4.5 Moat flows

Apart from the Evershed flow within the spot, there is also a large scale outflow pattern surrounding spots. Figure 16View Image shows a 15 minute time average of a sunspot flow map taken with HMI/SDO (External Linkhttp://sdo.gsfc.nasa.gov/)7. The spot is off disk center and viewed at an angle of 35° relative the local vertical. Within the spot (bounded by black contour) the Evershed flow reaches values exceeding 1.6 km s–1. Outside the spot, the granulation shows an overall redshift (blueshift) on the limb (center) side of about 0.5 km s–1, extending to about twice the spot radius.
View Image

Figure 16: Continuum image (left) and velocity map (right) of a sunspot at 𝜃 = 35° (N34W5) observed with HMI/SDO on January 6, 2011 (12-min average). The Evershed flow within the penumbra and the moat flow in the spot surroundings. The contour marks the outer spot boundary, the arrow points towards disk center, and the tick marks are in arcsec (courtesy of J. Löhner-Böttcher, KIS).

The area occupied by this flow patterns is called “moat region” and has typically extents out to about 2 sunspot radii. This flow patterns was first found by Sheeley Jr (1969) by tracking photospheric bright points and further studied through Doppler measurements by Sheeley Jr (1972). Harvey and Harvey (1973) studied further the behavior of the outward moving bright points and introduced the term “moving magnetic features (MMF)” to describe the time dependent magnetic structure of the moat region. They found that MMF activity is mostly limited to decaying sunspots and plays a role in transport of flux away from the spot. Most MMFs are dipolar but have on average a net flux with the polarity of the sunspot. No significant correlation with the presence of a penumbra was found. A very extensive study of the energy and mass flux of the moat region was conducted by Brickhouse and LaBonte (1988), who found that the radial extent of the moat region is about twice the spot diameter. The average moat flow velocity from their study is about 500 m s–1. Recently, the connection between the Evershed flow and moat flow has been addressed by several authors (see, e.g., Sainz Dalda and Martínez Pillet, 2005; Cabrera Solana et al., 2006; Vargas Domínguez et al., 2008; Zuccarello et al., 2009; Vargas Domínguez et al., 2010Jump To The Next Citation Point), however, so far the observational evidence is not conclusive to either proof or disproof a connection.

Helioseismic measurements of moat flows were performed by Gizon et al. (2000). They used inversions of the f -mode, which senses mainly the upper most 2 Mm of the convection zone and found good agreement with photospheric measurements. A more sophisticated inversion based on all ridges from f to p4 was presented by Gizon et al. (2009Jump To The Next Citation Point, 2010bJump To The Next Citation Point). The near surface flow agrees well with MMF tracking, and outflows with comparable amplitude were found down to a depth of 4.5 Mm. Recently, Featherstone et al. (2011) presented a helioseismic inversion combining ring-diagrams with three different resolution levels. They found that the moat flow consists of a two components, a superficial photospheric flow and a deeper reaching flow peaking at about 5 Mm depth.

On the theoretical side, Meyer et al. (1974Jump To The Next Citation Point) suggested that the moat flow is essentially a supergranular flow, which arises as sunspots are preferentially formed in a supergranular downflow vertex. Heat flux blockage by the extended penumbra leads to a reversal of the flow direction in the proximity of the spot turning the initially converging flows into outflows.

2D axisymmetric simulations by Hurlburt and Rucklidge (2000), Botha et al. (2006), and Botha et al. (2008) typically produce a 2 cell flow around sunspots, a converging flow in their proximity (which has been referred to as “collar flow”) and a diverging “moat” flow further out. Recently, this work has been expanded to 3D simulations in cylindrical geometry by Botha et al. (2011). While the basic results from the 2D axisymmetric simulations are confirmed, the collar flow breaks up into several cells in the azimuthal direction and allows for sunspot decay due to turbulent erosion. Since both, the 2D axisymmetric and 3D cylindrical simulations do not capture the effect of a penumbra, it is not clear how this collar flow would be further modified in a more realistic sunspot model. Zhao et al. (2010) suggested that a superficial Evershed flow is just added on top of it.

Large scale flows are also present in recent 3D MHD simulations of sunspots (Heinemann et al., 2007; Rempel et al., 2009aJump To The Next Citation Point,bJump To The Next Citation Point; Rempel, 2011a,c). Here outflows dominate the picture at all depth levels, i.e., there is no compelling evidence for the presence of a collar flow in simulations of sunspots with penumbrae. An outflow is also the flow response one would expect from the penumbral blockage of heat flux as suggested by Meyer et al. (1974Jump To The Next Citation Point). Converging collar flows are, however, found in simulations of pores (Cameron et al., 2007b; Kitiashvili et al., 2010b) and play a role in their formation and stabilization against decay. A converging flow around pores is also seen in observations (Wang and Zirin, 1992; Sobotka et al., 1999; Vargas Domínguez et al., 2010).

Recently, Cheung et al. (2010) simulated the formation of a pair of small (3 × 1021 Mx) sunspots through a flux emergence process in the upper most 7.5 Mm beneath the solar photosphere. Due to the large amount of high entropy plasma that emerges, a buoyantly driven large scale outflow surrounds the sunspots from early on in the simulation. Interestingly a coherent pair of spots was forming out of initially dispersed field despite diverging (azimuthally averaged) horizontal mean velocities. The analysis of the simulation revealed that mostly the transport of field due to the electromotive force resulting from small scale fluctuating motions dominated the spot formation, while large scale flows had a destructive effect throughout the process. The small-scale velocity field correlations allow in principle for a transition between the growing and decaying phase of sunspots without requiring changes in the large scale flow pattern as originally proposed by Meyer et al. (1974). However, this is still an untested hypothesis and numerical simulations are currently just progressing to the point at which processes on the scale of the moat region or entire active regions can be properly addressed. Substantial progress is likely over the next decade.

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