Research ArticleASTRONOMY

A low upper limit on the subsurface rise speed of solar active regions

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Science Advances  13 Jul 2016:
Vol. 2, no. 7, e1600557
DOI: 10.1126/sciadv.1600557
  • Fig. 1 Diagram of the setup for the simulation (bottom panel) and vertical slices through the simulation with a rise speed of 500 m/s at 13 and 3 hours before the emergence time (middle and top panels).

    In the bottom panel, the magnetic flux tube used to generate the bottom boundary condition is shown in gray. The major radius of the flux tube is given by R, the minor radius is given by a, and an untwisted magnetic field is oriented along the tube. Within the minor radius, the magnetic field has a Gaussian dependence of the form exp[−2x2/a2], where x is the distance from the center of the tube; the magnetic field is zero outside the tube. As the simulation progresses, the flux tube moves upward with rise speed vr. In the top two panels, the log of the magnetic field strength is color-coded (red is the strongest field, and light yellow is the weakest), and the arrows show the flows in the plane of the vertical slice (the largest arrows represent about 3 km/s). Upward and horizontal diverging flows are apparent during the emergence process in this case.

  • Fig. 2 Simulations of the emergence of magnetic flux through the photosphere reproduce many of the features of observed emergences.

    The top row shows, from left to right, the time evolution of the line-of-sight surface magnetic field associated with the emergence of AR11416 as seen by SDO/HMI. The images cover the time period from 14 hours before the emergence time to 8 hours after the emergence. The middle row shows the vertical surface magnetic field of a simulation for the case with a flux tube rising at a rise speed of 140 m/s. The bottom row shows vertical slices at y = 0 through the magnetic field strength in the same simulation. In the first two rows, positive (negative) line-of-sight magnetic field is shown in white (black). The gray scale is saturated at 120 G. In the bottom row, the color scale is the same as in Fig. 1.

  • Fig. 3 At 3 hours before the emergence time, the near-surface flows inferred from HMI observations are dominated by convection, whereas the simulations show a diverging flow that increases in strength with the rise speed of the flux tube at 20-Mm depth.

    The two panels in the left column show maps of the horizontal divergence of the flows measured from helioseismology (red for diverging flows and blue for converging flows), flow maps from helioseismology (black arrows), and line-of-sight magnetic field strength (from magnetograms, shaded gray regions for fields stronger than 60 G) for the HMI observations of AR11416 and AR11158. The four-panel group on the right shows simulations for 10-kG flux tubes with rise speeds of 70, 140, 280, and 500 m/s at 20-Mm depth. The simulations with rise speeds of 280 and 500 m/s produce strong diverging flows that are not seen in the observations. The longest arrows represent flows of 400 m/s.

  • Fig. 4 Comparison of the azimuthal average of the horizontal surface outflow from HMI observations with the surface outflows seen in the simulations rules out flux tubes with total flux 1022 Mx rising with speeds above 140 m/s at 20-Mm depth.

    The simulations (blue circles) show a radial surface outflow that increases with the rise speed of the flux tube through the bottom boundary of the simulation domain. The error bars for the simulations show upper limits on the noise in the seismology measurement procedure. The horizontal black arrows show the observations for AR11416 and AR11158 (the examples shown in Fig. 3). The red shaded region shows the one-σ variations in the azimuthal average of the horizontal outflow at a distance of 15 Mm from the emergence location for the sample of 70 observed active regions. The green diamond shows the reduced field strength case (error bars not shown; the errors are the same as the other simulations), and the green square shows the reduced cross-section case. The simulations with a rise speed of 140 m/s with the tube located in the strongest upflow or strongest downflow at the bottom boundary produce diverging flows of about 90 m/s. As discussed in the text, the surface flows driven by flux emergence depend not only on the rise speed but also on the geometry and field strength of the rising flux tube.

Supplementary Materials

  • Supplementary Materials

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    • fig. S1. Comparison of horizontal surface flows measured using LCT (red) and helioseismology (black) for AR11416.

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