sect. 3). This procedure is similar to that of Peter et al. (2004, 2006). The intensities in Fig. A.1 are displayed on a logarithmic scale with dynamic ranges of 3000 (O vi) and 50 (Mg x) to achieve a better contrast.

The bottom panels in Fig. A.1 and the movie show the current j, a measure of the Ohmic heating rate (∝ j2), in two different normalizations. The lower left panel shows j2 normalized by the average trend with height, i.e., the line-of-sight-integrated currents (∫y...dy) averaged along the x-direction and in time,  ⟨...⟩ x,t,

(A.1)

This normalization is necessary to see structures in the heating rate (∝ j2), which when averaged horizontally, drops roughly exponentially with a scale height of about 5 Mm (Bingert & Peter 2011).

To emphasize the temporal variability, the heating rate was normalized at each grid point in the 3D computational domain by the temporal average,  ⟨...⟩ t, at the respective grid point. This normalized quantity is then integrated along the line of sight, i.e.,

(A.2)

The term basically shows fluctuations along the line of sight, which is why it is indexed F. In the lower right panel of Fig. A.1, this quantity is plotted using a rainbow color table, where violet represents low values of and red represents high values.

A potential magnetic field is used as an upper boundary condition above the computational domain in the 3D MHD model. Of course, the magnetic field inside the box is computed self-consistently based on the MHD equations. As a result, increased currents are observed near the top boundary. These currents have no impact on the magnetic structure and plasma heating in the main part of the box. They are small compared to those at lower heights, which are responsible for heating the coronal plasma (note that the average currents decrease exponentially with height).


© ESO, 2011

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