3.2 Penumbral observations

3.2.1 Morphological description

The penumbra is a manifestation of small-scale structure. The variety of the intensity fine structure has recently been reviewed by Solanki (2003), Bellot Rubio (2007), Scharmer (2009), Schlichenmaier (2009) and Bellot Rubio (2010).

Intensity pattern:
In essence, there are bright and dark filaments, as well as penumbral grains. These features are barely visible at a resolution of about one arcsec. At smaller scales, these features exhibit structure on spatial scales of 0.1 arcsec in the inner penumbra (see, e.g., Scharmer et al., 2002Jump To The Next Citation Point) and of 0.35 arcsec in the mid and outer penumbra (Sütterlin, 2001): Bright filaments have dark cores (Scharmer et al., 2002; Sütterlin et al., 2004) and display inclined dark stripes4 along filaments (Ichimoto et al., 2007bJump To The Next Citation Point). Spruit et al. (2010) termed these stripes striations and interpreted them as corrugations, which form as a consequence of the fluting instability at the interface between the ambient magnetic field and the filament. In their explanation the overturning convection inside a field-free gap drags the inclined field lines downward such that the stripe migrates outwards as it is observed. Of course another scenario based on flow channels is also possible: The fluting instability could produce such migrating stripes at the interface between a magnetized flow channel and the ambient magnetic field, which wraps around the flow channel. In this scenario, the outward (Evershed) flow could drag the striations to migrate along the flow channel, and since the ambient magnetic field is inclined, the stripes appear inclined relative to the flow direction. The challenge to understand the intensity fine structure consists in measuring their spectroscopic and spectropolarimetric signatures with the goal to derive their thermodynamic properties as well as their velocity and magnetic field on scales as small as possible. Only recently, with the technological advance of adaptive optics and with observations from space, it has become possible to acquire data with a spatial resolution of 0.3 arcsec for exposure times as long as 5 sec or more. This is a necessity to collect enough photons to have high spatial, spectral, and polarimetric resolution.

At a spatial resolution of better than half an arcsec, it can be demonstrated that not only the intensity and velocity, but also the magnetic field consists of a filamentary structure (Title et al., 1993; Langhans et al., 2005Jump To The Next Citation Point; Tritschler et al., 2007Jump To The Next Citation Point; Ichimoto et al., 2007aJump To The Next Citation Point, 2008a; Bellot Rubio et al., 2007Jump To The Next Citation Point). Actually, at a spatial resolution of better than half an arcsec, all physical quantities in the penumbra show small-scale variations and predominantly filamentary (radially elongated) features. The latter is demonstrated in Figure 2View Image in which maps of intensity, velocity, and circular polarization are displayed at the SP/Hinode resolution of about 0.3 arcsec. Therefore, it is obvious that there is an intimate interaction between the convective flows and the magnetic fields.

However, at a spatial resolution worse than 1 arcsec, the penumbra looks fairly uniform and is on average brighter than the umbra, but less bright than in the surrounding granulation. But even if the penumbra is less bright on average, the small scale peak-to-peak intensity variation in the penumbra is larger and the spatial scales of the variations are smaller than in the granulation. The same is true for velocities in the penumbra. Line-of-sight (LOS) velocities in the penumbra of more than 5 km s–1 have been derived from Doppler shifts of photospheric lines (e.g., Wiehr, 1995Jump To The Next Citation Point; Bellot Rubio et al., 2007Jump To The Next Citation Point; Franz and Schlichenmaier, 2009Jump To The Next Citation Point) and radial flow channels with widths of less than half an arcsec are observed (e.g., Tritschler et al., 2004Jump To The Next Citation Point; Rimmele and Marino, 2006Jump To The Next Citation Point).

3.2.2 Evershed flow, uncombed magnetic field, and net circular polarization (NCP)

To understand the nature of the penumbral fine structure, it is essential to know the topology of the velocity field and the magnetic field. The first attempt to measure the flow field was undertaken by Evershed in 1908 (see Evershed, 1909) in order to test Hale’s tornado theory of sunspots. Yet, instead of a circular flow, Evershed found a radial outflow of plasma. Until today we lack a fully consistent theory for sunspots, although substantial progress in modeling the characteristic features of the penumbra has been made in recent years. We summarize first important observational aspects, before discussing models for sunspot fine structure.

View Image

Figure 3: The spot of NOAA 10933 observed with SP/Hinode at two different heliocentric angles: 𝜃 = 3° (left) and 47° (right). The upper row shows velocity maps inferred from the line wing of Fe i 630.15 nm. The bottom row shows so-called ‘Ichimoto’-grams, i.e., maps of Stokes V in the red wing of Fe i 630.25 nm, i.e., λ0 + 211 mA. The left spot is almost at disk center such that vertical motion and polarity reversals within the spot are best visible. The LOS into the right spot is inclined such that the horizontal flow component is dominant (courtesy of M. Franz, KIS).

Before we review this topic, we think it is instructive to describe Figure 3View Image, adhering to Franz (2011Jump To The Next Citation Point): The figure shows the velocity maps (upper row, determines from line wing bisector shift in Fe i 630.15 nm) and ‘Ichimotograms’ (bottom row) of a penumbra close to disk center (left column, spot 1) and a penumbra that is seen at a heliocentric angle of 47° (right column, spot 2): Spot 1: At disk center, horizontal velocity components do not contribute to the LOS velocity, such that the vertical velocity component is prominent. The blue elongated patches, which dominate the inner and mid penumbra, are associated with upflows of up to 1.5 km s–1. The yellow and red downflow patches are dominant in the very outer penumbra, but also exist in the mid and a few even in the inner penumbra. In the outer penumbra the downflow velocities exceed 5 km s–1, but are clipped at 1.5 km s–1 in the figure so that smaller velocities are better visible. The Ichimotogram is an image of Stokes-V in the red line wing at λ0 + 211 nm (such images were discussed by Ichimoto et al., 2007aJump To The Next Citation Point)5. In white patches the V-signal has opposite sign as in the overall spot and, hence, trace locations where the polarity is opposite to the spot polarity. These opposite polarity patches are co-spatial with downflow patches. Spot 2: At large heliocentric angles the horizontal velocity component becomes visible. Since the horizontal flow speeds are larger than the vertical velocities (see, e.g., Schlichenmaier and Schmidt, 2000Jump To The Next Citation Point), the velocity map is dominated by the horizontal (Evershed) flow, producing a blueshift on the center-side penumbra, and a redshift on the limb-side penumbra. The flow velocity are clipped at ± 3.5 km s–1. Velocities exceeding 4 km s–1 are common on both penumbral sides.

The flow field:
With high spatial resolution, it is now established that the flow has a filamentary structure (Tritschler et al., 2004Jump To The Next Citation Point; Rimmele and Marino, 2006Jump To The Next Citation Point). On azimuthal average, the flow is essentially horizontal with a small upward component in the inner and a small downward component in the outer penumbra (Schlichenmaier and Schmidt, 2000; Schmidt and Schlichenmaier, 2000; Tritschler et al., 2004; Langhans et al., 2005). Recent observations have revealed that radially aligned up- and downflows exist on small scales next to each other (Sainz Dalda and Bellot Rubio, 2008Jump To The Next Citation Point; Franz and Schlichenmaier, 2010Jump To The Next Citation Point). Regarding the height dependence of the flow, St John (1913) (see also Ichimoto, 1987, 1988) found that the flow velocity decreases with the formation height of the absorption line. In chromospheric lines the flow reverses its sign, which is being referred to as the inverse Evershed flow. Studying the line asymmetries of photospheric lines, one finds convincing evidence that the flow is predominantly present in the very deep photosphere, i.e., beneath τ = 0.1 (Maltby, 1964; Schlichenmaier et al., 2004Jump To The Next Citation Point; Bellot Rubio et al., 2006Jump To The Next Citation Point). The peaks of the flow velocities measured in the penumbra are substantially larger than what is measured in the granulation. Individual penumbral profiles exhibit line satellites that are Doppler shifted by up to 8 km s–1 (e.g., Wiehr, 1995). From inversions, velocities well above 10 km s–1 have been found by del Toro Iniesta et al. (2001). Bellot Rubio et al. (2004Jump To The Next Citation Point) find an azimuthally averaged Evershed out-flow velocity of about 6.5 km s–1, with local peaks of more than 10 km s–1, based on two component inversions (see below). The small-scale flow field of dark cored bright filaments is discussed in the context of convective roll models (at the end of Section 3.4.1).

The magnetic field:
Attempts to describe the magnetic field as being uniform along the line-of-sight are clearly inconsistent with the measured Stokes Q(λ ), U (λ), and V (λ) profiles (e.g., Westendorp Plaza et al., 2001a,b). In particular, the penumbral V-profiles with three or more lobes and non-vanishing NCP-values (see below) cannot be explained by one component Schlichenmaier and Collados (2002Jump To The Next Citation Point): Gradients and/or discontinuities along the line-of-sight must be present. Therefore, it was proposed that the magnetic field is interlocked or in other words uncombed (Solanki and Montavon, 1993Jump To The Next Citation Point). In order to keep things as simple as possible, the magnetic field is assumed to have two components with different inclinations. Indeed, if the observed Stokes profiles with a spatial resolution of about 1 arcsec are interpreted with two components by means of inversions techniques, the fits to the observations are substantially better and reproduce essential features of the line asymmetries, which is not possible with only one component (Bellot Rubio, 2004; Bellot Rubio et al., 2003, 2004; Borrero et al., 2004, 2005; Beck, 2008Jump To The Next Citation Point). Such inversions yield one less inclined magnetic component that is only slightly Doppler shifted, and a second component with somewhat weaker and more inclined, i.e., approximately horizontal field. This second component carries the Evershed flow, with spatially averaged flow speeds of about 6.5 km s–1. These inversions also show that the magnetic field of the second component is aligned with the associated flow, pointing slightly upwards in the inner and slightly downward in the outer penumbra. The inclination angle relative to the local vertical of the first magnetic field component increases from some 30° at the umbral-penumbral boundary to some 60° at the outer penumbral boundary. Inversions, which are optimized to locate the height of the flow layer, find that the flow is present in the very deep atmosphere, in the continuum forming layers (Bellot Rubio, 2003Jump To The Next Citation Point; Borrero et al., 2006; Jurčák and Sobotka, 2007; Jurčák and Bellot Rubio, 2008).

At 0.3 arcsec spatial resolution, spectropolarimetric measurements reveal that, at least in the inner penumbra, the more inclined magnetic component, which carries the flow, is associated with the dark cored bright filaments. Individual dark cores have a smaller degree of circular polarization than their lateral brightenings (Langhans et al., 2007Jump To The Next Citation Point). A thorough analysis shows that the latter statement is also true for the total polarization and that the dark core magnetic field is weaker and more inclined than in the lateral brightenings (Bellot Rubio et al., 2007). Additionally, these studies confirm that the dark cores harbor strong Evershed flows (Bellot Rubio et al., 2005Jump To The Next Citation Point).

The magnetic canopy:
Outside the white-light boundary of the penumbra, the inclined magnetic field continues into the chromosphere. It forms a magnetic canopy in the surroundings of the sunspot, rising with increasing distance up to a height of approximately 800 km (Solanki et al., 1992Jump To The Next Citation Point). In the canopy a radial outflow is present, which is interpreted as the continuation of the Evershed flow (Solanki et al., 1992; Rezaei et al., 2006). However, it is estimated that only a few tenth of the mass flows into the canopy. The rest of the penumbral Evershed flow must disappear within the penumbral downflow regions.

The net circular polarization (NCP):
The NCP, ∫ V (λ)d λ, is a quantity that intimately links the flow and the magnetic field: NCP can only be non-zero, if and only if velocity gradients along the line-of-sight are present (e.g., Sánchez Almeida and Lites, 1992). The magnitude and the size of the NCP depends on the gradient of the line-of-sight velocity, but also on the gradients in the magnetic field strength, inclination, and azimuth (Landolfi and Landi degl’Innocenti, 1996; Müller et al., 2002, 2006; Borrero et al., 2008Jump To The Next Citation Point). A predominantly horizontal flow channel embedded in a less inclined background magnetic field successfully explains symmetry properties of NCP maps of sunspots (Schlichenmaier et al., 2002) as well as the center to limb variation of NCP (Martínez Pillet, 2000; Borrero et al., 2007). Yet, some recent interpretations of NCP maps require that the flow component should be associated with stronger magnetic field (Tritschler et al., 2007Jump To The Next Citation Point; Ichimoto et al., 2008bJump To The Next Citation Point), rather than being associated with the same or weaker magnetic field in the flow channels, as we would expect from the models. Since there are also other indications for these stronger magnetic fields (e.g., Bellot Rubio, 2003; Cabrera Solana et al., 2008; Borrero and Solanki, 2008), the concept of embedded flow channels will need to be reviewed taking into account these new measurements. The magnetoconvective models described in Section 3.6.4 lead to flow channels with enhanced horizontal magnetic field strength consistent with these recent observational findings.

View Image

Figure 4: Two types of 3-lobe-V-profiles. The left profile of Fe i 630.15 nm and Fe i 630.25 nm displays a lobe in the blue wing. The right profile displays a redshifted lobe of opposite sign, which is associated with a second zero crossing. The bump in the left profile can be interpreted as a blueshifted magnetized flow component, with the same polarity as the main profile. The bump in the right profile is a signature of a redshifted magnetic component, which is of opposite polarity as the main profile. The plotted profiles are from a spot at disk center, but are also measured in spots off disk center (courtesy of M. Franz, KIS).

Magnetized or non-magnetized flow:
In terms of modeling the Evershed flow, it is crucial to know whether or not the flow is magnetized. While NCP can be generated by a field-free flow in a magnetized environment (e.g., Steiner, 2000), the observed V profiles in certain locations in the penumbra show more than two lobes (e.g., Schlichenmaier and Collados, 2002; Ichimoto et al., 2007aJump To The Next Citation Point; Beck, 2008, 2011; Franz and Schlichenmaier, 2010). Two example profiles of Stokes-V, which have more than two lobes, are displayed in Figure 4View Image. The profiles come from a spot close to disk center (𝜃 = 3∘). The left profile shows a bump in the blue wing (of the two iron lines at 630.15 nm and 630.25 nm). This bump is attributed to an magnetic upflow that is superposed with a contribution from the ambient magnetic field, which is roughly at rest. Both components have the same magnetic polarity. It can be shown that a non-magnetic upflow does not produce such a bump in Stokes-V, even though it makes a bump in Stokes-I. The right panel profile is crucial to understand the penumbra: It shows an extra bump of opposite sign in the red wing of Stokes-V. This bump must be generated by a redshifted component of opposite polarity! Hence, this profile can only be reproduced if (at least) two magnetic magnetic components of opposite polarity contribute to the profile (e.g., Franz, 2011)6. Note that a ‘typical’ magnetogram, which measures Stokes-V only at two wavelength positions, would show the spot polarity, and would miss the opposite polarity part of the profile. For a spot at disk center, Hinode/SP profiles show clear signatures of opposite polarity for about 40% of all downflow patches, i.e., for about 17% of all penumbral pixels. This is a lower limit, since these signatures are blended by noise.

Another clear evidence for the magnetic nature of the Evershed flow comes from the inversion results based on two components, which we described above. They also demonstrate that the Doppler shifted second component is magnetized. This result is inferred from spots off disk center, typically at ∘ 𝜃 ≈ 30.

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