3.7 Critical assessment of MHD simulations to date

While radiative MHD simulations capture the essential building blocks of penumbral fine structure, they are not fully realistic yet. Major shortcomings are related to the currently affordable resolution, which is sufficient to resolve individual filaments, but insufficient to properly resolve turbulent flows within filaments, i.e., these flows are currently forced to be more or less laminar. Also the initialization of these models is quite arbitrary since a self-consistent simulation of sunspot formation is still out of reach. Since there is strong evidence from observations that many aspects of penumbral structure and large scale flows around sunspots show hysteresis, it is likely that certain aspects of penumbral structure found in MHD simulations are tied to the initial state, which is typically an axisymmetric self-similar field configuration. Current limitations with regard to resolution and initial state will be relaxed in the future with more computing power becoming available.

Overall, MHD simulations are currently very successful in explaining the penumbral brightness, the filamentation resulting in a magnetic structure comparable to the uncombed penumbra (Solanki and Montavon, 1993), and the fast Evershed outflow along the almost horizontal component of the field. Since the outflow is essentially a convective flow (Scharmer et al., 2008; Rempel et al., 2009aJump To The Next Citation Point,bJump To The Next Citation Point; Rempel, 2011aJump To The Next Citation Point,bJump To The Next Citation Point) simulations show an Evershed flow in the deep photosphere, reaching its peak velocity near τ = 1 and falling off rapidly with height. This is in disagreement with the investigation of Rimmele (1995) and Stanchfield II et al. (1997), which found evidence for elevated flow channels. On the other hand, the bisector of spectral lines points toward outflows in the deep photosphere that decline with height (Schlichenmaier et al., 2004; Bellot Rubio et al., 2006). The currently most controversial aspect is the evidence (or lack of evidence) for overturning convection in observations of the penumbra. Most of the evidence in favor of overturning convection is based on twisting motions of filaments that are interpreted as overturning convection (Ichimoto et al., 2007b; Bharti et al., 2010). Márquez et al. (2006) analyzed proper motions in a sunspot penumbra based on local correlation tracking. In addition to the dominant Evershed flow, they found divergence from bright features and convergence toward dark features, very suggestive of overturning convection. Direct observations of overturning motions were presented by Sánchez Almeida et al. (2007), Zakharov et al. (2008) and Rimmele (2008). On the other hand, Bellot Rubio et al. (2005), Ichimoto et al. (2007a), Franz and Schlichenmaier (2009) and Bellot Rubio et al. (2010) did not find overturning motions along filaments. Most of the vertical flow they found is related to upflows in the inner and downflows in the outer penumbra near the endpoints of Evershed flow channels.

Recently, Bharti et al. (2011) analyzed the visibility of overturning motions in a MHD penumbra model through forward modeling of spectral lines and their degradation to the spatial and spectral resolution of observations. They concluded that the visibility of overturning motions depends strongly on the used spectral line and can be easily masked by projected Evershed flows, even if a sunspot is only a few degrees away from disk center. From their synthetic analysis, they propose that the C i 538.0 nm line is most promising to detect overturning motions. However, they did not consider the effect of line blends, present in the cooler parts of the penumbra, nor the fact that the line depression can be smaller than 5% in dark penumbral filaments, which makes a detection very difficult. Scharmer et al. (2011Jump To The Next Citation Point) and Joshi et al. (2011) claim direct evidence for overturning motions inside the penumbra using C i 538.0. Scharmer et al. (2011) finds a similar level of correlation between intensity and vertical velocity as found in the quiet Sun photosphere. The vertical RMS velocity is about 1.2 km s–1 and very similar to predictions from the above mentioned MHD simulations. While these recent results point clearly toward a convergence between observations and theoretical predictions, in both paper the results are only obtained after a stray-light correction was applied. Therefore rigorous evidence for the existence of overturning convection in penumbra is still missing.

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