Indications of 8-kilogauss magnetic field existence in the sunspot umbra

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ScienceDirect Advances in Space Research 57 (2016) 398–407 www.elsevier.com/locate/asr

Indications of 8-kilogauss magnetic field existence in the sunspot umbra V.G. Lozitsky Astronomical Observatory of Taras Shevchenko National University of Kyiv, Observatorna 3, Kyiv 01053, Ukraine Received 6 March 2015; received in revised form 27 August 2015; accepted 28 August 2015 Available online 4 September 2015

Abstract We present magnetic field diagnostics in two big sunspot of different magnetic polarity observed on 18 May 2002 and 29 October 2003. In these sunspots, according to visual measurements, magnetic field strength in Fe I 5250.2 Ǻ line was about 3500 gauss. The existence of stronger fields follows from the detailed study of fine spectral effects in I ± V and V profiles of Fe I 6301.5 and 6302.5 Ǻ lines, such as: (a) non-parallelism of bisectors in Fe I 6301.5 line related to distance about ±250 mǺ from the line center, and (b) weak secondary Stokes V peaks on distance, on the average, ±375 mǺ from the Fe I 6302.5 Ǻ center. Consequently, we argue that these peculiarities indicate to the fact that spatially unresolved magnetic fields exist in the sunspot umbra, their strength being about 8 kG. In small structures with such very strong fields magnetic polarity was the same as in the background field of the sunspot umbra, and Doppler velocity is about
1.9 km/s (lifting of plasma). Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Sun; Sunspots; Magnetic fields; Spatially unresolved structures; Extremely strong fields

1. Introduction Sunspots are well-visible manifestations of solar activity with slow evolution and long lifetime. Their diameters range from a few to 150–170 mega-meters (Mm) which is much more than spatial resolution of modern solar telescopes (Solanki, 2003; Babij et al., 2011). This is the reason why they are suitable objects for magnetic field measurements. First such measurements were made by Hale (1908) using observations of the Zeeman effect in solar spectral magnetosensitive lines. It was found that in developed sunspots with umbra and penumbra typical magnetic field strengths vary as rule, from 2000 to 3000 gauss (G). In small sunspot without penumbra (i.e. pores), direct measurements give somewhat lower values, from 1100 to 2500 G (Steshenko, 1967; Solanki, 2003). It was established that magnetic field strength in sunspots, in general, increases on the sunspot diameter. Due to this fact, to

E-mail address: [email protected] http://dx.doi.org/10.1016/j.asr.2015.08.032 0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.

study temporal changes of sunspot magnetic fields during the 11-year solar cycle, the fixation of sunspot diameter is needed (Lozitska, 2010). It was shown that for sunspots of 22–44 Mm, the average annual strengths in umbra vary in the range of 2100– 2900 G. Sunspots, similar to other features of the Sun, have a very fine structure of magnetic fields and velocities. The most distinctly one can see this structure in the sunspot penumbra. The smallest elements of this structure are likely to be spatially unresolved, as the true size of the mentioned elements is estimated at the level of several tens or even several units of kilometers (Sa´nchez Almeida, 1998), whereas the best spatial resolution on modern solar telescopes is 70–100 km. Due to this fact, direct magnetic field measurements give some average parameters of magnetic fields, which may, in a general case, strongly differ from local magnetic fields. This difference should be most essential in such places on the Sun where filling factor f is much smaller than 1 (f  1). However, in the sunspot umbra,

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where f  1 (Solanki, 2003), direct measurements give the reliable value of the local magnetic fields (Lozitska et al., 2015). Sometimes the strongest magnetic fields in sunspot umbrae reach 4000–5000 G. Livingston et al. (2006) reported one case only where magnetic field strength was 6100 G. Recently, Van Noort et al. (2013) first discovered the field over 7000 G in a sunspot penumbra, where velocities were about 20 km/s. Excellent comparative characteristics of above articles was made by the anonymous reviewer: ‘It is important to note that the magnetic field strengths in Livingston et al. (2006) and Van Noort et al. (2013) were determined by very different methods. In the case of Livingston et al. (2006) these are direct observations of Zeeman splitting in various spectral lines with large Lande factors based on the line intensity profile. In the case of Van Noort et al. (2013), they analyze full Stokes vector spectropolarimetry with an indirect Fourier technique to get information about the smallest spatial scales. The probable mechanisms behind the large magnetic field strengths are well developed in each paper. In the case of Livingston et al. (2006), very large sunspots horizontal force balance of the cool atmosphere requires additional support from a large magnetic field, while cooling also lowers the optical depth and depresses the level of the photosphere in the umbra, allow us to see larger fields. In the case of Van Noort, they also claim that the high field strengths they see in the penumbra actually originate deep between granules in the convection zone (again because the opacity is low) where field strengths should be higher corresponding to the larger gas pressure’. At present, it is unknown why and how often such extremely strong fields occur. Steshenko (1967) observed the field of 5350 G in a relatively small area (62 arc sec) of the umbra of a great sunspot, whereas outside this area the magnetic field was much weaker. Taking into account that both penumbra and umbra have very fine structure, it is most likely that the extremely strong fields (P7 kG) can occur in sunspot umbra too. As to spectral manifestations of such a case, we can expect a complicated picture of the Zeeman effect, with superposition of, at least, two components with different magnetic fields and filling factors: the first (background) component has a lower magnetic field but a bigger filling factor, while the second (subtelescopic) one has stronger magnetic fields but a smaller filling factor. In principle, the true physical parameters of both components could be determined on the basis of comparison of observed profiles with theoretical ones calculated for different models of magnetic field, velocity and atmosphere. The simplest case is when Zeeman splitting DkH in a small-scale (spatially unresolved) component is much bigger than spectral half-width Dk1/2 of magnetosensitive line (DkH  Dk1/2). In this case, two discrete and fully separate Zeeman pictures are observed in one and the same spectral line which corresponds to different magnetic fields and velocities. This allows for obtaining reliable magnetic

399

field parameters in each component independently from any assumption about models of the magnetic field and atmosphere. In a more complicated case DkH 6 Dk1/2 in both magnetic components (Gordovskyy and Lozitsky, 2014). This case also calls for a two-component model, but the problem is that the number of free parameters of such a model is too high, about ten. This leads to using some simplest assumptions that lead to ambiguity of final conclusions (Rachkovsky et al., 2005). An alternative approach is to use, for comparison, a simple theoretical one-component model, and to analyze the deviation of observations from such a model. For this purpose, the consideration of bisectors of I ± V profiles proves to be a very convenient and simple method (Lozitsky, 2015). This method is used in the present study. Also, a second (more direct) method is employed here, namely the search of spectral manifestations of full Zeeman splitting (DkH  Dk1/2) in a spectral line with a large Lande factor. 2. The instrument The observations were made with Echelle spectrograph of horizontal solar telescope of Astronomical Observatory of Taras Shevchenko National University of Kyiv, AO KNU (Kurochka et al., 1980). The optical scheme of this instrument is given in Fig. 1. In this Figure: M1 and M2 – coelostat flat mirrors with diameters of 310 and 350 mm, respectively, M3 – the main telescope mirror, with the diameter of 300 mm and focusing distance of 12,500 mm, M4 – throwing-back-mirror with the diameter of 150 mm, k/4
a quarter-wave plate, ES – enter slit of the spectrograph, P1 – splitting-beamprism made of Iceland spar, M5 – collimator’s mirror with the diameter of 150 mm and focus of 6000 mm, G – Echelle diffraction grating. This grating measures 100  150 mm, has 50 strokes per mm and diffraction angle 30°. In order to separate the different diffraction orders (from 31 to 56 in visual band), the glass prism P2 is used with the refraction angle of 12°. M6 is the camera’s mirror with the diameter of 500 mm and focus of 6500 mm, and PP is a photoplate. This instrument can simultaneously record the solar ˚ with the spectral resolution spectrum from 3800 to 6600 A of nearly 200,000 (i.e. 30 mǺ) in the green region and with the temporal resolution of about several seconds. The spatial resolution of observations depends mainly on image vibration and equals, as rule, 2–3 arc sec during the morning observations. As rule, typical equivalent length of the spectrograph exit slit is about 35 arc sec, i.e. 25 Mm. Although the spatial resolution of observations on the instrument is low, it has the following advantages: ˚ , of the (a) a wide spectral range, from 3800 to 6600 A simultaneous recording; for this goal large (180  240 mm and 240  240 mm) ORWO WP3 photo-plates are used;

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Fig. 1. Optical scheme of horizontal solar telescope of Astronomical Observatory of Taras Shevchenko National University of Kyiv (see text).

Fig. 2. Active regions NOAA 9948 (left) and NOAA 10488 (right) observed by SOHO in white light. Spot under study is the greater in second case.

(b) I + V and I – V spectra are recorded simultaneously; (c) instrumental polarization on the instrument is relatively low as all angles of reflection before the polarization analyzer do not reach, as rule, 20°. The telescope has a photo-guide for retention of Sun’s image on the exit slit of spectrograph. For observations of the Sun in Ha line, a spectro-helioscope of classical type is used on the instrument too. Since 1970s two basic observations have been carried out regularly with the instrument: (i) photographical observations of Echelle I ± V spectra of active processes on the Sun (flares, sunspots, prominences, surges), and (ii) magnetic field measurements in sunspots using visual method. Thanks to using this instrument in the monitoring regime, many very interesting and violent processes have been observed, including more than ten X class flares, for instance, X17.2/4B super-flare of 28 October 2003 (Lozitsky, 2009). 3. Observations and line profiles Two big sunspots with strong magnetic field were observed, namely, 18 May 2002 (NOAA 9948) and 29 October 2003 (NOAA 10488) – see Fig. 2. The first sunspot had the diameter of about 36 Mm and the magnetic field of S polarity with strength of 3600 G according to visual measurements in Fe I 5250.2 Ǻ line made at the AO KNU; the heliocentric angle of this sunspot was l = 0.85. The second sunspot had l = 0.97, the size of about 46 Mm and the

magnetic field of 3400 G of N polarity. During the observations, the I + V and I – V spectra of the sunspots were recorded using ORWO WP3 plates. Exposures were 30 s and started at 13:34:00, 14:12:00 and 14:31:20 UT for first spot, and at 12:53:50 UT – for the second one. So long as the diameters of sunspots were 36 and 46 Mm versus 25 Mm of the enter slit of the instrument, the obtained spectra correspond to umbra and penumbra of sunspots, without the nearest photosphere. The magnetic fields in sunspots were investigated using Fe I 6301.5 and 6302.5 Ǻ lines, which have nearest heights of formation in the atmosphere but different effective Lande factors, geff = 1.669 b 2.487, respectively (Zemanek and Stefanov, 1976). In the first approximation, these lines can be considered as the same line which has two discrete values of Lande factor, with the ratio once in 1.5 times. This is highly valuable in the line ratio method (see, e.g., Stenflo, 1989) which allows for studying spatially unresolved magnetic fields. The observed I + V and I – V profiles have the following peculiarities (Figs. 3–6): (a) Fe I 6302.5 Ǻ line has partly separated Zeeman pand r-components, whereas Fe I 6301.5 Ǻ line – blended these components; (b) the splitting of I ± V profile bisectors in Fe I 6301.5 Ǻ line is non-monotonous in both sunspots. Namely, this splitting has the maximum in the line core, the minimum – in the middle wings, and the second maximum – in the far wings;

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401

1.0

I ±V

0.8

0.6

0.4

0.2 -1000

-500

0

500

1000

Distance f rom 6302.000 A ( in mA ) Fig. 3. Observed I ± V profiles of Fe I 6301.5 and 6302.5 Ǻ lines in the sunspot of 18 May 2002 related to the time interval of 13:34:00–13:34:30 UT. Named solar lines correspond to the positions of about
500 and +500 mǺ on the abscissa axis, whereas telluric O2 lines – 0 and 750 mǺ. For the FeI 6301.5 Ǻ line, the bisectors are presented by stroke lines.

1.0

I ±V

0.8

0.6

0.4

0.2 -1000

-500 λ - 6302.000

0 A ( in

500 m A )

1000

Fig. 4. The same as in Fig. 3 for the sunspot of 18 May 2002, but for the time interval of 14:31:20–14:31:50 UT.

1.00

I ±V

0.80

0.60

0.40

0.20 -1000

-500 0 λ - 6302.000 A ( i n mA)

500

1000

Fig. 5. Observed I ± V profiles of Fe I 6301.5 and 6302.5 Ǻ lines in the sunspot of 18 May 2002 related to the time interval of 14:12:00–14:12:30 UT.

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1.0

I ±V

0.8

0.6

0.4

0.2 -1000

-500

0

500

1000

λ - 6302.000 A ( in mA) Fig. 6. The same as in Figs. 3–5, but for the sunspot of 29 October 2003.

4. Bisectors for homogeneous magnetic field To compare the observations with the theory, the profiles of lines were calculated within the framework of Unno (1956) theory. On the basis of Stokes I and V profiles, their combinations I + V and I
V were made, and for such profiles – their bisectors. Fig. 7 illustrates the results of calculations for relative absorption coefficient g0 = 4.0 and different angles c between the magnetic line and the line of sight: c = 0° (pure longitudinal field), 45° (field of intermediate orientation) and 75° (almost transversal field). In this Figure, the intensity levels I in profile are plotted along the vertical axis, and along the horizontal axis – the relative distance v from the line center normalized by Doppler half-width DkD, i.e. v = Dk/DkD, where Dk is linear distance from the line center. The case presented in Fig. 7 corresponds to vH = DkH/ DkD = 1, where DkH is Zeeman splitting. This is the case of close blending of the Zeeman p and r components. For the Fe I 6301.5 Ǻ line, it corresponds to about 3500 G, i.e. approximately the same magnetic field strength which was measured in the Fe I 5250.2 Ǻ line.

1.0 0°

45 °

75 °

75 °

45 °

0°

0.8

St okes I

(c) the second maximum of bisector splitting in Fe I 6301.5 Ǻ line corresponds to the distance of about ±250 mǺ from the line center. In fact, from Figs. 3– 6 it follows that on larger distances this splitting begins to decrease. The best illustration of this effect is Fig. 5: one can see that in the abscissa interval from
1000 to
800 mǺ the splitting of I ± V profiles is very small whereas in next interval
800. . .
500 mǺ it is much bigger; (d) as a rule, the position of central p component in the Fe I 6302.5 line coincides well in both I + V and I
V profiles. The problem of visible splitting of this component in sunspots has been discussed by many authors (see. Staude, 1973).

0.6

0.4

0.2

0.0 -1.5

-1.0

-0.5

0.0 v

0.5

1.0

1.5

Fig. 7. The theoretical shape of bisectors of I ± V profiles according to Unno (1956) theory for g0 = 4.0, vH = 1 and different angles c between magnetic line and line of sight.

From Fig. 7 it follows that in case of c = 0°, when central p component is absent, the bisectors of I + V and I
V profiles are parallel, and their splittings correspond to v = 1. This is the case where we obtain magnetic field magnitude from observations with circular polarization analyzer. If c = 45°, the relatively weak central p component occurs in the Zeeman triplet picture. In the I + V and I
V profiles, this component unites with r components which gives asymmetrical summary profile, with nonparallel bisectors of I + V and I
V profiles. It is important to note that in this case splitting of bisectors is maximum in the line core and decreases monotonically in the direction of the line wings. No peak of bisectors splitting is expected in the far wings, contrary to our observations. Also, in Fig. 7 one can see that even in the line core the value of the observed bisector splitting is smaller for c = 45° than for c = 0°. As a result, rather longitudinal component B|| = Bcos c can be obtained from such observations than the magnetic field magnitude. In case of c = 75°, the shape of bisectors is the same in the qualitative respect: their splitting increases monotoni-

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B ¼ 3:23  104 DkH ;

ð1Þ

where B is given in G, and DkH – in Ǻ. From (1) follows that for DkH = 250 mǺ, B = 8075 G. Probable errors are ±200 G here. So long as both Fe I 6301.5 and 6302.5 Ǻ lines have nearest depths of formation in the atmosphere and the same temperature sensitivity, we should observe similar spectral peculiarities in the second line, too. Unfortunately, we cannot apply similar method to Fe I 6302.5 Ǻ because it has a larger Lande factor (1.5 times) and it is blended by the telluric line at its ‘rot’ wing. Therefore, best approach in this case is to analyze the Stokes V profiles – this parameter can give the necessary information even in places of spectral continuum where bisectors of profiles cannot be constructed generally.

(vH  1), the amplitude of this distribution is proportional to the magnetic field strength B, and Stokes V peak separation DkV is the same as in Stokes I intensity gradient, dI/dk (see, e.g., Jefferies et al., 1989). However, if the splitting is strong (vH  1), then DkV  2 DkH (Lozitska and Lozitsky, 1994). This is the very case where the magnetic field magnitude can be measured independently from the angle c between the magnetic line and the line of sight. If the magnetic field is two-component, with essentially different strengths in each component, we should observe the double Stokes V distribution, with two positive and two negative peaks. The spectral splitting of these peaks depends on magnetic field strengths in both components, and amplitudes of peaks are dependent on their filling factors. The most obvious and remarkable effects in this sense were observed in the sunspot of 29 October 2003 (Figs. 8 and 9). In Fig. 8, the observed Stokes V in the area of 6302.0 ± 1.0 Ǻ is presented for five positions of this sunspot which differ spatially by 1 Mm; the numbers from
27 to
19 correspond to the numbers of photometrical sections on the spectrogram. The dependencies for
25,
23,
21 and
19 sections are lifted by 0.1, 0.2, 0.3 and 0.4, respectively, for the sake of clarity. The vertical dashed lines S1 and S2 denote the local peculiarities of opposite polarity which have a relatively small ‘red’ shift, about
40 mǺ (i. e.
1.9 km/s), in relation to the Fe I 6302.5 Ǻ center. It is important to note that the above-mentioned local peculiarities on S1 and S2 lines are presented in each section from
27 to
19, with approximately the same amplitude. Naturally, noise fluctuations are rather strong here and in order to decrease these fluctuations it is necessary to average all data. The results of such averaging over all five photometrical sections are presented in Fig. 9, where three main effects in Fe I 6302.5 Ǻ are visible:

S1

0.5 0.4 0.3 St o k e s V

cally from the line core to the wings. In addition, the range of this effect is greater than for c = 45°. In case of observational data, the heliocentric angles are about 32° for the first sunspot and 15° – for the second. So long as in the sunspot umbra the angles between the magnetic lines and the line of sight are small (Solanki, 2003), we can expect that in our case these angles do not exceed 45°. This means that, theoretically, the observed bisectors must have the monotonous increase in splitting from the line core to its wings, if the magnetic field is really homogeneous. Comparing Figs. 3, 4 and 6 with Fig. 7, one can see that the observed bisector splitting in Fe I 6301.5 Ǻ does not correspond to the case of homogeneous magnetic field. The main deviation from the theory lies in the local increase in the bisector splitting on distances of about ±250 mǺ from the line center for both sunspots. Theoretically, such peculiarity is excluded for a homogeneous field. One of the possible interpretations is that this peculiarity occurs due to superposition of two Zeeman effect pictures: the first (background) component with lower magnetic field but bigger filling factor, and second (subtelescopic) one – with stronger magnetic field but smaller filling factor (Gordovskyy and Lozitsky, 2014). From this point of view, the magnetic polarities of both components should be the same, while the magnetic field strengths should be very different. A simple estimation of the field value in the strong component can be obtained if we assume that the above-mentioned effects on ±250 mǺ (local increase in the bisector splitting) correspond to the Zeeman splitting DkH in spatially unresolved magnetic structures. For the Fe I 6301.5 Ǻ line, taking into account its effective Lande factor geff = 1.669, the magnetic field strength in the strong component can be determined via the formula

403

0.2 0.1 0.0

S2

-19

-21 -23 -25 -27

-0.1

5. Stokes V profiles Theoretically, if a magnetic field is one-component and homogeneous, Stokes V profile has a shape of single antisymmetrical distribution. For a small magnetic splitting

-1000

-500

0 500 λ - 6302.000 A (i n mA)

1000

Fig. 8. Comparison of observed Stokes V profiles of Fe I 6301.5 and 6302.5 Ǻ lines for five positions in the central part of the umbra for the sunspot of 29 October 2003.

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are in the umbra center only, whereas elsewhere they are absent.

0.15 0.10

'Red' σ comp.

'Violet' σ comp.

6. Discussion

St okes V

0.05

6.1. Instrumental polarization

0.00 -0.05 -0.10 -0.15 -1000

-500

0 λ - 6302.000 A (in m A)

500

1000

Fig. 9. Averaged by 5 Mm Stokes V in the area of Fe I 6301.5 and 6302.5 Ǻ for central part of the sunspot umbra of 29 October 2003. The vertical lines denote the position of ‘violet’ and ‘red’ Zeeman r components of Fe I 6302.5 Ǻ which correspond to about 8 kG. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

1. Strong (about ±10%) primary peaks of Stokes V distribution, with spectral separation DkV = 298 ± 2 mǺ, and Zeeman splitting DkH = 149 ± 1 mǺ. Taking into account that for the Fe I 6302.5 Ǻ line the connection between DkH and B is B ¼ 2:15  104 DkH ;

ð2Þ

then for DkH = 149 ± 1 mǺ we have B = 3200 ± 30 G. 2. Small stokes V inversion in the central part of the line. This effect was discussed earlier by many authors, see e.g. Staude (1973). 3. Well-visible secondary peaks with amplitudes of ±(3  4)% and separation of DkV = 750 ± 8 mǺ are denoted by solid vertical lines in Fig. 8. This means that DkH = 375 ± 4 mǺ, and B = 8060 ± 120 G are in excellent agreement with simple estimation by Fe I 6301.5 Ǻ line (8075 ± 200 G, see para 4 above). In order to check these estimations against the observed Stokes V of Fe I 6301.5 Ǻ line, simulations were made of the expected profile of secondary peaks in this line. It was taken into account that that Fe I 6301.5 Ǻ has an anomalous Zeeman splitting. Each r components of this line has four sub-components with relative splittings: 1.171, 1.503, 1.835 and 2.167 and intensities 0.100, 0.150, 0.150 and 0.100, respectively (Zemanek and Stefanov, 1976). The simulation results are presented in Fig. 9 via the dashed line. It can be seen that the calculated profile fits well with the observed pattern. Thus, also in this respect the results for both lines are in good agreement. Similar profiles for the spot of May 18, 2002 do not show such a clear presence of secondary peaks. This is illustrated in Fig. 10, where observations are compared for three positions: the center of the spot umbra, the center of the spot umbra +6 Mm and the middle penumbra. We can see that the weak indications of the secondary peaks

The influence of instrumental polarization (IP) has been studied by many authors, beginning from Ja¨ger (1972, 1974), Kotov (1973), Grigorjev and Golovko (1975), etc. Naturally, for magnetic field measurements on the Sun, a best case is modern polarization-free telescope like GREGOR (Schmidt et al., 2012). If, however, we use a telescope of any traditional type, horizontal of tower, we should take into account the main effects occuring due to IP. For horizontal solar telescope similar to that in the present study, they are following. 1. For magnetic field measurements by I + V and I
V profiles, the essential influence of IP occurs due to the linear-to-circular transformation effect (LCT-effect). If linear polarization is zero, observed I + V and I
V profiles are not distorted by IP. In this connection, we can expect an insignificant role of IP for observations of magnetic features with almost longitudinal field, e. g., for a sunspot near the disc center. 2. The IP value depends on the angles of reflection on mirrors of a telescope. For instruments with small angles, the value of IP is accordingly smaller. For the Horizontal Solar Telescope of Kyiv Observatory, the greatest angles occur on coelostat mirrors. As a rule, then the angles of reflection do not exceed 20°. 3. The phase polarization of the horizontal solar telescope may be approximately presented as an effect of equivalent phase plate with a path difference equals k/15  k/30. The highest phase polarization is observed in the morning and in the evening, and the lowest one – in the afternoon. 4. The phase polarization of the telescope may lead to a considerable distortion of line profiles, but only in the wavelength range of the Zeeman p and r components. For instance, IP cannot distort the nearest spectral continuum where split Zeeman components are absent. 5. For a line like Fe I 6301.5 Ǻ, taking into account its Lande factor and half-width, the influence of IP is close to zero at the distance of 250 mǺ from the line center, if the magnetic field is about 3200 G. We cannot expect a significant IP impact even at very high angles of inclination of magnetic field lines, around 60°. Especially, we cannot expect any large local splitting of bisectors at distances of ±250 mǺ caused by instrumental polarization. Summarizing the above paragraphs 1–5, we can conclude that, apparently, the instrumental polarization could not determine the diagnostic manifestations to the fields about 8 kG, although its specific manifestations still have to be presented in the spectrum. The latter assumption is

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0.5

S1

405

S2

0.4 Sunspot penumbra

I ±V

0.3 0.2

Umbra, 6 Mm f rom center

0.1 0.0

Center of umbra

-0.1 -0.2 -1000

-500 0 λ 6302.000A (in mA)

500

1000

Fig. 10. Comparison of the observed Stokes V profiles of Fe I 6301.5 and 6302.5 Ǻ lines for three positions in the sunspot of 18 May 2002, 14:12 UT.

confirmed by Fig. 9. One can see that in Fe I 6302.5 core (which corresponds to abscissa numbers about 500 on Fig. 9) a well visible non-monotonic changes of Stokes V presents when dV/dk twice changes its sign. Notice, such effect is possible in three cases (see, e.g., Rachkovsky, 1962; Staude, 1973; Grigorjev and Golovko, 1975; Lozitsky and Sheminova, 1992):

polarized), it may not significantly affect the polarized components in the Zeeman effect, especially at greater distances from the center of line. As a result, it is highly unlikely that the above-named peculiarities were caused by scattering light.

(a) presence of relatively weak (300–600 G) spatially unresolved magnetic field of opposite polarity, (b) anomalous dispersion, and (c) instrumental polarization.

For our photographical observations, grains of photoemulsion can produce noise effects, as rule, at the level of 1–2% in units of spectral continuum if exposures were optimal during the observations. There are two obvious ways for checking the data taking into account possible influence of noise of the spectra:

It is important to note that in (a) and (b) cases, we should have two positive and two negative peaks of Stokes V, and, in addition, V = 0 exact in line center. On the contrary, on Fig. 9 we can see V – 0 in the line Fe I 6302.5 center. Such case is possible if IP has obvious influence in the line center.

6.3. Noise of the spectra

(i) By comparing original observed profiles of lines for several different places on the Sun (see, e.g., Fig. 8, as well as Figs. 3–6), and (ii) By averaging observed profiles by significant spatial section on the Sun (see Fig. 9).

6.2. Stray light The influence of the scattered light significantly depends on the size of a spot and the optical scheme of the instrument. For large spots (as in this paper), this influence is much less than for small spots and pores. The presence of the scattered light appears as a central un-polarized component coinciding with the Zeeman p component. This component, if it is really significant in intensity, can be easily detected by observations of spectral line with large Lande factor which has fully separated p and r components. It is easy to check on our spectra. Examining Figs. 3–6, we can see that the Fe I 6302.5 Ǻ line has a relatively weak central component. Our calculations based on the Unno (1956) theory have shown that this is a typical view of this line at the field inclination angles up to 45°. This means that the proportion of the scattered light is negligible in the observed intensities. In addition, since scattered light is unpolarized (or weakly

From this point of view, our results reflect reliable effects regarding spectral indications of the existence of 8kilogauss magnetic fields. In fact, the specific peculiarities on Fig. 8 repeat systematically for different places on the Sun occurring on the same wavelengths marked by S1 and S2 lines. In addition, specific shape of bisectors in I ± V profiles are analogous for both sunspots and for different times of the same sunspot (Figs. 3–6). Furthermore, averaged Stokes V profiles on Fig. 9 have specific secondary peaks (marked by ‘violet’ r comp. and ‘red’ r comp.) with amplitudes of 3–4% which is much more than noise effects in this case. 6.4. Telluric and unidentified lines Naturally, ‘experimentum crucis’ in our investigation is direct observations of possible discrete fully split peculiarities in Stokes V with the opposite sign of polarization

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(Figs. 8 and 9). Fortunately, these peculiarities (i.e. secondary Stokes V peaks) were observed at distances of about 100 mǺ from the intensive telluric blends O2 6302.000 and 6302.764 Ǻ. This is quite enough for drawing reliable conclusions in the framework of our technique. As to unidentified lines, our observations demonstrate such effect in the sunspots of 18 May 2002 (Figs. 3–5). We can see an obviously asymmetrical profile of the telluric line O2 6302.000 Ǻ, with additional depression at the wavelength of 6302.090 Ǻ, exactly in the same place where a secondary ‘violet’ peak was observed in the other sunspot, of 29 October 2003 (Fig. 9) ! Fortunately, in the second sunspot, of 29 October 2003, this unidentified line was very weak or absent, which indicates to almost symmetrical profile of O2 6302.000 Ǻ line. This problem was discussed in detail with Dr. Mykola Gordovskyy. He presented excellent Hinode profiles of Fe I 6301.5 and 6302.5 Ǻ lines obtained in different places on the Sun – sunspots, plages, undisturbed photosphere (possible common investigation is planned in a separate paper). Dr. Gordovskyy found an interesting effect: the above-mentioned unidentified solar line between Fe I 6301.5 and 6302.5 Ǻ is very variable in the area of sunspots and its intensity can reach about 10 % in the units of the continuum level. Furthemore, this blend seems to be split in the I ± V spectra, similar to the magnetosensitive line with effective Lande factor geff 
0.3. Of course, this circumstance needs to be considered carefully in future studies. We should take into account that, in the first approximation, two types of sunspots exist: ‘warm’ sunspots like that of 29 October 2003 without the blend of 6302.090 Ǻ and ‘could’ sunspots like that of 18 May 2002 where this blend can occur. 6.5. Pressure balance One of the anonymous referees adheres to the following point of view: but if the two magnetic components form at the same height, this is in clear violation of magnetic pressure balance within the sunspot umbra. The stronger magnetic component must be deeper in the umbral atmosphere by several hundred kilometers to maintain equilibrium, and there the atmosphere will be warmer and have a different opacity, which will change the intrinsic amplitude of Stokes V0 . This definitely holds true, but for simple untwisted flux tubes only. If a flux tube is twisted as in a force-free magnetic field, much stronger field can occur in such a case. For example, Kirichek et al. (2013) show that in a force-free configuration the magnetic field can be amplified by 320 times as compared with the external background field. 7. Conclusion From our analysis it follows that maximum magnetic field strength in a sunspot umbra can reach about 8 kG,

being concentrated in small-scale magnetic elements of the same polarity as background field with strength of about 3 kG. According to observations, Doppler velocities are negative here (lifting of plasma) and their values are
1.9 km/s. If we compare this conclusion with the results of Van Noort et al. (2013), we can establish close magnetic field values (8 kG and >7 kG, respectively), but very different (about ten times) values of plasma velocity. In addition, the sight of plasma motions is different: it is lifting in our case and lowering in the cited article. Nevertheless, it is necessary to point out that our results concern the sunspot umbra whereas Van Noort et al. (2013) results were obtained in the penumbra, where physical conditions should be somewhat different. From our results it also follows that spatially unresolved structures with extremely strong fields of about 8 kG can occur in the spot umbra in great areas with the diameter no less than 5 Mm (as in the sunspot of October 29, 2003). A rough estimate of the filling factor by the ratio of the amplitudes of the primary and secondary peaks of Stokes V gives the value of about 20–30%, i.e. sufficient for self-observations, even with photographical method. A remarkable feature of the spectral manifestations of such very strong fields is very narrow spectral lines. One can see in Fig. 9 that the secondary peaks of Stokes V for Fe I 6302.5 Ǻ have a width of about 65% versus the primary peaks. A similar effect was observed earlier in flares (see, e.g., Lozitsky, 2011, 2015; Lozitsky and Staude, 2008). Spectral evidence on other interesting effect was detected here, namely, discrete field values, which can reach 104
105 G. Unfortunately, for a field of 104 G, such near-placed lines as Fe I 6301.5 and 6302.5 Ǻ should be considered as mutually blended. This means that Zeeman effect manifestations in these lines must be considered commonly, with the account of possible influence of the nearest spectral blend. In addition, many molecular lines occur in the spectra of a sunspot umbra, and these lines can mask weak spectral manifestation of very strong fields. Acknowledgements The author is obliged cordially to Prof. Ju¨rgen Staude, Dr. Mykola Gordovskyy and Dr. Natalia Lozitska for helpful discussions and advises, Prof. Valery Skomorovsky for making of the polarization optics for magnetic field measurements, and the anonymous referee for useful notes and comments. This study was funded by the Taras Shevchenko National University of Kyiv, the project No.11BF023-02. References Babij, V.P., Efimenko, V.M., Lozitsky, V.G., 2011. Statistical characteristics of large sunspots in solar activity cycles 17–23. Kinematics Phys. Celestial Bodies 27 (4), 191–196.

V.G. Lozitsky / Advances in Space Research 57 (2016) 398–407 Gordovskyy, M., Lozitsky, V.G., 2014. Observations of unresolved photospheric magnetic fields in solar flares using FeI and CrI lines. Solar Phys. 289 (10), 3681–3701. Grigorjev, V.M., Golovko, A.A., 1975. A study of the instrumental phase polarization of the horizontal solar telescope. Solnechnyje Dannyje 8, 78–85. Hale, G.E., 1908. On the probable existence of a magnetic field in sunspots. Astrophys. J. 28 (4), 315–343. Ja¨ger, F.W., 1972. Instrumental polarization concerning magnetographic measurements. I. Solar Phys. 27 (2), 481–488. Ja¨ger, F.W., 1974. Instrumental polarization concerning magnetographic measurements. II. Solar Phys. 29 (2), 499–508. Jefferies, John, Lites, Bruce W., Skumanich, A., 1989. Transfer of line radiation in a magnetic field. Astrophys. J. 343, 920–935. Kirichek, E.A., Solov’ev, A.A., Lozitskaya, N.I., Lozitskii, V.G., 2013. Magnetic fields in a limb flare on July 19, 2012. Geomag. Aeron. 53 (7), 831–834. Kotov, V.A., 1973. On the influence of instrumental polarization on magnetic field measurements. Izv. Krymskoj Astrofiz. Obs. 48, 78–84. Kurochka, E.V., Kurochka, L.N., Lozitsky, V.G., et al., 1980. Horizontal solar telescope of the Kiev University astronomical observatory. Vestnik Kiev Univ Seria Astronomii 22, 48–56. Livingston, W., Harvey, J.W., Malanushenko, O.V., 2006. Sunspots with the strongest magnetic fields. Solar Phys. 239, 41–68. Lozitska, N., Lozitsky, V., 1994. Small-scale magnetic fluxtube diagnostics in a solar flare. Solar Phys. 151 (2), 319–331. Lozitska, N.I., 2010. Inter-annual variations of magnetic fields in sunpots: comparison of different indexes. Kosm Nauka i Tekhnologia 16 (4), 30–36. Lozitska, N.I., Lozitsky, V.G., Andryeyeva, O.A., et al., 2015. Methodical problems of magnetic field measurements in umbra of sunspots. Adv. Space Res. 55, 897–907. Lozitsky, V.G., 2009. Magnetic fields anf FeI line profiles in the major solar flare on October 28, 2003. Astron. Lett. 35 (2), 136–142.

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Lozitsky, V.G., 2015. Small-scale magnetic field diagnostics in solar flares using bisectors of I V profiles. Adv. Space Res. 55, 958–967. Lozitsky, V.G., Sheminova, V.A., 1992. Influence of anomalous dispersion on magnetic field measurements using line ratio method. Kinematics Phys. Celestial Bodies 8 (1), 12–29. Lozitsky, V.G., Staude, J., 2008. Observational evidences for multicomponent magnetic field structure in solar flares. J. Astrophys. Astron. 29, 387–404. Lozitsky, V.G., 2011. Observational evidences for extremely strong magnetic fields in solar flares. Int. J. Astron. Astrophys. 1 (3), 147–154. Rachkovsky, D.N., 1962. Magneto-optical effect in spectral lines of sunspots. Bull. Crimean Astrophys. Obs. 27, 148–162. Rachkovsky, D.N., Tsap, T.T., Lozitsky, V.G., 2005. Small-scale magnetic field diagnostics outside sunspots: comparison of different methods. J. Astrophys. Astron. 26, 435–445. Sa´nchez, Almeida J., 1998. Optically thin irregularities in the penumbrae of sunspots. Astrophys. J. 497 (2), 967–971. Schmidt, W., von der Lu¨he, O., Volkmer, R., Denker, C., et al., 2012. The 1.5 meter solar telescope GREGOR. In: Astron. Nachrichten 333 (9), 796–809. Solanki, S., 2003. Sunspots: an overview. Astron. Astrophys. Rev. 11 (2– 3), 153–286. Staude, J., 1973. On the interpretation of some peculiarities observed in zeeman-split line contours in sunspots. Solar Phys. 32 (2), 403–408. Stenflo, J.O., 1989. Small-scale magnetic structures on the Sun. Astron. Astrophys. Rev. 1, 3–48. Steshenko, N.V., 1967. Magnetic fields of small sunspots and pores. Bull. Crimean Astrophys. Obs. 37, 21–28. Unno, W., 1956. Line formation of a normal Zeeman triplet. Publ. Astron. Soc. Jpn. 8, 108–125. Van Noort, M., Lagg, A., Tiwari S.K., Solanki, S.K., 2013. Peripheral downflows in sunspot penumbrae. Astron. Astrophys. 557, id.A24, 14 pp. Zemanek, E.N., Stefanov, A.P., 1976. Splitting of some spectral lines of FeI in magnetic field. Vestnik Kiev Univ Seria Astronomii 18, 20–36.