Numerical modelling of footpoint-driven magneto-acoustic wave propagation in a localised solar flux tube
Download the paper, The Astrophysical Journal, 2011.
Figures
Figure 1
Figure 2
Figure 1: Vertical dependences of logarithms of the density ρ and the temperature T in the computational domain. These profiles are constructed using atmospheric parameters for the average quiet Sun (VAL IIIC; Vernazza et al. 1981) for the lower part of the model, and McWhirter et al. (1975) coronal model for the upper (corona) region.
Figure 2: Vertical dependence of the ratio of the minimum to the maximum values of the sound speed taken along the cross section in the x-direction in the computational domain.
Figure 3a
Figure 3b
Figure 3a, 3b: Initial state of the computational configuration. The logarithm of the background pressure, log(P0) (a), the temperature, T (b), the magnetic field components, B0x (c) and B0z (d) are shown. The z-axis corresponds to altitude and the x horizontal axis is parallel to the solar surface. The orange lines visualise the magnetic field structure of the flux tube. The white lines are the iso-plasma-β contours, labelled by their values. The photosphere, chromosphere, transition region, and corona levels are highlighted schematically in the plot. Also, the position of the periodic driver (red ellipse) is illustrated at the footpoint region.
Figure 4a
Figure 4c
Figure 4b
Figure 4d
Figure 4a, 4b, 4c, 4d: Snapshots of the field-aligned (V∥) and transverse (V⊥) components of the velocity response showing the temporal development of the initial perturbation generated by 30 s vertical periodic driver at different times in the open magnetic flux tube. The colour scale shows the V∥ and V⊥ perturbations in km/s at times given in the bottom left corner of each pair of images. The colour curves (i.e., white and orange) are the same as on Figure 3. The angle and length of the white arrows correspond to the velocity vector field.
Figure 5a
Figure 5c
Figure 5b
Figure 5d
Figure 5a, 5b, 5c, 5d: Snapshots of the relative pressure difference ΔP/P0 and temperature ΔT perturbation from the initial state in a magnetic flux tube at different times (same as Figure 3). The colour scale shows the relative difference of pressure and temperature (in Kelvin) perturbations. The magnetic field lines and iso-plasma-β contours are the same as in Figure 3.
Figure 6a
Figure 6c
Figure 6b
Figure 6d
Figure 6a, 6b, 6c, 6d: Same as Figure 4 but generated by 30 s periodic horizontal driver.
Figure 7a
Figure 7c
Figure 7b
Figure 7d
Figure 7a, 7b, 7c, 7d: Relative pressure difference ΔP/P0 and temperature ΔT perturbation from the initial state in the magnetic flux tube at different times. Wave excitation is due to periodic horizontal motion. The colour scale shows the relative difference of pressure and temperature perturbations. The coloured (ie, white and orange) curves are the same as in Figure 5.
Figures 8a-8d
Figure 8a, 8b, 8c, 8d: Time series of the relative pressure difference ΔP/P0 and temperature ΔT perturbation showing the development of a guided wave at the transition region from the vertical harmonic source. Only the zoomed out portion centered around the transition region is shown in the plots.
Figures 9a-9d
Figure 9a, 9b, 9c, 9d: The same as Figure 8 but generated by the horizontal periodic driver.
Figure 10a
Figure 10c
Figure 10b
Figure 10d
Figure 10a, 10b, 10c, 10d: Altitude vs. time rendering of transverse (V⊥) and field-aligned (V∥) components of the velocity at x = 2.0 Mm, for vertical (upper panels) and transverse driving of perturbations. The white lines show the altitude variations of selected iso-plasma-β contours with time, labeled by their appropriate value.
Figure 11a
Figure 11c
Figure 11b
Figure 11d
Figure 11a, 11b, 11c, 11d: ω-k diagrams of the V∥ and V⊥ velocity components taken along the horizontal cross section at the chromosphere region, ie, at 0.85 Mm in the vertical direction. The upper and lower panels correspond to the V∥ and V⊥ velocity components generated by the vertical and horizontal photospheric drivers, respectively.
Figure 12a
Figure 12c
Figure 12b
Figure 12d
Figure 12a, 12b, 12c, 12d: Same as Figure 11 but the velocity components are taken along the horizontal cross section at the vertical height 1.5 Mm.
Figure 13
Figure 13: ω-k diagrams of the vertical V∥ and horizontal V⊥ velocity components in the transition and solar corona regions. Fourier transform performed on time-distance series are taken at heights h = 1.8, 1.85, 2.53, and 3.03Mm. The four panels are the ω-k diagrams of V∥ and V⊥ velocity components excited by vertical photospheric driver in each row, respectively.
Figure 14
Figure 14: Same as Figure 13 but the V∥ and V⊥ velocity components are now generated by a horizontal photospheric driver.
Videos
The omega-k diagrams of the vertical and horizontal velocity component.
Fourier transform performed on time-distance series are taken at heights h=0-4.0 Mm.
omega_k_Vpl_0-1976 (1).movVertical velocity component
omega_k_Vpd_0-1976.movHorizontal velocity component