4.5 Rotational properties of supergranules

A good measure of the influence of the global rotation Ω of the Sun on the dynamics of a structure of size L and typical velocity V is given by the Rossby number:
Ro = --V-- = (2Ω τ)−1. 2 ΩL

The second expression uses the lifetime of the structure τ = L ∕V. In numbers, taking τSG = 1.7 d and a rotation period of 25 – 30 d leads to RoSG ∼ 2– 3. This is not a large value, indicating that the Coriolis acceleration should have an effect on the dynamics of supergranules. This effect has been observed by Gizon and Duvall Jr (2003Jump To The Next Citation Point), who showed (Figure 5View Imagea) that the correlation between vertical vorticity and horizontal divergence of supergranules changes sign at the equator: it is negative in the northern hemisphere and positive in the southern one. Hence, supergranules, which may be seen as outflowing cells, behave like anticyclones in the Earth’s atmosphere (the vertical vorticity of anticyclones changes sign at the equator, see Figure 5View Imageb). These anticyclones are surrounded by cyclonic vorticity associated with downward flows; because these downdrafts have a somewhat smaller scale, this cyclonic vorticity is less conspicuous in measurements than the anticyclonic contribution of supergranules, but it has actually been singled out in the work of Komm et al. (2007).

View Image

Figure 5: (a) Correlation between the horizontal divergence and vertical vorticity of the supergranulation flow as a function of latitude (from Gizon and Duvall Jr, 2003Jump To The Next Citation Point). (b) Schematic view of anticyclones at the surface of the rotating Sun.

The first reports on the rotational properties of supergranulation focused on the rotation rate of the supergranulation pattern (Duvall Jr, 1980Jump To The Next Citation PointSnodgrass and Ulrich, 1990Jump To The Next Citation Point). Using Dopplergrams, they found, surprisingly, that supergranulation is rotating 4% faster than the plasma. This is now referred to as the superrotation of supergranules. In recent years, local helioseismology has proven extremely useful to study the rotational properties of supergranules. Their superrotation was confirmed by Duvall Jr and Gizon (2000) using the time-distance technique applied to f -modes. Beck and Schou (2000) estimated that the supergranulation rotation rate is larger than the solar rotation rate at any depth probed by helioseismology. Analysing time series of divergence maps inferred from time-distance helioseismology applied to MDI data, Gizon et al. (2003Jump To The Next Citation Point) found that the supergranulation pattern had wave-like properties with a typical period of 6 – 9 d, fairly longer than the lifetime of individual supergranules. They showed that the power spectrum of the supergranulation signal close to the equator presented a power excess in the prograde direction (with a slight equatorwards deviation in both hemispheres), thus explaining the anomalous superrotation rate of the pattern. The dispersion relation for the wave appears to be only weakly dependent on the latitude (Gizon and Duvall Jr, 2004Jump To The Next Citation Point). Schou (2003) confirmed these findings with direct Doppler shift measurements and found that wave motions were mostly aligned with the direction of propagation of the pattern. These results brought some extremely interesting new light on the supergranulation phenomenon and led to the conjecture that supergranulation could be a manifestation of oscillatory convection, a typical property of convection in the presence of rotation and/or magnetic fields (see Section 5).

However, Rast et al. (2004) and Lisle et al. (2004Jump To The Next Citation Point) questioned the interpretation of the observed power spectrum in terms of oscillations and suggested an alternative explanation in terms of two superimposed steady flow components identified as mesogranulation and supergranulation advected by giant cell circulations. According to Gizon and Birch (2005Jump To The Next Citation Point), this interpretation is not supported by observations. They argue that the finding of Lisle et al. (2004) that supergranules tend to align in the direction of the Sun’s rotation axis under the influence of giant cells can be explained naturally in terms of wave dynamics. Even more recently, Hathaway et al. (2006) argued that the supergranulation pattern superrotation inferred from Doppler shifts was due to projection effects on the line-of-sight signal. Using correlation tracking of divergence maps derived from intensity maps (Meunier et al., 2007c) and comparing it with direct Doppler tracking, Meunier and Roudier (2007) confirmed the existence of projection effects with the latter method, but found that the supergranulation pattern inferred from divergence maps was still superrotating, albeit at smaller angular velocities than those inferred by Duvall Jr (1980) and Snodgrass and Ulrich (1990Jump To The Next Citation Point). For a detailed discussion on the identification of supergranulation rotational properties with helioseismology, we refer the reader to the review article by Gizon and Birch (2005) on local helioseismology.

For the sake of completeness on the topic of rotation, we finally mention the observations by Kuhn et al. (2000) of small-scale 100 m high “hills” at the solar surface, which they interpreted as Rossby waves. Recently, Williams et al. (2007) argued that these structures actually resulted from the vertical convective motions associated with supergranules.

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