Dependence of emergence morphology on twist

Figures 4.1 and 4.2, respectively, show time sequences of the emergence of the untwisted (λ= 0) and the twisted (λ = 0.5) flux tube. In both figures, the temperature distribution of the background stratification is shown in greyscale. The absolute field strength|B|is indicated by the colour-coding. In each panel, theτ_Ross= 1level is indicated by a purple line running across the horizontal extent of the domain.

We first describe features that are common to both simulations. In both cases, the buoyancy force accelerates the flux tube upwards. The buoyant acceleration of each flux tube is accompanied by a co-acceleration of non-magnetic material above it. The upwards displacement of non-magnetic material above the tube is indicated by the local elevation of theτ_Ross = 1level (see the snapshots att= 4min andt = 8min in Figs. 4.1 and 4.2) with respect to the average geometrical height of the same optical depth. Radiative cool-ing of material near the surface causes it to become denser than material in the underlycool-ing layer. This top heavy configuration is unstable to perturbations displacing material in the vertical direction. With the flux tube rising towards the surface, the overly dense material is able to descend by sliding around the rising tube. The sinking of the dense material into the superadiabatically stratified convection zone instigates the development of two down-flows, one on either side of the emerging tube. In Figs 4.1 and 4.2, the two downflows show up as two ‘fingers’ of cool (dark in the greyscale) material reaching into the opti-cally thick layers (i.e. the convection zone). The pressure deficit in the wake of the rising tube with respect to the surroundings gives a pressure gradient that deflects the developing downflows towards the wake.

The tube expands as it rises into layers of lower external pressure. In the convec-tion zone, expansion in the vertical and horizontal direcconvec-tions occur at comparable rates.

Once the magnetic structure has reached the surface, the expansion becomes markedly asymmetric with respect to the vertical and horizontal directions. The reason for this is simple: expansion in the vertical direction requires lifting of material into the stably strat-ified layer, which requires work to be done against gravity. This explanation follows that of Archontis et al. (2004), who carried out idealized simulations of flux emergence into the corona. To make the computation feasible, their simulations ignore radiative transfer

4.2 Simulation results

Figure 4.1: Time sequence of the emergence of an untwisted magnetic flux tube (λ = 0). The background greyscale indicates the temperature stratification. The absolute field strength |B| is indicated by the colour-coding. In each of the panels, the purple line running across the horizontal extent of the domain indicates theτ_Ross = 1level.

and convection in the layers underlying the corona. However, their background atmo-sphere does contain a stably stratified layer mimicking the photoatmo-sphere. Although our simulation setups are different, both yield the result that a flux tube emerging into the photosphere expands preferentially in the horizontal direction.

The upper panel of Fig. 4.3 shows profiles of the longitudinal magnetic fieldB_l(upper panel) att = 10 min. The profiles were evaluated at the level of constant geometrical height (z = 0 km). The solid and dashed lines show the profiles for the untwisted and twisted cases respectively. The profiles ofB_lin the upper panel show that the twisted tube has a core with field strengths of up to 900 G. In comparison, the untwisted tube has a relatively weak field of200G.

The lower panel of Fig. 4.3 shows the corresponding profiles of the x−component of the velocity at t = 10 min. The strong horizontal expansion of the emerging mag-netic structure leads to the creation of two shock fronts propagating in opposite horizontal directions. This is illustrated by the profiles of the horizontal velocity in Fig. 4.3. The

Figure 4.2: Same as Fig. 4.1, but for a twisted flux tube (λ= 0.5).

horizontal velocity profile has maximum amplitude just outside the magnetic structure (compare with the upper panel of the same figure). The non-magnetic material residing immediately outside the tube can have speeds reaching10−15 km s⁻¹, corresponding to Mach numbers of M ≈ 1 −2. The expanding flux tube acts like a piston, which does work on the surrounding non-magnetic material. The acceleration of the material in the neighbourhood of the tube is so strong that they reach supersonic speeds and shocks form. In Fig. 4.3, the pair of shock fronts propagating in opposite directions are centered atx= 9Mm and atx= 15Mm respectively. Viscous dissipation in the shock fronts lead to localized specific entropy production, enhanced temperature and radiative cooling.

The kinetic energy density in the supersonic outflows driven is several times larger than the kinetic energy density of the granular flow at the surface, which has typical horizontal speeds of2−4km s⁻¹. Suppose such a flux tube were to emerge at the solar surface. Its expansion would be so strong, that we expect the resulting outflows to modify the granulation pattern. Our 3D simulations of flux emergence, which will be presented in Chapter 5, indeed confirm this expectation.

From previous work in the literature (Schüssler 1979, Longcope et al. 1996) and from our study presented in Section 2.3.2, we know that an initially untwisted flux tube

4.2 Simulation results

Figure 4.3: Profiles of the longitudinal magnetic field Bl (upper panel) and of the hor-izontal velocity v_x (lower panel), both taken at time t = 10 min at the level z = 0.

The solid lines and dashed lines indicate the profiles for the untwisted and twisted cases respectively.

rising under its own buoyancy separates into a pair of counter-rotating vortex rolls after transversing a distance a few times its diameter. A similar behaviour is found in the simulation presented in this chapter. By t = 8 min, the initially untwisted tube (see Fig. 4.1) is separating into two vortex rolls. This is the reason that in Fig. 4.3, we find that in the twisted tube, the maximum of the longitudinal field is strongest in the core, whereas the longitudinal field in the untwisted tube is relatively weak.