A Paradox in Measuring the Magnetic Field of the Sun

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1 ISSN , Bulletin of the Crimean Astrophysical Observatory, 28, Vol. 14, pp Allerton Press, Inc., 27. Original Russian Text V.A. Kotov, 28, published in Izvestiya Krymskoi Astrofizicheskoi Observatorii, 28, Vol. 14, pp A Paradox in Measuring the Magnetic Field of the Sun V. A. Kotov Research Institute Crimean Astrophysical Observatory, pos. Nauchny, 9849 Crimea, Ukraine vkotov@crao.crimea.ua Received February 7, 27 Abstract Significant discrepancies are often observed among the values of the mean magnetic field (MMF) of the Sun as a star observed by various instruments using various spectral lines. This is conventionally attributed to the measurement errors and saturation of a solar magnetograph in fine-structure photospheric elements with a strong magnetic field. Measurements of the longitudinal MMF performed in at six observatories are compared in this paper. It is shown that the degree of discrepancy (slopes b of linear regression lines) varies significantly over the phase of the 11-year cycle. This gives rise to a paradox: the magnetograph calibration is affected by the state of the Sun itself. The proposed explanation is based on quantum properties of light, namely, nonlocality and coupling of photons whose polarization at the telescope spectrograph output is determined by spacious parts of the solar disk. In this case, the degree of coupling, or identity, of photons depends on the field distribution in the photosphere and the instrument design (as Bohr said, the instrument inevitably affects the result ). The puzzling values of slope b are readily explained by the dependence of the coupling on the solar-cycle phase. The very statistical nature of light makes discrepancies unavoidable and requires the simple averaging of data to obtain the best approximation of the actual MMF. A 39-year time series of the MMF absolute value is presented, which is indicative of significant variations in the magnitude of the solar magnetic field with a cycle period of 1.5(7) yr. DOI: 1.313/S Keywords: Sun, magnetic field, photons, nonlocality 1. INTRODUCTION Magnetic field is one of the main attributes of the active Sun. The Babcock (1953) magnetograph is the most efficient device for measuring the solar magnetic field during more than half a century. By observing the degree of circular polarization, such a magnetograph detects the Zeeman effect for a photospheric spectral line with a nonzero Lande factor g (hereinafter, only measurements of the longitudinal component of the field are discussed). However, it has been known for a long time that the results of measurements by different instruments in different lines differ strongly even for the quiescent photosphere outside active regions. The discrepancies are believed to be caused mainly by measurement errors and saturation of the magnetograph signals in magnetic rope fibril filament fluxtube elements of the photosphere with angular widths less than an arcsecond with a strong magnetic field of about kg, as well as by different temperature sensitivity of different lines (Howard and Stenflo, 1972; Stenflo, 1973; Demidov et al., 22, 25a, 25b). In the case of measurements of the local fields in sunspots and active regions, additional discrepancies are caused by variations in the line profile and expansion of the solar magnetic fluxtubes with height in the solar atmosphere (Howard and Stenflo, 1972; Gopasyuk et al., 1973, 2). About 35 years ago, the main reason for discrepancies about the quiescent photosphere has been attributed to the superfine structure of the field, and the method of magnetic field ratio, or δ-effect (measured using different lines), began to be widely used to interpret the magnetic measurements of the photosphere (Wang and Sheeley, 1995; Demidov et al., 22, 25b). However, attention has been recently focused on quantitative discrepancies in the results by different authors who analyzed discrepancies in measurements by different instruments in different lines (Kotov, 23). This gives rise to ambiguity in interpreting the origins of such discrepancies based on the concepts of superfine structure and saturation. It is difficult to draw specific conclusions on the measurement accuracy, especially concerning different instruments, for scanning local fields in spots, active regions, faculae regions, and even the quiescent photosphere. This can be caused by a number of reasons, including the effect of spectral and spatial resolution and the spatial mismatch; variations in the line profile, which are difficult to take into account; errors in radial-velocity and brightness compensation; nonsimultaneous measurements; etc. For example, magnetograms obtained in Crimea (Gopasyuk et al., 1973, 2) showed such large differences in the magnetic field values measured using different spectral lines 79

2 8 KOTOV Table 1. MMF data obtained in Observatory Years Line, nm N, G S, G k Crimea Fe I λ Crimea Fe I λ Mount Wilson Fe I λ Stanford " Sayan Mountains " Sutherland K I λ Kitt Peak Fe I λ All data* * Total normalized MMF series. that it is unclear at all which lines give the actual field. Strong quantitative differences in the results of different observatories obtained using different lines were recently pointed out by Demidov et al. (25a). Therefore, it is especially interesting to measure the mean magnetic field (MMF) of the Sun as a star using one or several lines (within the context of this paper, the MMF has the same meaning as the overall magnetic field (OMF) of the Sun). Here, the entire visibledisk photosphere plays the role of a magnetic etalon. Since the diurnal variations in the MMF of this etalon are fairly small, measurements by various instruments in the same UT day can be considered simultaneous. The MMF has been successfully observed at CrO for the first time by Severny (1969) and colleagues. The first MMF catalog complied using CrAO data of was published by Kotov and Severny (1983). At present, published or free-access web data of MMF observations obtained at six observatories cover almost four solar cycles from 1968 to 26 (see Section 2). However, observers have noted many times the strong differences in MMF values measured by different instruments, which often exceed the errors (Scherrer et al., 1977a). As in the case of local fields, the generally adopted explanation refers to the instrumental errors. However, this cannot explain seasonal variations in the degree of discrepancy (Kotov et al., 1998a; Kotov, 23). On the other hand, the history of observational astrophysics shows that new facts and phenomena are most often discovered when weak signals (in our case, the MMF of the Sun) are studied. Are the spreading veils of the MMF a regularity indicative of a new, additional reason of discrepancies? Each new consequence gives rise to a new view of things (E. Mach), and even uninteresting stuff like errors and noise can be of great interest. 2. MMF OF THE SUN IN The world catalog of the MMF, comprising now about 18 daily values of the longitudinal magnetic field B, has existed since 1968 (see the Internet, Kotov and Severny, 1983; Kotov et al., 1998b; and Solar Geophysical Data). The catalog was compiled at six observatories: the Crimean Astronomical Observatory (CrAO), the Mount Wilson Observatory (MWO), the Wilcox Solar Observatory (WSO, Stanford University), the Sayan Solar Observatory (SSO, SIBIZMIR, Irkutsk), the Sutherland Observatory (Sutherland, South Africa, the BiSON group at the Birmingham University), and the Kitt Peak Observatory (KPO, National Solar Observatory, SOLIS-VSM data). The field was measured using the Fe I λ63.15 nm line (g = 5/3) at Kitt Peak and by atomic resonance spectroscopy using the K I λ525.2 nm line at Sutherland. Observations at other observatories are (were for MWO) carried out using the Fe I λ525.2 nm line (g = 3). Additional measurements were also performed at CrAO in using Fe I λ nm (g = 2). The MMF is weak. It varies mainly within ±1.5 G due to rotation of the Sun and slow evolution of the large-scale fields. Therefore, special techniques for controlling the zero level were employed in each magnetograph. Information on methods of MMF measurement and the data can be found in Sherrer et al. (1977a, 1977b), Kotov et al. (1998a, 1988b), Chaplin et al. (23), and Demidov et al. (25b). The WSO and KPO data were downloaded from the sites and respectively. Information on individual data sets used in the general catalog are given in Table 1, where N is the number of daily values of the MMF, is the typical error of a single measurement, S is the standard deviation for the data set, and k is the normalizing factor for merging the data of the six observatories for different spectral lines in a single time series. BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

3 A PARADOX IN MEASURING THE MAGNETIC FIELD OF THE SUN , N = 1795 (a) B, G.5 15 SGD (b) W Year Fig. 1. Temporal behavior of annual or semiannual average values of (a) the absolute value of the MMF (in G) in and (b) the Wolf numbers W according to Solar Geophysical Data. The horizontal axis is in years. The typical error of B is comparable to the dot size. The dashed line shows the average value for B. The numbers from 2 to 23 are the numbers of cycles. No other correction or saturation factors are employed. Positive values of B correspond to the N polarity, and all uncertainties are standard ±σ errors. To merge the measurements obtained at the six observatories using different lines in a single time series, the average standard deviation S is calculated using the seven values of S from Table 1 and then the normalizing factors k = S /S (see the last column in Table 1) are calculated for each observatory and each line. The complete normalized series with N = 1795 and S =.62 G is obtained by merging all data sets multiplied by the corresponding factors k. (The factors k are used below only to obtain the single time series of the MMF absolute value and are not used to analyze original measurements or to compare the data obtained by different instruments in different lines.) The linear-regression equations have the usual form y = a + bx, where x and y are the MMF values (in G) for two considered data sets. The regression factors (slopes) b will be compared neglecting small biases a, and the factors b will be treated as mean ratios of MMF absolute values measured using two different lines or at two different observatories using the same line. The weak Zeeman effect is observed by measuring the degree of circular polarization p ~ in the line. In this case, the nonlinear instrumental effects are a fortiori absent, so that a univocal correspondence should exist between p and B with accuracy up to the δ-effect, random errors, and the effect of line-profile asymmetry (Demidov et al., 25b). It would be specially noted that the MMF is determined by large-scale, i.e., background fields of the quiet Sun, while the contributions by sunspot and active-region fields are negligible (Severny, 1971; Kotov et al., 1977). In fact, the MMF is a polarity mismatch on the visible hemisphere of the Sun, i.e., diurnal excess of one polarity over the other. 3. THE 39-YEAR BEHAVIOR OF THE MMF ABOSLUTE VALUE The discussion requires knowledge of variation in B over the solar cycle. The cyclic variation in the MMF absolute value was reported for the first time by Kotov and Demidov (198) based of CrAO data obtained in The annual average value of B showed a threefold decrease from the solar maximum to the solar minimum. This result was confirmed using more extended MMF series obtained at four observatories in (Kotov and Setyaeva, 22). At present, the most complete series of MMF data covering almost four solar cycles is available. It is obtained at six observatories in four lines and compiled using the refined normalization of data series. The result of annual or semiannual averaging of B (the last is for ) is shown in Fig. 1a. This plot shows a distinct cyclical variation with a mean harmonic amplitude of.2 G. A comparison with the behavior of the Wolf number W (Fig. 1b) shows that the curve B on average lags behind the W curve by BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

4 82 KOTOV 2 CrAO 1 B, G WSO Fig. 2. Comparison of MMF values measured at Crimea (CrAO) and Stanford (WSO) from May 3 until September 2, 23, and shown by dots connected by line segments. The vertical bar is the typical error of CrAO data. The error of Stanford data is comparable to the dot size. The number of UT day of the year is given along the horizontal axis..7(7). Therefore, the maxima of B approximately coincide with the epochs of altering the polar poles. The power spectrum of the MMF absolute value yields a cycle period of 1.5(7) yr (hereinafter, the standard error for the last significant digits is given in parentheses). The 39-year average absolute value is.46(4) G for the adopted MMF normalization. This value during the solar maximum is less than for the solar minimum by about a factor of 3. The following two facts are also noteworthy: (a) the absolute maximum of annual average value of B was observed in 1991 and (b) B does not exhibit any noticeable trend in 39 years. This strengthens the conclusion by Kotov and Setyaeva (22) on the absence of secular variation in the average photospheric magnetic field, at least during the last four cycles. (Indirect data, such as measurements of the radial component of the interplanetary magnetic field at the Earth s orbit or the geomagnetic index, led to the conclusion on an increase in the coronal magnetic field by a proximately a factor of 2 during almost the entire 2th century (Lockwood et al., 1999). 4. COMPARISON OF CRIMEA AND STANFORD DATA As an example, Fig. 2 shows a part of MMF measurements carried out at Crimea and Stanford in 23. The 27-day periodicity caused by the two-sector structure is clearly seen. However, the Crimean values are on average higher than the WSO values by about a factor of 1.5. As for all observations performed in 23, the absolute values of the Crimean fields, according to Table 2, are larger than the Stanford ones by about a factor of 1.8, and the corresponding correlation coefficient r =.94. The data of the same observatories obtained from March 22 until November 23, 24, are shown in Fig. 3. Here, the values of B measured at CrAO are on average higher than B by about a factor of 1.8 according to the WSO data (Table 2). And it is clearly seen that since about August 1 (day 214) the two-sector structure has been replaced by the four-sector structure with a further overall decrease in the MMF absolute values. The entire set of CrAO WSO measurements carried out in correspond to the slope b =.45(1) which, however, varied strongly from year to year (Table 2). One could conclude that this spread is random and is caused mainly by the fairly large error of the Crimean measurements. However, similar annual variations in the slope take place if the measurements of other observatories, e.g., WSO and Mount Wilson (Table 3), are compared; see also Kotov et al. (1998a) and Kotov (23). 5. CRAO STANFORD BISON KITT PEAK CORRELATIONS The CrAO and Stanford magnetographs are oldfashioned, i.e., comprising high-resolution spectrographs and photomultipliers as photodetectors. The BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

5 A PARADOX IN MEASURING THE MAGNETIC FIELD OF THE SUN 83 Table 2. Equations for the Crimea (x) Stanford(y) linear regression (S x and S y are the corresponding standard deviations and n is the number of compared MMF pairs) Year n S x, G S y, G Equation r y = +.12(2) +.17(4) x y = +.6(2) +.9(3) x y = +.3(7) +.7(6) x y = +.1(4) +.37(8) x y =.5(3) +.24(9) x y =.3(3) +.17(12) x y = +.5(3) +.21(9) x y = +.7(4) +.37(8) x y = +.2(3) +.36(4) x y = +.11(3) +.4(4) x y = +.7(3) +.42(5) x y = +.11(2) +.55(3) x y =.1(2) +.56(2) x y = +.2(2) +.55(3) x y = +.8(3) +.4(7) x y = +.6(1) +.58(5) x y = +.7(1) +.45(1) x.78 main feature of the Stanford instrument is the use of an image slicer, which increases the optical flux tens times in comparison with the CrAO magnetograph. The BiSON measurements are obtained by atomic resonance spectroscopy using a magnetooptical filter without a spectrograph. The corresponding sensitivity is more than an order of magnitude better than at CrAO and, formally, better than at Stanford by a factor of 5 (Table 1). No less advanced instrumentation is used at Kitt Peak: (a) the line is extracted by a unique interference polarization filter, (b) an image of the Sun is recorded by large CCD matrix (the size is probably ), (c) the field is measured in each pixel of 1 arcsec in size, (d) and the MMF is B, G CrAO, 24 WSO, Fig. 3. Same as in Fig. 2, but for the period from March 22 until November 23, 24. BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

6 84 KOTOV Table 3. Equations for the Mount Wilson (x) Stanford(y) linear regression Year n S x, G S y, G Equation r y = +.6(2) +.8(2) x y = +.4(1) +.5(2) x y = +.8(1) +.23(4) x y =.1(2) +.33(4) x y = +.9(3) +.28(3) x y =.1(3) +.48(4) x y = +.6(3) +.54(4) x y = +.3(3) + 1.2(7) x.8 Table 4. Comparison of BiSON (x) WSO (y) and BiSON (x) CrAO (y) observations Year n S x, G S y, G Equation r BiSON WSO y =.7(3) +.38(4) x y =.8(2) +.53(3) x y =.4(1) +.58(3) x y =.3(1) +.54(4) x y =.1(1) +.35(4) x y = +.2(1) +.48(5) x y = +.1(3) +.73(5) x y = +.14(2) +.75(4) x.81 BiSON CrAO y =.31(8) +.77(17) x y = +.15(7) + 1.5(3) x y = +.13(6) +.48(21) x y = +.2(4) + 1.6(7) x y = +.9(4) + 1.1(9) x.85 found by averaging the signals of all pixels. (In addition, for the first time in the world, the mean absolute longitudinal magnetic field of the Sun as a star is determined every day at Kitt Peak. Namely, the mean absolute value of the longitudinal magnetic fields of the CCD pixels covering almost the entire solar disk is calculated. See Kotov (27) on the analysis of these absolutely new solar-physics data and the preliminary results. Operation of the Sayan magnetograph is generally the same as of the CrAO and WSO instruments, but photomultipliers in the former magnetograph were replaced by a CCD linear array in 1998 (Demidov et al., 25b.) Due to various technical reasons, in particular, different spectral resolution, the line sensitivity, and optical-flux level, typical errors of MMF values measured by the six instruments are strongly different and amount to ±.15 G for CrAO (525. line), ±.7 G for Mount Wilson, ±.5 G for Stanford and Sayan, and ±.1 G for BiSON and Kitt Peak. The BiSON measurements performed in can be compared with simultaneous Crimean and Stanford observations (comparison with the Sayan data for 1993 is discussed in Section 1). The results of correlation calculations are given in Table 4, which shows that the slope spread is always (at the corresponding cycle phases or, to be more correct, year by year) the same as in the case where measurements of other observatories are compared. Table 5 shows correlations found by comparing the annual or semiannual Kitt-Peak data sets with the corresponding data obtained at Stanford and CrAO. It is seen in both tables that the slopes for the compared data-set pairs differ up to more than 3σ. BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

7 A PARADOX IN MEASURING THE MAGNETIC FIELD OF THE SUN 85 Table 5. Comparison of Kitt Peak (x) Stanford (y) and Kitt Peak (x) CrAO (y) observations. A and B denote that first and second half-year Year n S x, G S y, G Equation r KPO WSO 23-B y = +.5(7) +.48(6) x A y = +.3(2) +.45(3) x B y = +.1(2) +.57(4) x A y = +.2(2) +.4(4) x B y = +.2(2) +.52(4) x A y =.2(2) +.44(6) x B y = +.1(1) +.4(3) x.83 KPO CrAO y =.2(4) +.61(6) x y =.12(4) +.91(9) x y =.1(2) +.74(8) x THE SUN ITSELF DETERMINES THE DEGREE OF MMF DISCREPANCY Variation in b with the 11-year behavior of the solar activity, demonstrated by Figs. 4 and 5, is especially interesting. The results are obtained for two pairs of MMF data series: MWO WSO in and CrAO WSO in The annual average values of B according to Fig. 1 are used as the solaractivity index, while the slopes b are taken from Tables 2 and 3. It is seen that b tends to increase toward the solar-activity maximum, i.e., with increasing absolute value of the MMF, and to a decrease toward the solar-activity minimum. Note, however, that in 26, at the end of cycle 23, the Crimea Stanford slope b did not show the expected decrease, but instead increased significantly. We attribute this increase to variations in the large-scale structure of the field, i.e., to the fact that the true magnetic cycle is not 1.5, but 21 years (it should be emphasized that the cycle duration in the last 1 years was 1.5 years instead of the usual 11.1 years). The same conclusion can be drawn also from a comparison of the behavior of B with other slope pairs for all six observatories, including the slopes obtained by comparing BiSON data with CrAO and WSO data. The general rule is as follows: the slope b increases in the solar-maximum years and decreases during the solar minimum (for the selected system of x and y axes and the regression y x), but noticeable deviations stipulated by the 21-year cycle can occur. This rule is seen fairly well for the CrAO Stanford data in Fig. 5. Note that the main conclusion of the paper, i.e., systematic variations in b over the solar cycle (or, more exactly, season by season or year by year), does not depend on the adopted type of regression, y x or x y. (The empirical regression coefficients b x y or b y x have the same signs as r and are related by the formula b x y b y x = r 2.) The correlation coefficient r varies in a similar way, but this trivial fact is easily explained by variations in the annual average values of B and, correspondingly, the standard deviations S for the compared series over the solar cycle. It is important to note that measurements for the same 525. line carried out at different magnetographs differ as strongly as the measurements for different lines at the same instrument (Kotov et al., 1998a; Kotov, 23). Figures 6 and 7 show the correlation dependences of the MMF according to the CrAO and Stanford data obtained in 1999 and 23. The numbers of compared data pairs are n = 13 and 132 and the correlation B 1..5 MWO WSO b Fig. 4. Variations in the slope b over the solar-cycle phase for Mount Wilson and Stanford observations according to Table 3 ( ; circles, dashed curve, and the right axis). The time in years is reckoned along the horizontal axis. The triangles and the solid line segments show the behavior of annual values of B (in G, the left-hand axis), while the vertical bars are the mean errors of B and b. BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

8 86 KOTOV B CrAO WSO b Year 2 25 Fig. 5. Same as in Fig. 4, but for CrAO and Stanford observations in B (WSO) , n = 13 r =.7, b =.36 1 coefficients r =.7 and.94 for 1999 and 23, respectively. The slopes for these two years differ by about a factor of 1.5: B(WSO) = +.2(3) +.36(4) B(CrAO), (1) B(WSO) =.1(2) +.56(2) B(CrAO). (2) The significance of these differences exceeds 4σ. Thus, the following paradox is encountered: the Sun affects the magnetograph calibration of the degree of difference of two instruments. Meanwhile, this is impossible from the viewpoint of common sense. The usual laboratory practice and the theory of experiment teach that, concerning our experiment with the Sun, the ratio δ and the slope b should be constant up to errors and independent of the solar magnetic state. Indeed, in this case, the small polarization of light from the same magnetic standard is measured almost simultaneously in the absence of nonlinear instrumental effects by two instruments with almost identical principles of operation. 7. CALIBTATION AND SATURATION Calibration of a magnetograph includes determination of the ratio between the magnetic field and the degree of circular polarization in the line wings. The calibration procedure is simple and, in principle, is the same n any observatory where a spectrograph is used (a similar differential technique was also used in the BiSON and Kitt Peak methods; certain features of B (WSO) 2 23, n = 132 r =.94, b = B (CrAO) Fig. 6. Comparison of the mean magnetic field B (in G) measured at Crimea and Stanford in the same UT days of The dashed line is the linear regression. The slope is equal to b =.36 (the number of pairs n = 13) B (CrAO) Fig. 7. Same as in Fig. 6, but for the measurements of 23 (n = 132 and b =.56). BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

9 A PARADOX IN MEASURING THE MAGNETIC FIELD OF THE SUN 87 SOLIS-VSM KPO measurements are discussed below). Namely, light with 1% circular polarization is obtained using a polarizer, the line at the spectrograph focal plane is shifted by some method of the photometer center by the Doppler shift λ C, which is less then the line halfwidth λ W, and the calibration signal C is recorded. Then the Zeeman-splitting formula λ B = gλ 2 B (3) is used to find the factor K relating C and B (the wavelength λ and the splitting λ B are in cm). With allowance for all imaginable sources of error, including uncertainties of λ W and λ C, errors of signal compensation for brightness and radial velocity, the asymmetry and fluctuations of the line profile and its instrumental broadening, variations due to atmospheric transparency and guiding, possible residual nonlinearities of the electromechanical devices, noise in electronics, and random errors one can with extreme confidence state that the resulting relative error K cannot exceed 15%. This is confirmed by five standard deviations S given in Table 1 (CrAO, MWO, SSO, and KPO): these values deviate by no more that 13% from the overall average S ' =.69 G. (The Stanford and BiSON data are exceptions. The fact that the values of S for these two observatories are about 4% lower than S ' for other observatories remains a mystery.) Temporal variations in b can be caused by timedependent technical differences of the instruments and the dependence of the average values of B and/or the δ-effect on the solar-cycle phase. Within the framework of the fine-rope model, the latter can be related to the varying relative contribution of strong and weak fields to the total MMF signal (Demidov et al., 22, 25b), as well as to the evolution of the large-scale magnetic field distribution during a cycle. Accordingly, this can result in strengthening or weakening of the saturation during a cycle, whereas the saturation effect itself (Howard and Stenflo, 1972) is caused by strong fields resulting in such a line splitting, then the extremums of the Stokes parameter V in the line wings reach the output slits of the magnetograph or even go beyond. This should give rise to a decrease in the longitudinal-field signal. In the case of the WSO magnetograph, the lineprofile segment in which the polarization is measured corresponds to distances of.9 and 8.4 pm, and the measured segments of the line profile are centered at distances of d = 4.7 pm at both sides of the line center. In the case of Crimea, these parameters are pm and d = 6.3 pm, respectively. According to the model of concentrated magnetic flux ropes, it can naturally be believed that a maximum of B should be accompanied by an increase in the number of ropes, as well as probably in the average absolute values of their magnetic fields and their distribution in the photosphere. Such a model predicts that the slope b in Fig. 5 should decrease with increasing B due to the higher sensitivity of the WSO magnetograph to saturation: d is much lower than at Crimea. However, the opposite picture is observed: the slope increases with increasing B and decreases with decreasing B, i.e., toward the solar-activity minimum (except for the minimum of 26 discussed above). No less unclear is why b strongly varies over a solar cycle according to MWO WSO measurements (Fig. 4). Indeed, the output slits of both magnetographs are located close to each other: d = 4.7 pm. Next, the Sayn magnetograph with d = 3.5 pm should be most sensitive to the δ-effect among four instruments (CrAO, MWO, WSO, and SSO), which measure the MMF using the 525. line. However, this instrument has a maximal value of S =.77 G among the seven individual cases presented in Table 1. These facts contradict the model dominated by the concept of saturation and superfine magnetic structure. Differences in b or, essentially, in the MMF scales determined by different magnetographs are similar to discrepancies in the locally measured field by virtue of different lines, i.e., to the δ-effect. In that case, however, the following explanation was conventionally accepted: the effect of saturation due to fine-structure flux ropes with strong fields, the effect of temperature sensitivity of the line, and the effect of divergence of the magnetic field lines. Unfortunately, this generalized hypothesis encounters difficulties as well (Kotov, 23). For example, Demidov et al. (25b) pointed out that the profile of the Stokes parameter V is strongly asymmetric over the line profile, and this asymmetry becomes more pronounced with decreasing B. This is attributed to an increase in noise, but the actual reason is unclear since, according to the model of fine ropes, the asymmetry should become more pronounced with increasing B. Moreover, the Kitt Peak measurements obtained without using output slits in the line wings should be free of saturation. The BiSON method is also almost free of saturation (Chaplin et al., 23). It is surprising, however, that the BiSON standard deviation S =.43 G is almost the same as the Stanford one (.41 G). In our opinion, the problem is more serious and fundamental than simple discrepancies in the magnetic fields measured by different instruments using different lines. 8. A NEW ENIGMA: TWO CHANNELS OF THE SAME MAGNETOGRAPH Since 1973, CrAO measurements have differed from observations at other observatories. Both light BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

10 88 KOTOV Table 6. Comparison of MMF measurements by two channels at CrAO (x and y are channels I and II, respectively) Year n S x, G S y, G Equation r y = +.13(13) (12) x y =.35(8) +.41(11) x y =.11(12) + 1.7(5) x y =.2(9) +.95(28) x y =.1(6) (11) x y =.(6) (1) x y = +.23(6) +.9(14) x y =.5(5) (11) x y =.3(6) (9) x y =.9(5) + 1.3(12) x y =.12(7) (22) x y =.18(2) + 1.4(9) x.81 beams created as the light enters the spectrograph after passing through the splitting Rochon prism (the ordinary and extraordinary beams with orthogonal polarizations (Kotov et al., 1982)) are used in the upgraded BST-1 telescope. Hence, two magnetographs called channel I and II actually operate at the BST-1 beginning with These magnetographs are almost independent, but they have a common system of feeding the telescope and the guiding system until the input of light into the spectrograph, the input slit of the spectrograph, the calibrating polarizer, and the electrooptical KDP crystal, together with a common modulating voltage and generator. However, these channels all have different optical elements inside the spectrograph, including the gratings, optical filters, and photodetectors (photomultipliers) and electronics together with separate amplifiers, synchronous-phase detectors and rectifiers, brightness and radial-velocity compensators, calibrating mechanisms, potentiometers, and integration and storage devices. The output slits have been installed identically, d = 6.3 pm, so that the effect of saturation should be the same for both channels. In , the MMF was almost always measured simultaneously by both channels of the BST-1. However, the averaged results of both channels have been published for the world catalog. In rare cases where the result of one channel is absent, the result of the operable channel has been published. The double measurements using the 525. line were carried out most regularly in The results of comparing the two channels are summarized in Table 6. It is seen that for a linear-regression validity >.95 (r >.5), the slope b varies by a factor of about 3 4, in a similar way as for MMF measurements according to different magnetographs in different years. There is no correlation (the MMF is undistinguishable against noise) during the solar minimum in All these features are illustrated in Fig. 8 (of course, zero values of b in have only nominal meaning, reflecting just the complete absence of correlation). Note also that the most pronounced deviations of b from the behavior of B in are obviously stipulated by the small number of observation in those years (Table 6). 9. DISTRIBUTIONS OF THE MMF It is interesting to know the MMF distribution for both channels. According to the simple logic of statistics, the distribution of B should tend to Gaussian if the number of trials or measurements is sufficiently large. Kotov (23) found that two magnetographs, the Crimean (based on the published data, i.e., for two-channel average values) and Sayan, the distributions m(b) are almost Gaussian. On the contrary, the MWO and WSO data have anomalous distributions close to an exponential distribution with the probability density p(b) ~ m(b) ~ e B /τ, (4) where τ is the coherence or damping parameter. The origin of the anomaly in the MWO WSO data is unclear. We believe that it is related to the quantum properties of light and the influence of the instrument itself, i.e., the act of measuring, on the state of photons and the results. The main source of the anomaly, or quantum nonlinearity, can be the image slicers used BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

11 A PARADOX IN MEASURING THE MAGNETIC FIELD OF THE SUN 89 B CrAO, b Year Fig. 8. Same as in Fig. 5, but for channel I and II observations at CrAO in m 1 5 CrAO-I, N = 1169 S =.5 G (a) 75 5 CrAO-II, N = 1143 S =.7 G (b) B Fig. 9. Distribution of the MMF according to the CrAO measurements: (a) channel I ( , N = 1169), (b) channel II ( , N = 1143; one value, B = 3.28 G, is outside the figure area). The solid lines are the fitting Gaussian curves with standard deviations S =.5 and.7 G, respectively. in the MWO and WSO spectrographs (details are discussed below; see also Kotov, 23). Figure 9 shows the distributions of all CrAO data obtained in using two channels separately. These distributions have been plausibly fitted to Gaussian curves with rms deviations of.5 and.7 G for channels I and II, respectively. (This is close to the standard deviations of.52 and.91 G of two data series (Table 7). Both distributions have almost zero means: +.1(15) and.27(27) G for channels I and II, respectively. The 4% difference between the parameters S and S for the two channels considered should be attributed to different sensitivities and calibration uncertainties.) BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

12 9 KOTOV Table 7. Resulting correlation between different magnetographs (x y format) Magnetographs Time interval, years n S x, G S y, G Equation r KPO WSO y = +.1(1) +.47(1) x.88 KPO CrAO y =.6(2) +.67(4) x.84 BiSON CrAO y = +.1(3) + 1.2(6) x.82 SSO MWO y =.3(5) +.47(4) x.81 CrAO WSO y = +.7(1) +.45(1) x.78 SSO WSO y =.5(2) +.51(3) x.77 CrAO: I II y =.4(2) + 1.3(4) x.74 BiSON WSO y =.(1) +.51(1) x.71 SSO BiSON y =.3(7) +.91(28) x.66 MWO WSO y = +.2(1) +.35(2) x.58 CrAO MWO y = +.3(3) +.27(4) x.26 Figure 1 shows the distributions of all CrAO data obtained in (N = 2537; the averaged values of B measured in the two channels were used) and Stanford data obtained in (N = 937). The Crimean distribution fits well with a Gaussian curve with the parameter S =.61 G close to a value of S =.67 G for the Crimean data series. However, the Stanford data distribution is strongly non-gaussian and fits well with an exponent with the parameter τ =.3 G. It is such a difference of these distributions that allowed us to put forward the hypothesis that the quantum nature of light (nonlocality or indistinguishability) influences measurements of the Zeeman polarization of the Sun and stars (Belinskii, 1997; Santori et al., 22; Kotov, 23). The means of the Crimean and Stanford distributions are.35(14) G and +.3(5) G, respectively. The BiSON distribution is shown in Fig. 11. It has a mean value of +.27(1) G and is qualitatively similar to the Stanford distribution, i.e., exponential. The quantum properties of light can be the reason for this anomaly as well. Namely, the interaction of solar photons with laboratory photons (emission from potassium vapor) is inevitable in resonance spectroscopy, which changes the polarization of light due to photon coalescence. It is interesting to note that S and τ are almost the same for both the Stanford and BiSON distributions. m 15 1 (a) CrAO, N = 2537 S =.61 G (b) WSO, N = 937 τ =.3 G B Fig. 1. Distribution of the MMF according to all observations performed at (a) CrAO in (N = 2537) and (b) at Stanford in (N = 937). One value, B = G, is outside the plot area. The solid curves are the fits (see text). BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

13 A PARADOX IN MEASURING THE MAGNETIC FIELD OF THE SUN 91 m 3 BiSON, N = 1988 τ =.3 G m 6 SOLIS-VSM, N = 677, S =.45 G Fig. 11. Same as in Fig. 1b, but for the BiSON data: , N = 1988, and τ =.3 G. The SOLIS-VSM (Kitt Peak) distribution is shown in Fig. 12. It is more or less close to the Gaussian distribution with a mean of.1 (.23) G and the parameter S =.45 G (the latter is less than the standard deviation of.6 G of the data series). However, the amount of data available at present is sufficient to definitively conclude that the distribution is Gaussian. In fact, although the number of measurements (677) is about twice as large than, e.g., the number of Sayan measurements (313), these measurements correspond only to the decaying part of the 23th cycle, while CCD measurements were carried out for different phases of the cycle. Deviations for Gaussianity and the asymmetry of Fig. 12 can be attributed to the limited time of observations perhaps in connection with the limited measurement interval (a little over three years). In addition, according to the SOLIS-VSM Internet site, these data are being corrected at present and the zero calibration is being refined. In our opinion, the fact that the SOLIS-VSM distribution is close to Gaussian is ensured by the absence of the interaction of light beams explicitly present in Mount Wilson, Stanford, and BiSON observations. 1. RESULTING CORRELATION Table 7 shows b and r calculated without selection by year for all published data obtained in 1968 to 26 at six observatories, including a comparison of the two CrAO channels. (The CrAO data in this table were obtained using the 525. line. The standard deviations S x and S y for different observatories are determined for simultaneous pairs of the compared data series. In the case of comparison of the SSO and Californian data series, the former was shifted by one day back 1 2 B B Fig. 12. Same as in Fig. 1a, but for SOLIS-VSM: 23 26, N = 677, and S =.45 G. relative to the MWO and WSO observatories, since the SSO observations were usually made at the beginning of a UT day, while the MWO WSO observations, at the end of a UT day. The compared observatory pairs are listed in the table according to decreasing r.) The correlation coefficient of the two CrAO channels is.74 (n = 1153). It is close to the correlation coefficients of the Crimea Stanford (r =.78 and n = 1222) and Sayan Stanford (r =.77 and n = 256) measurements, but much higher than for the Mount Wilson Stanford measurements (r =.58, n = 1442). The Kitt Peak correlations with both Crimea and Stanford are almost the same. At the same time, the CrAO BiSON correlation is somewhat better than the Stanford Sayan correlation. This is surprising since the typical Crimean error is larger than for Stanford and SSO by a factor of 3 (Table 1). The only possible explanation is that the discrepancies are determined not so much by formal errors as the measurement features, the very act of measurement, which is inherently deeply related to the quantum, statistical nature of light. It was noted above that the degree of correlation depends on the mean value of B, i.e., on the solaractivity phase. Therefore, the high Kitt Peak Stanford and Kitt Peak Crimea correlations in (Table 7) should be attributed to the increased value of B in those years, especially in Note, in particular, that the best correlation for all compared data-set pairs, including all annual data sets for 39 years, was also observed near the solar-activity maxima with a high annual average value of B (Fig. 1a): namely, r =.94 for Crimea Stanford observations in 1991 and 23 and for BiSON Crimea observations in 2 (Tables 2 and 4). BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

14 92 KOTOV The weak Crimea Mount Wilson correlation in should be attributed to the strong noise of Crimean observations in those years. The majority of the observations were performed using the MBST (now BST-2) telescope with and old magnetograph, i.e., before the upgrade of the BST-1 and magnetograph in The decrease in correlation was probably also contributed two by a decrease in the average value of B during the solar minimum of and an increase in the error of the MWO instrumental zero point determined by a signal corresponding to the switched-off modulating voltage of the crystal. (More rigorous methods of the zero-point control are used at CrAO, WSO, and SSO. See Scherrer et al., 1977a; Kotov et al., 1998b; Demidov et al., 25b.) With allowance for the above-mentioned reasons, we excluded from Table 7 all old Crimean measurements obtained in using mainly the old magnetograph. Then the average correlation coefficients of this observatory with other observatories are.86 for Kitt Peak,.83 for Crimea,.75 for Sayan and Stanford,.73 for BiSON, and.72 for Mount Wilson. (Of course, this comparison is limited since, for a while, we have forgotten about the strong difference in n and about the fact that the measurements were performed during different phases of the cycle.) And another paradox appears: the quality of the worst CrAO measurements that have the biggest formal error turns out to be about the same as the quality of the best, advanced Kitt Peak measurements and somewhat better than the quality of other observatories (!?). 11. IS THE QUANTUM NATURE OF LIGHT INVOLVED? Annual data sets (Tables 2 6) show that b has significant year-to-year variations, so the problem of interpreting the photospheric Zeeman effect becomes even more serious. For example, one can attribute the MMF discrepancies and the temporal variations in b to variations in the solar magnetic standard itself, which lead to fluctuation of the annual-average values of B, b, and r: (a) active regions and the background (large-scale) fields are partially displaced toward the equator during a solar cycle; (b) background field structures during the minimum become smaller and more mixed in polarity in comparison with the solar-maximum years; (c) the average magnetic field at the polar caps becomes higher during a solar minimum; (d) the absolute values of the MMF and the quiescent-photosphere field increase during the solar-maximum years (Fig. 1; see also Kotov and Demidov, 198; Kotov and Setyaeva, 22); (e) the density distribution of magnetic flux ropes in the quiescent photosphere, or the filling factor, changes, as well as the typical rope field (Demidov et al., 25a, 25b). However, these facts cannot explain the behavior of b since the phenomenon of ropes, or δ-effect, should have the same effects on both of the compared instruments, especially if they have the same d, and therefore cannot lead to significant temporal variations in the slope, which is clearly seen in, e.g., Figs The correlation between b and B in Figs. 4, 5, and 8, as well as the absence of correlation of b with the locations of the magnetograph output slits with respect to the line center, i.e., with the sensitivity of the instrument of saturation, also contradicts the above-mentioned items. All of the observational data, more extended than previously (Kotov, 23), implies that the measurement itself, namely, the instrument light system, is the reason. The quantum nature of light and the effect of the act of measurement on photons are probably involved. The nature of disorder in the measurements of the magnetic field of the Sun (in this case, the MMF) can be related to the phenomenon of coupling (coalescence entanglement identity nonlocality) of photons and the influence of the receiving system itself on the formation of the light field (Belinskii, 1997; Bouwmeester et al., 1997; Santori et al., 22). In particular, analysis of the formation of the spectral line in the magnetized solar photosphere and the subsequent act of observation ignores the quantum nature of light, except for, of course, the Zeeman splitting of the atomic levels and the polarization of photons. However, a certain quantum effect, in particular, the phenomena of coupling (complexity, mutual dependence, or entanglement) and indistinguishability, and the coalescence of photons, should not in fact be neglected. We do not touch the complex issue on the quantum coupling of photons in processes of emission and transfer of radiation in the solar atmosphere, especially in the presence of a magnetic field, as well as the known problem of Stark depolarization of radiation, whose role in uncertain. However, the coupling (coalescence or identity) of photons should inevitably occur during measurement with a magnetograph since the diffraction grating or filter, electrooptical modulator, and polarizer are used. In this case, light (its partially polarized photons) is partially absorbed or transformed in the modulator polarizer. The remaining photons pass the grating and/or filter and are detected by the photodetector. According to Bohr, the result of detection is strongly dependent on the characteristics of the instrument and on the act of measurement itself. BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol

15 A PARADOX IN MEASURING THE MAGNETIC FIELD OF THE SUN 93 In the case considered, the quantum states of photons, i.e., their polarization and, correspondingly, the magnetograph signal, are to a significant extent determined by the entire light beam in the spectrograph. Distortion of a magnetograph signal is an unavoidable consequence and an important feature of the quantum-mechanical approach. It is impossible to draw conclusions on an electromagnetic field measurement without allowance for the effect of the instrument interacting with the optical field (photons). The quantum nature of light itself poses limits the accuracy and objectiveness of measurements and at the same time becomes the main source of intrinsic star light instrument noise and statistical distortions of a signal (see Belinskii (1997) on theoretical issues of the problem). This recalls the discussion between Bohr and Einstein in the 193s on the implication of quantum realism : does a certain quantum state of a particle (the direction of photon polarization or the coordinate and momentum of an electron) exist before the act of measurement? Einstein insisted that a nonmeasured, but definite state should exist before the measurement, although we cannot know what it is. On the contrary, Bohr believed that the nonmeasured parameters exist only potentially with probabilities determined by the equations of quantum mechanics, and it is measurement that makes the wavefunction collapse to a certain measured value. The progress in theory (the Bell theorem or inequalities) and experiments on verification of quantum realism at the end of the 2th century confirmed that Bohr was right: The instrument inevitably affects the result of measurement or, according to Glanz (1995), Quantum experiments showed that the main reality is the measurement itself. The polarization of twin photons, which have close frequencies and quantum states, is changed by the act of measurement due to the coupling and coalescence. The influence coalescence factor depends on the specific design of the instrument, detection method, and polarization of light, i.e., in the case considered, on the actual value and distribution of the field on the visible hemisphere of the Sun. 12. MEASURING THE SUN Consider, for example, measurement of the MMF in a parallel light beam from the Sun as a star. In the case of the BST-1 telescope at CrAO, three plane mirrors illuminating the input slit of the spectrograph with light from the entire solar disk are used for this purpose. It is conventionally believed that the wavefront and its polarization inside the spectrograph are formed by all individual photons entering the spectrograph at a given time. Upon passing through the modulator, the light beam ray packet train front is incident on a collimator mirror, then it is directed to a grating, etc. Finally, according to the laws of linear optics and interference, a Zeeman-split line profile with nonzero polarization of light in the line wings is formed in the focal plane of the camera, i.e., at the photometer. The polarization gives rise to fluctuations of the radiation flux with the modulator frequency. This is what wave geometric optics and classical quantum physics teach. (In the case of Kitt Peak, the light in the telescope passed through a filter, and the image is obtained on a CCD matrix. The longitudinal field SOLIS-VSM is determined in each pixel of an angular size of about 1 arcsec, and then the results are averaged over the entire solar disk. The BiSON measurements by atomic resonance spectroscopy also have certain features.) Meanwhile, progress in techniques and high-frequency laser fiber computer technologies and photodetectors achieved in the last decade have made it possible to carry out experiments with light at frequencies comparable to femtosecond light pulses, i.e., with individual photons (1 fs = 1 15 s; recall that the period of the first Bohr orbit is.15 fs, while the 525. line corresponds to a period of 1.75 fs). It turned out that individual photons behave in an evasive way and pronouncedly exhibit such quantum properties as coupling, coalescence, nonlocality, and identity. As Bohm (1967) wrote, An observer participates actively in the act of observation, and this participation inevitably perturbs the observed system: the measurement itself, i.e., the instrument, perturbs the optical field. (By the way, this yields the Heisenberg uncertainty principle: each measurement bears a certain minimum amount of uncertainty.) In our case, it is erroneous to believe that individual photons, each having a certain polarization state, propagate from the solar photosphere to a spectrograph and are then, independently of each other, incident on some part of the grating, interfere, and form the total line profile upon the summation of distinct photo -events. To be more correct, this is only one side of the dualism of a photon field. In fact, the quantum, polarization, properties of single photons are determined cooperatively by the entire light beam, whose size depends on the diffraction parameters of the spectrograph. This is especially important for observations of the Sun as a star when a diffuse image of the solar disk is formed inside the spectrograph on the grating. In our case, the coherence size D of the beam amounts to about.3d (here, D is the size of diffuse disk image on the grating) for an input slit of width.4 cm. The polarization of photons from such a beam is determined by summing (probably in a nonadditive way) the photon parameters in a significant part of the disk (D is the size of this part). Moreover, each point of the line profile is BULLETIN OF THE CRIMEAN ASTROPHYSICAL OBSERVATORY Vol