A dynamo model for axisymmetric and non-axisymmetric solar magnetic fields

More and more observations are showing a relatively weak, but persistent, non-axisymmetric magnetic field co-existing with the dominant axisymmetric field on the Sun. Its existence indicates that the non-axisymmetric magnetic field plays an important role in the origin of solar activity. A linear non-axisymmetric  α²– Ω  dynamo model is derived to explore the characteristics of the axisymmetric  ( m = 0)  and the first non-axisymmetric  ( m = 1)  modes and to provide a theoretical basis with which to explain the 'active longitude', 'flip-flop' and other non-axisymmetric phenomena. The model consists of an updated solar internal differential rotation, a turbulent diffusivity varying with depth, and an α-effect working at the tachocline in a rotating spherical system. The difference between the  α²–Ω  and the  α–Ω  models and the conditions that favour the non-axisymmetric modes under solar-like parameters are also presented.     

Damped Oscillations of Coronal Loops

A mechanism of damped oscillations of a coronal loop is investigated. The loop is treated as a thin toroidal flux rope with two stationary photospheric footpoints, carrying both toroidal and poloidal currents. The forces and the flux-rope dynamics are described within the framework of ideal magnetohydrodynamics (MHD). The main features of the theory are the following: i) Oscillatory motions are determined by the Lorentz force that acts on curved current-carrying plasma structures and ii) damping is caused by drag that provides the momentum coupling between the flux rope and the ambient coronal plasma. The oscillation is restricted to the vertical plane of the flux rope. The initial equilibrium flux rope is set into oscillation by a pulse of upflow of the ambient plasma. The theory is applied to two events of oscillating loops observed by the Transition Region and Coronal Explorer (TRACE). It is shown that the Lorentz force and drag with a reasonable value of the coupling coefficient (c _d ) and without anomalous dissipation are able to accurately account for the observed damped oscillations. The analysis shows that the variations in the observed intensity can be explained by the minor radial expansion and contraction. For the two events, the values of the drag coefficient consistent with the observed damping times are in the range c _d ≈2 – 5, with specific values being dependent on parameters such as the loop density, ambient magnetic field, and the loop geometry. This range is consistent with a previous MHD simulation study and with values used to reproduce the observed trajectories of coronal mass ejections (CMEs).     

Prediction of Space Weather Using an Asymmetric Cone Model for Halo CMEs

Halo coronal mass ejections (HCMEs) are responsible of the most severe geomagnetic storms. A prediction of their geoeffectiveness and travel time to Earth’s vicinity is crucial to forecast space weather. Unfortunately, coronagraphic observations are subjected to projection effects and do not provide true characteristics of CMEs. Recently, Michalek (Solar Phys. 237, 101, 2006) developed an asymmetric cone model to obtain the space speed, width, and source location of HCMEs. We applied this technique to obtain the parameters of all front-sided HCMEs observed by the SOHO/LASCO experiment during a period from the beginning of 2001 until the end of 2002 (solar cycle 23). These parameters were applied for space weather forecasting. Our study finds that the space speeds are strongly correlated with the travel times of HCMEs to Earth’s vicinity and with the magnitudes related to geomagnetic disturbances.     

在太阳磁场大气中FeIλ 5324.19(?)谱线的形成深度

本文在用Unno-Beckers方程计算光球和黑子本影磁场内FeIλ5324.19谱线形成过程中,计算了该谱线Stokes参数随5000连续谱光学深度分布的贡献函数及形成深度随波长的变化。计算结果表明:磁光效应的存在给该线横向磁场定标参数Q、U的形成深度的确定带来一定的复杂性,对I和V的形成深度的确定没有明显的影响。结合北京天文台太阳磁场望远镜半宽0.15的双折射滤光器,确定所观测磁场信息的形成深度。当对日面中心观测,在滤光器调至线心时,I形成在光球层及黑子高度100公里左右,在偏离线心0.15时V分量形成高度亦如此,Q、U分量的情况较复杂。     

The challenge of predicting the occurrence of intense storms

Geomagnetic super-storms of October and November 2003 are compared in order to identify solar and interplanetary variables that influence the magnitude of geomagnetic storms. Although these superstorms (D_ST < -300 nT) are associated with high speed CMEs, their DST indices show large variation. The most intense storm of November 20, 2003 (D_St∼ - 472 nT) had its source in a comparatively small active region and was associated with a relatively weaker, M-class flare, while the others had their origins in large active regions and were associated with strong X-class flares. An attempt has been made to implement a logistic regression model for the prediction of the occurrence of intense/superintense geomagnetic storms. The model parameters (regression coefficients) were estimated from a training data-set extracted from a data-set of 64 geo-effective CMEs observed during 1996–2002. The results indicate that logistic regression models can be effectively used for predicting the occurrence of major geomagnetic storms from a set of solar and interplanetary factors. The model validation shows that 100% of the intense storms (-200 nT < D_St < -100 nT) and only 50% of the super-intense (DST < -200 nT) storms could be correctly predicted.     

Sunspot numbers based on historic records in the 1610s: Early telescopic observations by Simon Marius and others

Hoyt & Schatten (1998) claim that Simon Marius would have observed the sun from 1617 Jun 7 to 1618 Dec 31 (Gregorian calendar) all days, except three short gaps in 1618, but would never have detected a sunspot – based on a quotation from Marius in Wolf (1857), but mis‐interpreted by Hoyt & Schatten. Marius himself specified in early 1619 that for one and a half year... rather few or more often no spots could be detected... which was never observed before (Marius 1619). The generic statement by Marius can be interpreted such that the active day fraction was below 0.5 (but not zero) from fall 1617 to spring 1619 and that it was 1 before fall 1617 (since August 1611). Hoyt & Schatten cite Zinner (1952), who referred to Zinner (1942), where observing dates by Marius since 1611 are given but which were not used by Hoyt & Schatten. We present all relevant texts from Marius where he clearly stated that he observed many spots in different form on and since 1611 Aug 3 (Julian) = Aug 13 (Greg.) (on the first day together with Ahasverus Schmidnerus); 14 spots on 1612 May 30 (Julian) = Jun 9 (Greg.), which is consistent with drawings by Galilei and Jungius for that day, the latter is shown here for the first time; at least one spot on 1611 Oct 3 and/or 11 (Julian), i.e. Oct 13 and/or 21 (Greg.), when he changed his sunspot observing technique; he also mentioned that he has drawn sunspots for 1611 Nov 17 (Julian) = Nov 27 (Greg.); in addition to those clearly datable detections, there is evidence in the texts for regular observations. For all the information that can be compared to other observers, the data from Marius could be confirmed, so that his texts are highly credible. We also correct several shortcomings or apparent errors in the database by Hoyt & Schatten (1998) regarding 1612 (Harriot), 1615 (Saxonius, Tard´e), 1616 (Tard´e), 1617–1619 (Marius, Riccioli/Argoli), and Malapert (for 1618, 1620, and 1621). Furthermore, Schmidnerus, Cysat, David & Johann Fabricius, Tanner, Perovius, Argoli, and Wely are not mentioned as observers for 1611, 1612, 1618, 1620, and 1621 in Hoyt & Schatten. Marius and Schmidnerus are among the earliest datable telescopic sunspot observers (1611 Aug 3, Julian), namely after Harriot, the two Fabricius (father and son), Scheiner, and Cysat. Sunspots records by Malapert from 1618 to 1621 show that the last low‐latitude spot was seen in Dec 1620, while the first high‐latitude spots were noticed in June and Oct 1620, so that the Schwabe cycle turnover (minimum) took place around that time, which is also consistent with the sunspot trend mentioned by Marius and with naked‐eye spots and likely true aurorae. We consider discrepancies in the Hoyt & Schatten (1998) systematics, we compile the active day fractions for the 1610s, and we critically discuss very recent publications on Marius which include the following Maunder Minimum. Our work should be seen as a call to go back to the historical sources. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

R-N场中雷达回波延迟实验的后后牛顿修正

从球对称引力场中光子在赤道面上的运动微分方程出发,采用后牛顿近似方法,讨论了Reissner-Nordstr(o|¨)m度规场中雷达回波延迟实验的后后牛顿修正.通过计算给出了后牛顿以及后后牛顿的修正结果,当荷电量Q为零时,该结果适用于电中性天体,其后牛顿部分的修正与经典文献一致.文中采用的近似展开方法同样适用于讨论更高阶的修正.雷达回波的高阶修正对目前展开的高精度空间引力试验有着重要的参考价值.     

Center to limb variation of penumbral Stokes V profiles

We investigated the horizontal and the vertical component of the Evershed flow (EF). To this end, we computed average Stokes V profiles for various velocity classes in penumbrae at different heliocentric angles. Our results show that for blueshifted profiles an additional lobe with the same polarity as the spot is present in the blue side of the average Stokes V profile. The amplitude of the additional lobe grows with increasing blueshift and with increasing heliocentric angle. For small redshifts, the profiles show an additional lobe with the opposite polarity as the spot on the red side of the average Stokes V profile. Even at disk center, the original polarity of the average Stokes V profile is reversed for strong redshifts. The transition between the different types of Stokes V profiles is continuous and indicates that not only the vertical, but also the horizontal EF is a magnetized stream of plasma in a magnetic background field (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Probability distribution functions for the Sun's magnetic field

Magnetoconvection structures the Sun's magnetic field cover a vast range of scales, down to the magnetic diffusion scale that is orders of magnitude smaller than the resolution of current telescopes. The statistical properties of this structuring are governed by probability density functions (PDFs) for the flux densities and by the angular distribution functions for the orientations of the field vectors. The magnetic structuring on sub‐pixel scales greatly affects the field properties averaged over the resolution element due to the non‐linear relation between polarization and magnetic field. Here we use a Hinode SOT/SP data set for the quiet Sun disk center to explore the complex behavior of the 6301–6302 Å Stokes line profile system and identify the observables that allow us to determine the distribution functions in the most robust and least model dependent way. The angular distribution is found to be strongly peaked around the vertical direction for large flux densities but widens with decreasing flux density to become isotropic in the limit of zero flux density. The noise‐corrected PDFs for the vertical, horizontal, and total flux densities all have a narrowly peaked maximum at zero flux density that can be fitted with a stretched exponential, while the extended wings decline quadratically (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)