4.1 Methods

Let us recall that supergranulation is first of all a feature of the surface velocity field at the surface of the quiet Sun. Three methods are currently able to detect the associated signal. These are Doppler imaging, granule tracking, and local helioseismology.

4.1.1 Dopplergrams

Doppler imaging is the oldest technique used to monitor supergranulation (the first detection by Hart (1954Jump To The Next Citation Point) was on a Doppler signal). A SOHO/MDI view of supergranulation is shown in Figure 2View Image. An inconvenience of Doppler imaging is that it only provides the line-of-sight component of the velocity field, which except at the disc centre or at the solar limb is a mixture of the horizontal and vertical velocity field components. In this figure, one clearly notices that the supergranulation velocity field is mainly horizontal, as the signal almost disappears near the disc centre.

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Figure 2: A Dopplergram revealing the supergranulation pattern (credits SOHO/MDI/ESA).

4.1.2 Tracking

Another way to infer the velocity fields of the solar plasma in the photosphere is to track various structures visible at the surface. The idea is that small-scale structures like granules (see Section 3.1 below) are simply advected by large-scale flows. This technique is used in three different algorithms: the local correlation tracking (LCT), the coherent structure tracking (CST), and the ball-tracking (BT). The first one determines the motion of features on an image by maximising the correlation between small sub-images (November and Simon, 1988). The second method identifies coherent structures in the image by a segmentation process and then measures their displacement (e.g., Roudier et al., 1999aRieutord et al., 2007Tkaczuk et al., 2007). The third algorithm (BT) follows the displacement of floating balls over the intensity surface of images. The motion of the floating balls traces the mean motion of granules; this is presumably more effective computationally speaking than LCT and CST (Potts et al., 2004).

The principles and accuracy of granule tracking with LCT or CST were tested by Rieutord et al. (2001Jump To The Next Citation Point) using synthetic data extracted from numerical simulations. They showed that flows at scales larger than 2.5 Mm are well reproduced by the displacements of granules. At shorter scales, the random motion of granules (which are dynamical structures) generates a noise that blurs the signal. The 2.5 Mm lower limit was recently confirmed by Rieutord et al. (2010Jump To The Next Citation Point) with observations using the Hinode/SOT data.

Since the spatial resolution of the granule tracking technique is well above the one needed for supergranulation, this method is well adapted to derive the horizontal components of the supergranulation flow, and it does not suffer from a projection effect, unlike Doppler imaging. An example of the flow fields obtained by Rieutord et al. (2008Jump To The Next Citation Point) using this technique is shown in Figure 3View Image.

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Figure 3: The supergranulation horizontal velocity field as obtained by granule tracking (from Rieutord et al., 2008Jump To The Next Citation Point).

4.1.3 Local helioseismology

This method uses the propagation of acoustic or surface gravity waves (f -modes) to determine the velocity of the medium over which they propagate. Basically, if the wave velocity is c and that of the fluid is V, a plane wave travelling downstream shows a velocity V + c whereas the one travelling upstream moves with a velocity V − c. The sum of the two measured velocities gives that of the fluid. However, the phase velocity of the waves is not directly measurable: the observable quantity is the local oscillation of the fluid which results from the superposition of many travelling waves. A proper filtering is thus needed to select the desired wave; this operation requires a true machinery. We refer the reader to the review of Gizon and Birch (2005Jump To The Next Citation Point) for a detailed introduction to this subject. Here, we just want to recall some basic information about the output of this technique: the spatial resolution at which velocity fields can be measured is around 5 Mm, and the time resolution for time-distance helioseismology is around 8 h. This is lower than what can be achieved with other methods but, in exchange, this technique is the only one that can probe the vertical profiles of the velocities and image the subphotospheric dynamics. Typically, vertical variations can be evaluated down to 10 – 15 Mm below the surface, but the accuracy of measurements deeper than 10 Mm is still debated. A comparison between the tracking and helioseismic reconstructions of large-scale solar surface flows was done by Švanda et al. (2007), who found very good agreement between the two.

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