Hinode observations reveal boundary layers of magnetic elements in the solar photosphere
R. Rezaei, O. Steiner, S. Wedemeyer-Böhm, R. Schlichenmaier, W. Schmidt, B. W. Lites
AAstronomy & Astrophysics manuscript no. rrezaei + al07 c (cid:13) ESO 2018October 25, 2018 L etter to the E ditor Hinode observations reveal boundary layers of magnetic elementsin the solar photosphere
R. Rezaei , O. Steiner , S. Wedemeyer-B¨ohm , R. Schlichenmaier , W. Schmidt , and B.W. Lites Kiepenheuer-Institut f¨ur Sonnenphysik, Sch¨oneckstrasse 6, D-79104 Freiburg, Germany Institute of Theoretical Astrophysics, P.O. Box 1029, Blindern, N-0316 Oslo, Norway High Altitude Observatory, NCAR, P.O. Box 3000, Boulder, CO 80307, USAE-mail: [rrezaei; steiner; schliche; wolfgang]@kis.uni-freiburg.de, [email protected], [email protected] 27 July 2007 / Accepted 31 October 2007
ABSTRACT
Aims.
We study the structure of the magnetic elements in network-cell interiors.
Methods.
A quiet Sun area close to the disc centre was observed with the spectro-polarimeter of the Solar Optical Telescope on boardthe Hinode space mission, which yielded the best spatial resolution ever achieved in polarimetric data of the Fe i
630 nm line pair. Forcomparison and interpretation, we synthesize a similar data set from a three-dimensional magneto-hydrodynamic simulation.
Results.
We find several examples of magnetic elements, either roundish (tube) or elongated (sheet), which show a central areaof negative Stokes- V area asymmetry framed or surrounded by a peripheral area with larger positive asymmetry. This pattern waspredicted some eight years ago on the basis of numerical simulations. Here, we observationally confirm its existence for the first time. Conclusions.
We gather convincing evidence that this pattern of Stokes- V area asymmetry is caused by the funnel-shaped boundaryof magnetic elements that separates the flux concentration from the weak-field environment. On this basis, we conclude that electriccurrent sheets induced by such magnetic boundary layers are common in the photosphere. Key words.
Sun: photosphere – Sun: magnetic fields
1. Introduction
With ever increasing polarimetric sensitivity and spatial resolu-tion, it becomes now clear that even the most quiescent areason the solar surface harbour ample amounts of magnetic flux.This flux becomes visible in small patches of field concentra-tions, called magnetic elements for short. While horizontal fieldstend to occur near the edge of granules, the present investigationfocusses on fields predominantly oriented in the vertical direc-tion and mainly occurring in the intergranular space (Lites et al.2007b,a). There, magnetic elements are often visible in G-bandfiltergrams as point-like objects. In more active regions, mag-netic elements of extended size appear in the form of ‘crinkles’,‘ribbon bands’, ‘flowers’, etc. (Berger et al. 2004), which showa sub-structure consisting of a dark central area surrounded by astriation of bright material and further outside by a downdraft ofplasma (Langangen et al. 2007). While Doppler measurementsof this downdraft are at the limit of spatial resolution with thebest ground-based solar telescopes, spectro-polarimetric mea-surements have less spatial resolution due to image degradationby atmospheric seeing over the required long integration times.Measurements with the spectro-polarimeter on board theHinode satellite have a superior spatial resolution of approxi-mately 0 . (cid:48)(cid:48) thanks to excellent pointing capabilities (Shimizuet al. 2007) and the absence of seeing. Using Hinode data, weshow examples of unipolar magnetic elements of the network-cell interiors that possess a distinct sub-structure, which is strik-ingly manifested in maps of the asymmetry of spectral lines inthe circularly polarized light — the Stokes- V area asymmetry.The areas of the blue and the red lobes of Stokes- V profilesare identical when formed in a static atmosphere, but become asymmetric in the presence of gradients in the velocity and mag-netic field strength (Illing et al. 1975; Solanki & Pahlke 1988;Sanchez Almeida et al. 1989; Landolfi & Landi degl’Innocenti1996). Hence, the variation in the Stokes- V asymmetry acrossmagnetic elements gives information on their magnetic field andplasma flow properties. Since this information is involved, wecomputed synthetic Stokes- V profiles of magnetic elements thatoccur in a three-dimensional simulation of magneto-convectionand compare their asymmetry with the measured ones in orderto understand their origin.
2. Observation and data reduction
The observations were carried out on 10 March, 2007 with thespectro-polarimeter (SP) of the Solar Optical Telescope (SOT)on board of the Hinode space satellite (Kosugi et al. 2007;Tsuneta et al. 2007; Suematsu et al. 2007). The four Stokes pro-files of the Fe i
630 nm line pair were recorded in a quiet Sunarea close to the disc centre. The integration time of 4.8 s led toan rms noise level in the polarization signal of σ ≈ . × − I c .The data calibration for the SP is described in Ichimoto et al.(2007) and Tarbell (2006). The field of view comprises an areaof 162 (cid:48)(cid:48) × (cid:48)(cid:48) with a spatial sampling of 0 . (cid:48)(cid:48) along the slitand 0 . (cid:48)(cid:48) in the scanning direction. The spatial resolution of theresulting spectro-polarimetric maps is approximately 0 . (cid:48)(cid:48) , andthe spectral sampling is 2.15 pm. The rms continuum contrastat 630.0 nm is around 7.5 %, far above the 3 % value typicallyobserved from the ground at the same wavelength (Rezaei et al.2007; Khomenko et al. 2005). This same data set served Liteset al. (2007a,b) in an investigation of the horizontal magneticfields in the quiet Sun. a r X i v : . [ a s t r o - ph ] N ov Rezaei et al.: Variation of area asymmetry across a magnetic element
Fig. 1.
Columns a-c : observational data obtained with the spectro-polarimeter of Hinode / SOT.
Columns d and f : synthetic data fromthe 3-D MHD simulation.
Columns e and g : same as d and f but after application of the SOT-PSF to the synthetic intensity maps.
Rows from top to bottom : the sign of the Stokes- V area asymmetry for the line Fe i i − , V tot of Fe i V tot . Distance between tick marks is 0 . (cid:48)(cid:48) .
3. Numerical simulation
The three-dimensional magnetohydrodynamic simulation com-prises an area of 4 800 × , corresponding to 6 . (cid:48)(cid:48) × . (cid:48)(cid:48) and spans a height range of 2 800 km from the top layers of theconvection zone to the middle chromosphere. Details of the sim-ulation, carried out with the CO BOLD code, can be found inScha ff enberger et al. (2005, 2006).Initially, a homogeneous vertical magnetic field with astrength of 1 mT was superposed on a model of relaxed ther-mal convection. After relaxation, fields of mixed polarity occurthroughout the photosphere with an area-fractional imbalancetypically of 3:1 for fields stronger than 1 mT. Similar polarityimbalances of even larger fields of view also occur in observa-tional data (Lites 2002). Because of the periodic side boundariesand the conditions that the magnetic field must remain vertical atthe top and bottom boundaries, the horizontally averaged verticalnet magnetic-flux density remains 1 mT throughout the simula-tion. This value compares very well with the mean flux densityof 1.12 mT reported by Lites et al. (2007a) for the Hinode dataset. The mean absolute horizontal field strength is 2.5 mT in theupper photosphere of the simulation, 2.5 times the net verticalflux density. Lites et al. (2007a) report a ratio of 5.The grid constant of the computational domain in the hori-zontal direction is 0 . (cid:48)(cid:48) (120 grid cells), three times smallerthan the spatial sampling of the Hinode SP data. The simu-lation was advanced for 4400 s of real time. The results pre-sented here refer to the last 2400 s, well after the initial relax-ation phase. Using the SIR code (Ruiz Cobo & del Toro Iniesta1992; Bellot Rubio 2003), we synthesized the Stokes profiles ofthe Fe i
630 nm line pair from a large number of simulation snap-shots with a spectral sampling of 2 pm. Profiles were computedalong vertical lines-of-sight for each grid point. To the result-ing intensity maps, we additionally applied a theoretical point- spread function (PSF) that models the spatial resolution capabil-ity of the SOT optics (Wedemeyer-B¨ohm 2008).
4. Data analysis
The line parameters extracted from both the calibrated Stokesdata of the observation and from the simulation include the areaand amplitude asymmetry of Stokes- V , the line-core and line-wing velocities, and the total (signed) circular polarization V tot = (cid:90) λ λ b V ( λ ) / I c d λ − (cid:90) λ r λ V ( λ ) / I c d λ , (1)where λ is the zero-crossing wavelength of a regular Stokes- V profile, and λ r and λ b denote fixed wavelengths in the red andblue continua of the lines (similar to Rezaei et al. 2007). Therelative Stokes- V area asymmetry (Solanki & Stenflo 1984) isdefined as δ A = (cid:32)(cid:90) λ λ b | V ( λ ) | d λ − (cid:90) λ r λ | V ( λ ) | d λ (cid:33) (cid:30)(cid:90) λ r λ b | V ( λ ) | d λ . (2)Figure 1 shows a few selected examples of magnetic ele-ments from the Hinode data (columns a-c) and the simulation(columns d-g). The observed ones are all taken from networkcell interiors. Columns e and g are based on the same syntheticdata as are columns d and f, respectively, but degraded with thetheoretical PSF for SOT. The top row displays the sign of thearea asymmetry: black corresponds to negative and white to pos-itive area asymmetries. Gray indicates that the Stokes- V profilehas a signal below the 3 σ noise level (65 % of the total field ofview) or that it has an irregular shape (20 %), where most of thelatter would classify as regular when lowering the noise level.This same threshold also applies to the simulation data of thepanels in columns d-g, where we ignore V -profiles with an am-plitude less than 3 . × − I c for comparison with the Hinode ezaei et al.: Variation of area asymmetry across a magnetic element 3 Fig. 2.
Variation in δ A across magnetic elements from theHinode data (top row) and the simulation (bottom row) . Fromleft to right and top to bottom, the sections are taken from thedata corresponding to columns a, b, d, and f of Fig. 1.data. In the rightmost two panels, this threshold is 5 times lowerin order to highlight the case of a weak magnetic element thatwould have barely been detected with Hinode.The line-wing velocity of Fe i I Doppler shiftin the intensity interval 0.8-0 . I c . We set the convective blueshift of the line-core velocity in the quiet Sun to − . − .Because of the low degree of polarization, the line-wing velocityis not spoilt by magnetic influence.The third row displays V tot , whose contours are shown in allthe panels. It is a linear measure of the magnetic flux densityaccording to Lites et al. (1999) and Lites et al. (2007b). Fromthe fourth row, which shows the continuum intensity at 630 nm,we see that the magnetic flux concentration occurs mainly in theintergranular space.
5. Results and discussion
Both the observation and the simulation show magnetic elementsof either sheet like or roundish shape, possessing the same strik-ing pattern with regard to the Stokes- V asymmetry: a central re-gion with negative Stokes- V area asymmetry is framed or sur-rounded by a narrow seam of pixels having positive area asym-metry (Fig. 1, first row). Plotting δ A across a magnetic element,we find that | δ A | is typically larger in the periphery than in thecentral region of the magnetic flux concentration. Representativecross sections that demonstrate this behaviour are shown inFig. 2 for both the observation and the simulation. Along with δ A in the top right panel of Fig. 2, Fig. 4 also gives the corre-sponding observed Stokes- V profiles. Also from Fig. 1 we seethat the magnetic elements are located within and surrounded bya downdraft.For gaining deeper insight, we now consider in Fig. 3 thevertical cross section through the simulation snapshot shown incolumn d of Fig. 1 for the position y = . (cid:48)(cid:48) . It displays themagnetic field strength (colour-coded) together with the veloc-ity field, projected on the vertical plane (white arrows). The hor-izontally running curve indicates optical depth τ
500 nm =
1. Amagnetic flux concentration is forming in the downdraft and hasreached a field strength of 0.13 T at τ
500 nm =
1. Close to the sur-face of optical depth unity and through the photosphere, a rela-tively sharp, funnel-shaped boundary separates the magnetic fluxconcentration from the weak-field or field-free surroundings.
Fig. 3.
Vertical cross section through the simulation box cor-responding to position y = . (cid:48)(cid:48) of the column d of Fig. 1.It displays the logarithmic magnetic field strength (from 1.0 to10 . mT, colour-coded), together with the velocity field, pro-jected on the vertical plane (white arrows) and the electric cur-rent density normal to the plane (black contours). Optical depth τ
500 nm = V profiles from vertical lines-of-sighthave either positive or negative area asymmetry, δ A . Outside thisrange, the Stokes-V signal is below the 3 σ noise level of the ob-servations. δ A ( x ) is plotted in the lower left panel of Fig. 2.The inner vertical white lines indicate a central part of theflux concentration (880 < x < V pro-files have δ A <
0. This is because their lines-of-sight sam-ple increasing field strength and increasing downflow veloc-ity with increasing continuum optical depth (Solanki & Pahlke1988). This situation changes drastically in the peripheral region840 ≤ x <
880 km and 1120 < x ≤ δ A >
0. Here, the downflow speed stillincreases with optical depth; but because of the funnel-shapedflux concentration, lines-of-sight traverse a magnetic boundarylayer, where the field strength rapidly drops with increasing op-tical depth. The combination of increasing velocity and decreas-ing field strength produces positive area asymmetry. From this,we conclude that the narrow seam of positive area asymmetryin the periphery of magnetic flux elements seen in the Hinodedata is a consequence of their well-defined boundary (or magne-topause) that expands with height in a funnel-like manner.As an immediate consequence of Amp`ere’s law, this bound-ary carries an electric current sheet. The black contours in Fig. 3indicate a current density of 0.5 Am − , encircling higher valuesof up to 4.0 Am − . This refers to the current component perpen-dicular to the section plane, which flows in the opposite directionon either side of the magnetic flux concentration.If the magnetic flux concentration is inclined enough with re-spect to the viewing direction, lines-of-sight traverse the bound-ary layer on only one side of the flux concentration, which leadsto a one-sided seam of positive area asymmetry. This is almostthe case in Fig. 3 (and corresponding δ A -panel of Fig. 1), wherethe flux concentration is slightly inclined to the right making theseam of positive δ A to the left much narrower than that on the Rezaei et al.: Variation of area asymmetry across a magnetic element
Fig. 4.
Stokes- V profiles from the Hinode data across the magnetic element of column b of Fig. 1. δ A ( x ) for the same section isshown in Fig. 2 (top right panel).right side. In fact, most magnetic elements in the field of view ofthe observation show a one-sided pattern like in the upper rightcorner of the synthetic δ A -map in columns d or e.Because the mean magnetic flux density in the network cellinterior is low, granular flow gathers only small amounts offlux so that only small and weak magnetic flux concentrationsform (Steiner 2003). They form and disperse with the onsetand cessation of intergranular downdrafts. Therefore we observestrong downflows associated with the magnetic elements con-sidered in this work. Indeed, Grossmann-Doerth et al. (1996),Sigwarth et al. (1999), and Mart´ınez Pillet et al. (1997) also ob-serve mainly downflows associated with weak magnetic signals.In combination with increasing field strength, these downflowsgive rise to negative area asymmetry. Yet, the peripheral posi-tive area asymmetry is larger (Fig. 2) and may partially balanceor even outweigh the negative contribution when observing at alower spatial resolution.Langangen et al. (2007) finds that the downdraft velocitynear the edges of magnetic elements is larger than in the cen-tral part. Here we find in both observations and simulation themaximum speed in the centre of the flux concentration. In thesimulation this is because the magnetic element forms as a con-sequence of an intergranular downdraft, with peak velocity inthe centre. This is di ff erent from the regime of a mature strongflux concentration for which simulations exhibit veritable down-flow jets near their edges but not in the centre (Steiner et al.1998; Shelyag et al. 2007). This regime might be more represen-tative of the active region elements observed by Langangen et al.(2007).Grossmann-Doerth et al. (1988, 1989) and Solanki (1989)first pointed to the peripheral, canopy-like magnetopause ofmagnetic elements as the origin of the observed positive Stokes- V area asymmetry. Steiner (1999) found this e ff ect at work in atwo-dimensional MHD-simulation, but also found that the cen-tral region of the magnetic flux sheet tends to have negative val-ues and that a delicate balance with the peripheral region ex-ists in which the positive values may dominate and outweighthe negative ones. These findings have recently been confirmedin a three-dimensional environment by Shelyag et al. (2007).Bellot Rubio et al. (2000) came to a similar conclusion based onsemi-empirical modelling. Leka & Steiner (2001) found a simi-lar pattern in the Stokes- V area asymmetry in pores and magneticknots. Here, for the first time, we find this pattern in observationsof small-scale magnetic elements in the network cell interior.
6. Conclusion
Spectro-polarimetric data of a quiet Sun area close to the disccentre obtained with SOT on board Hinode were analysed. Wefind magnetic elements of either a roundish (tube) or an elon-gated (sheet) shape, which show Stokes- V profiles of negativearea asymmetry in the centre, surrounded or framed by pixelsof larger, positive area asymmetry. A comparison with results from 3-D MHD-simulations suggests that this peculiar patternin Stokes- V area asymmetry (first predicted by Steiner 1999) isdue to the confined nature of the field in magnetic elements witha funnel-shaped boundary layer that gives rise to a steep gradientin field strength along the line of sight.We also conclude that this kind of magnetic element of theinternetwork is accompanied by electric current sheets. Whilethese conclusions are evident from the comparison, we cannotexclude the hypothesis that a suitable magnetic structuring onscales not resolved by the present observation and simulationwould lead to the observed pattern in δ A . Acknowledgements.
Hinode is a Japanese mission developed and launched byISAS / JAXA, with NAOJ as the domestic partner and NASA and STFC (UK)as international partners. It is operated by these agencies in co-operation withESA and NSC (Norway). Part of this work was supported by the DeutscheForschungsgemeinschaft (SCHM 1168 / References
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