The potential field source surface (PFSS) equations are commonly used to model the coronal magnetic field of the Sun and other stars. As with any computational model, solving equations using a numerical scheme introduces errors due to discretisation. We present a set of tests for quantifying these errors by taking advantage of analytic solutions to the PFSS equations when the input field is proportional to a single spherical harmonic. From the spherical harmonic solutions we derive analytic equations for magnetic field lines traced through the three dimensional magnetic field solution. We propose these as a set of standard analytic solutions that all PFSS solvers should be tested against to quantify their inherent errors. We apply these tests to the pfsspy software package, showing that it reproduces spherical harmonic solutions well with a slight overestimation of the unsigned open magnetic flux. It is also successful at reproducing analytic field line equations, with errors in field line footpoints typically much less than one degree.
Aims. We aim to develop a fast and consistent extrapolation method to model multiple layers of the solar atmosphere. Methods. The new approach combines the magnetohydrostatic (MHS) extrapolation which models the solar low atmosphere in a flat box and the nonlinear force-free field (NLFFF) extrapolation which models the solar corona with a chromospheric vector magnetogram deduced from the MHS extrapolation. We test our code with a snapshot of a radiative magnetohydrodynamic simulation of a solar flare. Comparisons are conducted by several metrics quantitatively. Results. Based on a number of te…
Identifying coronal sources of L1 solar wind disturbances using the Fisk heliospheric magnetic field and potential field extrapolations during three solar minima
We present a careful assess of the forced field extrapolation using Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) magnetogram. The convergence property is checked by several metrics. The extrapolated field lines below 3600km appear to be aligned with most Halpha fibrils observed by New Vacuum Solar Telescope (NVST). In the region where magnetic energy far larger than potential energy, field lines computed by forced field extrapolation still consistent with the patterns of Halpha fibrils while non-linear force free field (NLFFF) results show large misalignment. The horiz…
In the solar corona, magnetic flux rope is believed to be a fundamental structure accounts for magnetic free energy storage and solar eruptions. Up to the present, the extrapolation of magnetic field from boundary data is the primary way to obtain fully three-dimensional magnetic information of the corona. As a result, the ability of reliable recovering coronal magnetic flux rope is important for coronal field extrapolation. In this paper, our coronal field extrapolation code (CESE-MHD-NLFFF, Jiang & Feng 2012) is examined with an analytical magnetic flux rope model proposed by Titov & Demouli…
The magnetic field shapes the structure of the solar corona but we still know little about the interrelationships between the coronal magnetic field configurations and the resulting quasi-stationary structures observed in coronagraphic images (as streamers, plumes, coronal holes). One way to obtain information on the large-scale structure of the coronal magnetic field is to extrapolate it from photospheric data and compare the results with coronagraphic images. Our aim is to verify if this comparison can be a fast method to check systematically the reliability of the many methods available to …
Magnetic field in the solar corona is usually extrapolated from photospheric vector magnetogram using a nonlinear force-free field (NLFFF) model. NLFFF extrapolation needs a considerable effort to be devoted for its numerical realization. In this paper we present a new implementation of the magnetohydrodynamics (MHD)-relaxation method for NLFFF extrapolation. The magneto-frictional approach which is introduced for speeding the relaxation of the MHD system is novelly realized by the spacetime conservation-element and solution-element (CESE) scheme. A magnetic field splitting method is used to f…
Coronal mass ejections (CMEs) and high speed solar streams serve as perturbations to the background solar wind that have major implications in space weather dynamics. Therefore, a robust framework for accurate predictions of the background wind properties is a fundamental step towards the development of any space weather prediction toolbox. In this pilot study, we focus on the implementation and comparison of various models that are critical for a steady state, solar wind forecasting framework. Specifically, we perform case studies on Carrington rotations 2053, 2082 and 2104, and compare the p…
Context. On the sun, the magnetic field vector is measured routinely only in the photosphere. By using these photospheric measurements as boundary condition, we developed the magnetohydrostatic (MHS) extrapolation to model the solar atmosphere. The model makes assumption about the relative importance of magnetic and non-magnetic forces. While the solar corona is force-free, this is not the case in photosphere and chromosphere. Aim. The model has been tested with an exact equilibria in \cite{zw18}. Here we present a more challenging and realistic test of our model with radiative MHD simulation …
Solar magnetic fields play a key role in understanding the nature of the coronal phenomena. Global coronal magnetic fields are usually extrapolated from photospheric fields, for which farside data is taken when it was at the frontside, about two weeks earlier. For the first time we have constructed the extrapolations of global magnetic fields using frontside and artificial intelligence (AI)-generated farside magnetic fields at a near-real time basis. We generate the farside magnetograms from three channel farside observations of Solar Terrestrial Relations Observatory (STEREO) Ahead (A) and Be…
The solar atmosphere being magnetic in nature, the understanding of the structure and evolution of the magnetic field in different regions of the solar atmosphere has been an important task over the past decades. This task has been made complicated by the difficulties to measure the magnetic field in the corona, while it is currently known with a good accuracy in the photosphere and/or chromosphere. Thus, to determine the coronal magnetic field, a mathematical method has been developed based on the observed magnetic field. This is the so-called magnetic field extrapolation technique. This tech…
We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and Démoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version, having a parabolic current density profile, is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the i…
Chromospheric magnetic field extrapolations reveal the flux-rope configuration of a solar filament
High Altitude Observatory, NSF National Center for Atmospheric Research（美国国家大气研究中心高空观测站）；Institute of Physics, University of Graz（格拉茨大学物理研究所）；National Solar Observatory（美国国家太阳天文台）；School of Electrical and Electronic Engineering, University of Sheffield（谢菲尔德大学电气与电子工程学院）；Department of Astronomy, Eötvös Loránd University（罗兰大学天文学系）；Gyula Bay Zoltán Solar Observatory (GSO), Hungarian Solar Physics Foundation (HSPF)（久洛·巴约·佐尔坦太阳观测站（匈牙利太阳物理基金会））；Solar Physics and Space Plasma Research Centre (SP2RC), School of Mathematics and Statistics, The University of Sheffield（谢菲尔德大学数学与统计学院太阳物理与空间等离子体研究中心）；Kanzelhöhe Observatory for Solar and Environmental Research, University of Graz（格拉茨大学卡恩泽霍厄太阳能与环境研究观测站）
We use rotation stereoscopy to estimate the height of a steady-state solar feature relative to the photosphere, based on its apparent motion in the image plane recorded over several days of observation. The stereoscopy algorithm is adapted to work with either one- or two-dimensional data (i.e. from images or from observations that record the projected position of the source along an arbitrary axis). The accuracy of the algorithm is tested on simulated data, and then the algorithm is used to estimate the coronal radio source heights associated with the active region NOAA 10956, based on multifr…
Due to the absence of direct measurement, the magnetic field in the solar corona is usually extrapolated from the photosphere in numerical way. At the moment, the nonlinear force-free field (NLFFF) model dominates the physical models for field extrapolation in the low corona. Recently we have developed a new NLFFF model with MHD relaxation to reconstruct the coronal magnetic field. This method is based on CESE--MHD model with the conservation-element/solution-element (CESE) spacetime scheme. In this paper, we report the application of the CESE--MHD--NLFFF code to \SDO/HMI data with magnetogram…
Distribution of magnetic helicity and energy with height in solar atmosphere
State Key Laboratory of Solar Activity and Space Weather, National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台太阳活动与空间天气国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Two extrapolation models of the solar coronal magnetic field are compared using magnetogram data from the SDO/HMI instrument. The two models, a horizontal current-current sheet-source surface (HCCSSS) model and a potential field-source surface (PFSS) model differ in their treatment of coronal currents. Each model has its own critical variable, respectively the radius of a cusp surface and a source surface, and it is found that adjusting these heights over the period studied allows better fit between the models and the solar open flux at 1 AU as calculated from the Interplanetary Magnetic Field…
Magnetic reconnection is one of the primary mechanisms for triggering solar eruptive events, but direct observation of its rapid process has been of challenge. In this Letter we present, using a nonlinear force-free field (NLFFF) extrapolation technique, a visualization of field line connectivity changes resulting from tether-cutting reconnection over about 30 minutes during the 2011 February 13 M6.6 flare in NOAA AR 11158. Evidence for the tether-cutting reconnection was first collected through multiwavelength observations and then by the analysis of the field lines traced from positions of f…
For the extrapolation of magnetic fields into the solar corona from measurements taken in the photosphere (or chromosphere) force-free magnetic fields are typically used. This does not take into account that the lower layers of the solar atmosphere are not force-free. While some numerical extrapolation methods using magnetohydrostatic magnetic fields have been suggested, a complementary and numerically comparatively cheap method is to use analytical magnetohydrostatic equilibria to extrapolate the magnetic field. In this paper, we present a new family of solutions for a special class of analyt…
Coronal magnetic fields are responsible for the onset of solar flares and solar eruptions. However, the type of magnetic field parameters that can be used to measure the critical condition for a solar eruption is still unclear. As an effort to understand the possible condition for a solar flare, we have examined the non-dimensional parameter $κ$ introduced by Ishiguro & Kusano (2017), which contains information about magnetic twist distribution and magnetic flux in an active region (AR). We introduce a new parameter $κ^\ast$, as a proxy for $κ$, and we have analyzed the evolution of $κ^\ast$ d…
Extrapolations of solar photospheric vector magnetograms into three-dimensional magnetic fields in the chromosphere and corona are usually done under the assumption that the fields are force-free. The field calculations can be improved by preprocessing the photospheric magnetograms. We compare two preprocessing methods presently in use, namely the methods of Wiegelmann et al. (2006) and Fuhrmann et al. (2007). The two preprocessing methods were applied to a recently observed vector magnetogram. We examine the changes in the magnetogram effected by the two preprocessing algorithms. Furthermore,…
Understanding the mechanism(s) of the solar wind acceleration is important in astrophysics and geophysics. A promising model of the solar wind acceleration is known as the wave/turbulence-driven (WTD) model, in which Alfvén waves feed energy to the solar wind. In this study, we tested the WTD model with global measurement of wind speed from interplanetary scintillation (IPS) observations. For Carrington rotations in minimal and maximal activity phases, we selected field lines calculated by the potential-field source-surface method in high- and mid-latitudes and compared the simulated and obser…
In recent decades our understanding of solar active regions (ARs) has improved substantially due to observations made with better angular resolution and wider spectral coverage. While prior AR observations have shown that these structures were always brighter than the quiet Sun at centimeter wavelengths, recent observations at millimeter and submillimeter wavelengths have shown ARs with well defined dark umbrae. Given this new information, it is now necessary to update our understanding and models of the solar atmosphere in active regions. In this work, we present a data-constrained model of t…
Modeling the interface region between solar photosphere and corona is challenging, because the relative importance of magnetic and plasma forces change by several orders of magnitude. While the solar corona can be modeled by the force-free assumption, we need to take care about plasma forces (pressure gradient and gravity) in photosphere and chromosphere, here within the magneto-hydro-static (MHS) model. We solve the MHS equations with the help of an optimization principle and use vector magnetogram as boundary condition. Positive pressure and density are ensured by replacing them with two new…
In the solar corona, magnetic helicity slowly and continuously accumulates in response to plasma flows tangential to the photosphere and magnetic flux emergence through it. Analyzing this transfer of magnetic helicity is key for identifying its role in the dynamics of active regions (ARs). The connectivity-based helicity flux density method was recently developed for studying the 2D and 3D transfer of magnetic helicity in ARs. The method takes into account the 3D nature of magnetic helicity by explicitly using knowledge of the magnetic field connectivity, which allows it to faithfully track th…
Reliable measurements of the solar magnetic field are still restricted to the photosphere, and our present knowledge of the three-dimensional coronal magnetic field is largely based on extrapolation from photospheric magnetogram using physical models, e.g., the nonlinear force-free field (NLFFF) model as usually adopted. Most of the currently available NLFFF codes have been developed with computational volume like Cartesian box or spherical wedge while a global full-sphere extrapolation is still under developing. A high-performance global extrapolation code is in particular urgently needed con…
We present a new improved version of our force-free electrodynamics (FFE) numerical code in spherical coordinates that extrapolates the magnetic field in the inner solar corona from a photospheric vector magnetogram. The code satisfies the photospheric boundary condition and the condition divB=0 to machine accuracy. The performance of our method is evaluated with standard convergence parameters, and is found to be comparable to that of other nonlinear force-free extrapolations.
Possibilities in principle for satisfactory removal of the 180-azimuthal ambiguity in the transverse field of vector magnetograms and the extrapolation of magnetic fields independently of their position on the solar disk are shown. Revealed here is an exact correspondence between the estimated field and the nonpotential loop structure on the limb. The Metropolis's algorithm modified to work in spherical geometry is used to resolve the azimuthal ambiguity. Based on a version of the optimization method from Rudenko and Myshyakov (2009), we use corrected magnetograms as boundary conditions for ma…
We have performed numerical magnetohydrodynamic (MHD) simulations of two closed active regions (AR). The input magnetic field values were the coronal magnetic field computed as extrapolation coronal from observations of the photospheric magnetic field. The studied active regions, NOAA AR12565 and AR12567, were registered as different bipolar region. Our investigation, the 3D coronal extrapolations, as well as the numerical MHD experiments, revealed that actually they evolved together as a quadrupolar active region. The second region emerged later under the loops system of AR12565 and separated…
We analyze high-resolution spectropolarimetric observations of a flux emerging region (FER) in order to understand its magnetic and kinematic structure. Our spectropolarimetric observations in the He I 1083.0 nm spectral region of a FER are recorded with GRIS at the 1.5 m aperture GREGOR telescope. A Milne-Eddington based inversion code was employed to extract the photospheric information of the Si I spectral line, whereas the He I triplet line was analyzed with the Hazel inversion code, which takes into account the joint action of the Hanle and the Zeeman effect. The spectropolarimetric analy…
Extrapolation codes in Cartesian geometry for modelling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) on board solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS). We use Helioseismic and Magnetic Imager and Vector Sp…
Force-free extrapolations are widely used to study the magnetic field in the solar corona based on surface measurements. The extrapolations assume that the ratio of internal energy of the plasma to magnetic energy, the plasma-beta is negligible. Despite the widespread use of this assumption observations, models, and theoretical considerations show that beta is of the order of a few percent to more than 10%, and thus not small. We investigate what consequences this has for the reliability of extrapolation results. We use basic concepts starting with the force and the energy balance to infer rel…
Stellar mass loss rates are an important input ingredient for stellar evolution models since they determine stellar evolution parameters such as stellar spin-down and increase in stellar luminosity through the lifetime of a star. Due to the lack of direct observations of stellar winds from Sun-like stars stellar X-ray luminosity and stellar level of activity are commonly used as a proxy for estimating stellar mass loss rates. However, such an intuitive activity --- mass loss rate relation is not well defined. In this paper, I study the mass loss rate of the Sun as a function of its activity le…
The "solar-stellar connection" began as a relatively small field of research focused on understanding the processes that generate magnetic field in stars and which sometimes lead to a cyclic pattern of long-term variability in activity, as demonstrated by our Sun. This area of study has recently become more broadly pertinent to questions of exoplanet habitability and exo-space weather, as well as stellar evolution. In contrast to other areas of stellar research, individual stars in the solar-stellar connection often have a distinct identity and character in the literature, due primarily to the…
Refinement of global coronal and interplanetary magnetic field extrapolations constrained by remote-sensing and in-situ observations at the solar minimum
针对太阳磁场外推中的 Open Flux Problem，提出三个评估参数结合遥感与就地观测约束日冕和行星际磁场，确定了太阳极小期 PFSS+PFCS 和 CSSS 模型的最优自由参数，发现使用 HMI 综观图可缓解该问题。
The magnetic field plays an essential role in the initiation and evolution of different solar phenomena in the corona. The structure and evolution of the 3D coronal magnetic field are still not very well known. A way to get the 3D structure of the coronal magnetic field is by performing magnetic field extrapolations from the photosphere to the corona. In previous work, it was shown that by prescribing the 3D reconstructed loops' geometry, the magnetic field extrapolation finds a solution with a better agreement between the modeled field and the reconstructed loops. Also, it improves the qualit…
Energetics and Emission in a Simulated Solar Flare Initialised by a Non-Force Free Magnetic Field
University of Hertfordshire（赫特福德大学）；Statkraft AS（斯塔特勒克公司）；University of Oslo（奥斯陆大学）；Université Paris-Saclay（巴黎萨克雷大学）；Université Paris Cité（巴黎西岱大学）；CEA（法国原子能和替代能源委员会）；CNRS（法国国家科学研究中心）；University of Manchester（曼彻斯特大学）；New Jersey Institute of Technology（新泽理工学院）
What Determines the Brightness of the Magnetically Open Solar Corona?: Insights from Three-dimensional Radiative Magnetohydrodynamic Simulations and Observations
Solar twins are stars of key importance to the field of astronomy and offer a multitude of science applications. Only a small number ($\lesssim200$) of solar twins are known today, all of which are relatively close to our Sun ($\lesssim800\,pc$). The goal of our Survey for Distant Solar Twins (SDST) is to identify many more solar twin and solar analogue stars out to much larger distances ($\sim4\,kpc$). In this paper, we present a new method to identify solar twins using relatively low $S/N$, medium resolving power ($R\sim 28{,}000$) spectra that will be typical of such distant targets observe…
Variations in the propagation of globally-propagating disturbances (commonly called "EIT waves") through the low solar corona offer a unique opportunity to probe the plasma parameters of the solar atmosphere. Here, high-cadence observations of two "EIT wave" events taken using the Atmospheric Imaging Assembly (AIA) instrument onboard the Solar Dynamics Observatory (SDO) are combined with spectroscopic measurements from the Extreme ultraviolet Imaging Spectrometer (EIS) onboard the Hinode spacecraft and used to examine the variability of the quiet coronal magnetic-field strength. The combinatio…
The 3D magnetic topology of a solar active region (NOAA 10956) was reconstructed using a linear force-free field extrapolation constrained using the twin perspectives of \emph{STEREO}. A set of coronal field configurations was initially generated from extrapolations of the photospheric magnetic field observed by the Michelson Doppler Imager (MDI) on \emph{SOHO}. Using an EUV intensity-based cost function, the extrapolated field lines that were most consistent with 171Å passband images from the Extreme UltraViolet Imager (EUVI) on \emph{STEREO} were identified. This facilitated quantitative con…
The symposium has shown the dynamism of this rapidly evolving discipline. I shall concentrate here on some highlights and some complementary informations. I conclude on open questions with some perspectives on solar & stellar activity and related planets.
Simulations of magnetohydrodynamics convection in slowly rotating stars predict anti-solar differential rotation (DR) in which the equator rotates slower than poles. This anti-solar DR in the usual $αΩ$ dynamo model does not produce polarity reversal. Thus, the features of large-scale magnetic fields in slowly rotating stars are expected to be different than stars having solar-like DR. In this study, we perform mean-field kinematic dynamo modelling of different stars at different rotation periods. We consider anti-solar DR for the stars having rotation period larger than 30~days and solar-like…
The elemental composition of the Sun's hot atmosphere, the corona, shows a distinctive pattern that is different than the underlying surface, or photosphere (Pottasch 1963). Elements that are easy to ionize in the chromosphere are enhanced in abundance in the corona compared to their photospheric values. A similar pattern of behavior is often observed in the slow speed (< 500 km/s) solar wind (Meyer 1985), and in solar-like stellar coronae (Drake et al. 1997), while a reversed effect is seen in M-dwarfs (Liefke et al. 2008). Studies of the inverse effect have been hampered in the past because …
In this review, we discuss whether the present solar dynamo models can be extrapolated to explain various aspects of stellar activity. We begin with a summary of the following kinds of data for solar-like stars: (i) data pertaining to stellar cycles from Ca H/K emission over many years; (ii) X-ray data indicating hot coronal activity; (iii) starspot data (especially about giant polar spots); and (iv) data pertaining to stellar superflares. Then we describe the current status of solar dynamo modelling---giving an introduction to the flux transport dynamo model, the currently favoured model for …
Linking Solar Magnetism, Extreme Solar Particle Events and Stellar Superflares
Max Planck Institute for Solar System Research（马克斯·普朗克太阳系统研究所）；Space Physics and Astronomy Research Unit and Sodankylä Geophysical Observatory, University of Oulu（奥卢大学空间物理与天文学研究部及索丹屈莱地球物理观测站）；Institute for Space-Earth Environmental Research, Nagoya University（名古屋大学宇宙地球环境研究所）
The development of the Zeeman-Doppler Imagine (ZDI) technique has provided synoptic observations of surface magnetic fields of low-mass stars. This led the Stellar Astrophysics community to adopt modeling techniques that have been used in solar physics using solar magnetograms. However, many of these techniques have been neglected by the solar community due to their failure to reproduce solar observations. Nevertheless, some of these techniques are still used to simulate the coronae and winds of solar analogs. Here we present a comparative study between two MHD models for the solar corona and …
Modern Time-Series and Spectral Methods for Analyzing Solar and Stellar Oscillatory Signals
School of Aerospace, Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳）航天学院）；Faculty of Information Engineering and Automation, Kunming University of Science and Technology（昆明理工大学信息工程与自动化学院）
It is widely believed that loops observed in the solar atmosphere trace out magnetic field lines. However, the degree to which magnetic field extrapolations yield field lines that actually do follow loops has yet to be studied systematically. In this paper we apply three different extrapolation techniques - a simple potential model, a NLFF model based on photospheric vector data, and a NLFF model based on forward fitting magnetic sources with vertical currents - to 15 active regions that span a wide range of magnetic conditions. We use a distance metric to assess how well each of these models …
On the basis of the 30-year ago ground-based photometry and the recent Kepler space experiment there have been considered frequencies of occurrence and energetics of the solar-type stellar flares. It was concluded that frequencies of occurrence of such flares are proportional to sizes of stellar surfaces, and estimates of maximum flare radiation from the results of the ground-based photometry and space observations practically coincide.
This summary reports on papers presented at the Cool Stars-16 meeting in the splinter session "Solar and Stellar flares." Although many topics were discussed, the main themes were the commonality of interests, and of physics, between the solar and stellar flare communities, and the opportunities for important new observations in the near future.
The 2015 March 15 coronal mass ejection as one of the two that together drove the largest geomagnetic storm of solar cycle 24 so far was associated with sympathetic filament eruptions. We investigate the relations between the different filaments involved in the eruption. A surge-like small-scale filament motion is confirmed as the trigger that initiated the erupting filament with multi-wavelength observations and using a forced magnetic field extrapolation method. When the erupting filament moved to an open magnetic field region, it experienced an obvious acceleration process and was accompani…
