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Modern Solar Facilities – Advanced Solar Science, 233–240 F. Kneer, K. G. Puschmann, A. D. Wittmann (eds.) c  Universitätsverlag Göttingen 2007 On the inhomogeneities of the sunspot penumbra R. Schlichenmaier1,* , D. A. N. Müller2 , and C. Beck1,3 1 Kiepenheuer-Institut für Sonnenphysik, Freiburg, Germany 2 European Space Agency, c/o NASA Goddard Space Flight Center, Greenbelt, MD, USA 3 Instituto de Astrofı́sica de Canarias, La Laguna, Tenerife, Spain * Email: schliche@kis.uni-freiburg.de Abstract. The penumbra is ideally suited to challenge our understanding of magnetohydrodynamics. The energy transport takes place as magnetoconvection in inclined magnetic fields under the effect of strong radiative cooling at the surface. The relevant processes happen at small spatial scales. In this contribution we describe and elaborate on these small-scale inhomogeneities of a sunspot penumbra. We describe the penumbral properties inferred from imaging, spectroscopic and spectropolarimetric data, and discuss the question of how these observations can be understood in terms of proposed models and theoretical concepts. 1 Introduction Almost hundred years ago, Hale (1908a,b) performed the first spectropolarimetric measurements on the Sun and discovered that sunspots are manifestations of magnetic fields with strengths of up to 3000 G in their centers. He proposed the tornado theory to explain both the darkness of a spot by dust that is whirled up into the solar atmosphere and the magnetic field by the circular current by electrons. Investigating Doppler shifts in sunspots, Evershed (1909) measured radial rather than circular movements in sunspot penumbrae and concluded that his findings were ”entirely out of harmony with the splendid discovery of the Zeeman effect in sun-spots, made by Prof. Hale.” Until today, we lack a complete understanding of sunspots and penumbrae, but it seems obvious that the Evershed flow plays an essential role in the latter. The presence of the Evershed flow is intimately linked to the mere existence of the penumbra as demonstrated by the observations of Leka & Skumanich (1998). The filamentary bright and dark structure should be related to the flow field, in a similar way as the granular pattern of the quiet Sun is related to the granular flow field of hot up- and cool downflows. The magnetic field can – in principle – be inferred from the spectropolarimetric imprints of the Zeeman effect on photospheric absorption lines. However, this leads to unambiguous results only if the magnetic and velocity fields are homogeneous along the line-of-sight. Considerable complications in interpreting the line profiles arise if gradients or discontinuities are present in the volume of the solar atmosphere which is sampled by one resolution element. Such variations may be present laterally due to insufficient spatial resolution, but also along the line-of-sight from the depth layers that contribute to the observed line profile. 234 Schlichenmaier et al.: On inhomogeneities of the sunspot penumbra In this contribution, we make the case that the latter must be assumed to reconstruct some of the observed profile asymmetries. We summarize our knowledge of the inhomogeneities in the magnetic and velocity field of a sunspot penumbra, aiming at an understanding of radiative magneto-convection in inclined magnetic fields. 2 Penumbral properties The photospheric penumbral properties may be characterized by three different types of measurements: (1) imaging, (2) spectroscopy of lines that do not show the Zeeman effect, and (3) spectropolarimetric measurements of Zeeman sensitive lines. 2.1 Imaging At a spatial resolution of 1 or worse, the penumbra appears as a gray ring that surrounds the umbra. The radial bright and dark filaments only become apparent at a spatial resolution of about 0. 5. At a spatial resolution of about 0. 2 bright filaments show internal intensity variations: In the inner penumbra, predominantly on the center side, bright filaments show a dark elongated core (Scharmer et al. 2002; Sütterlin et al. 2004; Langhans et al. 2007). Such dark-cored bright filaments have a width of some 0. 2. 2.2 Spectroscopy As for the intensity, the length scale of variations in a Doppler map decreases with improving spatial resolution. At 1 no flow filaments are visible and the Doppler shifts only show a transition from red shifts on the limb side to blue shifts on the center side. To infer the flow vector at this spatial resolution, azimuthal cuts at constant distance from the spot center are constructed. The azimuthal mean reflects the vertical velocity component, while the amplitude of the variation...

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