A. C. Birch1, H. Schunker1, D. C. Braun2, R. Cameron1, L. Gizon1,3,5,6, B. Löptien1, M. Rempel4 & E. Guggenberger1
1 Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
2 NorthWest Research Associates, 3380 Mitchell Ln, Boulder, CO 80301, USA
3 Georg-August-Universität Göttingen, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
4 National Center for Atmospheric Research, High Altitude Observatory, 3080 Center Green Drive, Boulder, CO 80301, USA
5 Center for Space Science, New York University Abu Dhabi, PO Box 129188 Abu Dhabi, UAE
6 National Astronomical Observatory of Japan, Mitaka, Tokyo 181-8588, Japan
Solar active regions are thought to be the result of magnetic flux tubes rising from deep in the solar interior and penetrating the surface. The prevailing picture is that these flux tubes are formed in the stably stratified layer just below the convection zone. An alternative view is that they are formed in the convection zone itself.
Calculations based on the thin flux-tube approximation (these calculations assume that the flux tube radius is small compared to the scale height of the solar stratification) predict that flux tubes that rise from the base of the convection zone will reach a speed of close to 500 m s-1 at 20 Mm below the surface1. However, the thin flux tube model is not justified near the solar surface due to the compressibility of the solar environment near the surface, and realistic numerical simulations of magnetoconvection are required in this region2.
To better understand how active regions emerge, we used observations of surface flows coupled with numerical simulations of magnetoconvection to constrain the rise speed of magnetic flux tubes from the solar interior3.
To ensure we reliably capture surface flows associated with the emergence process we employ observations of many such regions. The high-resolution full-time coverage of HMI is ideal for this purpose. For this study, we used line-of-sight magnetic field, intensity, and Dopplergram observations of 70 emerging active regions observed from 2010 through to 2012, as described in ref. 4. From these we made flow maps with a 6 hour cadence and time-averaged magnetic field maps for each active region. Using both helioseismic holography and local correlation tracking (LCT5) of the granules in the continuum intensity, we measured the horizontal flows at the surface of the Sun as the active regions emerged. Comparison of the helioseismology and LCT results confirms that the two methods are measuring the same horizontal flows at the surface.
Figure 1 | Diagram of the setup for the simulation (bottom panel) and vertical slices through the simulation with a rise speed of 500 m s-1 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 [−2 x2 / 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-1). Upward and horizontal diverging flows are apparent during the emergence process in this case.
We carried out three-dimensional magneto-hydrodynamic simulations using the MURaM code to simulate the rise of a flux tube through the last 18~Mm below the solar surface (Fig. 1). We used the basic setup of ref. 2. The simulations consisted of a half torus of a magnetic flux tube injected, with a prescribed rise speed, through the bottom boundary of the simulation domain (48 × 48 × 20 Mm3). The simulations differed in the rise speed of the magnetic flux concentration (70 m s-1 to 500 m s-1). The simulations showed that the horizontal flows at the surface increase with the (imposed) upward rise speed of the magnetic flux concentrations: material is pushed to the sides by the upward motion of the flux concentrations.
Figure 2 | 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-1 at 20 Mm depth. The simulations with rise speeds of 280 and 500 m s-1 produce strong diverging flows that are not seen in the observations. The longest arrows represent flows of 400 m s-1.
By comparing the simulations and the observations of surface flows (see Fig. 2), we showed that magnetic flux concentrations cannot be rising more quickly than the local subsurface convective velocity, which is about 150 m s-1 at a depth of 20 Mm below the surface (see Fig. 3). The upper limit on the rise speed of magnetic flux concentrations obtained here (~150 m s-1) is about three times smaller than the rise speed predicted by thin flux tube calculations (500 m s-1 at 20 Mm). Although thin flux tube calculations reproduce the latitudes at which active regions emerge and also their tilt angles, these models cannot address the interaction of flux tubes with convection in the near-surface layers.
Figure 3 | 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 red shaded region shows the 1-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 a case where the field strength has been reduced by a half (error bars not shown; the errors are the same as the other simulations), and the green square shows a case where the tube cross-section has been reduced by a half. The simulations with a rise speed of 140 m s-1 with the tube located in the strongest upflow or strongest downflow at the bottom boundary produce diverging flows of about 90 m s-1.
This result shows that convection must play a key role in the flux emergence process and the prevailing theoretical picture must be modified to include the effect of convection in the solar interior. See the publication3 for more detail.
 Fan, Y., 2009, Living Rev. Sol. Phys., 6, 4
 Rempel, M. & Cheung, M. C. M., 2014, ApJ, 785, 90
 Birch, A. C., Schunker, H., Braun, D. C., Cameron, R., Gizon, L., Löptien, B., & Rempel, M., 2016, Sci. Adv., 2, e1600557
 Schunker, H., Braun, D. C., Birch, A. C., Burston, R. B., & Gizon, L., 2016, A&A, 595, A107
 Welsch, B. T., Fisher, G. H., Abbett, W. P., & Regnier, S., 2004, ApJ, 610, 1148