Small-scale background magnetic field on the sun in solar cycle 23

Based on SOHO/MDI data (an archive of magnetic maps with a resolution of ～2″), we have investigated the dynamics of the small-scale background magnetic field on the Sun in solar cycle 23. The cyclic variations and surface structure of the background magnetic field have been analyzed using the mean estimates of 〈B〉 and 〈B ²〉 of the observed magnetic field strength B for various solar surface areas and at various B levels. We have established that the cyclic variations of 〈2〉 at latitudes below 30° are essentially similar to those of the total radio flux F _10.7. A significant difference between the background magnetic fields in the northern and southern solar hemispheres persisting throughout the solar cycle has been detected. We have found the effect of background magnetic field growth toward the solar limb and concluded that the transversal component in the background magnetic field is significant. The relatively weak small-scale background magnetic fields are shown to form a special population with its own special laws of cyclic variation.     

Comparison of the magnetic fields in active prominences measured from the He I D3 and Hα lines

We present the results of magnetic field measurements in three active prominences, July 24, 1981, July 24, 1999, and July 12, 2004, obtained from observations with the echelle spectrograph of the horizontal solar telescope at the Astronomical Observatory of the Taras Shevchenko Kiev National University. The magnetic fields were measured from the Zeeman splitting of the I ± V profiles in the He I D₃ and H?? lines in the atmosphere at heights from 3 to 14 Mm. Our measurements of the effective magnetic fields B _eff from the shift of the profile centroids have shown that the magnetic fields averaged over the entrance slit area were within the range from ?600 to +1500 G. The amplitude values of the local fields have been estimated from the splitting of the bisectors of the central parts of the line profiles at 0.9 of the peak intensity. The corresponding fields B _0.9 have turned out to be approximately twice B _eff and reached 4000 G in absolute value. Narrow (1?C2 Mm) height peaks at heights of 6?C11 Mm have been found in the height distributions of the magnetic field. We have found an interesting effect in two prominences-an anticorrelation between the magnetic field strengths measured from the D₃ and H?? lines.     

Longitude variations of solar magnetic fields of different intensity in cycle 23 as inferred from the SOHO/MDI data

SOHO/MDI magnetograms have been used to analyze the longitude distribution of the squared solar magnetic field 〈B ²〉 in the activity cycle no. 23. The energy of the magnetic field (〈B ²〉) is shown to change with longitude. However, these variations hardly fit the concept of active longitudes. In the epochs of high solar activity, one can readily see a relationship between longitude variations of the medium-strong ((|B| > 50 G or |B| > 100 G) and relatively weak (|B| ≤ 50 G or |B| ≤ 100 G) fields at all latitudes. In other periods, this relationship is revealed mainly at the latitudes not higher than 30°. The background fields (|B| ≤ 25 G) also display longitude variations, which are, however, not related to those of the strong fields. This makes us think that the fields of solar activity are rather inclusions to the general field than the source of the latter.     

Statistics of magnetic fields for OB stars

Based on an analysis of the catalog of magnetic fields, we have investigated the statistical properties of the mean magnetic fields for OB stars. We show that the mean effective magnetic field B of a star can be used as a statistically significant characteristic of its magnetic field. No correlation has been found between the mean magnetic field strength B and projected rotational velocity of OB stars, which is consistent with the hypothesis about a fossil origin of the magnetic field. We have constructed the magnetic field distribution function for B stars, F(B), that has a power-law dependence on B with an exponent of ≈−1.82. We have found a sharp decrease in the function F(B) for B ⩽ 400 G that may be related to rapid dissipation of weak stellar surface magnetic fields.     

Differential rotation and sector structure of solar magnetic fields

The differential rotation and sector structure of solar magnetic fields has been studied using digitized data on photospheric magnetic fields recorded at the Mount Wilson Observatory during the period August 1959–May 1970. The power spectra show considerable power in high-frequency peaks, corresponding to harmonic components with wavelengths less than 1/10 solar rotation. Calculations for a series of shorter time intervals show how the distribution of power over the various harmonic components in the sector pattern varies strongly with the solar cycle. The equatorial rotation rate of solar magnetic fields is about 0.1 km s^-1 faster than that of the photospheric plasma determined from Doppler shifts. It is shown that the Doppler measurements mainly refer to the non-network regions. The differential flow of 0.1 km s^-1 forms streamlines around the magnetic fine structures. The different rotation rates of various solar features can be explained in terms of the rotation rates of magnetic and non-magnetic regions. The rotation rates of the magnetic fields in active and quiet regions agree at the equator. At higher latitudes, however, the background fields deviate less from solid-body rotation, indicating that their source is below the deepest layers to which the sunspot magnetic fields penetrate. This suggests that turbulent diffusion of the field in old active regions may not be the main source for the background magnetic field, but that the source is located close to a rigidly rotating solar core with a synodic rotation period of 26.87 days.     

Comments on solar linear force-free field and application of FFT analysis

We begin with some comments on the methods of computation of the magnetic fields of solar active regions in terms of force-free field, and point out some mistakes in the solutions. Then we propose a method of quasi-linear force-free field, and probe the application of fast Fourier transform (FFT) in its computation. The magnetic field of the active region NOAA 9165 on 2000-09-15 is taken as an example, and three different methods are used in the determination of the configuration of magnetic lines. The results are then compared with the fine Hα filtergrams of Ganyu Station of Purple Mountain Observatory.     

Some properties of finite energy constant-α force-free magnetic fields in a half-space

Some useful properties of a finite energy, constant-α, force-free magnetic field B _α occupying a half-space D are presented. In particular:

1. Fourier and Green representations of B _α are obtained and used to derive conditions for the existence and uniqueness of a B _α having a given normal component B _z on the boundary ?D.
2. The asymptotic behaviour of B _α at infinity as well as stability results against changes in the boundary condition on ?D and in the value of α are established.
3. The energy of B _α is shown to be smaller than the energy of the open field having the same B _z on ?D, thus confirming an earlier conjecture (Aly, 1984).
4. B _α is proved to not be a Taylor-Heyvaerts-Priest state, in spite of the fact that its relative helicity H is finite and that it is the only solution of the Lagrange-Euler equation associated with the problem of minimizing the energy among all the fields having the same value of H and the same B _z on ?D.

     

Zonal structure and meridional drift of large-scale solar magnetic fields

Digitized synoptic charts of photospheric magnetic fields were analyzed for the past 4 incomplete solar activity cycles (1969–2000). The zonal structure and cyclic evolution of large-scale solar magnetic fields were investigated using the calculated values of the radial B _r, |B _r|, meridional B _θ, |B _θ|, and azimuthal B _φ, |B _φ| components of the solar magnetic field averaged over a Carrington rotation (CR). The time–latitude diagrams of all 6 parameters and their correlation analysis clearly reveal a zonal structure and two types of the meridional poleward drift of magnetic fields with the characteristic times of travel from the equator to the poles equal to ∼16–18 and ∼2–3 years. A conclusion is made that we observe two different processes of reorganization of magnetic fields in the Sun that are related to generation of magnetic fields and their subsequent redistribution in the process of emergence from the field generation region to the solar surface. Redistribution is supposed to be caused by some external forces (presumably, by sub-surface plasma flows in the convection zone).     

The ion H 3 + in a strong magnetic field

A first detailed study of the low-lying electronic states of the H ₃ ⁺ molecular ion in linear configuration, parallel to a magnetic field, is carried out for B=0–4.414×10¹³ G in the Born-Oppenheimer approximation. The variational method is employed with a single, physically adequate trial function which includes, in particular, explicitly the electronic correlation term in the form exp?(γ r ₁₂), where γ is a variational parameter. The state of the lowest total energy (ground state) depends on the magnetic field strength. It evolves from spin-singlet ¹Σ _g for small magnetic fields B?5×10⁸ G to weakly-bound spin-triplet ³Σ _u for intermediate fields and eventually to spin-triplet ³Π _u state for B?5×10¹⁰ G.     

Dayside H circulation at Mercury and neutral particle emission

In this study we discuss the proton circulation and the neutral atom emission at Mercury. The H⁺ distribution in space, energy and pitch angle has been simulated by means of a single-particle Monte Carlo model. The applied electric and magnetic field model has been parameterized to take into account different boundary conditions such as interplanetary magnetic field and cross-tail potential drop. Particular attention has been paid to the estimation of the surface-sputtered neutral atoms and the energetic neutral atoms generated via charge-exchange process. The peculiar configuration of the hermean magnetosphere, as it is expected after the Mariner-10 observation of a weak magnetic field, allows a significant part of the incoming solar wind to enter Mercury's environment. For the Bz<−10 nT conditions, intense ion fluxes are expected in the cusp regions, which are extremely large when compared to the Earth's ones. The solar wind particles are likely to rapidly leave the hermean magnetosphere or precipitate onto the planetary surface, thus originating neutral particle emission via ion-sputtering. Two instruments, proposed to fly on board ESA mission BepiColombo (namely: the NPA-IS SERENA suite on the MPO segment and the ENA instrument on the MMO segment) will monitor the neutral signal as well as the precipitating ion particles. The modeled distribution presented here may be considered as a reference tool for the future observations.     

Relationship between Powerful Flares and Dynamic Evolution of the Magnetic Field at the Solar Surface

Powerful flares are closely related to the evolution of the complex magnetic field configuration at the solar surface. The strength of the magnetic field and speed of its evolution are two vital parameters in the study of the change of magnetic field in the solar atmosphere. We propose a dynamic and quantitative depiction of the changes in complexity of the active region: E=u×B, where u is the velocity of the footpoint motion of the magnetic field lines and B is the magnetic field. E represents the dynamic evolution of the velocity field and the magnetic field, shows the sweeping motions of magnetic footpoints, exhibits the buildup process of current, and relates to the changes in nonpotentiality of the active region in the photosphere. It is actually the induced electric field in the photosphere. It can be deduced observationally from velocities computed by the local correlation tracking (LCT) technique and vector magnetic fields derived from vector magnetograms. The relationship between E and ten X-class flares of four active regions (NOAA 10720, 10486, 9077, and 8100) has been studied. It is found that (1) the initial brightenings of flare kernels are roughly located near the inversion lines where the intensities of E are very high, (2) the daily averages of the mean densities of E and its normal component (E _n) decrease after flares for most cases we studied, whereas those of the tangential component of E (E _t) show no obvious regularities before and after flares, and (3) the daily averages of the mean densities of E _t are always higher than those of E _n, which cannot be naturally deduced by the daily averages of the mean densities of B _n and B _t.     

Evolution of Relative Magnetic Helicity: Method of Computation and Its Application to a Simulated Solar Corona above an Active Region

For a better understanding of solar magnetic field evolution it is appropriate to evaluate the magnetic helicity based on observations and to compare it with numerical simulation results. We have developed a method for calculating the vector potential of a magnetic field given in a finite volume; the method requires the magnetic flux to be balanced on all the side boundaries of the considered volume. Our method uses a fast Laplace/Poisson solver to obtain the vector potentials for a given magnetic field and for the corresponding potential (current-free) field. This allows an efficient calculation of the relative magnetic helicity in a finite 3D volume. We tested our approach on a theoretical model (Low and Lou, Astrophys. J. 352, 343, 1990) and also applied our method to the magnetic field above active region NOAA 8210 obtained by a photospheric-data-driven MHD model. We found that the amount of accumulated relative magnetic helicity coincides well with the relative helicity inflow through the boundaries in the ideal and non-ideal cases. The temporal evolution of relative magnetic helicity is consistent with that of magnetic energy. The maximum value of normalized helicity, H _m/Φ²=0.0298, is reached just before a drastic energy release by magnetic reconnection. This value is close to the corresponding value inferred from the formula that connects the magnetic flux and the accumulated magnetic helicity based on the observations of solar active regions.     

Towards Calibration of the Mean Magnetic Field of the sun

The 1968–2000 data on the mean magnetic field (MMF, longitudinal component) of the Sun are analysed to study long-time trends of the Sun's magnetic field and to check MMF calibration. It is found that, within the error limits, the mean intensity of photospheric magnetic field (the MMF strength, |H|), did not change over the last 33 years. It clearly shows, however, the presence of an 11-year periodicity caused by the solar activity cycle. Time variations of |H| correlate well with those of the radial component, |B _r|, of the interplanetary magnetic field (IMF). This correlation (r=0.69) appears to be significantly higher than that between |B _r| and the results of a potential source-surface extrapolation, to the Earth's orbit, of synoptic magnetic charts of the photosphere (using the so-called `saturation' factor <sup>–1</sup> for magnetograph measurements performed in the line Fei 525.0 nm; Wang and Sheeley, 1995). It seems therefore that the true source surface of IMF is the `quiet' photosphere – background fields and coronal holes, like those for MMF. The average `effective' magnetic strength of the photospheric field is determined to be about 1.9 G. It is also shown that there is an approximate linear relation between |B <sub>r</sub>| and MMF intensity |H| (in gauss)|B <sub>r</sub>|(H <sub>0</sub>)<sub>min</sub>×(1+C|H|)where =1.5×10<sup>–5</sup> normalizes the photospheric field strength to 1 AU distance from the Sun, (H <sub>0</sub>)<sub>min</sub>=1.2 G is some minimal `effective' intensity of photospheric background fields and C=1.3 G^–1 an empirical constant. It is noted that good correlation between time variations of |H| and |B _r| makes suspicious a correction of the photospheric magnetic fields with the use of saturation factor ^–1.     

A search for forward scattering of sunlight from lunar libration clouds

An attempt to determine the radiance of forward scattered sunlight from particles in lunar libration regions was made with the white light coronagraph on Skylab. The libration regions could not be distinguished against the solar K + F coronal background; an upper limit to the libration cloud radiance is determined to be $\text{2·5 × 10}{}^{\mathrm{?11}}\text{B}{}_{\mathrm{?}}$, where $\text{B}{}_{\mathrm{?}}$ is the mean radiance of the solar disk. Employing a model of the particle composition and size distribution which has been proposed for the interplanetary medium, we determine upper limits for the density enhancements in the libration region from the upper limit of the forward scattered radiance presented herein. Similarly, the actual spatial density enhancement is calculated using the earlier observations of the libration region backscattered radiance (Roach, 1975). Enhancements of a factor of 10²–10³ are thus determined, depending upon material composition and size distribution used. By combining the forward and backscatter observations, it is possible to eliminate from consideration clouds whose power law particle size distribution exponent k is 2·5 and complex index of refraction m is 1·33?0.05i and 1·50?0.05i (i.e. absorbing ice and quartz particles, respectively). Finally, the radiance contrast of a possible model libration cloud is calculated with respect to the K- and F-corona/zodiaal light background and is shown to be a maximum in the vicinity of solar elongation angle ～30 deg.     

Gamma-ray lines and neutrons from solar flares

An analysis, with a representative (canonical) example of solar-flare-generated equatorial disturbances, is presented for the temporal and spatial changes in the solar wind plasma and magnetic field environment between the Sun and one astronomical unit (AU). Our objective is to search for first order global consequences rather than to make a parametric study. The analysis - an extension of earlier planar studies - considers all three plasma velocity and magnetic field components (V _r, V_φ, V₀, and B _r, B₀, B_φ) in any convenient heliospheric plane of symmetry such as the ecliptic plane, the solar equatorial plane, or the heliospheric equatorial plane chosen for its ability (in a tilted coordinate system) to order northern and southern hemispheric magnetic topology and latitudinal solar wind flows. Latitudinal velocity and magnetic field gradients in and near the plane of symmetry are considered to provide higher-order corrections of a specialized nature and, accordingly, are neglected, as is dissipation, except at shock waves. The representative disturbance is examined for the canonical case in which one describes the temporal and spatial changes in a homogeneous solar wind caused by a solar-flare-generated shock wave. The ‘canonical’ solar flare is assumed to produce a shock wave that has a velocity of 1000 km s^#X2212;1 at 0.08 AU. We have examined all plasma and field parameters at three radial locations: central meridian and 33° W and 90° W of the flare's central meridian. A higher shock velocity (3000 km s^#X2212;1) was also used to demonstrate the model's ability to simulate a strongly-kinked interplanetary field. Among the global (first-order) results are the following: (i) incorporation of a small meridional magnetic field in the ambient magnetic spiral field has negligible effect on the results; (ii) the magnetic field demonstrates strong kinking within the interplanetary shocked flow, even reversed polarity that - coupled with low temperature and low density - suggests a viable explanation for observed ‘magnetic clouds’ with accompanying double-streaming of electrons at directions ～ 90° to the heliocentric radius.     

Magnetic fields and Fe I line profiles in the major solar flare on October 28, 2003

Strong (“kilogauss”) small-scale magnetic fields were detected outside a sunspot near the seismic source of the major X17.2/4B solar flare on October 28, 2003. Echelle Zeeman spectrograms of the flare were obtained with the horizontal solar telescope at the Astronomical Observatory of the Taras Shevchenko Kiev National University. Analysis of the Stokes I ± V profiles for the Fe I 5232.9, 5247.1, 5250.2, and 5397.1 Å lines has revealed a number of characteristic spectral features. These are indicative of both background fields with a strength of ≈300 G and small-scale fields with a strength of 1300–3100 G. Evidence for the presence of another small-scale field component of opposite polarity with a strength of 8–10 kG has been found. A redshift (downflow) with a velocity of 1 km s^?1 was observed in the latter component.     

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.     

Solar Cycle Phase Dependence of Supergranular Fractal Dimension

We study the complexity of supergranular cells using the intensity patterns obtained from the Kodaikanal Solar Observatory during the 23rd solar cycle. Our data consists of visually identified supergranular cells, from which a fractal dimension D for supergranulation is obtained according to the relation P?∝?A ^D/2, where A is the area and P is the perimeter of the supergranular cells. We find a difference in the fractal dimension between active and quiet region cells in the ascending phase, during the peak and in the descending phase which is conjectured to be due to the magnetic activity level.