4.4 Sunspot evolution past emergence process

After the appearance of an active region in the photosphere, sunspots show a transition from an active initial phase toward a more passive later phase. In the active phase both polarities continue to separate and move away from the original emergence site, in the later passive phase sunspots do not show strong motions with respect to ambient plasma (Švanda et al., 2009). It has been suggested that this change of behavior is related to the subsurface connectivity of sunspots. The early stage with the strong separation of both polarities is the natural consequence of an Ω-shaped loop emerging into the photosphere. The related asymmetries between the leading and following spots have been well studied in thin flux tube simulations (Fan et al., 1993; Caligari et al., 1995) and are also reproduced by 3D simulations (Fan, 2008). Extrapolating these results past the appearance time of active regions in the photosphere would predict rather strong separation of polarities if the magnetic field remains rooted in the tachocline. A process that would stop the separation process, requires a dramatic change in field connectivity. Whatever the underlying process is, it has to be very reliable since we do not observe active regions with peculiar behavior in that respect. The two possible scenarios discussed in literature are reconnection of sunspots leading to shallow U-loops (Schrijver and Title, 1999Jump To The Next Citation Point) and dynamical disconnection (Fan et al., 1994Jump To The Next Citation Point; Schüssler and Rempel, 2005Jump To The Next Citation Point). The latter leads to rather shallow sunspots in which the magnetic field strength drops to sub-equipartition values at about 5 – 10 Mm depth. The magnetic field would become passive to turbulent motions there, which effectively disconnects the sunspot from the magnetic root at the base of the convection zone. While this process was simulated within a time evolved one-dimensional self-similar sunspot model, a self-consistent ab initio 3D simulation is still outstanding. On the other hand, it is also not clear whether a rather shallow sunspot would be stable enough to explain live times of several weeks, which is certainly longer than the overturning time scale of convection in the surface layers. Simulations of sunspots in 6 – 8 Mm deep domains (Rempel et al., 2009bJump To The Next Citation Point,aJump To The Next Citation Point) require fixing the magnetic field at the bottom boundary to prevent a rapid decay within a few hours. Recent simulations by Rempel (2011cJump To The Next Citation Point) in up to 16 Mm deep domains show strong evidence that this constraint can be significantly relaxed since the intrinsic convective time scales increase dramatically with depth. Rempel (2011cJump To The Next Citation Point) found that sunspot lifetimes of about 1 – 2 days can be achieved in a 16 Mm deep domain regardless of the bottom boundary condition; extrapolating this result should yield lifetimes of about 10 days for sunspots anchored in 50 Mm depth. The latter is substantially deeper than the disconnection depth that was suggested by Fan et al. (1994), Schrijver and Title (1999) and Schüssler and Rempel (2005). Addressing this problem fully consistently requires to model all stages of the flux emergence process from the base of the convection zone into the photosphere and beyond, which will likely become feasible within the next decade.

To date the decay of sunspots has been primarily addressed by simplified turbulent decay models, such as Petrovay and van Driel-Gesztelyi (1997), Rüdiger and Kitchatinov (2000) and Kitchatinov and Olemskoi (2006). With proper assumptions about the quenching of the turbulent magnetic diffusivity these models can describe the overall flux loss rates and shape of the decay curve, a more detailed modeling requires taking fully into account the interaction of the sunspot with the surrounding convection zone as well large scale flows (moat). The 3D interaction of sunspots with convective flows was recently modeled by Botha et al. (2011Jump To The Next Citation Point) in an idealized setup and by Rempel (2011cJump To The Next Citation Point) using radiative MHD models.

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