Supergranulation and Scale Emergence

Energy transport in the outer 30% of the sun's radius takes place primarily via thermally-driven convection. The physical parameter regime characterizing solar interior conditions is such that this convection is expected (and observed) to be strongly turbulent. Observations of the sun's photosphere can reveal the surface imprint of this convection, showing up as structures on more or less well-defined spatial scale. Granulation (Figure 1A) is the only such scale that is unambiguously convective, in that upflows (downflow) are spatially well correlated with positive (negative) temperature fluctuations. Supergranulation (see Figure 1B), a pattern on a scale 20-30 times larger, is observed primarily in horizontal velocity and lacks the convective signature seen in granulation. Supergranulation is usually assumed to be a surface imprint of a deeper convective scale, but why this scale (and no other) becomes imprinted in this fashion remains unexplained.

Figure 1A: G-Band image of approximately 15000 by 15000 kilometer piece of the solar photosphere, showing granulation. Bright areas correspond to hotter rising fluid, and darker lanes to colder sinking fluid. Supergranular cells have a typical length scale of about 1000 km, and a lifetime of a few hours. The small bright points are associated with strong concentration of magnetic fields. Cropped from an image by R. Shine, Lockheed/Palo-Alto. Click on the image to see an animation from data taken at the Swedish Vacuum Solar Telescope (mpeg 480KB).
Figure 1B: Doppler image of the solar disk, showing line-of-sight velocity. Solar rotation has been subtracted, and acoustic oscillations have been removed by temporal averaging. The remaining pattern is called supergranulation, and is a primarily horizontal flow, as evidenced by the fact that the signal is strongest near the solar limb and vanishes at disk center. Image by D. Hathaway using data from SOHO/MDI.

Using Monte Carlo simulations, we have been exploring the possibility that supergranulation is an emergent length scale, building up as small magnetic elements are randomly displaced by the granular flow, occasionally colliding and aggregating to form larger magnetic clusters that, we postulate, can seed the supergranular downflow structure. The simulations are carried out on a 2D computational plane representing a piece of the solar photosphere, and share many similarities with diffusion-limited aggregation, a well-studied mechanism in the theory of pattern formation. Our simulations (see Figure 2 for a sample) indicate that for reasonable model parameter values, solar-like distributions of magnetic flux concentrations are produced, with length scales commensurate with supergranulation can indeed emerge in this manner.

Figure 2A: A typical spatial distribution of clusters produced by our Monte carlo simulation. Blue and Red code the magnetic polarity. Only clusters of size larger than 10 magnetic elements are shown. Click on the image to see an animation (mpeg, 19MB).
Figure 2B: High resolution magnetogram of a quiet Sun region, away from active regions or other large-scale magnetic structures, showing magnetic flux concentrations of opposite polarities (red/green). Magnetographic data from SOHO/MDI.

We are currently investigating whether the same aggregation process, fed by the decay of sunspots and active regions, could form plage-like structures, and how the characteristics of such structures --or any other emerging scales-- are affected by the injection rate of small magnetic structures. Long term plans include the coupling to simulations of total solar irradiance, also in development in our group, with the aim of building a working model for the contribution of the magnetic network to solar irradiance variations, that could be extended all the way back to the Maunder Minimum.

Who in the group works on this: Ashley Crouch, Paul Charbonneau. Kim Thibault.

Recent publications by group members on this topic:

Thibault, K., Crouch, A., Charbonneau, P. 2006, Solar supergranulation as a result of granular advective interaction: a numerical simulation. Canadian Undergraduate Physics Journal, 4, 7-10
Crouch, A., Charbonneau, P., & Thibault, K. 2007, Supergranulation as an emergent length scale, The Astrophysical Journal, 662, 715-729
Thibault, K., Charbonneau, P., & Crouch, A. 2011, The buildup of a scale-free photospheric magnetic network, The Astrophysical Journal, 757, id187