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Magnetic Stars, 2011, pp. 104 ­ 125

Magnetic Field Measurements of CP Stars from Hydrogen Line Cores
Kudryavtsev D. O., Romanyuk I. I.
Special Astrophysical Observatory, Nizhny Arkhyz, Russia

Abstract. We present the results of measurements of magnetic fields of chemically peculiar (CP) stars, performed from the shifts between the circularly polarized components of metal and hydrogen lines (the Babcock method). The observations are carried out with an analyzer of circular polarization at the 6­m telescope of the SAO RAS. We found that for the absolute ma jority of the ob jects studied (in 22 CP stars out of 23), the magnetic fields, determined from the Zeeman shifts in the hydrogen line cores, are significantly lower than those obtained from metal lines in the same spectra. This disparity varies between the stars. We show that instrumental effects can not produce the above features, and discuss the possible causes of the observed effect. The condition discovered reveals a more complicated structure of magnetic fields of CP stars than a simple dipole, in particular, a reduction of the field strength in the upper atmosphere with the vertical gradient, significantly higher than the dipole. Key words: spheres stars: magnetic fields ­ stars: chemically peculiar ­ stars: atmo-

1

Intro duction

Our recent measurements have shown that the magnetic fields, determined using the classical method (Babcock, 1947) from the shifts between the circularly polarized Zeeman components, appear to be smaller when the measurements are done based on the cores of hydrogen lines than those performed the same way, but from the lines of metals. We published our first results in (Kudryavtsev & Romanyuk, 2009). They show that the differences between the magnetic field values reach 1­2 kG, which is significantly higher than the possible measurement error. Hydrogen line cores are formed in higher atmospheric layers than the hydrogen line wings and metal lines. Therefore, the effect of a decrease of magnetic field, measured from the hydrogen line cores (as compared with that measured from metals) that we discovered may indicate the existence of a large radial gradient, i.e. a height­wise magnetic field decrease for most of the magnetic CP stars we observed. The observations were performed at the Main Stellar Spectrograph of 6­m BTA telescope of the Special Astrophysical Observatory of Russian Academy of Sciences (SAO RAS) with the Zeeman analyzer in the spectral region width of about 250 ° centered on the H line, and sometimes on the A H line. In all cases we determined the longitudinal component of magnetic field Be . In each of the Zeeman spectra we measured a sufficiently large (from 50 to 100, depending on the temperature and the star's rotation velocity) number of lines belonging to neutral and ionized metals. Line
This paper is based on data obtained at the Russian 6­m telescope


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centre positions were determined by fitting the line profile with a Gaussian, both in the case of hydrogen line cores and in the case of metal lines. We do not anticipate any instrumental errors systematically distorting the measurements based on the cores of hydrogen lines. Only in case of very strong magnetic fields, which can show partial splitting of Zeeman components of metal lines, the field obtained from the hydrogen lines, possessing the most simple splitting picture, may turn out to be smaller than the field observed based on the metal lines due to methodological reasons. We shall hereby examine this question in detail. As the result obtained once more raises the question about the magnetic field topology in CP stars, let us have a detailed look at the results of our measurements and compare them with the data published by other authors.

2

Measurements of Longitudinal Magnetic Field From Hydrogen and Metal Lines
Search for the Vertical (Radial) Magnetic Field Gradient
Factors Complicating the Task

2.1
2.1.1

Before we consider the search for a vertical field gradient, let us denote the factors that can complicate the task: in the first place, this is the topology of magnetic fields and inhomogeneous distribution of elements over the surface. The observed periodic synchronous magnetic, spectral and photometric variability of CP stars is adequately represented by an oblique rotator model in the form of a rotating star with chemical and thermal inhomogeneities on the surface and a dipole magnetic field. The dipole axis does not coincide with the rotational axis. The oblique rotator model has been successfully applied in several studies carried out in the late 60's and early 70's of the twentieth century by Preston (for example, Preston, 1971) to explain the variability of magnetic CP stars. A nonuniform distribution of chemical elements on the surfaces of CP stars was confirmed in dozens of works, and subsequently the methods of inhomogeneous surface mapping were developed (e. g. Khokhlova, 1976). Investigations on the structure of deviations of the magnetic field structure from the dipole structure have a long history as well. The models became more complex -- from simple (a noncentral displaced dipole (Landstreet, 1970) to the complex combinations of multipoles of different orders (e. g. Landstreet, 1988). Later, there were developed magnetic field mapping methods allowing to describe the magnetic fields of any complexity (e. g. Piskunov, 1992, 2000). Kochukhov et al. (2001), Piskunov & Kochukhov (2002) and other authors describe reconstruction programmes of the magnetic field vector on the surface of a star without any preliminary assumptions about its structure, with or without account of the inhomogeneities of chemical composition. Mapping of several stars performed using this method showed that the magnetic field topology of CP stars can be very complex (Kochukhov, 2004). If vertical inhomogeneities of the field and chemical composition in the atmosphere do exist, then it is extremely difficult to find them in a thin (less than 1% of the stellar diameter) atmosphere, as the horizontal inhomogeneities are appeared much stronger in the spectra and would mask the vertical effect. Currently the one and only way is prosed to study the vertical structure of the field and the distribution of chemical composition -- a thorough study of line profiles, formed at different optical depths in the atmospheres of CP stars.


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2.1.2

Field Measurements from Metal Lines at Different Formation Depths

A search for a vertical field gradient in magnetic stars was first proposed by Babcock (1949) and Preston (1965) via measuring the Zeeman shifts of the lines formed at different depths in the atmosphere. Yet they did not implement this idea. The first measurements of magnetic fields from the lines in the spectral regions up to (high layers) and after (deep layers of the atmosphere) the Balmer jump were performed for three stars by Wolff (1978). For the star 2 CVn, she found a smaller value of the longitudinal field and the amplitude of its variability in the region shorter than the jump, what indicated a 25% decrease of the field in the 2 CVn upper atmosphere. Romanyuk (1980) has as well independently found a decrease of the field Be with height in the atmospheres of CP stars 2 CVn and 53 Cam from high intensity lines, formed in higher atmospheric layers than the weak lines, showing a larger field. Later Romanyuk (1986, 1993) made a detailed examination of the 2 CVn spectrum based on the lines of different elements in the spectral regions before and after the Balmer jump and confirmed the decreasing of its longitudinal magnetic field with height. Especially large differences in the Be value were found from the lines of rare earth elements. Note that the above results were obtained by measuring the Zeeman shifts between the circularly polarized components of metal lines from the spectra obtained with photographic plates at the 6­m BTA telescope. First digital detectors worked in the red spectral region. It was only at the end of the twentieth century when the registration with CCD chips in the near­ultraviolet spectral region became possible at the 6­m telescope. We performed Zeeman observations of several magnetic CP stars in the range of 3400 ­ 4200 ° with the NES echelle spectrograph with high spectral resolution. Using the A Babcock method we measured the longitudinal component of the magnetic field Be . We confirmed our previous result for 2 CVn: its longitudinal magnetic field decreases with height by about 25% (or 400 ­ 500 G) in the observed layer of the atmosphere (Romanyuk et al., 2007). Therefore, we estimated that 2 CVn magnetic field decreases with height with a gradient of a few tenths of G/km. For other stars we did not obtain sufficient data, however, we should note one trend -- the longitudinal field Be decreases with height. Nesvacil et al. (2004) proposed another method. They did not measure the longitudinal component Be , but the mean modulus of the magnetic field Bs from the split Zeeman components of spectral lines formed at different depths in the atmosphere in the spectral regions before and after the Balmer jump. The measurements were performed based on high­resolution unpolarized spectra obtained at the ESO's UVES VLT spectrograph. For all the three investigated magnetic stars, HD 965, HD 116114 and HD 137949 the authors obtained an increase of the Bs value with height. Therefore, conflicting results were obtained, although different stars were investigated. Sufficiently hot stars with strong fields at the BTA, and cold and slow rotators with narrow split lines on the VLT. In addition, we measured the longitudinal component of the field Be , yet at the VLT the surface field Bs measurements were done. Note here that the main factor affecting the measurement accuracy of the longitudinal component of the field at the 6­m telescope is a strong transmission decrease of the circular polarization analyzer in the spectral region shorter than the Balmer jump. Consequently, the S/N ratio of the obtained spectra in the < 3646 ° region appeared to be significantly smaller than that in the long­wave A region. When measuring the mean modulus of the field, the ma jor distorting factor -- an increase of spectral line blending with decreasing wavelength. Since the Lande factors of the lines in general differ quite weakly, an increase of blending does not greatly affect the accuracy of the longitudinal field component measurements. In both cases the differences in field strength reached noticeable quantities, more than 300 ­ 500 G, which is larger than the typical measurement errors. We have no reason to doubt the reality of different field values at different depths in the atmospheres of CP stars. In case of a simple dipole


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field, the strength of the field itself decreases proportionally to the cube of the distance from the dipole centre, i. e. from the centre of the star. Therefore, at a distance of the atmospheric thickness (a few tenths of percent of the diameter) it may decrease by no more than 0.01 from its value (or 30 ­ 50 G for typical magnetic CP stars). Hence we may conclude that the evidence of the existence of a radial gradient, exceeding the dipole gradient, is obtained. This indicates, in turn, that a field structure much more complicated than a simple dipole is quite widespread. Recent works discovered the stratification of elements in the atmosphere. Hence, this fact should be taken into account in the analysis of characteristics of the field distribution with height. This issue will be considered further in the discussion of results of our study. The effect of inhomogeneous horizontal distribution of elements on the results of investigations of the vertical field structure and the stratification of elements is anyhow difficult to assess. The solution can be found, in our opinion, measuring the magnetic fields from hydrogen lines. There is no reason to believe that there is any significant variation in the distribution of hydrogen abundance over the surface. Therefore, investigating the distribution of polarization (or Zeeman shifts) of the hydrogen line core and wings, we may hope to detect the features of the vertical structure of magnetic fields. The cores of hydrogen lines are formed in higher layers of the atmosphere than the usual metal lines. A comparison of measurements obtained from them can as well yield data on the vertical structure of magnetic fields of CP stars.

2.2

Results from the Landstreet Balmer Line Magnetometer

Hydrogen lines are very broad, hence the classical method (Babcock, 1947) could not be used in the photographic studies of stellar magnetism. Measurements of magnetic fields from hydrogen lines were for the first time performed by John Landstreet on the photoelectric Balmer magnetometer he designed (Angel & Landstreet, 1970). This device measured the V ­Stokes parameter in the wings of hydrogen lines, mainly H . The 5 ° A­wide spectral region at the distance of 5 ° from the A hydrogen line core was cut with an interference filter, while the shifts in the spectrum, associated with the differences in radial velocities of different ob jects, were offset by the tilt of the filter. The longitudinal magnetic field Be was obtained from the measurements of circular polarization caused by the Zeeman effect in the wings of hydrogen lines. The formation regions of hydrogen line wings and metal lines must approximately coincide. The calibrations performed showed that in general there is a good agreement with the measurements obtained earlier from metal lines using the photographic method. Nevertheless, the field obtained photoelectrically is not necessarily an identical match with the one obtained photographically due to significant differences in the techniques of observations and reduction, and due to the fact that, unlike metals, hydrogen is distributed uniformly throughout stellar surfaces. Landstreet and his team studied a number of known magnetic CP stars with an anharmonic photographic curve of the longitudinal field Be component variability. In most of cases, hydrogen curves of the longitudinal field appeared to be much closer to the sine, yet several stars still showed anharmonicity of Be curves. The results were interpreted as follows: hydrogen is distributed uniformly over the surface of the star, and the harmonious sine curve indicates a dipole field. Stars with an anharmonic hydrogen curve possess magnetic fields different from the dipole. Anharmonicity of the "metal" curve is linked both with an inhomogeneous distribution of elements over the surface and with nondipole topology of the field. The studies of vertical topology via analyzing the distribution of circular polarization in hydrogen lines were not carried out. However, note (as we demonstrate further in Section 4) that although the curves of magnetic fields obtained from hydrogen line wings and metal lines may differ, magnetic field strengths obtained using these two methods do not show systematic differences.


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2.3

Measurements with LSD Techniques

By the end of the twentieth century the observations on hydrogen magnetometers were over, the latter being replaced with the CCDs. Classic Zeeman measurements were at first performed on them only from metal lines. Practice has shown that we can significantly improve the accuracy of magnetic field measurements summing the signals of the V ­Stokes parameter from many lines. Although a transition from polarization values to magnetic fields may cause calibration problems and the results may not coincide with those measured using the classical method, the multi­line technique turns out to be very effective for the detection of stellar magnetic fields. It was called LSD, or the Least Squares Deconvolution technique. This method has been implemented by Donati et al. (1999) on the MUSICOS spectrograph. A large series of observations of the earlier known magnetic stars was carried out on this instrument (Wade et al., 2000), which showed a good agreement with the data obtained by other means.

2.4

Measurements with FORS1

The measurements of circular polarization in hydrogen lines continued on the new magnetometer FORS1 VLT (Bagnulo et al., 2002). Circularly polarized spectra with low (R = 2000) resolution in the spectral range 3500 ­ 5800 ° are observed with this device. The instrument simultaneously A registers all the available hydrogen lines from H to the Balmer limit (3646 ° and metal lines. A), The device has a very high efficiency, it can provide high accuracy of observations (typical errors -- tens of gauss). However, it has its drawbacks, there are problems with calibration and referencing of the obtained values of magnetic fields to the data from previous studies.

3

Comparison of Magnetic Field Measurements Obtained with Different Techniques

Measurement of stellar magnetic fields is a rather complex methodological task. To detect such fine and weak effects, as the radial magnetic field gradient, a detailed study and elimination of various instrumental causes that may affect the accuracy of the results are required. Analysis of all observations shows that a vast amount of data on the magnetic fields of CP stars was obtained from the measurements of the longitudinal component Be . From all the proposed and implemented options and methods determining this value, the most successful are the following: 1) measurement of shifts between the circularly polarized components of lines from the spectra, obtained with photographic plates (the so­called photographic method, proposed by Babcock in 1947); 2) measurement of circular polarization in hydrogen line wings (the photoelectric method, Angel & Landstreet, 1970); 3) measurement of shifts between the circularly polarized line components from the spectra obtained with CCD chips (the modified Babcock photographic method, see, e. g. Mathys, 1991; Mathys & Hubrig, 1997; Kudryavtsev et al., 2006); 4) multi­line LSD techniques that appeared relatively recently (Donati et al., 1999; Bagnulo et al., 2002). In case of the dipole stellar field and a uniformly distributed over the surface chemical composition, the measurement results obtained from lines of different elements and with the use of different methods would be roughly the same. But it is well known that CP stars have chemical compositions inhomogeneously distributed over the surface: the elements are often concentrated in spots or rings around magnetic poles. In view of the foresaid it is of interest to compare the longitudinal field data for the same stars obtained using different methods.


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In (Romanyuk et al., in preparation) we compare the measurement results for 28 magnetic stars, for which the rotation periods are known, and for which the curves of the longitudinal field Be components were identified both from the hydrogen line wings and from metal lines. We have rather reliably found the extrema of Be curves, and analyzed the degree of mutual conformity of every curve for each star. The analysis is as follows. The longitudinal field Be is stronger from hydrogen for 7 stars, stronger from metals for 7 stars as well, equal (within the measurement error) for 12 stars, and for 2 ob jects we lack sufficient measurement data to make a comparison. Analyzing these data we can come to two conclusions. 1) for approximately half of all the studied stars there are significant and crucial differences in the longitudinal field strength obtained from metal and hydrogen lines, at that the distribution is equal, 7 stars show a stronger field from metals, and 7 from hydrogen lines. Typically, these are stars with strong fields. For the second half (as a rule, these are stars with weaker fields) within the measurement errors the Be curves do not differ in amplitude. Certainly, relative accuracy of measurements of such stars is lower and the individual differences are less visible. 2) Although the amplitudes and shapes of "metal" and "hydrogen" Be curves for individual stars may vary, in general, there are no systematic differences: the fields defined from the lines of metals may be higher, lower or equal to the fields measured from hydrogen lines. No observational evidence was found that the strength of the longitudinal magnetic field, obtained using the photoelectric method based on the measurements of circular polarization in the wings of hydrogen H line (or other lines) is systematically higher or lower than the field strength obtained from the measurements of shifts between the centres of left and right circularly polarized metal lines. The features are observed only in the degree of differences between the Be curves and sines. As early as in 1977, Borra & Landstreet (1977) noted that systematically the "hydrogen" curves are more harmonious than metal curves, what is associated with homogeneous distribution of hydrogen over the surface. The conclusions about the absence of systematic differences have an important practical significance: they indicate reliability and good mutual agreement of calibrations made by different authors determining the longitudinal field Be component using different methods and at various telescopes. This also means that different instrumental effects are correctly taken into account, or else systematic deviations would appear, irrespective of the ob ject observed. On the other hand, we can see that for approximately half of the stars from Romanyuk et al., in preparation) there are significant differences (both upward and downward) in the field value obtained from metal and hydrogen lines. Apparently, this is a consequence of peculiarities of inhomogeneous distribution of metals over the surface. Individual characteristics of the field topology for each of the stars play a certain role as well, but it is a more complex issue and modelling is needed in order to solve it. Therefore, a question arises as of how to explain a significant and systematically smaller field value obtained from the hydrogen line cores in comparison with that found from metal lines from the same spectra, previously deduced (Kudryavtsev & Romanyuk, 2009). Based on the analysis above we can argue that such a systematic difference is neither related to instrumental factors, nor to the peculiarities of the distribution of chemical composition over the surfaces of magnetic stars. It remains to assume that the differences we found are linked with the topology of magnetic fields of CP stars, most likely -- with the peculiarities of their vertical structure. Hence we are back again with the problem of searching the radial gradient of magnetic fields. Theoretically, the right thing to do is to choose the following method: to measure the magnetic fields from different parts of hydrogen line profiles. The hydrogen line cores are formed in the stellar atmosphere certainly higher than their wings. As the hydrogen is distributed uniformly over the surface of CP stars, the effect of horizontal inhomogeneities of chemical composition will not be


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present, and the influence of the field topology will be minimized. By measuring the field in different regions of the hydrogen line profile formed at different optical depths, we could do a vertical section of the field by height in the atmosphere. However in practice this task is very hard to implement. The polarization signal (the V ­Stokes parameter) of the Zeeman effect sharply decreases with distance from the hydrogen line core, the situation is complicated by blends of different metal lines. To date, the greatest number of V ­Stokes parameter measurements in the wings of hydrogen lines was obtained on the photoelectric Landstreet's Balmer magnetometer (Angel & Landstreet, 1970). The observations with this instrument were most often performed in the wing of the H line in a 5 ° wide filter centered at the distance of 5 ° from the core of this line. Circular polarization A A was measured in the most optimal site of the hydrogen line profile. As a rule, for a typical H hydrogen line it could be adopted that the value of V ­Stokes parameter equal to 1% corresponds to the magnetic field Be of 13 kG. The investigations thus made do not concern the topmost layers of the observed atmosphere. Based on the fact that there are no significant systematic differences in the field strength, deduced from the lines of metals (using both the classical and LSD­method) and found from the observations of circular polarization on hydrogen magnetometers, we attempt to estimate the existence of the radial field gradient higher than the dipole gradient based on a comparison of measurements of the field from the metal lines and hydrogen line cores using the classical "photographic" method proposed by Babcock (1958a,b). In the following sections we will set out the methodology of observations and data reduction, as well as the results of our observations.

4

Observations and Data Reduction

Our observations have been obtained with the Main Stellar Spectrograph (Panchuk, 1998) of the 6m telescope equipped with an image slicer and a circular polarization analyzer (Chountonov, 2004) and a 2000â2000 pixel CCD with the spectral resolution R = 15000. For our observations we used the spectral range 4760 ­ 5000 ° which includes 50 ­ 100 metal lines (mostly Fe and Cr for our stars) and A, the H line. Several spectra were obtained in the region of other hydrogen lines (H, H ). The data reduction was performed within the MIDAS context LONG and using our own codes (Kudryavtsev, 2000) developed for the reduction of the Zeeman spectra and measurement of longitudinal magnetic fields. The technique of our measurements has been already described (see, e. g. Kudryavtsev et al., 2006). Longitudinal magnetic field values were measured from the Zeeman shift between the line positions in the right­hand and left­hand circularly polarized spectra, using standard Babcock's formulae. For the metal lines we used the mean Lande factor z = 1.23. With multiple measured lines this is a good approach and will not lead to additional errors. The positions of spectral lines were determined via fitting the profiles with a Gaussian. The same procedure was applied to measure the positions of the H line core. The central part of the line, well­described by the Gaussian profile is adopted as a line core. A typical procedure of the hydrogen line core centre determination is demonstrated in Fig. 1. The errors for metal lines are based on the scatter of individual values and derived using standard statistics expressions. The errors of the H line measurements are derived from the procedure of Gaussian fitting as the biggest error of the line centre finding in pairs of Zeeman spectra. Note that the measurements from hydrogen and metal lines are done from one and the same spectrum, which minimizes all the possible systematic errors. In Fig. 2 we show a spectral region of the star 53 Cam in right­hand and left­hand circular polarizations, and the Stokes V parameter for this region. One can see that the Stokes V values in metal lines are greater than that in H . Particularly this effect is caused by the fact that metal lines have generally higher Lande factors (z =


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Figure 1: Hydrogen line core centre determination by fitting the line profile with a Gaussian

53 Cam
Stokes V

Metal lines: Be = +3620 +- 110 H core: Be = +1570 +- 550

Right circular polarization Left circular polarization 4860 4865 Wavelength, A 4870 4875

4850

4855

Figure 2: Spectra of the right­hand and left­hand circular polarizations and V ­Stokes parameter for the star 53 Cam in the H region


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Table 1: Longitudinal magnetic field Be extrema for 53 Cam method H (V ­Stokes) metals (photo) metals (photo) metals (photo) metals (CCD) metals (LSD) Be (extrema) -4900/ + 3900 -4500/ + 3700 -5800/ + 3400 -3200/ + 4200 -5400/ + 4300 -4600/ + 3300 [n] [18] [12] [8] [16] [30] [10] Citations Hill et al. (1998) Babcock (1958a) Preston & Stepien (1968) Glagolevskij et al. (1978) our CCD (this paper) Wade et al. (2000)

1.23 on average), and therefore are more sensitive to the magnetic field, while H has z = 1.0. A more significant effect -- lower steepness of the hydrogen line profile. But in the Zeeman measurements we correct for the difference in the Lande factors, and the magnetic field is determined from the line centre positions, hence the steepness of the profile may have an impact only on the accuracy of measurements. Nevertheless the measured longitudinal magnetic field Be shows quite different values for metal lines and for the core of H line.

5
5.1

Results of Magnetic Field Gradient Measurements Obtained at 6­m Telescop e
53 Cam Longitudinal Magnetic Field From Metals and Hydrogen

In this section we present the results of magnetic field measurements from the hydrogen line cores and metal lines for 23 magnetic CP stars. We performed more than 30 observations in different phases of rotation period for one of these stars, 53 Cam. Since this ob ject is often used as a magnetic standard and was thoroughly studied using different techniques, let us give it special consideration. As a first step, we analyze the previously obtained results of measurements of 53 Cam longitudinal magnetic field. Its Be curves were obtained repeatedly using different techniques. Compare the extrema of these curves in Table 1. The columns represent: the observational technique, extreme values of the longitudinal magnetic field component Be , number of observations [n] and references. Wade et al. (2000) compared Babcock's "metal" curve (Babcock, 1958a), the hydrogen curve by Hill et al. (1998) and the "metal" LSD Be curve they obtained. It is noted that Babcock's photographic metal curve is strongly anharmonic, the hydrogen curve obtained on Landstreet's Balmer magnetometer is almost sinusoidal, and the shape of the curve obtained using the LSD method from metal lines occupies an intermediate position between them: it is anharmonic, but to a smaller extent than Babcock's curve. Our observations performed at the BTA (both photographically and CCD­based), show that our curve for 53 Cam is anharmonic and agrees well with Babcock's curve (Babcock, 1958a). For greater clarity Fig. 3 shows different curves of the longitudinal field for 53 Cam: open circles -- the curve of Hill et al. (1998), triangles -- Preston & Stepien (1968), stars -- the LSD curve of Wade et al. (2000), filled circles -- our curve from metal lines. Thus, we can conclude that all methods of observation of the longitudinal component yield approximately the same value of 53 Cam longitudinal field. Some differences are observed only in the form of the Be curves. More surprising is the fact of significant differences in the field strength, obtained from the cores of hydrogen lines not only in comparison with metals, but with the hydrogen curve of Hill et al. (1998). Consider this question in detail. Our measurements of the magnetic field from metal


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53 Cam
6000 4000 2000
Be, G

0 -2000 -