ESTRATO POBLADORES TURISTAS

Figure 4.4: Temporal evolution of magnetic (black) and kinetic (red) energy above the corona.

dynamics of these eruptions in more detail. The kinetic energies of these eruptions are0.6−3.6× 1025erg, while the modulation of the magnetic energy during the eruptions is1−4×1026erg. The first rise in kinetic energy (t= 175 min) corresponds to the initial emergence of the magnetic field into corona. The magnetic energy gradually increases throughout the simulation, as more magnetic energy is being brought into the atmosphere by the emergence of new magnetic flux.

4.2

First Confined Eruption

We now focus on the first eruption. In Fig 4.5 we show the magnetic field topology at t = 274.24 min. Left column shows the side and right column the top view of the field lines. The magnetic lobes come into contact early in the simulation (beforet= 214.25 min, Fig 4.1c). The blue field lines in Fig 4.5a are the field lines, which have been traced from the apex of each emerging lobe. Therefore, these field lines could be considered as the envelope field lines of each bipole. Notice that viewed from the top (Fig 4.5b), the two sets of blue lines (connecting P1-N1 and P2-N2) have been compressed and adopted an orientation almost parallel to the PIL between P1-N2. A current sheet is formed along the interface between the two systems, marked as upper current sheet in Fig 4.5a. Reconnection between the two lobes of blue field lines form lines connecting the outer polarities (N1-P2, grey colour) and the inner polarities (P1-N2, green colour shown in Fig 4.10c as they are relevant to the second eruption).

4.2 First Confined Eruption 45

For clarity, Fig 4.5c and Fig 4.5d show only the blue and the grey field lines. Notice that the grey lines located higher up have the shape of the blue lines at their flanks. These lines relax downwards and adopt a less-curved orientation (as they are projected onto the xy-plane). We will refer to the grey lines as the overlying field of the flux rope, which will be defined later.

Field lines of the magnetic lobes, which are located lower in height and they have emerged later in the simulation, are more sheared (pink lines connecting P1-N1 and P2-N2, Fig 4.5a and Fig 4.5b). The footpoints of these field lines near the outer polarities have adopted a J-like config- uration, due to the rotation of these polarities (see velocity vectors inside the polarities, Fig 4.2b). This J-shape is less apparent near the inner polarities, as the two (pink) sets of field lines come very close together and they start to be deformed (e.g. due to compression of the material there and/or due to reconnection).

(a) Side view. (b) Top view.

4.2 First Confined Eruption 46

(e) Side view. (f) Top view.

Figure 4.5: The magnetic field line topology at just before the eruption att = 274.24 min. The overall magnetic field line topology shown in side view (a) & top view (b). The white crosses indicate the locations where the current sheets are formed. Panels (c) and (d) show the top part of the magnetic field lines system. Blue field lines are part of the outermost magnetic field lobes and the grey field lines result from the reconnection between the two sets of blue field lines. Panels (e) and (f) show the bottom part of the magnetic field line system. Pink field lines are sheared and rotated field lines from each magnetic bipole found lower in height and orange field lines are the result of reconnection between the two sets of pink field lines.

As the pink field lines approach each other above the P1-N2 PIL, a current sheet is formed there, which we name as the lower current sheet. Through this lower current sheet, the (pink) field lines reconnect, forming field lines connecting the outer polarities (N1-P2, orange colour) and the inner polarities (P1-N2, arcade field lines, not shown here). Eventually the orange field lines, which have a mirror S shape, pass through the center of a newly developed flux rope. This system is isolated in Fig 4.5e and Fig 4.5f. Notice that the orange lines have a small amount of twist due to the sheared nature of the pink field lines and the reconnection happening in three dimensions. Also, another current sheet is formed (named as middle current sheet) in between the flux rope lines (orange) and the grey lines.

Now we trace the height-time profile of the flux rope by locating the maximum of the normal component of the magnetic field on a plane perpendicular to the P1-N2 PIL and plot it in Fig 4.6a (black). We have not traced the height before t = 271.38 min, because we could not spot the center of the flux rope. We find that the flux rope is already on non-linear ascent from t = 271.38 min untilt = 275.67 min. The rising motion slows down during the time period t = 275.67−278.53 min. Then we find the rapid rise eruptive phase, which is followed by gradual saturation aftert= 283 min.

4.2 First Confined Eruption 47

(a) (b)

Figure 4.6: Black line: height-time profile of the first flux rope. (a) Red line: temporal evolution of the average absolute magnetic tension in a cross-sectional cut area above the flux rope. (b) Red line: temporal evolution of the average azimuthal magnetic flux in the same area above the flux rope.

Figure 4.7: MaximumJ/B as a function of time for the lower (blue), middle (black) and upper (red) current sheet.

To understand the dynamics of the flux rope’s motion, we follow the temporal evolution of the maximumJ/B at the lower (blue), middle (black) and upper (red) current sheets in Fig 4.7. During the evolution of the eruption, the lower current sheet acts as the flare current sheet and the middle as the “breakout” current sheet, as we explain in the following.