Differential Rotation of the Solar Corona from Magnetic Field Data

A method for investigating the differential rotation of the solar corona using the coronal magnetic field as a tracer is proposed. The magnetic field is calculated in the potential approximation from observational data at the photospheric level. The time interval from June 24, 1976, to December 31, 2004, is considered. The magnetic field has been calculated for all latitudes from the equator to ±75? with a 5? step at distances from the base of the corona 1.0 R_⊙ to 2.45 R_⊙ near the source surface. The coronal rotation periods at 14 distances from the solar center have been determined by the method of periodogram analysis. The coronal rotation is shown to become progressively less differential with increasing heliocentric distance; it does not become rigid even near the source surface. The change in the coronal rotation periods with time is considered. At the cycleminimumthe rotation has been found to bemost differential, especially at small distances from the solar center. The change in coronal rotation with time is consistent with the tilt of the solar magnetic equator. The results from the magnetic field are compared with those obtained from the brightness of the green coronal Fe XIV 530.3 nm line. The consistency between these results confirms the reliability of the proposed method for studying the coronal rotation. Studying the rotation of the coronal magnetic field gives hope for the possibility of using this method to diagnose the differential rotation in subphotospheric layers.     

The Floor in the Solar Wind Magnetic Field Revisited

Svalgaard and Cliver (Astrophys. J. Lett. 661, L203, 2007) proposed that the solar-wind magnetic-field strength [B] at Earth has a ??floor?? value of ??4.6 nT in yearly averages, which is approached but not broached at solar minima. They attributed the floor to a constant baseline solar open flux. In both 2008 and 2009, the notion of such a floor was undercut by annual B averages of ??4 nT. Here we present a revised view of both the level and the concept of the floor. Two independent correlations indicate that B has a floor of ??2.8 nT in yearly averages. These are i) a relationship between solar polar-field strength and yearly averages of B for the last four 11-year minima (B _MIN), and ii) a precursor relationship between peak sunspot number for cycles 14??C?23 and B _MIN at their preceding minima. These correlations suggest that at 11-year minima, B consists of i) a floor of ??2.8 nT, and ii) a component primarily due to the solar polar fields that varies from ??0 nT to ??3 nT. The solar polar fields provide the ??seed?? for the subsequent sunspot maximum. Removing the ??2.8 nT floor from B _MIN brings the percentage decrease in B between the 1996 and 2009 minima into agreement with the corresponding decrease in solar polar-field strength. Based on a decomposition of the solar wind (from 1972??C?2009) into high-speed streams, coronal mass ejections, and slow solar wind, we suggest that the source of the floor in B is the slow solar wind. During 2009, Earth was in slow solar-wind flows ??70% of the time. We propose that the floor corresponds to a baseline (non-cyclic or ground state) open solar flux of ??8×10¹³ Wb, which originates in persistent small-scale (supergranular and granular) field.     

Inference of Solar Magnetic Field Parameters from Data with Limited Wavelength Sampling

We investigate the diagnostic potential of polarimetric measurements with filtergraph instruments. Numerical simulations are used to explore the possibility of inferring the magnetic field vector, its filling factor, and the thermodynamics of model atmospheres when only a few wavelength measurements are available. These simulations assume the magnetic Sun to be represented by Milne–Eddington atmospheres. The results indicate that two wavelength measurements are insufficient to reliably determine the magnetic parameters, regardless of whether magnetograph techniques or least-squares fitting inversions are used. However, as few as four measurements analyzed with the inversion technique provide enough information to retrieve the intrinsic magnetic field with an accuracy better than 10% in most cases.     

Solar Wind Speed and Expansion Rate of the Coronal Magnetic Field in Solar Maximum and Minimum Phases

Relationships between solar wind speed and expansion rate of the coronal magnetic field have been studied mainly by in-ecliptic observations of artificial satellites and some off-ecliptic data by Ulysses. In this paper, we use the solar wind speed estimated by interplanetary scintillation (IPS) observations in the whole heliosphere. Two synoptic maps of SWS estimated by IPS observations are constructed for two Carrington rotations CR 1830 and 1901; CR 1830 starting on the 11th of June, 1990 is in the maximum phase of solar activity cycle and CR 1901 starting on the 29th of September, 1995 is in the minimum phase. Each of the maps consist of 64800 (360×180) data points. Similar synoptic maps of expansion rate of the coronal magnetic field (RBR) calculated by the so-called potential model are also constructed under a radial field assumption for CR 1830 and CR1901. Highly significant correlation (r=–0.66) is found between the SWS and the RBR during CR1901 in the solar minimum phase; that is, high-speed winds emanate from photospheric areas corresponding to low expansion rate of the coronal magnetic field and low speed winds emanate from photospheric areas of high expansion rate. A similar result is found during CR 1830 in solar maximum phase, though the correlation is relatively low (r=–0.29). The correlation is improved when both the data during CR 1830 and CR 1901 are used together; the correlation coefficient becomes –0.67 in this case. These results suggest that the correlation analysis between the SWS and the RBR can be applied to estimate the solar wind speed from the expansion rate of the coronal magnetic field, though the correlation between them may depend on the solar activity cycle. We need further study of correlation analysis for the entire solar cycle to get an accurate empirical equation for the estimation of solar wind speed. If the solar wind speed is estimated successfully by an empirical equation, it can be used as an initial condition of a solar wind model for space weather forecasts.     

Constraints on the Solar Internal Magnetic Field from a Buoyancy Driven Solar Dynamo

We report here results from a dynamo model developed on the lines of the Babcock-Leighton idea that the poloidal field is generated at the surface of the Sun from the decay of active regions. In this model magnetic buoyancy is handled with a realistic recipe – wherein toroidal flux is made to erupt from the overshoot layer wherever it exceeds a specified critical field B _c (10⁵ G). The erupted toroidal field is then acted upon by the α-effect near the surface to give rise to the poloidal field. In this paper we study the effect of buoyancy on the dynamo generated magnetic fields. Specifically, we show that the mechanism of buoyant eruption and the subsequent depletion of the toroidal field inside the overshoot layer, is capable of constraining the magnitude and distribution of the magnetic field there. We also believe that a critical study of this mechanism may give us new information regarding the solar interior and end with an example, where we propose a method for estimating an upper limit of the difusivity within the overshoot layer. This revised version was published online in July 2006 with corrections to the Cover Date.     

Contribution to the Solar Mean Magnetic Field from Different Solar Regions

Seven-year-long seeing-free observations of solar magnetic fields with the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) were used to study the sources of the solar mean magnetic field, SMMF, defined as the net line-of-sight magnetic flux divided over the solar disk area. To evaluate the contribution of different regions to the SMMF, we separated all the pixels of each SDO/HMI magnetogram into three subsets: weak (\(B^{\mathrm{W}}\)), intermediate (\(B^{\mathrm{I}}\)), and strong (\(B^{\mathrm{S}}\)) fields. The \(B^{\mathrm{W}}\) component represents areas with magnetic flux densities below the chosen threshold; the \(B^{\mathrm{I}}\) component is mainly represented by network fields, remains of decayed active regions (ARs), and ephemeral regions. The \(B^{\mathrm{S}}\) component consists of magnetic elements in ARs. To derive the contribution of a subset to the total SMMF, the linear regression coefficients between the corresponding component and the SMMF were calculated. We found that i) when the threshold level of 30 Mx?cm^?2 is applied, the \(B^{\mathrm{I}}\) and \(B^{\mathrm{S}}\) components together contribute from 65% to 95% of the SMMF, while the fraction of the occupied area varies in a range of 2?–?6% of the disk area; ii) as the threshold magnitude is lowered to 6 Mx?cm^?2, the contribution from \(B^{\mathrm{I}}+B^{\mathrm{S}}\) grows to 98%, and the fraction of the occupied area reaches a value of about 40% of the solar disk. In summary, we found that regardless of the threshold level, only a small part of the solar disk area contributes to the SMMF. This means that the photospheric magnetic structure is an intermittent inherently porous medium, resembling a percolation cluster. These findings suggest that the long-standing concept that continuous vast unipolar areas on the solar surface are the source of the SMMF may need to be reconsidered.     

Correlation between Expansion Rate of the Coronal Magnetic Field and Solar Wind Speed in a Solar Activity Cycle

Thirteen synoptic maps of expansion rate of the coronal magnetic field (CMF; RBR) calculated by the so-called ‘potential model’ are constructed for 13 Carrington rotations from the maximum phase of solar activity cycle 22 through the maximum phase of cycle 23. Similar 13 synoptic maps of solar wind speed (SWS) estimated by interplanetary scintillation observations are constructed for the same 13 Carrington rotations as the ones for the RBR. The correlation diagrams between the RBR and the SWS are plotted with the data of these 13 synoptic maps. It is found that the correlation is negative and high in this time period. It is further found that the linear correlation is improved if the data are classified into two groups by the magnitude of radial component of photospheric magnetic field, |B^pho_r|; group 1, 0.0 G ≦ |B_r^pho| < 17.8 G and group 2, 17.8 G ≦ |B_r^pho|. There exists a strong negative correlation between the RBR and the SWS for the group 1 in contrast with a weak negative correlation for the group 2. Group 1 has a double peak in the density distribution of data points in the correlation diagram; a sharp peak for high-speed solar wind and a low peak for low-speed solar wind. These two peaks are located just on the axis of maximum variance of data points in the correlation diagram. This result suggests that the solar wind consists of two major components and both the high-speed and the low-speed winds emanating from weak photospheric magnetic regions are accelerated by the same mechanism in the course of solar activity cycle. It is also pointed out that the SWS can be estimated by the RBR of group 1 with an empirical formula obtained in this paper during the entire solar activity cycle.     

Intermittency of the Solar Magnetic Field and Solar Magnetic Activity Cycle

Small-scale solar magnetic fields demonstrate features of fractal intermittent behavior, which requires quantification. For this purpose we investigate how the observational estimate of the solar magnetic flux density \(B\) depends on resolution \(D\) in order to obtain the scaling \(\ln B_{D} = - k \ln D +a\) in a reasonably wide range. The quantity \(k\) demonstrates cyclic variations typical of a solar activity cycle. In addition, \(k\) depends on the magnetic flux density, i.e. the ratio of the magnetic flux to the area over which the flux is calculated, at a given instant. The quantity \(a\) demonstrates some cyclic variation, but it is much weaker than in the case of \(k\). The scaling obtained generalizes previous scalings found for the particular cycle phases. The scaling is typical of fractal structures. In our opinion, the results obtained trace small-scale action in the solar convective zone and its coexistence with the conventional large-scale solar dynamo based on differential rotation and mirror-asymmetric convection.     

The Magnetic Field of the Solar Corona from Pulsar Observations

We present a novel experiment with the capacity to independently measure both the electron density and the magnetic field of the solar corona. We achieve this through measurement of the excess Faraday rotation resulting from propagation of the polarised emission from a number of pulsars through the magnetic field of the solar corona. This method yields independent measures of the integrated electron density, via dispersion of the pulsed signal and the magnetic field, via the amount of Faraday rotation. In principle this allows the determination of the integrated magnetic field through the solar corona along many lines of sight without any assumptions regarding the electron density distribution. We present a detection of an increase in the rotation measure of the pulsar J1801-2304 of approximately 170 rad m² at an elongation of 0.96° from the centre of the solar disc. This corresponds to a lower limit of the magnetic field strength along this line of sight of >41.8 nT. The lack of precision in the integrated electron density measurement restricts this result to a limit, but application of coronal plasma models can further constrain this to approximately 0.5 μT, along a path passing 2.7 solar radii from the solar limb, which is consistent with predictions obtained using extensions to the source surface models published by the Wilcox Solar Observatory.     

日冕磁场重建方法在研究太阳爆发活动中的应用

太阳是与地球关系最为密切的天体.发生在日面上的剧烈爆发性活动可能对人类的生存环境产生巨大影响甚至是灾难性后果.包含太阳耀斑、暗条爆发和日冕物质抛射在内的太阳爆发活动是同一物理过程的不同表现形式,其能量来源于爆发前储存在日冕中的磁场自由能.因此,了解日冕磁场的3维结构是理解太阳爆发的触发机制以及活动区的稳定性等现象的前提.由于观测技术限制,目前尚无法对日冕磁场进行常规观测,因此发展了多种利用可常规观测的光球磁场来重建日冕磁场的方法.主要评述近10 yr来各种日冕磁场重建方法在研究太阳爆发活动中的应用.     

Studying Solar Eruptions from Reconstructed Coronal Magnetic Field

The Sun is the celestial body in the sky with the closest relationship with the Earth. The violent eruptive activities happening on the Sun can greatly impact the human living environment and lead to disastrous consequences. It is well accepted that solar eruptions including the solar flare, prominence eruption and coronal mass ejection are the different manifestations of a single physical process powered by the magnetic free energy gradually stored in the corona prior to eruptions. Therefore, mapping the three-dimensional structure of coronal magnetic field is a prerequisite to understand the initiation mechanism of solar eruptions. Due to the technological and methodological difficulties, routine observations of the coronal magnetic field are still unavailable. Therefore, a number of methods have been developed to reconstruct the coronal magnetic field. This paper mainly reviews the applications of various reconstruction methods to the studies of the solar eruptions in the recent ten years.     

Fluctuations of the Solar Dynamo Observed in the Solar Wind and Interplanetary Magnetic Field at 1 AU and in the Outer Heliosphere

Recent helioseismic observations have found strong fluctuations at a period of about 1.3 years in the rotation speed around the tachocline in the deep solar convection layer. Similar mid-term quasi-periodicities (MTQP; periods between 1–2 years) are known to occur in various solar atmospheric and heliospheric parameters for centuries. Since the deep convection layer is the expected location of the solar magnetic dynamo, its fluctuations could modulate magnetic flux generation and cause related MTQP fluctuations at the solar surface and beyond. Accordingly, it is likely that the heliospheric MTQP periodicities reflect similar changes in solar dynamo activity. Here we study the occurrence of the MTQP periodicities in the near and distant heliosphere in the solar wind speed and interplanetary magnetic field observed by several satellites at 1 AU and by four interplanetary probes (Pioneer 10 and 11 and Voyager 1 and 2) in the outer heliosphere. The overall structure of MTQP fluctuations in the different locations of the heliosphere is very consistent, verifying the solar (not heliospheric) origin of these periodicities. We find that the mid-term periodicities were particularly strong during solar cycle 22 and were observed at two different periods of 1.3 and 1.7 years simultaneously. These periodicities were latitudinally organized so that the 1.3-year periodicity was found in solar wind speed at low latitudes and the 1.7-year periodicity in IMF intensity at mid-latitudes. While all heliospheric results on the 1.3-year periodicity are in a good agreement with helioseismic observations, the 1.7-year periodicity has so far not been detected in helioseismic observations. This may be due to temporal changes or due to the helioseismic method where hemispherically antisymmetric fluctuations would so far have remained hidden. In fact, there is evidence that MTQP fluctuations may occur antisymmetrically in the northern and southern solar hemisphere. Moreover, we note that the MTQP pattern was quite different during solar cycles 21 and 22, implying fundamental differences in solar dynamo action between the two halves of the magnetic cycle.     

Solar Wind Speed and Expansion Rate of the Coronal Magnetic Field during Carrington Rotation 1909

The synoptic map of the solar wind speed (SWS) estimated by the computer-assisted tomography (CAT) method with interplanetary scintillation observations is constructed for the 1909 Carrington rotation. A similar synoptic map of expansion rate (RBR) of the coronal magnetic field calculated by the so-called 'potential model' with the photospheric magnetic field is also constructed under the radial field assumption (RF model). These maps consist of 64800 (180×360) data points of equal area. We examine for the first time relations between the SWS estimated by the CAT technique and the RBR calculated by the RF model. A highly significant correlation is found between the SWS and the RBR. A simple correlation coefficient is about –0.72; that is, high-velocity winds emanate from photospheric areas corresponding to a low expansion rate of the coronal magnetic field, and low-velocity winds emanate from photospheric areas of high expansion rate. This result suggests that there is some acceleration mechanism relating to the coronal field expansion.     

Magnetic Power Spectra Derived from Ground and Space Measurements of the Solar Magnetic Fields

We study magnetic power spectra of active and quiet regions by using Big Bear Solar Observatory and SOHO/MDI measurements of longitudinal magnetic fields. The MDI power spectra were corrected with Gaussian Modulation Transfer Function. We obtained reliable magnetic power spectra in the high wave numbers range, up to k=4.6 Mm⁻¹, which corresponds to a spatial scale l=1.4 Mm. We find that the occurrence of the spectral discontinuity at high wave numbers, k≥3 Mm⁻¹, largely depends on the spatial resolution of the data and it appears at progressively higher wave numbers as the resolution of the data improves. The spectral discontinuity in the raw spectra is located at wave numbers about 3 times smaller than wave numbers, corresponding to the resolution of the data, and about 1.5–2.0 times smaller in the case of the noise- and-resolution corrected spectra. The magnetic power spectra for active and quiet regions are different: active-region power spectra are described as ∼k ^−1.7, while in a quiet region the spectrum behaves as ∼k ^−1.3. We suggest that the difference can be due to small-scale dynamo action in the quiet-Sun photosphere. Our estimations show that the dynamo can generate more than 6% of the observed magnetic power.     

A Study of Correlation between Solar Wind Data Observed at Two Points in Interplanetary Space During the Recent Solar Maximum

Identifying co-rotating structures in solar wind enables us to predict solar wind variation at the Earth and, hence, geomagnetic disturbances. However, co-rotating structures during solar maximum are sometimes difficult to see. We correlated solar wind data obtained by two spacecraft, Nozomi heading towards Mars and ACE at the L1 point, from late 1999 through early 2002. There were intervals when the solar wind showed specific co-rotating structures even in the midst of the solar maximum, whereas no correlation was found during the other intervals. The coefficient was generally higher between Nozomi and ACE than for the 27-day recurrence at ACE, while there was some correlation, especially when the difference in longitude between the two spacecraft was less than 120°. Although frequency of occurrence of CMEs is partly responsible for the correlation, the results can be interpreted in terms of rapid changes in co-rotating high-speed streams from near-equatorial coronal holes at the solar maximum.     

太阳磁场理论外推研究进展

太阳磁场是研究太阳物理的关键。目前对太阳磁场的精确测量只限于光球层。对日冕磁场结构的了解,则多是以观测的光球磁场作为边界条件,在某种理论模型下进行外推。势场模型、线性无力场模型和非线性无力场模型是无力场假设下的三种理论外推模型。文章介绍了太阳磁场理论外推的基本方法和最新进展,和对三种模型中使用较多的外推方法,列举了它们在天文研究中的一些应用,同时也简略讨论了外推方法中存在的一些问题。     

太阳剩余磁场研究进展

太阳剩余磁场是指形成于太阳主序星阶段之前，深藏在太阳辐射核内部的原始磁场。由于太阳内部高电导率和准静态等因素，其剩余磁场耗散相当缓慢，而得以保留至今。太阳剩余磁场的存在不仅能够解释太阳活动的很多不对称性现象，如南北不对称性、活动经度与活动穴、低纬度冕洞和Maunder极小期等，还能通过改变自激发发电机模型的边值条件而影响整个太阳表面磁场的分布与演化。从观测结果和理论模型两方面评述了太阳剩余磁场的研究成果及最新进展，并简单讨论了进一步努力的方向。     

Understanding the Behavior of the Heliospheric Magnetic Field and the Solar Wind During the Unusual Solar Minimum Between Cycles 23 and 24

The properties of the heliospheric magnetic field and the solar wind were substantially different in the unusual solar minimum between Cycles 23 and 24: the magnetic-field strength was substantially reduced, as were the flow properties of the solar wind, such as the mass flux. Explanations for these changes are offered that do not require any substantial reconsideration of the general understandings of the behavior of the heliospheric magnetic field and the solar wind that were developed in the minimum of Cycle 22?–?23. Solar-wind composition data are used to demonstrate that there are two distinct regions of solar wind: solar wind likely to originate from the stalk of the streamer belt (the highly elongated loops that underlie the heliospheric current sheet), and solar wind from outside this region. The region outside the streamer-stalk region is noticeably larger in the minimum of Cycle 23?–?24; however, the increased area can account for the reduction in the heliospheric magnetic-field strength in this minimum. Thus, the total magnetic flux contained in this region is the same in the two minima. Various correlations among the solar-wind mass flux and coronal electron temperature inferred from solar-wind charge states were developed for the Cycle 22?–?23 solar minimum. The data for the minimum of Cycle 23?–?24 suggest that the correlations still hold, and thus the basic acceleration mechanism is unchanged in this minimum.     

太阳磁场观测研究

简要回顾了近几年国际上太阳磁场研究的一些重要进展，包括耀斑与磁切和电流的关系，电流螺度和磁螺度，磁场拓扑性，三维磁场外推，色球磁场研究，日冕磁场研究，内网络磁元，磁流和振荡，极区磁场观测以及色球磁元观测等方面内容，同时也介绍了怀柔太阳观测站最近所取得的主要成果，自20世纪90年代以来，YOHKOH高分辨率的太阳X射线数据，SOHO的多波段大尺度观测，TRACE的高分辨太阳过渡区资料，为研究太阳磁场从内部到距离几十太阳半径处的大范围演化提供了依据，高效的空间资料结合长期的地面资料，将是正派推动太阳磁场研究的重要手段和必然趋势。     

Modeling Technogenous Contamination of the Near-Earth Space

In analyzing the technogenous contamination of the near-earth space (NES), the following issues have usually been considered: the estimation of the current level of NES contamination by objects of various size; the modeling of technogenous contamination evolution; the estimation of the probability of spacecraft collisions with space objects (SOs) of various size and the possible implications of hazardous collisions; the determination of characteristics of the flux of SOs of various size through the observation zones of ground-based and onboard means of measurement. The main difficulty in solving the aforementioned problems lies in the deficiency of the experimental data. The available measurement information was obtained in relatively small domains of multidimensional space: the altitude of a point–the latitude of a point–the SO size–the time. As a consequence, additional (a priori) information is invoked for determining the technogenous contamination characteristics at various points of the region mentioned above. The efficient use of experimental data and a priori information constitutes the basic problem of space debris modeling. This paper briefly outlines the data on three space debris (SD) models: ORDEM2000 (Orbital Debris Engineering Model, 2000), MASTER'99 (Meteoroid and Space Debris Terrestrial Environment Reference Model, 2000) and SDPA (Nazarenko, 1997, 2000; Nazarenko and Menshikov, 2001). The features of modeling techniques and the comparative characteristics of technogenous contamination are discussed in the paper.