4.6 Multiscale convection and magnetic fields

As shown in Section 2.2, the magnetic dissipation scale at the solar surface is ℓη ∼ 100 m or slightly less. Hence, convection at the solar surface is strongly coupled to the Sun’s magnetic dynamics at all observable scales, including that of supergranulation. The particular role played by magnetic fields in the supergranulation problem and the large amount of observational information available on this topic justify a dedicated subsection. In the following, we first look at the correlations between supergranulation and the magnetic network and then describe the properties of internetwork fields, whose dynamics can hardly be dissociated from the formation of the magnetic network. After a short detour to the observations of the interactions between supergranulation and active regions, we finally review several studies of the dependence of supergranulation on the global solar magnetic activity.

4.6.1 Supergranulation and the magnetic network

The discovery of the chromospheric network in Ca+K spectroheliograms (the K-line of Ca+ at 393.4 nm) dates back to Deslandres (1899). Such a spectroheliogram is shown in Figure 6View Image. Leighton et al. (1962) and Simon and Leighton (1964Jump To The Next Citation Point) performed a comparative study between magnetograms, spectroheliograms, and Dopplergrams, which revealed a strong correlation between the chromospheric network, the magnetic field distribution of the quiet Sun and supergranulation. For this reason, both magnetograms and spectroheliograms are used to trace supergranulation (e.g., Lisle et al., 2000Jump To The Next Citation PointDel Moro et al., 2007). It should be kept in mind, however, that the dynamical interactions between magnetic fields and supergranulation are actually not well understood theoretically. This problem will be discussed at length in Section 8.

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Figure 6: A view of the chromospheric network at the Ca+K3 line at 393.37 nm (from Meudon Observatory).

The magnetic network refers to a distribution of magnetic field concentrations (associated with bright points in spectroheliograms) with typical field strengths of the order of 1 kG (see reviews by Solanki, 1993de Wijn et al., 2009Jump To The Next Citation Point), primarily located on the boundaries of supergranules (Simon et al., 1988), in downflow areas. Several differences between supergranulation and the magnetic network have been noticed, including a 2% relative difference in the rotation rate of the two patterns (see Snodgrass and Ulrich (1990) and Section 4.5 above). The magnetic network is not regularly distributed on the boundaries of supergranulation cells but rather concentrates into localised structures (see Figure 7View Image). Estimates for the lifetime and size of supergranules inferred from magnetograms or spectroheliograms are significantly smaller than those based on direct velocimetric measurements (Wang and Zirin, 1989Schrijver et al., 1997Hagenaar et al., 1997Jump To The Next Citation Point). For instance, Hagenaar et al. (1997), using correlations of maps of the chromospheric network, obtained a typical size of 16 Mm. As far as the horizontal velocities are concerned, the tracking of magnetic network elements gives values around 350 m s–1, close to the estimates derived from granule tracking (Lisle et al., 2000). Krijger and Roudier (2003) found that the chromospheric network is well reproduced by letting magnetic elements that are emerging be passively advected by the surface (supergranulation) flow field.

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Figure 7: Magnetic field distribution (grey scale levels) on the supergranulation boundaries. The black dots show the final positions of floating corks that have been advected by the velocity field computed from the average motion of granules. The distribution of corks very neatly matches that of the magnetic field. (from Roudier et al., 2009Jump To The Next Citation Point).

These results suggest that the formation of the magnetic network is in some way related to the supergranulation flow. It is however probably too simplistic and misleading to make a one-to-one correspondence between the single scale of supergranulation and the network distribution of magnetic bright points. Several studies with the Swedish Solar Telescope at La Palma observatory indicate that strong correlations between flows at scales comparable to or smaller than mesoscales (i.e., significantly smaller than supergranulation) and intense magnetic elements exist (Domínguez Cerdeña, 2003Domínguez Cerdeña et al., 2003Jump To The Next Citation Point). A recent study by Roudier et al. (2009), combining spectropolarimetric and photometric Hinode measurements, also demonstrated a very clear correlation between the motions at mesoscales and those of the magnetic network (see also de Wijn and Müller, 2009).

4.6.2 Internetwork fields

One of the major advances on solar magnetism in the last ten years has been the detection of quiet Sun magnetic fields at scales much smaller than that of granulation (e.g., Domínguez Cerdeña et al., 2003Jump To The Next Citation PointBerger et al., 2004Trujillo Bueno et al., 2004Jump To The Next Citation PointRouppe van der Voort et al., 2005Jump To The Next Citation PointLites et al., 2008Jump To The Next Citation Point). The ubiquity of these fields and their energetics suggest that the dynamics of internetwork fields could also be an important piece of the supergranulation puzzle (see also Section 4.6.5 below). It is therefore useful to recall their main properties before discussing the physics of supergranulation in the next sections. Note that the following summary is not meant to be exhaustive. For a dedicated review, we refer the reader to the recent work of de Wijn et al. (2009Jump To The Next Citation Point).

Internetwork fields refer to mixed-polarity fields that populate the interior of supergranules. Their strength is on average thought to be much weaker than that of network fields, but magnetic bright points are also observed in the internetwork, (e.g., Muller, 1983Nisenson et al., 2003de Wijn et al., 2005Lites et al., 2008Jump To The Next Citation Point). Besides, network and internetwork fields are known to be in permanent interaction (e.g., Martin, 1988Jump To The Next Citation Point). In the light of nowadays high-resolution observations, the historical dichotomy between network and internetwork fields appears to be rather blurred (this point will be further discussed in Section 8.1).

Internetwork magnetism was originally discovered by Livingston and Harvey (19711975) and subsequently studied by many authors (e.g., Martin, 1988Jump To The Next Citation PointKeller et al., 1994Jump To The Next Citation PointLin, 1995Jump To The Next Citation Point) at resolutions not exceeding 1” (730 km). Observations with the solar telescope at La Palma observatory revealed the existence of such fields at scales comparable and even smaller than the granulation scale (Domínguez Cerdeña et al., 2003Jump To The Next Citation PointRoudier and Muller, 2004Rouppe van der Voort et al., 2005). Recent studies based on Hinode observations (Orozco Suárez et al., 2007Jump To The Next Citation PointLites et al., 2008Jump To The Next Citation Point) reported magnetic field variations at scales comparable to or smaller than 100 km.

The strength of internetwork fields, their distribution at granulation and subgranulation scales and their preferred orientation are still a matter of debate. Almost every possible value in the 5 – 500 G range can be found in literature for the typical field strengths within the internetwork (Martin, 1988Keller et al., 1994Lin, 1995Domínguez Cerdeña et al., 2003Trujillo Bueno et al., 2004Jump To The Next Citation PointLites et al., 2008Jump To The Next Citation Point). This wide dispersion is explained by several factors. The most important one is certainly that Zeeman spectropolarimetry, one of the most frequently used tools to study solar magnetism, is affected by cancellation effects when the magnetic field reverses sign at scales smaller than the instrument resolution (Trujillo Bueno et al., 2004Jump To The Next Citation Pointde Wijn et al., 2009). Hence, very small-scale fields still partially escape detection via this method. Recent Zeeman spectropolarimetry estimates of the average field strength based on Hinode observations (Lites et al., 2008Jump To The Next Citation Point) are 11 G for longitudinal fields and 60 G for transverse fields (horizontal fields at disc centre), but wide excursions from these average values are detected and the observed signatures may also be compatible with stronger, less space-filling magnetic fields. On the side of Hanle spectropolarimetry, Trujillo Bueno et al. (2004) report an average field strength of 130 G, with stronger fields in the intergranular lanes and much weaker fields in the bright centres of granules.

The previously mentioned Zeeman estimates seem to indicate that internetwork fields have a tendency to be horizontal (Orozco Suárez et al., 2007Bommier et al., 2007Lites et al., 2008), sometimes even bridging over granules, but other studies have come to the opposite conclusion that internetwork fields are mostly isotropic (Martínez González et al., 2008Asensio Ramos, 2009Bommier et al., 2009). Using Zeeman and Hanle diagnostics in a complementary way, López Ariste et al. (2010Jump To The Next Citation Point) very recently came to the conclusion that internetwork fields are mostly isotropic and highly disordered, with a typical magnetic energy containing scale of 10 km.

4.6.3 The magnetic power spectrum of the quiet photosphere

The scale-by-scale distribution of magnetic energy and the power spectrum of magnetic fields in the quiet photosphere are other important quantities to look at, as they may give us some clues on the type of MHD physics at work in the subgranulation to supergranulation range. Based on various types of analysis (structure statistics, wavelets, etc.), several authors have notably argued that solar magnetic fields, from the global solar scales to the smallest scales available to observations, may have a fractal or multifractal structure (Lawrence et al., 1995Komm, 1995Nesme-Ribes et al., 1996Meunier, 1999Janßen et al., 2003Stenflo and Holzreuter, 20022003aJump To The Next Citation Point,bAbramenko, 2005).

Explicit studies of the power spectrum of the quiet Sun are currently limited to the range 1 – 100 Mm and to the line-of-sight component of the magnetic field. Most spectra available in literature have been obtained from either ground-based observations or SOHO/MDI magnetograms. We have been unable to find any study of the magnetic power spectrum of the quiet Sun covering scales well below 1 Mm, at which internetwork fields can now be detected with Hinode.

At scales below 10 Mm, the magnetic power spectrum of the quiet photosphere has been found to be rather flat and decreasing with decreasing scales. Scalings in that mesoscale interval range from −1 k to k− 1.4 (Lee et al., 1997Jump To The Next Citation PointAbramenko et al., 2001Jump To The Next Citation PointHarvey et al., 2007Jump To The Next Citation PointMcAteer et al., 2009Longcope and Parnell, 2009Jump To The Next Citation Point). At scales larger than 10 Mm, a slightly positive flat slope ∼ k1.3–k0 has been reported by several authors (Lee et al., 1997Jump To The Next Citation PointAbramenko et al., 2001Jump To The Next Citation PointLongcope and Parnell, 2009).

4.6.4 Supergranulation and flows in active regions

Proceeding along the description of the interactions between supergranulation and magnetic fields, one may also consider the properties of surface flows at scales comparable to supergranulation within active regions and in the vicinity of sunspots. The reason for this is twofold. First, we may wonder how the supergranulation pattern evolves locally during the formation or decay of an active region. Second, the properties of flows around sunspots may give us some hints of the effect of strong magnetic flux concentrations on the flow dynamics in the quiet photosphere.

As far as the first point is concerned, the information is fairly scarce at the moment. Rieutord et al. (2010Jump To The Next Citation Point) recently reported the disappearance of the supergranulation spectral peak in the kinetic energy power spectrum of solar convection during the emergence of two magnetic pores. While the pores (of a size comparable to that of a granule) are emerging, the supergranulation flow becomes very weak just like if the surrounding magnetic flux associated with the pores had a significant impact on the flow. A related observation by Hindman et al. (2009Jump To The Next Citation Point) shows that the fairly regular tiling of the surface of the quiet Sun associated with supergranulation is somewhat disorganised and washed away within magnetic active regions.

On the second point, many studies in the past have focused on the detection and characterisation of intrinsic flows associated with sunspot regions (see Solanki, 2003 and Thomas and Weiss, 2008 for exhaustive descriptions of sunspot structure and dynamics) and significant observational progress has been made on this problem in recent years thanks to local helioseismology (Lindsey et al., 1996Gizon et al., 2000Jump To The Next Citation PointZhao et al., 2001Haber et al., 2001Braun and Lindsey, 2003Haber et al., 2004Zhao et al., 20042009Hindman et al., 2009Jump To The Next Citation Point). The general picture that has progressively emerged is the following (see Hindman et al., 2009Jump To The Next Citation Point, and Figure 8View Image): an annular outflow called the moat flow (Sheeley Jr, 1969) is observed at the surface, close to the sunspot. There is a corresponding return flow at depths smaller than 2 Mm, so the moat circulation is fairly shallow. In contrast, further away from the sunspot umbra, larger-scale circulations characterised by a surface inflow and a deep (> 10 Mm) outflow are inferred from helioseismic inversions.

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Figure 8: Structure of flows surrounding a sunspot, as inferred from helioseismology (from Hindman et al., 2009).

Several authors studied the structure of the moat flow using Doppler signal (Sheeley Jr and Bhatnagar, 1971Sheeley Jr, 1972Jump To The Next Citation Point), by tracking surface features, such as granules (Muller and Mena, 1987Shine et al., 1987) or small-scale magnetic elements (Sheeley Jr, 1972Harvey and Harvey, 1973Hagenaar and Shine, 2005), or using helioseismology (Gizon et al., 2000). One of the conclusions of these studies is that the outflow has properties similar to those of supergranulation (see notably Brickhouse and Labonte, 1988), albeit with a larger velocity ∼ 1 km s–1. It is however unclear whether or not this flow has anything to do with the regular supergranulation, as the outflow is centred on a strong field region in that case whereas it is the supergranulation inflow vertices that coincide with magnetic flux concentrations in the quiet Sun. As far as supergranulation is concerned, nevertheless, the lesson to be learned from helioseismology of sunspot regions is that magnetoconvection in strong fields has the naturally ability to produce a variety of coherent outflows and inflows at various horizontal and vertical scales in the vicinity of regions of strong magnetic flux. This phenomenology may be worth exploring further in the somewhat scaled-down system consisting of the supergranulation flow and local flux concentrations associated with the magnetic network in the quiet Sun (see Section 8.2 in this review).

4.6.5 Supergranulation variations over the solar cycle

In view of the association between supergranulation and the magnetic network, it is finally natural to wonder if and how the size of supergranules varies with solar activity.

Singh and Bappu (1981), studying spectroheliograms spanning a period of seven solar maxima, found a decrease of the typical size of the chromospheric network between the maxima and the minima of the cycle. Their results are in line with those of Kariyappa and Sivaraman (1994), Berrilli et al. (1999Jump To The Next Citation Point) and Raju and Singh (2002), but appear to be at odds with those of Wang (1988Jump To The Next Citation Point) and Münzer et al. (1989), who both reported an increase of network cell sizes in regions of stronger magnetic activity, and with those of Meunier (2003), who found from MDI magnetograms spanning the first half of Cycle 23 an increase of the size of magnetic elements at supergranulation-like scales with solar activity (note that Berrilli et al., 1999 also used data obtained at the beginning of Cycle 23 close to the activity minimum). These somehow contradicting results show that magnetic tracers must be used with care for this kind of measurements. The results are indeed sensitive to the thresholds used to identify the various field components (e.g., network or internetwork). Disentangling all these effects is not an easy task.

Recent studies have thus attempted to use proxies independent of magnetic tracers of supergranulation to measure its size, notably velocity features like positive divergences. DeRosa and Toomre (2004), using two data sets obtained at periods of different levels of magnetic activity, found smaller supergranulation cell sizes in the period of high activity. A similar conclusion was reached by Meunier et al. (2008). Meunier et al. (2007aJump To The Next Citation Point) found a decrease of the typical cell sizes with increasing field strength within supergranules, but noted that larger supergranulation cells were associated with stronger network fields at their boundaries. Hence, it seems that a negative or a positive correlation can be obtained, depending on whether the level of magnetic activity is defined with respect to internetwork or network fields. Meunier et al. (2007aJump To The Next Citation Point) also reported the absence of large supergranulation cells for supergranules with large internetwork magnetic field strengths, indicating that internetwork fields do have a dynamical influence on supergranules. We refer the reader to Meunier et al. (2007aJump To The Next Citation Point) for a more exhaustive discussion of the previous results and of the possible shortcomings and biases of these various studies.

Finally, on the helioseismic side, the dispersion relation for the supergranulation oscillations found by Gizon et al. (2003Jump To The Next Citation Point) appears to be only weakly dependent on the phase of the solar cycle (Gizon and Duvall Jr, 2004). However, the same authors reported a decrease in the lifetime and power anisotropy of the pattern from solar minimum to solar maximum.


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