Photospheric Magnetic Field: Relationship Between North–South Asymmetry and Flux Imbalance

Photospheric magnetic fields were studied using the Kitt Peak synoptic maps for 1976?–?2003. Only strong magnetic fields (B>100 G) of the equatorial region were taken into account. The north–south asymmetry of the magnetic fluxes was considered as well as the imbalance between positive and negative fluxes. The north–south asymmetry displays a regular alternation of the dominant hemisphere during the solar cycle: the northern hemisphere dominated in the ascending phase, the southern one in the descending phase during Solar Cycles 21?–?23. The sign of the imbalance did not change during the 11 years from one polar-field reversal to the next and always coincided with the sign of the Sun’s polar magnetic field in the northern hemisphere. The dominant sign of leading sunspots in one of the hemispheres determines the sign of the magnetic-flux imbalance. The sign of the north–south asymmetry of the magnetic fluxes and the sign of the imbalance of the positive and the negative fluxes are related to the quarter of the 22-year magnetic cycle where the magnetic configuration of the Sun remains constant (from the minimum where the sunspot sign changes according to Hale’s law to the magnetic-field reversal and from the reversal to the minimum). The sign of the north–south asymmetry for the time interval considered was determined by the phase of the 11-year cycle (before or after the reversal); the sign of the imbalance of the positive and the negative fluxes depends on both the phase of the 11-year cycle and on the parity of the solar cycle. The results obtained demonstrate the connection of the magnetic fields in active regions with the Sun’s polar magnetic field in the northern hemisphere.     

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.     

Particle and field environment of Uranus

In 1985 the spin axis of Uranus points within 10° of the Sun and the planet's position is very near the solar apex direction. A Uranus mission with an encounter near 1985 might expect to measure the unusual particle and field configuration of a “pole-on” magnetosphere and also properties of the interstellar medium. We give here estimates of the particle and field environment of Uranus based on extrapolation of solar wind data from 1 AU and on scaling relations for an Earth-type magnetosphere. Since the magnetic moment of Uranus is unknown, all magnetospheric parameters are derived as a function of the dipole strength. The onset of special magnetospheric properties are identified as the dipole moment increases from small to large values. A fairly complete set of magnetospheric parameters is given for a specific dipole moment to illustrate the case of a large moment.     

Persistent 22-year cycle in sunspot activity: Evidence for a relic solar magnetic field

We use the recently presented group sunspot number series to show that a persistent 22-year cyclicity exists in sunspot activity throughout the entire period of about 400 years of direct sunspot observations. The amplitude of this cyclicity is about 10% of the present sunspot activity level. A 22-year cyclicity in sunspot activity is naturally produced by the 22-year magnetic polarity cycle in the presence of a relic dipole magnetic field. Accordingly, a persistent 22-year cyclicity in sunspot activity gives an evidence for the existence of such a relic magnetic field in the Sun. The stable phase and the roughly constant amplitude of this cyclicity during times of very different sunspot activity level strongly support this interpretation.     

Enigmas in measurements of solar magnetic field

The mean magnetic field (MMF) of the photosphere of the Sun as a star was measured in 2001?C2010 at the Crimean Astrophysical Observatory using two Fe I absorption lines with ?? = 524.7 nm and ?? = 525.0 nm. The regression coefficient b for 1054 pairs of daily values measured simultaneously on both lines equals 0.82 (a correlation coefficient is 0.94; magnetic field strengths determined by the line with ?? = 525.0 nm are lower than those for the line with ?? = 524.7 nm). However, the b value varied significantly along with phases of the 11-year cycle from 0.88 in 2003 to 0.49 in 2009. It is difficult to ascribe these variations to purely instrumental or solar causes. Moreover, the semiannual value of b decreased with the decrease in the absolute strength of the MMF, which contradicts the model of thin magnetic flux ropes of the photosphere. Similar behavior of b was also observed in the comparison of MMF measured at the Crimean Astrophysical Observatory and Stanford by the line with ?? = 525.0 nm. The inconsistency of the results obtained by these two iron lines on different instruments has been noted. It has been concluded that the variance in and odd behavior of b are predetermined not only by the instrument and the Sun (by the so-called fine structure of the photosphere field), but also by the act of measuring. When recording solar (and stellar) magnetic fields and modeling atmospheric processes, quantum effects have to be taken into account, such as nonlocality, indistinguishability, and the entanglement of photons, as well as that a photon only acquires its properties at the exact moment of its detection. The best approximation to reality can be achieved by averaging the MMF measurements carried out with different magnetographs and in different spectral lines.     

Regularities in the growth of background magnetic fields

The cyclicity in the latitudinal distribution of the growth and decay rates of the total magnetic fluxes for weak magnetic fields is investigated. The synoptic maps of the line-of-sight solar magnetic field strength obtained at the Kitt Peak Observatory (USA) from January 1, 1977, to September 30, 2003, are used as the observational material. The latitudinal distributions of the growth rates of total magnetic fluxes with various strengths constructed from them and their evolution during three solar cycles have been compared with the analogous distribution of the total powers of rotation with various periods as well as the relative sunspot numbers and areas. The results obtained allow a unified picture of the development of solar cycles for weak and strong magnetic fields to be formulated. A new cycle begins with the growth of weak magnetic fields with a strength of 0–200 G at latitudes 20°–25° in both hemispheres. This occurs one year before the activity minimum determined from sunspots. Two years later, the growth rate of the total magnetic flux, which begins to propagate equatorward and poleward, reaches a maximum. This process coincides with the onset of the growth of strong sunspot magnetic fields at the corresponding latitudes and the formation of zones with a stable rotation. Subsequently, a fall-off in growth rate and then a flux decay for weak magnetic fields correspond to the growth of the sunspot areas. In light of the dynamo theory, the results obtained suggest that strong and weak magnetic fields are generated near the bottom of the convection zone, while the observed differences in their behavior are determined by the interaction of emerging magnetic flux tubes of various strengths with turbulent plasma motions inside the Sun.     

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.     

New results of magnetic field measurements for BP Tau

We present measurements of the longitudinal magnetic field component B _‖ of the young star BP Tau in the He I 5876 emission line formation region, i.e., in the accretion flow near the stellar surface. The values obtained (?1.7 kG and ?1.0 kG in 2000 and 2001, respectively) agree with the results of similar measurements by other authors. At the same time, we show that the previously obtained field strength at the magnetic pole, B _p, and the inclination of the magnetic axis to the rotation axis, β, are untrustworthy. In our opinion, based on the B _‖ measurements available to date, it is not possible to conclude whether the star’s magnetic field is a dipole one or has a more complex configuration and to solve the question of whether this field is stationary. However, we argue that at least in the He I 5876 line formation region, the star’s magnetic field is not stationary and can be restructured in a time of the order of several hours. Nonstationary small-scale magnetic fields of active regions on the stellar surface and/or magnetospheric field line reconnection due to the twisting of these field lines as the star rotates could be responsible for the short-term magnetic field variability. It seems highly likely that there are no strictly periodic variations in brightness and emission line profiles in BP Tau due to the irregular restructuring of the star’s magnetic field.     

Reversals of the Sun’s Polar Magnetic Fields in Relation to Activity Complexes and Coronal Holes

A spatiotemporal analysis of long-term measurements of the Sun’s magnetic field was carried out to study changes in its zonal structure and reversals of the polar fields in Cycles 21?–?24. A causal relationship between activity complexes, their remnant magnetic fields, and high-latitude magnetic fields has been demonstrated in the current cycle. The appearance of unipolar magnetic regions near the poles is largely determined by the decay of long-lived activity complexes. The nonuniform distribution of sunspot activity and its north–south asymmetry result in the asymmetry of remnant fields that are transported poleward due to meridional circulation. The asymmetry of high-latitude magnetic fields leads to an asynchrony of polar-field reversals in both hemispheres. The interaction of high-latitude unipolar magnetic regions with the polar fields affects the embedded coronal holes. The evolution of large-scale magnetic fields was also studied in a time–latitude aspect. It is shown that regular reversals of the Sun’s polar fields resulted from cyclic changes in high-latitude magnetic fields. A triple polarity reversal of the polar fields in Cycle 21 and short-term polarity alternations at the poles were interpreted taking into account the interaction of the remnant fields with the Sun’s polar fields.     

Kink mode <Emphasis Type="Italic">m</Emphasis> = 1 in a thin plasma filament with discontinuous vertical magnetic field

In this paper, we study the conditions of realization and stability of kink modes with azimuthal wave numbers m = ±1 in a cylindrical plasma filament with a twisted magnetic field and a homogeneous current along its axis. We assume that there are vertical constant magnetic fields inside and outside of the filament; the filament is surrounded by current-free plasma; and outside of its boundary, the azimuthal magnetic field decreases inversely in proportion to the distance from the filament’s border. The dispersion equations for stable and unstable modes are obtained in the approximation of “thin” plasma filament. The analysis of the equations for the case of discontinuous vertical magnetic field at the filament’s boundary is provided. The conditions of propagation of the wave modes have been defined. We have obtained that the unstable modes with m = ±1 cannot be realized. The results of this work can be applied to the interpretation of the solar magnetic flux tubes’ behavior using measurements provided by the spacecrafts.     

Magnetic field measurement of the star HD 35298

Based on the spectropolarimetric data obtained at the 6-m telescope, a study of the magnetic field and physical parameters of the magnetic He-weak star HD 35298 was performed. A comparison of the results of magnetic field measurements by various methods has been carried out. The star’s magnetic field varies in the range from ?3 to +3 kG. The field geometry is explained in terms of the oblique rotator model. The obtained magnetic field variation curve can be described by a central dipole with the dipole axis inclined to the axis of rotation by β = 60°, and the magnetic field strength at the pole of B _p = 11.5 kG. The data on the variability of spectral lines of some metals are presented, allowing to make an assumption that the stellar surface is heavily spotted.     

On the origin and structure of stellar magnetic fields

Newly formed stars have magnetic fields provided by the compression of the interstellar field, and contrary to a widely accepted idea these fields are not destroyed by convective motions. For the same reason, the fallacy of ‘turbulent diffusion’, turbulent dynamo action is not possible in any star. Thus all stellar magnetic fields have a common origin, and persist throughout the lifetime of each star, including degenerate phases. This common origin, and a general similarity in stellar evolutionary processes, suggest that the fields may develop similar structural characteristics and MHD effects. This would open new possibilities of coordinating the studies of different types of stars and relating them to solar physics which has tended to become isolated from general stellar physics. As an initial step we consider three features of solar magnetic fields and their MHD effects. First, the solar magnetic field comprises two separate components: a poloidal field and a toroidal field. The former is a dipole field, permeating the entire Sun and closely aligned with the rotational axis; at the surface it is always concealed by much stronger elements of the toroidal field. The latter is probably wound from the former by differential rotation at latitudes below about 35°, where sections emerge through the solar surface and are then carried polewards. The second feature of solar magnetic fields is that all flux is concentrated into flux tubes of strength some kG, isolated within a much larger volume of non-magnetic plasma. The third feature is that the flux tubes are helically twisted into flux ropes (up to ?10²²Mx) and smaller elements ranging down to flux fibres (? 10¹⁸Mx). Some implications of similar features in other stars are discussed.     

Large-Scale Magnetic Field and Sunspot Cycles

Hα magnetic synoptic charts of the Sun are processed for 1915–1999 and the spherical harmonics are calculated. It is shown that the polarity distribution of the magnetic field on Hα charts is similar to the polarity distribution of the Stanford magnetic field observations during 1975–1999. The index of activity of the large-scale magnetic field A(t), representing the sum of the intensities of dipole and octupole components, is introduced. It is shown that the cycle of the large-scale magnetic field of the Sun precedes on the average by 5.5 years the sunspot activity cycle, W(t). This means that the weak large-scale magnetic fields of the Sun do not result from decay and diffusion of strong fields from active regions as it is supposed in all modern theories of the solar cycle. On the basis of the new data the intensity of the current solar cycle 23 is predicted and some aspects of the theory of the solar cycle are discussed.     

Magnetic Neutron Stars. I. Static Field Configurations

The paper is the first in a series dealing with the structure of magnetic and rotating neutron stars including general relativistic effects. The geometry of fossile magnetic fields frozen in the highly conductive neutron star matter in a non-rotating (or weakly rotating) star is studied. § 2 treats the general poloidal field in a vacuum outside the star. The geometry of magnetic fields within the star — whose matter is governed by a barytropic equation of state — is restricted by the condition that the magnetic force density should be curl-free to maintain equilibrium (§ 3). Numerical results are obtained for a poloidal and a toroidal dipole field (§ 4).     

On global and local magnetic fields of flare stars with YZ CMi and OT Ser as examples

Global magnetic fields of flare stars evolve very fast—at times of tens–hundreds of days. In our opinion, this is due to mutual addition of local magnetic fields generated by the differential rotation of these objects.With the example of two flare stars,OT Ser and YZCMi, we consider possiblemechanisms of generation and disspation of local and global magnetic fields and the mechanism of “magnetic deceleration” of these stars according to the scheme “differential rotation–generation of local magnetic fields–fluorescence of energy accumulated by local magnetic fields during flares.” We also estimated the rotation energy and global magnetic field for OT Ser and YZCMi. It is shown that even strong dissipation of the accumulated local magnetic energy in the flare on February 9, 2008 (UT 20:22:00) in YZCMi has not had any impact on the global magnetic field.     

Small-scale magnetic field diagnostics outside sunspots: Comparison of different methods

We analyse different observational data related to the problem of intrinsic magnetic field strength in small-scale fluxtubes outside sunspots. We conclude that the kG range of fluxtube fields follows from not only classical line ratio method, but also from other old and new techniques. For the quiet regions on the Sun, the most probable mode of such fields has a magnetic field strength of 1.2–1.5 kG assuming the rectangular field profile. To best interpret the observations, a weak background field between fluxtubes should be assumed, and its magnetic field strength is expected to increase with the filling factor of fluxtubes. The alternative point of view about subkilogauss fluxtube fields is critically examined, and possible sources of different conclusions are presented.     

Turbulent dynamo near tachocline and reconstruction of azimuthal magnetic field in the solar convection zone

In order to extend the abilities of the αΩ dynamo model to explain the observed regularities and anomalies of the solar magnetic activity, the negative buoyancy phenomenon and the magnetic quenching of the α effect were included in the model, as well as newest helioseismically determined inner rotation of the Sun were used. Magnetic buoyancy constrains the magnitude of toroidal field produced by the Ω effect near the bottom of the solar convection zone (SCZ). Therefore, we examined two “antibuoyancy” effects: i) macroscopic turbulent diamagnetism and ii) magnetic advection caused by vertical inhomogeneity of fluid density in the SCZ, which we call the ∇ρ effect. The Sun's rotation substantially modifies the ∇ρ effect. The reconstruction of the toroidal field was examined assuming the balance between mean‐field magnetic buoyancy, turbulent diamagnetism and the rotationally modified ∇ρ effect. It is shown that at high latitudes antibuoyancy effects block the magnetic fields in the deep layers of the SCZ, and so the most likely these deep‐rooted fields could not become apparent at the surface as sunspots. In the near‐equatorial region, however, the upward ∇ρ effect can facilitate magnetic fields of about 3000 – 4000 G to emerge through the surface at the sunspot belt. Allowance for the radial inhomogeneity of turbulent velocity in derivations of the helicity parameter resulted in a change of sign of the α effect from positive to negative in the northern hemisphere near the bottom of the SCZ. The change of sign is very important for direction of the Parker's dynamo‐waves propagation and for parity of excited magnetic fields. The period of the dynamo‐wave calculated with allowance for the magnetic quenching is about seven years, that agrees by order of magnitude with the observed mean duration of the sunspot cycles. Using the modern helioseismology data to define dynamo‐parameters, we conclude that north‐south asymmetry should exist in the meridional field. At low latitudes in deep layers of the SCZ, the αΩ dynamo excites most efficiency the dipolar mode of the meridional field. Meanwhile, in high‐latitude regions a quadrupolar mode dominates in the meridional field. The obtained configuration of the net meridional field is likely to explain the magnetic anomaly of polar fields (the apparent magnetic “monopole”) observed near the maxima of solar cycles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Statistical interrelation of 22-yr-long variations in the data on parameters of the Earth’s rotation and magnetic fields of the Earth and the Sun

By means of spectral analysis, oscillations have been detected in many-year time series of deviations in the duration of days from the standard that cannot be explained within the framework of existing gravitational theory. The solution of the problem of the origin and structure of these oscillations is associated with the essence of the phenomena taking place inside the Earth and the mechanisms of energy transfer by external fields and the Sun. The effect of the Sun on the Earth’s rotation also leads to the formation of a unified cyclic background, resulting in correlated oscillations in all shells of the Earth, as well as in its atmosphere and its nucleus. Ground magnetic fields of the Earth and the Sun play the leading role in the abovementioned unified cyclic process. The results of spectral autoregressive and wavelet analyses of experimental data concerning deviations in the duration of days from the standard in the years 1832–2006, ground geomagnetic field intensities in 1832–2006, and the mean magnetic field of the Sun during the period from 1975 to 2005 have been discussed in this paper to reveal and compare correlating oscillations. To analyze a short-period (31-yr-long) series of daily data on the mean magnetic field of the Sun, the results of wavelet transformations (the Morlet wavelet) of the detected amplitude of a burst envelope with a carrier frequency of 13 cycles/yr have been obtained.     

Determination of the Coronal and Interplanetary Magnetic Field Strength and Radial Profiles from Large-Scale Photospheric Magnetic Fields

We propose a new model for the magnetic field at different distances from the Sun during different phases of the solar cycle. The model depends on the observed large-scale non-polar (\({\pm}\, 55^{\circ }\)) photospheric magnetic field and on the magnetic field measured at polar regions from \(55^{\circ }\) N to \(90^{\circ }\) N and from \(55^{\circ }\) S to \(90^{\circ }\) S, which are the visible manifestations of cyclic changes in the toroidal and poloidal components of the global magnetic field of the Sun. The modeled magnetic field is determined as the superposition of the non-polar and polar photospheric magnetic field and considers cycle variations. The agreement between the model predictions and magnetic fields derived from direct in situ measurements at different distances from the Sun, obtained with different methods and at different solar activity phases, is quite satisfactory. From a comparison of the magnetic fields as observed and calculated from the model at 1 AU, we conclude that the model magnetic field variations adequately explain the main features of the interplanetary magnetic field (IMF) radial, \(B_{\mathrm{x}}\), component cycle evolution at Earth’s orbit. The modeled magnetic field averaged over a Carrington rotation (CR) correlates with the IMF \(B_{\mathrm{x}}\) component also averaged over a CR at Earth’s orbit with a coefficient of 0.691, while for seven CR-averaged data, the correlation reaches 0.81. The radial profiles of the modeled magnetic field are compared with those of already existing models. In contrast to existing models, ours provides realistic magnetic-field radial distributions over a wide range of heliospheric distances at different cycle phases, taking into account the cycle variations of the solar toroidal and poloidal magnetic fields. The model is a good approximation of the cycle behavior of the magnetic field in the heliosphere. In addition, the decrease in the non-polar and polar photospheric magnetic fields is shown. Furthermore, the magnetic field during solar cycle maxima and minima decreased from Cycle 21 to Cycle 24. This implies that both the toroidal and poloidal components, and therefore the solar global magnetic field, decreased from Cycle 21 to Cycle 24.     

Soft X-ray Solar Activities Associated with Interplanetary Magnetic Flux Ropes

We studied the soft X-ray solar events that could be associated with the interplanetary magnetic flux ropes observed by the WIND satellite during 1995 through 1998. The timings of the launches of the magnetic flux ropes from the Sun were estimated using flux rope speeds derived by the fitting of a cylindrical model. In the reasonable time window, soft X-ray solar signatures were found in approximately 70% of the flux ropes. Parameters (e.g., axis direction, strength of magnetic field, radius, and helicity) of the magnetic flux ropes obtained by the model fitting were compared with the characteristics of the corresponding soft X-ray events observed by Yohkoh. According to the result of the comparison, the magnetic flux ropes with strong magnetic fields or high speeds were observed in association with higher soft X-ray solar activities.