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1.
We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components B x (x), B y (x), B z (x), the force-free parameter α(x), the electric current density j(x), and are accurate to second-order (of the nonlinear force-free α-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena.  相似文献   

2.
In this study we use a numerical simulation of an artificial coronal mass ejection (CME) to validate a method for calculating propagation directions and kinematical profiles of interplanetary CMEs (ICMEs). In this method observations from heliospheric images are constrained with in-situ plasma and field data at 1 AU. These data are used to convert measured ICME elongations into distance by applying the harmonic mean approach, which assumes a spherical shape of the ICME front. We used synthetic white-light images, similar to those observed by STEREO-A/HI, for three different separation angles between remote and in-situ spacecraft of 30°, 60°, and 90°. To validate the results of the method, the images were compared to the apex speed profile of the modeled ICME, as obtained from a top view. This profile reflects the “true” apex kinematics because it is not affected by scattering or projection effects. In this way it is possible to determine the accuracy of the method for revealing ICME propagation directions and kinematics. We found that the direction obtained by the constrained harmonic mean method is not very sensitive to the separation angle (30° sep: ?=W7; 60° sep: ?=W12; 90° sep: ?=W15; true dir.: E0/W0). For all three cases the derived kinematics agree relatively well with the real kinematics. The best consistency is obtained for the 30° case, while with growing separation angle the ICME speed at 1 AU is increasingly overestimated (30° sep: ΔV arr≈??50 km?s?1, 60° sep: ΔV arr≈+?75 km?s?1, 90° sep: ΔV arr≈+?125 km?s?1). Especially for future L4/L5 missions, the 60° separation case is highly interesting in order to improve space-weather forecasts.  相似文献   

3.
The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) provides photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semianalytic and numeric equilibria and applied to vector magnetograms from Hinode and ground-based observations. Recently we implemented a new version which takes into account measurement errors in photospheric vector magnetograms. Photospheric field measurements are often affected by measurement errors and finite nonmagnetic forces inconsistent for use as a boundary for a force-free field in the corona. To deal with these uncertainties, we developed two improvements: i) preprocessing of the surface measurements to make them compatible with a force-free field, and ii) new code which keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which must be optimized for use with data from SDO/HMI. In this work we describe the corresponding analysis method and evaluate the force-free equilibria by how well force-freeness and solenoidal conditions are fulfilled, by the angle between magnetic field and electric current, and by comparing projections of magnetic field lines with coronal images from the Atmospheric Imaging Assembly (SDO/AIA). We also compute the available free magnetic energy and discuss the potential influence of control parameters.  相似文献   

4.
The type II solar radio burst recorded on 13 June 2010 by the Hiraiso Solar Observatory Radio Spectrograph was employed to estimate the magnetic-field strength in the solar corona. The burst was characterized by a well-pronounced band splitting, which we used to estimate the density jump at the shock and Alfvén Mach number using the Rankine–Hugoniot relation. We convert the plasma frequency of the type II burst into height [R] in solar radii using an appropriate density model, and then we estimated the shock speed [V s], coronal Alfvén velocity [V A], and the magnetic-field strength at different heights. The relative bandwidth of the band splitting was found to be in the range 0.2?–?0.25, corresponding to a density jump of X=1.44?–?1.56, and an Alfvén Mach number of M A=1.35?–?1.45. The inferred mean shock speed was on the order of V≈667 km?s?1. From the dependencies V(R) and M A(R) we found that the Alfvén speed slightly decreases at R≈1.3?–?1.5 R⊙. The magnetic-field strength decreases from a value between 2.7 and 1.7 G at R≈1.3?–?1.5 R⊙, depending on the coronal-density model employed. Our results are in good agreement with the empirical scaling by Dulk and McLean (Solar Phys. 57, 279, 1978) and Gopalswamy et al. (Astrophys. J. 744, 72, 2012). Our results show that the type II band-splitting method is an important tool for inferring the coronal magnetic field, especially when independent measurements are made from white-light observations.  相似文献   

5.
Recent magnetic modeling efforts have shown substantial misalignment between theoretical models and observed coronal loop morphology as observed by STEREO/EUVI, regardless of the type of model used. Both potential field and non-linear force-free field (NLFFF) models yielded overall misalignment angles of 20??C?40 degrees, depending on the complexity of the active region (Sandman et al., Solar Phys. 259, 1, 2009; DeRosa et al., Astrophys. J. 696, 1780, 2009) We demonstrate that with new, alternative forward-fitting techniques, we can achieve a significant reduction in the misalignment angles compared with potential field source surface (PFSS) models and NLFFF models. Fitting a series of submerged dipoles to the field directions of stereoscopically triangulated loops in four active regions (30 April, 9 May, 19 May, and 11 December 2007), we find that 3??C?5 dipoles per active region yield misalignment angles of ???11°??C?18°, a factor of two smaller than those given by previously established extrapolation methods. We investigate the spatial and temporal variation of misalignment angles with subsets of loops for each active region, as well as loops observed prior to and following a flare and filament eruption, and find that the spatial variation of median misalignment angles within an active region (up to 75%) exceeds the temporal variation associated with the flare (up to 40%). We also examine estimates of the stereoscopic error of our analysis. The corrected values yield a residual misalignment of 7°??C?13°, which is attributed to the non-potentiality due to currents in the active regions.  相似文献   

6.
A model of a coronal region of enhanced Fexv and Fexvi emission is developed and its energy balance is examined using extreme ultraviolet observations from OSO-7 together with calculations of possible force-free coronal magnetic field configurations. The coronal emissions overlying the photospheric boundary between regions of opposite magnetic polarity are found to be associated with generally non-potential (current-carrying) magnetic fields in the forms of arches with footpoints in regions of opposite polarity. The orientation of these arches relative to the neutral line changes with degree of ionization of the emitting ion (which we infer from our limb observations to be a function of height) and may be evidence of differing electric currents along various field lines. The appearance of a coronal arch, seen side-on, can conveniently be represented by a parabola and a detailed analysis (Appendix) shows this to be a realistic approximation that should be generally useful in analyzing two-dimensional pictures of coronal structures. Applying this analysis to the most prominent coronal region observed in the radiations of Fexv and Fexvi, we find a maximum in the electron temperature, T e , of 2.6 × 106K at the top of arches whose heights are 20000–40000 km and whose footpoints are separated by ≈ 100000 km. A temperature gradient of ▽T e ≈5 × 10-5K cm-1 is found in this coronal structure. Radiative losses are typically fifteen times greater than conductive losses and the energy deposition required to maintain the coronal feature is nearly uniformly distributed along its length.  相似文献   

7.
J. Javaraiah 《Solar physics》2013,287(1-2):197-214
Using the Solar Optical Observing Network (SOON) sunspot-group data for the period 1985?–?2010, the variations in the annual mean equatorial-rotation rates of the sunspot groups are determined and compared with the known variations in the solar equatorial-rotation rates determined from the following data: i) the plasma rotation rates at 0.94R⊙,0.95R⊙,…,1.0R⊙ measured by the Global Oscillation Network Group (GONG) during the period 1995?–?2010, ii) the data on the soft-X-ray corona determined from Yohkoh/SXT full-disk images for the years 1992?–?2001, iii) the data on small bright coronal structures (SBCS) that were traced in Solar and Heliospheric Observatory (SOHO)/EIT images during the period 1998?–?2006, and iv) the Mount Wilson Doppler-velocity measurements during the period 1986?–?2007. A large portion (up to ≈?30° latitude) of the mean differential-rotation profile of the sunspot groups lies between those of the internal differential-rotation rates at 0.94R⊙ and 0.98R⊙. The variation in the yearly mean equatorial-rotation rate of the sunspot groups seems to be lagging behind that of the equatorial-rotation rate determined from the GONG measurements by one to two years. The amplitude of the GONG measurements is very small. The solar-cycle variation in the equatorial-rotation rate of the solar corona closely matches that determined from the sunspot-group data. The variation in the equatorial-rotation rate determined from the Mount Wilson Doppler-velocity data closely resembles the corresponding variation in the equatorial-rotation rate determined from the sunspot-group data that included the values of the abnormal angular motions (>?|3°|?day?1) of the sunspot groups. Implications of these results are pointed out.  相似文献   

8.
We study the association of solar flares with coronal mass ejections (CMEs) during the deep, extended solar minimum of 2007?–?2009, using extreme-ultraviolet (EUV) and white-light (coronagraph) images from the Solar Terrestrial Relations Observatory (STEREO). Although all of the fast (v>900 km?s?1), wide (θ>100°) CMEs are associated with a flare that is at least identified in GOES soft X-ray light curves, a majority of flares with relatively high X-ray intensity for the deep solar minimum (e.g. ?1×10?6 W?m?2 or C1) are not associated with CMEs. Intense flares tend to occur in active regions with a strong and complex photospheric magnetic field, but the active regions that produce CME-associated flares tend to be small, including those that have no sunspots and therefore no NOAA active-region numbers. Other factors on scales similar to and larger than active regions seem to exist that contribute to the association of flares with CMEs. We find the possible low coronal signatures of CMEs, namely eruptions, dimmings, EUV waves, and Type III bursts, in 91 %, 74 %, 57 %, and 74 %, respectively, of the 35 flares that we associate with CMEs. None of these observables can fully replace direct observations of CMEs by coronagraphs.  相似文献   

9.
RX J1856.5–3754 is one of the brightest nearby isolated neutron stars, and considerable observational resources have been devoted to it. However, current models are unable to satisfactorily explain the data. We show that our latest models of a thin, magnetic, partially ionized hydrogen atmosphere on top of a condensed surface can fit the entire spectrum, from X-rays to optical, of RX J1856.5–3754, within the uncertainties. In our simplest model, the best-fit parameters are an interstellar column density N H≈1×1020 cm?2 and an emitting area with R ∞≈17 km (assuming a distance to RX J1856.5–3754 of 140 pc), temperature T ∞≈4.3×105 K, gravitational redshift z g ～0.22, atmospheric hydrogen column y H≈1 g cm?2, and magnetic field B≈(3–4)×1012 G; the values for the temperature and magnetic field indicate an effective average over the surface.  相似文献   

10.
We analyze multiwavelength observations of an M2.9/1N flare that occurred in AR NOAA 11112 on 16 October 2010. AIA 211 Å EUV images reveal the presence of a faster coronal wave (decelerating from ≈?1390 to ≈?830 km?s?1) propagating ahead of a slower wave (decelerating from ≈?416 to ≈?166 km?s?1) towards the western limb. The dynamic radio spectrum from Sagamore Hill radio telescope shows the presence of a metric type II radio burst, which reveals the presence of a coronal shock wave (speed ≈?800 km?s?1). The speed of the faster coronal wave, derived from AIA 211 Å images, is found to be comparable to the coronal shock speed. AIA 171 Å high-cadence observations showed that a coronal loop, which was located at a distance of ≈?0.32R ⊙ to the west of the flaring region, started to oscillate by the end of the impulsive phase of the flare. The results indicate that the faster coronal wave may be the first driver of the transversal oscillations of coronal loop. As the slower wave passed through the coronal loop, the oscillations became even stronger. There was a plasmoid eruption observed in EUV and a white-light CME was recorded, having velocity of ≈?340?–?350 km?s?1. STEREO 195 Å images show an EIT wave, propagating in the same direction as the lower-speed coronal wave observed in AIA, but decelerating from ≈?320 to ≈?254 km?s?1. These observations reveal the co-existence of both waves (i.e. coronal Moreton and EIT waves), and the type II radio burst seems to be associated with the coronal Moreton wave.  相似文献   

11.
We analyze and discuss the properties of decameter spikes observed in July?–?August 2002 by the UTR-2 radio telescope. These bursts have a short duration (about one second) and occur in a narrow frequency bandwidth (50?–?70 kHz). They are chaotically located in the dynamic spectrum. Decameter spikes are weak bursts: their fluxes do not exceed 200?–?300 s.f.u. An interesting feature of these spikes is the observed linear increase of the frequency bandwidth with frequency. This dependence can be explained in the framework of the plasma mechanism that causes the radio emission, taking into account that Langmuir waves are generated by fast electrons within a narrow angle θ≈13°?–?18° along the direction of the electron propagation. In the present article we consider the problem of the short lifetime of decameter spikes and discuss why electrons generate plasma waves in limited regions.  相似文献   

12.
We study the abundances of the elements He through Pb in Fe-rich impulsive solar energetic-particle (SEP) events with measurable abundances of ions with atomic number Z>2 observed on the Wind spacecraft, and their relationship with coronal mass ejections (CMEs) observed by the Large Angle and Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric Observatory (SOHO). On an average the element abundances in these events are similar to coronal abundances at low Z but, for heavier elements, enhancements rise as a power law in the mass-to-charge ratio A/Q of the ions (at coronal temperatures of 2.5?–?3 MK) to a factor of 3 at Ne, 9 at Fe, and 900 for 76≤Z≤82. Energy dependences of abundances are minimal in the 2?–?15 MeV amu?1 range. The 111 of these Fe-rich impulsive SEP events we found, between November 1994 and August 2013 using the Wind spacecraft, have a 69 % association rate with CMEs. The CMEs are narrow with a median width of 75°, are characteristically from western longitudes on the Sun, and have a median speed of ≈?600 km?s?1. Nearly all SEP onsets occur within 1.5?–?5 h of the CME onset. The faster (>?700 km?s?1), wider CMEs in our sample are related to SEPs with coronal abundances indicating hot coronal plasma with fully ionized He, C, N and O and moderate enhancements of heavier elements, relative to He, but slower (<?700 km?s?1), narrower CMEs emerge from cooler plasma where higher SEP mass-to-charge ratios, A/Q, yield much greater abundance enhancements, even for C/He and O/He. Apparently, the open magnetic-reconnection region where the impulsive SEPs are accelerated also provides the energy to drive out CME plasma, accounting for a strong, probably universal, impulsive SEP-CME association.  相似文献   

13.
We consider the modulation of nonthermal gyrosynchrotron emission from solar flares by the ballooning and radial oscillations of coronal loops. The damping mechanisms for fast magnetoacoustic modes are analyzed. We suggest a method for diagnosing the plasma of flare loops that allows their main parameters to be estimated from peculiarities of the microwave pulsations. Based on observational data obtained with the Nobeyama Radioheliograph (17 GHz) and using a technique developed for the event of May 8, 1998, we determined the particle density n≈3.7×1010 cm?3, the temperature T≈4×107 K, and the magnetic field strength B≈220 G in the region of flare energy release. A wavelet analysis for the solar flare of August 28, 1999, has revealed two main types of microwave oscillations with periods P1≈7, 14 s and P2≈2.4 s, which we attribute to the ballooning and radial oscillations of compact and extended flare loops, respectively. An analysis of the time profile for microwave emission shows evidence of coronal loop interaction. We determined flare plasma parameters for the compact (T≈5.3×107 K, n≈4.8≈1010 cm?3, B≈280 G) and extended (T≈2.1≈107 K, n≈1.2≈1010 cm?3, B≈160 G) loops. The results of the soft X-ray observations are consistent with the adopted model.  相似文献   

14.
The onset of the “Rush to the Poles” of polar-crown prominences and their associated coronal emission is a harbinger of solar maximum. Altrock (Solar Phys. 216, 343, 2003) showed that the “Rush” was well observed at 1.15 R o in the Fe xiv corona at the Sacramento Peak site of the National Solar Observatory prior to the maxima of Cycles 21 to 23. The data show that solar maximum in those cycles occurred when the center line of the Rush reached a critical latitude of 76°±2°. Furthermore, in the previous three cycles solar maximum occurred when the highest number of Fe xiv emission features per day (averaged over 365 days and both hemispheres) first reached latitudes 20°±1.7°. Applying the above conclusions to Cycle 24 is difficult due to the unusual nature of this cycle. Cycle 24 displays an intermittent Rush that is only well-defined in the northern hemisphere. In 2009 an initial slope of 4.6°?year?1 was found in the north, compared to an average of 9.4±1.7°?year?1 in the previous cycles. An early fit to the Rush would have reached 76° at 2014.6. However, in 2010 the slope increased to 7.5°?year?1 (an increase did not occur in the previous three cycles). Extending that rate to 76°±2° indicates that the solar maximum in the northern hemisphere already occurred at 2011.6±0.3. In the southern hemisphere the Rush to the Poles, if it exists, is very poorly defined. A linear fit to several maxima would reach 76° in the south at 2014.2. In 1999, persistent Fe xiv coronal emission known as the “extended solar cycle” appeared near 70° in the North and began migrating towards the equator at a rate 40 % slower than the previous two solar cycles. However, in 2009 and 2010 an acceleration occurred. Currently the greatest number of emission features is at 21° in the North and 24° in the South. This indicates that solar maximum is occurring now in the North but not yet in the South.  相似文献   

15.
Geomagnetic field variations during five major Solar Energetic Particle (SEP) events of solar cycle 23 have been investigated in the present study. The SEP events of 1 October 2001, 4 November 2001, 22 November 2001, 21 April 2002 and 14 May 2005 have been selected to study the geomagnetic field variations at two high-latitude stations, Thule (77.5° N, 69.2° W) and Resolute Bay (74.4° E, 94.5° W) of the northern polar cap. We have used the GOES proton flux in seven different energy channels (0.8–4 MeV, 4–9 MeV, 9–15 MeV, 15–40 MeV, 40–80 MeV, 80–165 MeV, 165–500 MeV). All the proton events were associated with geoeffective or Earth directed CMEs that caused intense geomagnetic storms in response to geospace. We have taken high-latitude indices, AE and PC, under consideration and found fairly good correlation of these with the ground magnetic field records during the five proton events. The departures of the H component during the events were calculated from the quietest day of the month for each event and have been represented as ΔH THL and ΔH RES for Thule and Resolute Bay, respectively. The correspondence of spectral index, inferred from event integrated spectra, with ground magnetic signatures ΔH THL and ΔH RES along with Dst and PC indices have been brought out. From the correlation analysis we found a very strong correlation to exist between the geomagnetic field variation (ΔHs) and high-latitude indices AE and PC. To find the association of geomagnetic storm intensity with proton flux characteristics we derived the correspondence between the spectral indices and geomagnetic field variations (ΔHs) along with the Dst and AE index. We found a strong correlation (0.88) to exist between the spectral indices and ΔHs and also between spectral indices and AE and PC.  相似文献   

16.
Knowledge regarding the coronal magnetic field is important for the understanding of many phenomena, like flares and coronal mass ejections. Because of the low plasma beta in the solar corona, the coronal magnetic field is often assumed to be force-free and we use photospheric vector magnetograph data to extrapolate the magnetic field into the corona with the help of a nonlinear force-free optimization code. Unfortunately, the measurements of the photospheric magnetic field contain inconsistencies and noise. In particular, the transversal components (say B x and B y) of current vector magnetographs have their uncertainties. Furthermore, the magnetic field in the photosphere is not necessarily force free and often not consistent with the assumption of a force-free field above the magnetogram. We develop a preprocessing procedure to drive the observed non–force-free data towards suitable boundary conditions for a force-free extrapolation. As a result, we get a data set which is as close as possible to the measured data and consistent with the force-free assumption.  相似文献   

17.
We study event-to-event variations in the abundance enhancements of the elements He through Pb for Fe-rich impulsive solar energetic-particle (SEP) events, and their relationship with properties of associated coronal mass ejections (CMEs) and solar flares. Using a least-squares procedure we fit the power-law enhancement of element abundances as a function of their mass-to-charge ratio A/Q to determine both the power and the coronal temperature (which determines Q) in each of 111 impulsive SEP events identified previously. Individual SEP events with the steepest element enhancements, e.g. ～?(A/Q)6, tend to be smaller, lower-fluence events with steeper energy spectra that are associated with B- and C-class X-ray flares, with cooler (～?2.5 MK) coronal plasma, and with narrow (°), slower (?1) CMEs. On the other hand, higher-fluence SEP events have flatter energy spectra, less-dramatic heavy-element enhancements, e.g. ～?(A/Q)3, and come from somewhat hotter coronal plasma (～?3.2 MK) associated with C-, M-, and even X-class X-ray flares and with wider CMEs. Enhancements in 3He/4He are uncorrelated with those in heavy elements. However, events with 3He/4He≥0.1 are even more strongly associated with narrow, slow CMEs, with cooler coronal plasma, and with B- and C-class X-ray flares than are other Fe-rich impulsive SEP events with smaller enhancements of 3He.  相似文献   

18.
We statistically analyzed the kinematical evolution and wave pulse characteristics of 60 strong large-scale EUV wave events that occurred during January 2007 to February 2011 with the STEREO twin spacecraft. For the start velocity, the arithmetic mean is 312±115 km?s?1 (within a range of 100?–?630 km?s?1). For the mean (linear) velocity, the arithmetic mean is 254±76 km?s?1 (within a range of 130?–?470 km?s?1). 52 % of all waves under study show a distinct deceleration during their propagation (a≤?50 m?s?2), the other 48 % are consistent with a constant speed within the uncertainties (?50≤a≤50 m?s?2). The start velocity and the acceleration are strongly anticorrelated with c≈?0.8, i.e. initially faster events undergo stronger deceleration than slower events. The (smooth) transition between constant propagation for slow events and deceleration in faster events occurs at an EUV wave start-velocity of v≈230 km?s?1, which corresponds well to the fast-mode speed in the quiet corona. These findings provide strong evidence that the EUV waves under study are indeed large-amplitude fast-mode MHD waves. This interpretation is also supported by the correlations obtained between the peak velocity and the peak amplitude, impulsiveness, and build-up time of the disturbance. We obtained the following association rates of EUV wave events with other solar phenomena: 95 % are associated with a coronal mass ejection (CME), 74 % to a solar flare, 15 % to interplanetary type II bursts, and 22 % to coronal type II bursts. These findings are consistent with the interpretation that the associated CMEs are the driving agents of the EUV waves.  相似文献   

19.
W. T. Thompson 《Solar physics》2013,283(2):489-504
Triangulation measurements using observations from the two Solar Terrestrial Relations Observatory (STEREO) spacecraft, combined with observations from the Solar Dynamics Observatory (SDO), are used to characterize the behavior of a prominence involved in two successive coronal mass ejections 6?–?7 December 2010. The STEREO separation at the time was 171.6°, which was functionally equivalent to a separation of 8.4°, and thus very favorable for feature co-identification above the limb. The first eruption at ≈?14:16 UT on 6 December of the middle branch of the prominence starts off a series of magnetic reconfigurations in the right branch, which itself erupts at ≈?2:06 UT the next day, about 12 hours after the first eruption. The cool prominence material seen at 304?Å drains back down to the surface, but a flux-rope-like magnetic structure is seen to erupt in both 195?Å by the STEREO/Extreme Ultraviolet Imager (EUVI), and in white light by the STEREO/COR1 inner coronagraph. In between the two eruptions, two different signs of helicity are seen in the measured twist of the right branch. This is interpreted to be caused by the overall prominence channel being composed of different segments with alternating helicity signs. The erupting parts on 6 and 7 December both show positive twist, but negative twist is seen in between these positive sections. Negative twist is consistent with the dextral chirality signs seen in the He ii line at 304?Å prior to both eruptions. However, during the period between the eruptions, a region of positive twist grows and replaces the region of negative twist, and finally erupts. We interpret these observations in the light of models that predict that helicity cancellation can be an important factor in the triggering of flares and coronal mass ejections.  相似文献   

20.
We performed for the first time stereoscopic triangulation of coronal loops in active regions over the entire range of spacecraft separation angles (?? sep??6°,43°,89°,127°,and 170°). The accuracy of stereoscopic correlation depends mostly on the viewing angle with respect to the solar surface for each spacecraft, which affects the stereoscopic correspondence identification of loops in image pairs. From a simple theoretical model we predict an optimum range of ?? sep??22°??C?125°, which is also experimentally confirmed. The best accuracy is generally obtained when an active region passes the central meridian (viewed from Earth), which yields a symmetric view for both STEREO spacecraft and causes minimum horizontal foreshortening. For the extended angular range of ?? sep??6°??C?127° we find a mean 3D misalignment angle of ?? PF??21°??C?39° of stereoscopically triangulated loops with magnetic potential-field models, and ?? FFF??15°??C?21° for a force-free field model, which is partly caused by stereoscopic uncertainties ?? SE??9°. We predict optimum conditions for solar stereoscopy during the time intervals of 2012??C?2014, 2016??C?2017, and 2021??C?2023.  相似文献   

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