The magnetic configuration of a delta-spot
Horst Balthasar, Christian Beck, Rohan E. Louis, Meetu Verma, Carsten Denker
aa r X i v : . [ a s t r o - ph . S R ] D ec Solar Polarization 7ASP Conference Series, Vol. **Volume Number**K. N. Nagendra, J. O. Stenflo, Z. Qu and M. Sampoorna eds. c (cid:13) The magnetic configuration of a δ -spot H. Balthasar , C. Beck , R.E. Louis , M. Verma , and C. Denker Leibniz-Institut f¨ur Astrophysik Potsdam, An der Sternwarte 16, 14482Potsdam, Germany National Solar Observatory, Sacramento Peak, 3010 Coronal Loop, SunspotNew Mexico 88349, U.S.A. Max-Planck-Institut f¨ur Sonnensystemforschung, Max-Planck-Straße 2,37191 Katlenburg-Lindau, Germany
Abstract.
Sunspots, which harbor both magnetic polarities within one penumbra,are called δ -spots. They are often associated with flares. Nevertheless, there are onlyvery few detailed observations of the spatially resolved magnetic field configuration.We present an investigation performed with the Tenerife Infrared Polarimeter at theVacuum Tower Telescope in Tenerife. We observed a sunspot with a main umbra andseveral additional umbral cores, one of them with opposite magnetic polarity (the δ -umbra). The δ -spot is divided into two parts by a line along which central emissionsof the spectral line Ca ii δ -umbra, and the magnetic field decreases rapidly with height, faster thanin the main umbra. The horizontal magnetic field in the direction connecting main and δ -umbra is rather smooth, but in one location next to a bright penumbral feature at somedistance to the δ -umbra, we encounter a change of the magnetic azimuth by 90 ◦ fromone pixel to the next. Near the δ -umbra, but just outside, we encounter a blue-shift ofthe spectral line profiles which we interpret as Evershed flow away from the δ -umbra.Significant electric current densities are observed at the dividing line of the spot andinside the δ -umbra.
1. Introduction
Normally, the two magnetic polarities appear in two or more separated sunspots. K ¨unzel(1960) described cases where both polarities appear within a single penumbra, andhe named them δ -sunspot groups. They are frequently associated with flares (seeSammis et al. 2000). K ¨unzel (1964) later suggested to extend the Hale classificationof sunspots to include δ -spots.Flares can be ignited when shear flows along the Polarity Inversion Line (PIL)build up magnetic shear or twist. Therefore, velocities in and around δ -spots have beeninvestigated frequently. Tan et al. (2009) observed a shear flow of 0.6 km s − betweentwo umbrae of opposite polarity before an X3.4 flare. After the flare, the flow was re-duced to 0.3 km s − . Denker et al. (2007) investigated a case where a shear flow did notchange the magnetic shear su ffi ciently and concluded that a shear flow might even re-duce magnetic shear. Lites et al. (2002) found flows converging at the PIL. Remarkable1 Balthasar etal. U3 U40 10 20 30 40 50 0 10 20 30 40 50 60010203040 x [Mm] y [ M m ] Figure 1. Slit reconstructed continuum images of the spot near Fe i ii downflows near the PIL have been reported by Mart´ınez Pillet et al. (1994), who found14 km s − , while Takizawa et al. (2012) detected values between 1.5 and 1.7 km s − .Doppler velocities of ±
10 km s − were detected by Fischer et al. (2012) during flaringactivity. Min & Chae (2009) observed that the opposite polarity part of a sunspot ro-tated around its center by 540 ◦ within five days. Such rotation can cause coronal massejections as demonstrated by T ¨or¨ok et al. (2013). Wang et al. (2013) reported a forma-tion of a penumbra between dark features of opposite polarity associated with a C7.4flare. After the flare, a new δ -spot was created. Jennings et al. (2002) used the Mg i line at 12.32 µ m to observe a large sunspot group just prior to the occurrance of anM2-flare. The flare was initialized by flux cancellation at a location where oppositepolarities were close together.In this work, we observed a δ -sunspot to investigate its detailed magnetic structureand to search for special magnetic configurations that might lead to flares. Parts of theresults are published in Balthasar et al. (2013b).
2. Observations and data reduction
The sunspot group NOAA 11504 consisted on 2012, June 17 of three major spots, andone of them harbored smaller umbrae other than the main umbra. Close to the outerboundary but still inside the complex penumbra was an extended dark feature with op-posite magnetic polarity with respect to the main umbra. In the following, we call thisfeature the δ -umbra. The group was located 35 ◦ from disk center at 18 ◦ S / ◦ W (cos ϑ = ff erent spectral lines, Fe i i δ -spot 3 x [Mm] y [ M m ] Figure 2. Line core intensity of the line Ca ii was recorded with the Tenerife Infrared Polarimeter (TIP; Collados et al. 2007). AsBalthasar & G ¨om¨ory (2008) pointed out, these two lines originate from di ff erent atmo-spheric layers except for the cool cores of umbrae. Both lines form a normal Zeemantriplet with a splitting factor g e ff = .
5. The spectral dispersion was 2.19 pm, and alongthe slit, two pixel were binned resulting in an image scale of 0 . ′′
35 per pixel. During thetime period 10:00 – 10:38 UT we scanned the sunspot with 180 steps of 0 . ′′
36 width cor-responding to the slit width . Both spatial step widths correspond roughly to the theo-retical resolution of the telescope of 0 . ′′
39. For each scan position we accumulated tenexposures of 250 ms in each modulation state of TIP. Seeing influences were compen-sated by the Kiepenheuer Adaptive Optics System (KAOS; von der L ¨uhe et al. 2003;Berkefeld et al. 2010). The same data set was also used by Balthasar et al. (2013b).The magnetic vector field and the Doppler velocities of these two lines were de-rived with the Stokes Inversion based on Response functions (SIR). This code wasdeveloped by Ruiz Cobo & del Toro Iniesta (1992). We set three nodes for the temper-ature and kept magnetic field strength B , inclination γ , and azimuth ψ constant withheight, as well as the Doppler velocity v D . We obtained the height dependence of theseparameters by inverting the two lines separately. We used a single-component modelatmosphere. The SIR code provided also error estimates for the calculated quantities,and we processed these errors by error propagation to get the errors of the final physicalparameters. The next issue was to solve the magnetic azimuth ambiguity. In the firststep, we assumed a single azimuth center in the main umbra and chose that directionwhich had the smaller di ff erence to the radial orientation. It had to be considered thatthis orientation is inward because of the negative polarity on the main umbra. Thisway we obtained a roughly correct start azimuth (although the δ -umbra had its ownazimuth center) for the minimum energy method provided by Leka et al. (2009). Withthis method, the term |∇ · ~ B | + w | J z | is minimized. J z is the vertical component of Balthasar etal.the electric current density and w is a weighting factor. The output delivers a reliablemagnetic azimuth. Finally we rotated all images to the local reference frame.Next to TIP, we mounted a CCD-camera to record spectra of the line Ca ii i ff erentcases. If there was no central emission, as usual, we determined the minimum of apolynomial fit of fourth degree. If we detected central emission with a single peak,we applied a parabola fit to this central emission and calculated its maximum position.In some cases, we encountered a central reversal in the emission. In these cases, wefit a polynomial of fourth degree, and its central minimum was used to determine theDoppler velocity. Central emission occurs in the δ -spot along a line dividing the lowerright part of the penumbra in Fig. 1. In the following, we call this line the ‘CentralEmission Line’ (CEL). The CEL is partly co-spatial with the PIL, but not everywhere.Fig. 2 shows the line core intensities of the infrared Ca line and the maximum intensityof the central emission after subtraction of a parabel fit through the wings of the line.All maps were destretched with the method described by Verma et al. (2012) toget quadratic pixels with a side length of 260 km on the Sun.
3. Results
Slit reconstructed intensity maps are shown in Fig. 1. The spot exhibited a complexstructure of the penumbra, which harbored several dark features beside the main umbra.Most of them had the same polarity as the main umbra, but the bow-shaped feature inthe South-West part of the penumbra was the δ -umbra, i.e., it had the opposite polarity.The δ -umbra had the same polarity as the leading spot of the group, which is partly seenon the right side of Fig. 1. We also see some bright inclusions in the penumbra, andone of them, marked by an arrow in Fig. 1, seems to play a special role in the magneticconfiguration. Between main and δ -umbra there was a another small umbra U3, whichhad the same polarity as the main umbra. Another small umbra U4 close to the δ -umbraalso had the polarity of the main umbra.Maps of the Stokes-profiles at a selected slit position are shown in Fig. 3. Weakmulti-lobe Q -profiles appear at 12 Mm along the slit.Context images in the line cores of H α and the He i line at 1083.03 nm were ob-tained with the Chromospheric Telescope (ChroTel; Bethge et al. 2011, 2012). On thisday, the ChroTel observations started at 10:45 UT, and we used the first images of theseries shown in Fig. 4. In the helium image, we see mainly photospheric structuresbecause this line is normally weak compared to H α . In H α , the umbrae of the twoneighboring spots ( x , y ∼
60 Mm, 110 Mm and 150 Mm, 75 Mm) are well visible, whileit is very hard to identify the umbrae of the δ -spot ( x , y ∼
75 Mm, 70 Mm). Here, thephotospheric structures were completely covered by chromospheric features indicatingthat the magnetic field in the chromosphere plays an important role in δ -spots. Espe-cially, we detected a brightening in H α along the CEL. An even stronger brighteninghemagnetic configuration ofa δ -spot 5 I/I c V/I c Q/I c U/I c λ [nm] S lit po s iti on [ M m ] Figure 3. Maps of the Stokes-profiles I / I c , Q / I c , U / I c , and V / I c , normalized tothe continuum intensity at disk center I c for a selected slit position. Scalings are: I / I c V / I c ± − . , and Q / I c and U / I c ± . . Note the weak multi-lobe Q / I c -profiles at 12 Mm along the slit. occured in the prolongation of the CEL along the outer penumbral boundary of theleading spot of this group. The total magnetic field strength is shown in Fig. 5. In the main umbra we found 2600 Gin the Fe i i δ -umbra were 2250 G and 2030 G, respectively. Thefield strength dropped to 1500 G from the iron line and and 1400 G from the silicon linein the area between main and δ -umbra. Umbral core U3 exhibited 2000 G in the ironline, but only 1500 G in the silicon line.The magnetic inclination in Fig. 6 was close to 180 ◦ in the main umbra indicatingthe negative polarity. In and around the δ -umbra, we encountered small inclinationsbecause of the positive polarity here. Between the two umbrae the inclination changedrapidly from about 150 ◦ to about 60 ◦ , and only at the PIL it was horizontal (90 ◦ ). Inside Balthasar etal. Figure 4. Images obtained with ChroTel in the core of the He i line at 1083.03 nm(left) and in H α (right). Black and white contours mark penumbra and umbrae,respectively. U3 and U4, the field was less inclined than in its surroundings. The magnetic field wasalso more vertical at the CEL, where it was not cospatial with the PIL.The horizontal component of the magnetic field is shown in Fig. 7. We see asmooth transition from the main umbra to the δ -umbra. The strongest horizontal fieldsurrounded the δ -umbra. At some distance to the δ -umbra, close to a small brightfeature in the intensity maps, the field lines were almost perpendicular to each other. Atthis location, the Stokes profiles were anomalous (see Fig. 3), and a single-componentinversion was not able to reproduce these profiles. Lites et al. (2002) interpreted such aconfiguration by an interleaved system of magnetic field lines. Within the framework of our data we have two possibilities to determine the heightdependence of the magnetic field. The first option is to take the di ff erence of themagnetic quantities derived from the two lines and divide it by the height di ff erencefor the two lines. The height di ff erences were determined in the same way as byBalthasar & G ¨om¨ory (2008), who used the depression contribution functions for twodi ff erent model atmospheres and interpolated according to the local temperature. Theresults are shown in Fig. 8.
In the main umbra, we found a mean decrease of the total magnetic field strengthby 1.9 G km − , which is comparable to values published for other spots. The decreasewas much steeper in the δ -umbra, here we encountered 5.6 G km − . Along the com-mon part of PIL and CEL and in U3 the magnetic field decreased by 3–4 G km − , butalong the CEL where it was separated from the PIL, the magnetic field strength wasincreasing by 1 G km − . A fast decrease was also observed in U4. Outside the spot,the magnetic field is increasing with height because of the canopy e ff ect. The gradientof the absolute vertical component exhibited a similar behavior. In the δ -umbra, U3,and U4, the decrease was even slightly faster than for the total field strength indicatingthat the magnetic field became more horizontal above these features. Along the wholehemagnetic configuration ofa δ -spot 7 x [Mm] y [ M m ] B tot [G] Figure 5. Total magnetic field strength from Fe i i CEL, B z was increasing with height, while the total field strength was decreasing inthe common range of CEL and PIL. This discrepancy is explained by a fast decreaseof the horizontal magnetic field here. In the mid penumbra, we observed that the ver-tical component increased with height because the magnetic field was more vertical inhigher layers.The second option is applicable only for the vertical component of the magneticfield and starts from the condition that ∇ · ~ B is zero, and vertical partial derivatives mustbe compensated by the horizontal ones: ∂ B z ∂ z = − ∂ B x ∂ x + ∂ B y ∂ y ! (1)The horizontal derivatives were derived from di ff erences of the values from neighboringpixels, as described by Balthasar (2006).Qualitatively, the results were similar to those of the di ff erence method, but asBalthasar & G ¨om¨ory (2008) and Balthasar et al. (2013a) found, the values were smallerby a factor of about two as shown in Fig 9 . The vertical component of the magneticfield decreased faster with height in the δ -umbra, U3 and U4 than in the main umbra.Along the CEL, there was a tendency for an increasing B z with height. The horizontal partial derivatives of the magnetic field also allow us to determine thevertical component of electric current densities J z according to J z = µ ( ∇ × ~ B ) z = µ ∂ B y ∂ x − ∂ B x ∂ y ! , (2)where µ is the magnetic permeability. Partial derivatives were estimated from di ff er-ences between neighboring pixels. This procedure was used before by Balthasar (2006). Balthasar etal. x [Mm] y [ M m ] γ [ o ] Figure 6. Inclination of the magnetic field. x [Mm] y [ M m ] B hor [G] Figure 7. Horizontal component of the magnetic field. The strength is given bythe gray-scale and the azimuth by the white arrows.
The results are shown in Fig. 10. Positive current densities of more than 200 mA m − occurred near the outer boundary inside the δ -umbra along a line parallel to the PIL.The maximum value from the iron line is 273 ±
76 mA m − . Along the CEL, we de-tected negative current densities. Close to the δ -umbra the negative current densitiesmight be a counterpart to the positive values inside the δ -umbra. Negative current den-sities were still found in the part of the CEL, where it was separated from the PIL.Strong current densities are much more pronounced in the Fe i i δ -spot 9 x [Mm] y [ M m ] −6 −4 −2 0 2 ∆ B / ∆ h [G km −1 ] Figure 8. Height gradients of the total magnetic field B (left) and the absolutevalue of the vertical component B z (right) derived from the formation-height di ff er-ence of the two lines Fe i i x [Mm] y [ M m ] −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 dB z / dz [G km −1 ] Figure 9. Height gradients of the vertical component of the the magnetic fieldderived via ∇ · ~ B = i i The Doppler velocities were investigated by Balthasar et al. (2013b). The dominantfeature in the photosphere was the Evershed-e ff ect which was interrupted at the CEL.A special feature is a blueshift at the PIL which Balthasar et al. (2013b) interpreted asEvershed-e ff ect related to the δ -umbra. In the chromosphere above the CEL, small loca-tions exhibited downflows up to 8 km s − , derived from the line Ca ii x [Mm] y [ M m ] −150 −100 −50 0 50 100 150 J z [mA m −2 ] Figure 10. Vertical component of electric current densities from Fe i i ±
150 mA m − . these downflow patches was very close to the bright feature marked in Fig. 1. Anotherdownflow patch is located just outside the penumbra, similar as a patch observed byBalthasar et al. (2013a) near a single sunspot. Other locations along the CEL exhibitedupflows of the same order of magnitude as the downflows.Proper motions also were investigated by Balthasar et al. (2013b). They useda time series of magnetograms from the Helioseismic and Magnetic Imager (HMI,Schou et al. 2012) on board of the Solar Dynamic Observatory (SDO, Pesnell et al.2012) and applied the Di ff erential A ffi ne Velocity Estimator (DAVE) developed bySchuck (2005, 2006). This method delivered ‘magnetic flux transfer velocities’ (Schuck2006), that do not necessarily represent plasma flows. The flux transfer velocitiespointed towards the δ -umbra, where its Evershed e ff ect was visible as blue-shift. Aflow of 0.25 km s − away from the δ -umbra parallel to the CEL was detected, whichcrossed the PIL, where it was separated from the CEL. On the other side of the CEL,towards the main umbra, only 0.05 km s − were found, resulting in a shear imbalanceof 0.2 km s − . A counterclockwise spiral motion covered a part of the δ -umbra and U4,but we did not detect that the whole δ -umbra was rotating.
4. Discussion
The discrepancy between di ff erent methods to derive the height gradient of the verti-cal component of the magnetic field strength is a long-lasting problem in solar physicsand has been discussed by Leka & Metcalf (2003), Balthasar & G ¨om¨ory (2008), andBalthasar et al. (2013a). Determining geometrical heights from contribution or re-sponse functions has uncertainties, and one has to keep in mind that such functionscover an extended height range. Height gradients determined by this method but fromdi ff erent lines have similar values around 2 G km − (see Wittmann 1974; Balthasar & Schmidt1993; Moran et al. 2000; Leka & Metcalf 2003). To solve the problem with larger dif-hemagnetic configuration of a δ -spot 11ferences of the line formation, one would need to extend the solar atmosphere to muchmore than a few hundred kilometers. Similar gradients were also derived from height-dependent inversions as carried out by Westendorp Plaza et al. (2001), Mathew et al.(2003), and S´anchez Cuberes et al. (2005). However, comparing with a coronal C iv line at 154.8 nm, Hagyard et al. (1983) obtained gradients of 0.1–0.2 G km − . Using ∇ · ~ B , Hofmann & Rendtel (1989) obtained 0.32 G km − from data with low spatial res-olution. Many solar structures are rather small, i.e., at the spatial resolution limit ofpresent instruments or even below. Thus, features that do not belong to the same mag-netic structure enter the determination of the horizontal gradients and a ff ect the verticalgradients. Indications where found by Balthasar et al. (2013a) that higher spatial res-olution decreases this discrepancy. So far, the problem is not solved, but independentfrom the solution of this problem, we can state that the magnetic field decreases muchfaster with height above the δ -umbra than above the main umbra.The CEL might be the dividing line between the original spot and new emerg-ing flux forming the δ -umbra. The penumbral area between PIL and CEL then wouldbe the following part of the new bipolar flux. Penumbrae merged between main and δ -umbra, i.e., between opposite polarities, similar as observed by Wang et al. (2013),but not for the parts with the same polarity. This scenario explains that the Evershedflow belonging to the main umbra ended at the CEL. The horizontal flux transfer ve-locities were parallel to the CEL and did not cross it, in contrast to the PIL. Strongchanges of the magnetic field with height in this area are not surprising, and there wereelectric currents at the CEL. Such an emerging flux system would also explain that theCEL representing the dividing line between old and new flux is more important for theconfiguration of this δ -spot than the PIL.The observed chromospheric downflows above the CEL resemble the supersonicdownflows found by Mart´ınez Pillet et al. (1994) at the PIL of another sunspot, but inthe photosphere. We could not detect such large vertical velocities in the photosphere.Perhaps, the photospheric counterparts to the chromospheric flows were rather narrow,much less than the 2 ′′ in case of Mart´ınez Pillet et al. (1994), and they contributed onlya small fraction of the signal in our resolution element.The group NOAA 11504 produced a C1.8 flare about 19 hours before our obser-vations and a C3.9 flare seven hours after our observations as shown in Fig. 11. We didnot find a shear flow in this group next to the δ -umbra. The flow away from it parallelto the CEL is probably not strong enough to build up magnetic shear within a shortperiod. This indicates that a δ -spot can be quiet in the sense of flares for at least a day.
5. Conclusions
In the following, we summarize the most important findings with regard to this δ -spotin NOAA 11504. • The magnetic field strength of 2250 G in the δ -umbra is somewhat less than in themain umbra (2600 G in deep photospheric layers). • We find that the magnetic field transition between the main and the δ -umbra is rathersmooth. A small location, where the magnetic azimuth changes by about 90 ◦ from one pixel to the next, occurrs at some distance from the δ -umbra close to abright patch next to the PIL.2 Balthasar etal.
16 17 18 19June 201210 −9 −8 −7 −6 −5 −4 −3 X − r ay f l u x [ W m − ]
16 17 18 19June 201210 −9 −8 −7 −6 −5 −4 −3 X − r ay f l u x [ W m − ] XMCBA
Figure 11. X-ray flux in the 1.0–8.0 Å (top) and 0.5–4.0 Å (bottom) channelsof the of the GOES-satellite for the period 2012, June 16–18. The gray verticalbar marks our VTT-observing time.
For an easier readability, logarithmic scalemarks are repeated at the beginning of each day. • The magnetic field decreases much faster with height above the δ -umbra than abovethe main umbra. • Electric currents are detected at the CEL in deep photospheric layers and in the δ -umbra. • Around the main umbra, we observe the typical Evershed flow which ends in thesoutheastern part of the spot at the CEL. • Related to the δ -umbra, we detect a second system of Evershed flows. • Large velocities of ± − occur in the chromosphere above the CEL. • No major flare was observed within seven hours before or after our observations.We have shown that the CEL is more important than the PIL for this specificsunspot. We are able to explain this assuming that the CEL is the dividing line betweenold and new emerging bipolar flux. Thus, δ -spots can be stable, they do not alwaysproduce flares. The brightenings in H α and the occurrence of central emission in theCa ii δ -spot. Future observations should include also measurements of thehemagnetic configuration of a δ -spot 13chromospheric magnetic field. This will be possible with, e.g., with the GREGOR In-frared Spectrograph (Collados et al. 2012) or the GREGOR Fabry P´erot Interferometer(Puschmann et al. 2012) at the new GREGOR solar telescope (Schmidt et al. 2012) inTenerife. Acknowledgments.
The VTT and ChroTel are operated by the Kiepenheuer-Institutf¨ur Sonnenphysik (Germany) at the Spanish Observatorio del Teide of the Instituto deAstrof´ısica de Canarias. The HMI-data have been used by courtesy of NASA / SDO andthe HMI science team. MV expresses her gratitude for the generous financial support bythe German Academic Exchange Service (DAAD) in the form of a Ph.D. scholarship.CD and REL were supported by grant DE 787 / References
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