A paradox in measuring the magnetic field of the Sun

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 1968–2006 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 10.5(7) yr.     

Oscillations of the Sun: Results of observations in 1974–2007

Doppler measurements of the photosphere of the entire Sun carried out at the Crimean Astrophysical Observatory (CrAO) in 1974–2007 by the differential technique showed the presence of an enigmatic periodicity of P ₁ = 159.967(4) min. The phase of this oscillation was constant over the entire 34-year of surveys and interval. The true nature of this phenomenon is unknown. Pulsation with the former period P ₀ = 160.0101(15) min has been reliably detected only in the first nine years, from 1974 to 1982. It is noted that (a) the average amplitude of the P ₁ oscillation in the first half of the data was nearly 34% higher than in the second half and (b) the beat period of 400(14) d of these two pulsations is equal within error to the Jovian synodic period (399 d). A hypothesis is discussed relating the P ₁ oscillation to the superfast rotation of the inner solar core.     

A method for the determination of the lithium abundance in sunspots: Observations for 2011

Sunspot spectra for LiI 6708Å lines and for several FeI and CaI lines were obtained. Observations were performed in January and in August, 2011 using the TST-2 telescope with a charge-coupled camera at the Crimean Astrophysical Observatory. The sunspot models were calculated by using the observing profiles of FeI and CaI lines. Lithium abundance was determined by using the calculated sunspot models and LiI 6708Å observed profiles; this equals log(N _Li) = 0.98 and 0.95 (in the scale logA(H) = 12.0).     

The lithium content in sunspots: Observations of 2007

The spectra of sunspots were observed in the region of the LiI 6708 Å lines and several FeI and CaI lines. The observations were carried out with a CCD camera in May, June, and July 2007 using the BST-2 telescope of the Crimean Astrophysical Observatory. The spot models were calculated using the observed profiles of FeI and CaI lines. The lithium content was estimated at log(NLi) = 1.20, 1.15, and 1.00 (at the scale of logA(H) = 12.0) using the calculated spot models and observed LiI 6708 Å line profiles.     

Lithium abundance in the sunspot from the observational data of August 1981

A spectrum of a sunspot in the range of the Li I ?? 670.8 nm line and some lines of Ca I, Ti I, Al I, and Na I was measured. Observations were carried out with the TST-2 telescope of the Crimean astrophysical observatory on August 21, 1981. A model of the spot was calculated from the observed profiles of the Ca I, Ti I, Al I, and Na I lines. From the calculated model and the observed profile of the Li I ?? 670.8 nm line, the lithium abundance was estimated as log(N _Li) = 0.78 (in the scale of logA(H)= 12.0).     

Rotation of the Solar Equator

Regular measurements of the general magnetic field of the Sun, performed over about half a century at the Crimean Astrophysical Observatory, the J. Wilcox Solar Observatory, and five other observatories, are considered in detail for the time 1968?–?2016. They include more than twenty-six thousand daily values of the mean line-of-sight field strength of the visible solar hemisphere. On the basis of these values, the equatorial rotation period of the Sun is found to be 26.926(9) d (synodic). It is shown that its half-value coincides within error limits with both the main period of the magnetic four-sector structure, 13.4577(25) d, and the best-commensurate period of the slow motions of the major solar system bodies, 13.479(22) d (sidereal). The probability that the two periods coincide by chance is estimated to be about \(10^{-7}\). The true origin of this odd resonance is unknown.     

Determination of lithium abundance in sunspots: Observations in 1973

Spectra of sunspots in the region of the lithium 6708 ? line, as well as certain CaI, AlI, FeI, YI, ScI, VI lines, were studied. The observations were performed on July 8, 1973 using a BST-2 telescope at the Crimean Astrophysical Observatory. A sunspot model was developed based on the observed profiles of CaI, AlI, FeI, YI, ScI, and VI lines. Using the developed model and observed profile of the Li 6708 ? line, the abundance of lithium was determined. The obtained result is log(N_Li) = 0.95.     

Studies of magnetic fields in the solar photosphere using the line-ratio method

The longitudinal magnetic field measured using the Fe I λ 525 and Fe I λ 524.7 nm lines and global magnetic field of the sun differ depending on the observatory. To study the cause of these discrepancies, we calculate the H _‖(525)/H _‖(524.7) ratios for various combinations of magnetic elements and compare them with the corresponding observed values. We use the standard quiet model of the solar photosphere suggesting that there are magnetic fields of different polarities in the range between zero and several kilogauss. The magnetic element distribution is found as a function of magnetic field strength and the parameters of this distribution are determined for which the calculated H _‖(525)/H _‖(524.7) ratio agrees with the observed one. The sigma-components are found to be shifted differently for various points of the Fe I λ 525 nm profile calculated for the inhomogeneous magnetic field. The farther the point is from the line center, the larger the sigma-components shift. Such a peculiarity of the profiles may be responsible for the discrepancies in the measured values of the global magnetic field obtained at different observatories. The increase in modulus of the global magnetic field during the maxima of solar activity can be due to a larger fraction of magnetic elements with kilogauss magnetic fields.     

Forty years of measurements of the mean magnetic field of the Sun: View from today

During the last 40 years, the Crimean Astrophysical Observatory and five other observatories around the world have carried out more than 18 500 (daily) measurements of the mean magnetic field (MMF) of the Sun as a star. The main MMF periodicity is due to the equatorial rotation of the Sun with a synodic period of 26.92 ± 0.02 day (it was stable for decades, but “bifurcated” in the 23rd cycle). It is shown that (a) the average sidereal period of the equator, 25.122 ± 0.010 day, is in close resonant relations with orbital and axial rotations of Mercury (5: 2 and 5: 3, respectively); (b) the most powerful long period, 1.036 ± 0.007 years, is suspiciously close to the orbital period of the Earth and (c) coincides with the average synodic period of revolution of giant planets 1.036 ± 0.020 years; and (d) MMF reveals a significant period of 1.58 ± 0.02 years, which agrees, within errors, with the synodic period of Venus (1.60 years), and (e) a significant periodicity of 19.8 ± 2.5 years probably related to the 22-year magnetic cycle of the Sun. The nature of all these periodicities is mysterious.The assumption is made that the resonances originated at the early stages of formation of the Solar System, and their existence in the modern epoch is due to the specific features of the structure and dynamics of the central core of our star. It is found that the MMF level averaged over 40 years is practically zero, ?0.018 ± 0.015 G. The anomalous behavior of the 23rd cycle is pointed out; this is expressed in (1) violation of the Gnevyshev-Ohl rule for the pair of cycles 22–23, (2) accelerated rotation of the solar equator by 1.2%, and (3) considerable increase in the cycle duration (not smaller than 11.5 years), as compared to the average cycle duration in the 20th century (11.5 years). The problem of the so called magnetic “monopole” of the Sun is briefly discussed.     

Pulsations of the sun and a beat period of 399 days

Measurements of the Doppler effect of the solar photosphere have been carried out at the Crimean Astrophysical Observatory for 37 years, beginning in 1974 (in total, 2188 days or 13 247 h). The measurements use the differential center-to-limb method of registration of line-of-sight velocity with a solar magnetograph (in the iron absorption line λ512.4 nm). As a result of the experiment, two global pulsations of the sun with periods P ₀ = 9600.606(12) and P ₁ = 9597.936(16) s have been discovered. The nature of the periods is unknown. The first pulsation was detected in 1974–1982; the second, during nearly all the 37 years. The 2008–2010 data confirm the stability of the initial phase of the P ₁ pulsation with a mean (differential) amplitude of 0.25 m/s. The fact that the beat period of the two pulsations coincides with the synodic period of Jupiter’s orbital revolution, i.e., 399 days, raises a new, complex problem for solar physics and cosmogony.     

On Multi-Line Spectro-Polarimetric Diagnostics of the Quiet Sun’s Magnetic Fields

On the long way to establish reliable physical properties of the solar atmosphere from different kinds of magnetic field measurement, significant progress has been achieved, but many important issues are still waiting for solution. This is essential for the investigation of weak magnetic fields of the quiet Sun, which usually cover most of the solar surface. Weak magnetic fields significantly contribute to the formation of the interplanetary magnetic field. The problem of reliable diagnostics of such fields hardly ever has a simple solution using only single spectral line observations. A better chance is given by multi-spectral line spectro-polarimetric observations, especially with lines having very different properties. In the present study, we use simultaneous high-precision Stokes-meter measurements of the quiet solar magnetic fields in 15 lines in the vicinity of Fe?i?525.0?nm. These measurements cover the whole range of heliocentric distances. Magnetic field strength ratios of different spectral lines with respect to Fe?i 525.0?nm vary between 1.07 and 2.12. This ratio depends also on the heliocentric position, moving closer to the limb it decreases and approaches values of about unity in most cases. To interpret the observations, different model approaches are compared. SIR-inversions (Stokes Inversion based on Response functions) with a two-component atmospheric model approach reproduce the basic observables much better than with one-component atmospheres. Our best fits are connected with field strengths of 1?–?2?kG and filling factors of less than five percent. To check the justification for the recent re-calibration of the data from the Michelson Doppler Imager (MDI) onboard SOHO, we carried out a numerical experiment, and we confirm our former conclusion that there is no need for such a re-calibration.     

Starspots and active regions on IN Com: UBVRI photometry and linear polarization

The activity of the variable star IN Com is considered using the latest multicolor UBVRI photometry and linear polarimetric observations carried out during a decade. The photometric variability of the star is fully described using the zonal spottedness model developed at the Crimean Astrophysical Observatory (CrAO). Spotted regions cover up to 22% of the total stellar surface, with the difference in temperatures between the quiet photosphere and the spot umbra being 600 K. The spots are located at middle and low latitudes (40°–55°). The intrinsic broad-band linear polarization of IN Com and its rotational modulation in the U band due to local magnetic fields at the most spotted (active) stellar longitudes were detected for the first time.     

Investigation of the Differential Rotation by H�� Filaments and Long-Lived Magnetic Features for Solar Activity Cycles 20 and 21

For solar activity Cycles 20 and 21 (1966??C?1985) the solar differential rotation has been investigated using H?? filaments and relatively small-scale long-lived magnetic features with negative and positive polarities. We used annual averaged angular velocities of quiescent H?? filaments from H?? photoheliograms of the Abastumani Astrophysical Observatory film collection and selected long-lived magnetic features from the McIntosh atlas (McIntosh, Willock, and Thompson, Atlas of Stackplots, NGDC, 1991). We have determined coefficients of Faye??s formulas for H?? filaments as well as for long-lived magnetic features and have found that for Solar Cycles 20 and 21 the H?? filaments have lower rotation rates and rotated more differentially than the long-lived magnetic features.     

Rapid variability of the line He I λ 587.6 nm in the spectrum of the Herbig Ae/Be star WW Vul

We investigate the behavior of the relatively strong absorption line He I λ 587.6 nm in the spectrum of the rapid irregular variable star WW Vul (Sp A3) with the Algol-like brightness fadings. As many as 76 spectra of this star were acquired with the 2.6-m ZTSh telescope of the Crimean Astrophysical Observatory with the use of the medium-dispersion spectrograph SPEM. We show that the equivalent width of the He I line exhibits not only daily variations but also rapid oscillations with a typical period of several tens of minutes. Quasi-simultaneous observations of several standard stars with known energy distributions allowed us to calculate the monochromatic magnitudes of the variable at λ = 550 nm. There was no correlation between the equivalent widths of the line He I λ 587.6 nm and the monochromatic brightness of the star. At times we could identify the short-wave emission component of the He I line. We used the H_β profiles to confirm the spectral type A2–A3 of WW Vul.     

Connection between the magnetic field strengths and the helium abundance in helium-rich stars

Special Astrophysical Observatory, USSR Academy of Sciences; Crimean Astrophysical Observatory, USSR Academy of Sciences. Translated from Astrofizika, Vol. 33, No. 3, pp. 363–370, November–December, 1990.     

Photometric and magnetic variability of the Ap star GY And

We present the results of photometric and magnetic monitoring of a well-known long-period Ap star GY And. This research was inspired by the unusual “secular” variability of the B ? V color index. Photometric monitoring was carried out with the 60-cm reflector of the Crimean Laboratory of the Moscow State University, where 420 brightness estimates were obtained during 2011–2014 with the Johnson system broadband U, B, and V filters. Magnetic monitoring was carried out at the 1-m telescope of the Special Astrophysical Observatory. The duration of photometric observations is about 54 years, and the duration of magnetic monitoring is 64 years. As a result, we have refined the period and the parameters of variability of the magnetic field, and the photometric behavior. We demonstrate that the peculiar “secular” color variability is explained by the off-duty factor of the observations.     

Equipment and observational technique used to obtain dynamic spectra of the solar radio radiation at the KRIM station

The equipment and observational technique used to obtain dynamic spectra of the solar radio radiation at the KRIM station (Crimean Astrophysical Observatory) that is a part of the e-CAL-LISTO worldwide network are described. The parameters of an antenna fabricated in the Radioastronomy Laboratory of the Crimean Astrophysical Observatory and a method for excluding the instrumental distortions that was developed at the KRIM station are outlined.     

Magnetic field of solar prominences: The procedure of radio observations

The first successful radio astronomical results of measurements of the magnetic field of solar prominences are presented. The accuracy of polarization and magnetic field observations is 3 · · 10⁻⁴ and 2 G, respectively. The observations were made by the 22-meter radio telescope of the Crimean Astrophysical Observatory at wavelengths of 8 and 13.5 mm. It has been found that the value of the magnetic fields coincides with the optical one (from 7 to 30 G), but the image of radio polarization differs from the intensity.     

High-resolution spectrographs on medium-diameter telescopes

The problem of high-resolution spectroscopic observations on telescopes with diameters of D = 0.5–1.5 m is considered. Examples of the optimum technical solutions and survivability of certain telescopes and methods of observation are given in retrospect. Improvements in the technique of spectroscopy allow one to also consider the potential of those instruments that were not originally intended for use in high-resolution spectroscopy. Arguments in favor of using medium-diameter telescopes in modern high-resolution spectroscopy are discussed. This review is connected to the 100th anniversary of the 122-cm telescope of the Crimean Astrophysical Observatory.