We use The Sun Watcher with Active Pixel System detector and Image Processing (SWAP) imager onboard the Project for Onboard Autonomy 2 (PROBA2) mission to study the evolution of large-scale EUV structures in the solar corona observed throughout Solar Cycle 24 (from 2010 to 2019). We discuss the evolution of the on-disk coronal features and at different heights above the solar surface based on EUV intensity changes. We also look at the evolution of the corona in equatorial and polar regions and compare them at different phases of the solar cycle, as well as with sunspot number evolution and with the PROBA2/Lyman-Alpha Radiometer (LYRA) signal. The main results are as follows: The three time series (SWAP on-disk average brightness, sunspot number and LYRA irradiance) are very well correlated, with correlation coefficients around 0.9. The average rotation rate of bright features at latitudes of +15, 0, and -15 degrees was around 15 degree/day throughout the period studied. A secondary peak in EUV averaged intensity at the Poles was observed on the descending phase of SC24. These peaks (at North and South poles respectively) seem to be associated with the start of the development of the (polar) coronal holes. Large-scale off-limb structures were visible from around March 2010 to around March 2016, meaning that they were absent at the minimum phase of solar activity. A fan at the North pole persisted for more than 11 Carrington rotations (February 2014 to March 2015), and it could be seen up to altitudes of 1.6 Rs.
Time profiles of solar soft X-ray microflares and structure soft X-ray solar corona thermal background are studied on RHESSI data. The observations of 2003 year are analyzed. Decrease fluxe of solar soft X-ray microflares and thermal background of solar corona in the X-ray range 2-15 kev are revealed. The new model of solar corona heating in based on this new data are suggested.
During the total solar eclipse at Akademgorodok, Siberia, Russia, in 1 August 2008, we imaged the flash spectrum with a slitless spectrograph. We have spectroscopically determined the duration of totality, the epoch of the 2nd and 3rd contacts and the duration of the flash spectrum (63 s during ingress and 48 s during egress). Here we compare the 2008 flash spectra with those that we similarly obtained from the total solar eclipse of 29 March 2006, at Kastellorizo, Greece. Any changes of the intensity of the corona emission lines, in particularly those of [Fe X] and [Fe XIV], could give us val…
We propose that coronal heating in EUV coronal plumes is weaker, not stronger, than in adjacent non-plume coronal magnetic funnels. This expectation stems from (i) the observation that an EUV plume is born as the magnetic flux at the foot of the plume's magnetic funnel becomes tightly packed together, and (ii) the observation that coronal heating in quiet regions increases in proportion to the coast-line length of the underlying magnetic network. We do not rule out the possibility that coronal heating in EUV plumes might be stronger, not weaker, but we point out how the opposite is plausible. …
The history and present state of large-scale magnetohydrodynamic (MHD) modeling of the solar corona and the solar wind with steady or quasi-steady coronal physics is reviewed. We put the evolution of ideas leading to the recognition of the existence of an expanding solar atmosphere into historical context. The development and main features of the first generation of global corona and solar wind models are described in detail. This historical perspective is also applied to the present suite of global corona and solar wind models. We discuss the evolution of new ideas and their implementation in…
Measuring the global magnetic field of the solar corona remains exceptionally challenging. The fine-scale density structures observed in white light images taken during Total Solar Eclipses (TSEs) are currently the best proxy for inferring the magnetic field direction in the corona from the solar limb out to several solar radii (Rs). We present, for the first time, the topology of the coronal magnetic field continuously between 1 and 6 Rs, as quantitatively inferred with the Rolling Hough Transform (RHT) for 14 unique eclipse coronae that span almost two complete solar cycles. We find that the…
Ludendorff coronal flattening index of the Total Solar Eclipse (TSE) on March 9, 2016, was calculated at various distances in solar radius. As a result, we obtained the coronal flattening index $\left(ε=a+b\right)$ at a distance of 2 solar radii is 0.16. The $24^{th}$ solar cycle phase based on the 2016 TSE event obtained -0.64 which showed the corona is pre-minimum type. Resulted coronal flattening index value gives a predicted maximum amplitude of the monthly sunspot number ($W_{max}$) for the $25^{th}$ solar cycle to be $70\pm65$. Therefore, the solar activity for $25^{th}$ solar cycle pred…
We revisit in more detail a model for element abundance fractionation in the solar chromosphere, that gives rise to the "FIP Effect" in the solar corona and wind. Elements with first ionization potential below about 10 eV, i.e. those that are predominantly ionized in the chromosphere, are enriched in the corona by a factor 3-4. We model the propagation of Alfven waves through the chromosphere using a non-WKB treatment, and evaluate the ponderomotive force associated with these waves. Under solar conditions, this is generally pointed upwards in the chromosphere, and enhances the abundance of ch…
The solar coronal heating is a longstanding mystery in astrophysics. Considering that the solar magnetic field is spatially inhomogeneous with considerable magnetic gradient from solar surface to the corona, this work proposes a magnetic gradient pumping (MGP) mechanism and try to explain the formation of hot plasma upflows, such as the hot type II spicules and hot plasma ejections, etc. In MGP mechanism, the magnetic gradients drive the energetic particles to move upwards from the underlying solar atmosphere and form hot upflows. These upflow energetic particles deposit in corona and make it …
Time-evolving coronal modelling of the solar maximum around the solar storms in May 2024 by COCONUT
KU Leuven（荷语鲁汶大学）；University of Maria Curie-Skłodowska（玛丽亚·居里-斯可夫多夫斯卡大学）；Von Karman Institute For Fluid Dynamics（冯·卡门流体力学研究所）；University of Oslo（奥斯陆大学）
Solar corona, the last main layer of the atmosphere of the Sun, is detectable in the EUV and X-ray. The corona is expanding into space up to millions of kilometers and is observable during the eclipse. The temperature is increasing about millions of Kelvin. The investigation of this layer is significant for solar physicists because it is dynamic and features. Active regions (AR) and solar mass ejections (CMEs) are the important features in the solar corona. In this research, the solar limb and coronal width is studied from full-disk images at $284 Å$ taken by SOHO/EIT during eleven-year period…
Magnetic fields in the sun's outer atmosphere -- the corona -- control both solar-wind acceleration and the dynamics of solar eruptions. We present the first clear observational evidence of coronal magnetic nulls in off-limb linearly polarized observations of pseudostreamers, taken by the Coronal Multichannel Polarimeter (CoMP) telescope. These nulls represent regions where magnetic reconnection is likely to act as a catalyst for solar activity. CoMP linear-polarization observations also provide an independent, coronal proxy for magnetic expansion into the solar wind, a quantity often used to …
Coronal jets are transient, collimated eruptions that occur in regions of predominantly open magnetic field in the solar corona. Our understanding of these events has greatly evolved in recent years but several open questions, such as the contribution of coronal jets to the solar wind, remain. Here we present an overview of the observations and numerical modeling of coronal jets, followed by a brief description of "next-generation" simulations that include an advanced description of the energy transfer in the corona ("thermodynamic MHD"), large spherical computational domains, and the solar wi…
We analyze data from the Solar and Heliospheric Observatory to produce global maps of coronal outflow velocities and densities in the regions where the solar wind is undergoing acceleration. The maps use UV and white light coronal data obtained from the Ultraviolet Coronagraph Spectrometer and the Large Angle Spectroscopic Coronagraph, respectively, and a Doppler dimming analysis to determine the mean outflow velocities. The outflow velocities are defined on a sphere at 2.3 Rs from Sun-center and are organized by Carrington Rotations during the solar minimum period at the start of solar cycle …
The Sun's corona has interested researchers for multiple reasons, including the search for solution for the famous coronal heating problem and a purely practical consideration of predicting geomagnetic storms on Earth. There exist numerous different theories regarding the solar corona; therefore, it is important to be able to perform comparative analysis and validation of those theories. One way that could help us move towards the answers to those problems is the search for observational methods that could obtain information about the physical properties of the solar corona and provide means f…
The solar corona, anomalously hot outer atmosphere of the Sun, is traditionally described by magnetohydrodynamic, fluid-like approach. Here we review some recent developments when, instead, a full kinetic description is used. It is shown that some of the main unsolved problems of solar physics, such as coronal heating and solar flare particle acceleration can be viewed in a new light when the small-scale, kinetic plasma description methods are used.
Coronal Mass Ejections (CMEs) contributes to the perturbation of solar wind in the heliosphere. Thus, depending on the different phases of the solar cycle and the rate of CME occurrence, contribution of CMEs to solar wind parameters near the Earth changes. In the present study, we examine the long term occurrence rate of CMEs, their speeds, angular widths and masses. We attempt to find correlation between near sun parameters, determined using white light images from coronagraphs, with solar wind measurements near the Earth from in-situ instruments. Importantly, we attempt to find what fraction…
It has been known that some solar activity indicators show a double-peak feature in their evolution through a solar cycle, which is not conspicuous in sunspot number. In this letter, we investigate the high solar dynamic activity in the declining phase of the sunspot cycle by examining the evolution of polar and low latitude coronal hole areas and the statistics of splitting and merging events of coronal holes and coronal mass ejections detected by SOHO/LASCO C3 in solar cycle 23. Although the total coronal hole area is at its maximum near the sunspot minimum, in which polar coronal holes prev…
Coronal density, temperature and heat flux distributions for the equatorial and polar corona have been deduced by Lemaire [2012] from Saito's model of averaged coronal white light (WL) brightness and polarization observations. They are compared with those determined from a kinetic collisionless/exospheric model of the solar corona. This comparison indicates rather similar distributions at large radial distances (> 7 Rs) in the collisionless region. However, rather important differences are found close to the Sun in the acceleration region of the solar wind. The exospheric heat flux is directed…
The tenuous supersonic solar wind that streams from the top of the corona passes through a natural boundary -- the Alfvén surface -- that marks the causal disconnection of individual packets of plasma and magnetic flux from the Sun itself. The Alfvén surface is the locus where the radial motion of the accelerating solar wind passes the radial Alfvén speed, and therefore any displacement of material cannot carry information back down into the corona. It is thus the natural outer boundary of the solar corona, and the inner boundary of interplanetary space. Using a new and unique motion analysis …
Knowledge of the electron density distribution in the solar corona put constraints on the magnetic field configurations for coronal modeling and on initial conditions for solar wind modeling. We work with polarized SOHO/LASCO-C2 images from the last two recent minima of solar activity (1996-1997 and 2008-2010), devoid of coronal mass ejections. The goals are to derive the 4D electron density distributions in the corona by applying a newly developed time-dependent tomographic reconstruction method and to compare the results between the two solar minima and with two magnetohydrodynamic models. F…
The plasma $β$ is important to investigate the interchanging roles of plasma and magnetic pressure in the solar atmosphere. It can help to describe features over the photosphere and their changes at different heights. The goal is to obtain the plasma $β$ variations through the solar corona during the solar cycles 23 and 24. The plasma $β$ is reconstructed in different layers of the solar atmosphere. For this purpose, we use an updated version of COronal DEnsity and Temperature (CODET) model. In this version, we selected different features in the solar atmosphere such as Quiet Sun (QS), faculae…
The global structure of solar corona observed in optical window is governed by the global magnetic field with different characteristics over solar activity cycle. Ludendorff flattening index becomes a popular measure of the global structure of solar corona as observed during eclipse. In this study, 15 digital images of solar corona from 1991 to 2016 were analyzed in order to construct the coronal flattening profiles as a function of radius. In most of the cases, the profile can be modeled with 2nd order polynomial function so that the radius with maximum flattening index ($R_{\text{max}}$) can…
Transient collimated plasma eruptions in the solar corona, commonly known as coronal (or X-ray) jets, are among the most interesting manifestations of solar activity. It has been suggested that these events contribute to the mass and energy content of the corona and solar wind, but the extent of these contributions remains uncertain. We have recently modeled the formation and evolution of coronal jets using a three-dimensional (3D) magnetohydrodynamic (MHD) code with thermodynamics in a large spherical domain that includes the solar wind. Our model is coupled to 3D MHD flux-emergence simulatio…
Coronal heating is a big question for modern astronomy. Daily measurement of 985 solar spectral irradiances (SSIs) at the spectral intervals 1-39 nm and 116-2416 nm during March 1 2003 to October 28 2017 is utilized to investigate characteristics of solar rotation in the solar atmosphere by means of the Lomb \,-\, Scargle periodogram method to calculate their power spectra. The rotation period of coronal plasma is obtained to be 26.3 days, and that of the solar atmosphere at the bottom of the photosphere modulated by magnetic structures is 27.5 days. Here we report for the first time that unex…
We present observations of the extended solar cycle activity in white-light coronagraphs, and compare them with the more familiar features seen in the Fe XIV green-line corona. We show that the coronal activity zones seen in the emission corona can be tracked high into the corona. The peak latitude of the activity, which occurs near solar maximum, is found to be very similar at all heights. But we find that the equatorward drift of the activity zones is faster at greater heights, and that during the declining phase of the solar cycle, the lower branch of activity (that associated with the curr…
Strong magnetic fields are of vital importance to the physics of the solar corona. They easily move a rarefied coronal plasma. Physical origin of the main structural element of the corona, the so-called coronal streamers, is discussed. It is shown that the reconnecting current layers inside streamers determine their large-scale structure and evolution, including creation, disruption and recovery. Small-scale (fine) magnetic fields in the photosphere experience random motion. Their reconnection appears to be an important source of energy flux for quiet-corona heating. For active-corona heating,…
Total solar eclipses (TSEs) provide a unique opportunity to quantify the properties of the K-corona (electrons), F-corona (dust) and E-corona (ions) continuously from the solar surface out to a few solar radii. We apply a novel inversion method to separate emission from the K- and F-corona continua using unpolarized total brightness (tB) observations from five 0.5 nm bandpasses acquired during the 2019 July 2 TSE between 529.5 nm and 788.4 nm. The wavelength dependence relative to the photosphere (i.e., color) of the F-corona itself is used to infer the tB of the K- and F-corona for each line-…
The most violent space weather events (eruptive solar flares and coronal mass ejections) are driven by the release of free magnetic energy stored in the solar corona. Energy can build up on timescales of hours to days, and then may be suddenly released in the form of a magnetic eruption, which then propagates through interplanetary space, possibly impacting the Earth's space environment. Can we use the observed evolution of the magnetic and velocity fields in the solar photosphere to model the evolution of the overlying solar coronal field, including the storage and release of magnetic energy …
Recent analysis of high-cadence white-light images taken by the Solar-Terrestrial RElations Observatory (STEREO) near solar maximum has revealed that outflowing density structures are released in an ubiquitous manner in the solar wind. The present study investigates whether these density fluctuations could originate from the transient heating of the low corona observed during Coronal Bright Points (CBPs). We assume that part of the intense heating measured during CBPs occurs at the coronal base of open magnetic fields that channel the forming solar wind. We employ the solar wind model MULTI-VP…
We developed a new technique for registration of the far solar corona from ground-based observations at distances comparable to those obtained from space coronagraphs. It makes possible visualization of fine details of studied objects invisible by naked eye. Here we demonstrate that streamers of the electron corona sometimes punch the dust corona and that the shape of the dust corona may vary with time. We obtained several experimental evidences that the far coronal streamers (observed directly only from the space or stratosphere) emit only in discrete regions of the visible spectrum like reso…
We aim to study excitation of the observed 5-min oscillations in the solar corona by localized pulses that are launched in the photosphere. We solve the full set of nonlinear one-dimensional Euler equations numerically for the velocity pulse propagating in the solar atmosphere that is determined by the realistic temperature profile. Numerical simulations show that an initial velocity pulse quickly steepens into a leading shock, while the nonlinear wake in the chromosphere leads to the formation of consecutive pulses. The time interval between arrivals of two neighboring pulses to a detection p…
In order to study the solar corona during eclipses, a new telescope was constructed. Three coronal images were obtained simultaneously from one objective of the telescope as the coronal radiation passed through three polarisers (whose transmission directions were turned through 0^{\circ}, 60^{\circ}, and 120^{\circ} to the chosen direction); one image without polariser was also obtained. The telescope was used to observe the solar corona during the eclipse of 1 August 2008. We obtained distributions of the polarisation brightness, K-corona brightness, degree of the K-corona polarisation and to…
The hot solar corona exists because of the balance between radiative and conductive cooling and some counteracting heating mechanism which remains one of the major puzzles in solar physics. The coronal thermal equilibrium is perturbed by magnetoacoustic waves which are abundantly present in the corona, causing a misbalance between the heating and cooling rates. Due to this misbalance, the wave experiences a back-reaction, either losing or gaining energy from the energy supply that heats the plasma, at the time scales comparable to the wave period. In particular, the plasma can be subject to wa…
Determining the mechanisms responsible for the heating of the coronal plasma and maintaining and accelerating the solar wind are long standing goals in solar physics. There is a clear need to constrain the energy, mass and momentum flux through the solar corona and advance our knowledge of the physical process contributing to these fluxes. Furthermore, the accurate forecasting of Space Weather conditions at the near-Earth environment and, more generally, the plasma conditions of the solar wind throughout the heliosphere, require detailed knowledge of these fluxes in the near-Sun corona. Here w…
Operating experience from fusion research shows how Spitzer resistivity may render ohmic heating in the chromosphere self limiting and thus serve to define the lower margin of the transition region. Its upper margin is at about 6000 K, where radiative cooling of He:H plasma decelerates sharply. The third and last stage in the proposed scheme is expansion into the tenuous plasma of space, which leads to the acceleration of ions to high energies, long recorded by spacecraft instruments. There is thus dynamic continuity all the way from the solar interior, the energy source for spinning columns i…
It is well established that the transverse MHD waves are ubiquitous in the solar corona. One of the possible mechanisms for heating both open (e.g. coronal holes) and closed (e.g. coronal loops) magnetic field regions of the solar corona is due to the MHD wave-driven turbulence. In this work, we have studied the variation in the filling factor of overdense structures in the solar corona due to the generation of the transverse MHD wave-driven turbulence. Using 3D MHD simulations, we estimate the density filling factor of an open magnetic structure by calculating the fraction of the volume occup…
Homogeneous coronal data set (HCDS) of the green corona (Fe XIV) and coronal index of the solar activity (CI) have been used to study time-latitudinal distribution in solar cycles 18-24 and compared with similar distribution of sunspots, the magnetic fields and the solar radio flux 10.7 cm. The most important results are: (a) distribution of coronal intensities related to the cycle maximum are different for individual cycles, (b) the poleward migration of the HCDS from mid latitudes in each cycle exists, even in extremely weak Cycle 24, and the same is valid for the equatorward migration (c) t…
The coronal magnetic field, despite its overwhelming importance to the physics and dynamics of the corona, has only rarely been measured. Here, the electron density maps derived from images acquired during the total solar eclipse of August 21st, 2017 are employed to demonstrate a new technique to measure the coronal magnetic fields. The strength of the coronal magnetic fields is derived with a semiempirical formula relating the plasma magnetic energy density to the gravitational potential energy. The resulting values are compared with those provided by more advanced coronal field reconstructio…
We have studied the corona as seen at the eclipses of 1878, 1900, 1901 and others. These eclipses occurred during extended sunspot minimum conditions. We compare these data with those of the recent solar minimum corona, using data from the eclipses of July 22 2009 and August 1 2008. An attempt to characterize the global solar magnetic fields is made. We speculate on the origin of the non-dipolar structure seen in the 2008 and 2009 eclipse images.
A turbulent dynamo in spherical geometry with an outer corona is simulated to study the sign of magnetic helicity in the outer parts. In agreement with earlier studies, the sign in the outer corona is found to be opposite to that inside the dynamo. Line-of-sight observations of polarized emission are synthesized to explore the feasibility of using the local reduction of Faraday depolarization to infer the sign of helicity of magnetic fields in the solar corona. This approach was previously identified as an observational diagnostic in the context of galactic magnetic fields. Based on our simula…
Radio Wave Propagation as a Probe of the Solar Corona and Solar Wind
Indian Institute of Astrophysics（印度天体物理研究所）；Indian Institute of Science Education and Research（印度科学教育与研究学院）；Physical Research Laboratory（物理研究实验室）；University of Glasgow（格拉斯哥大学）
The distribution of magnetic flux across the solar photosphere results in a complex web of coronal magnetic field structures. To understand this complexity, the magnetic skeleton of the coronal field can be calculated. The skeleton highlights the separatrix surfaces that divide the field into topologically distinct regions, allowing open-field regions on the solar surface to be located. Furthermore, separatrix surfaces and their intersections (separators) are important likely energy release sites. This paper investigates, throughout the solar cycle, the nature of coronal magnetic-field topolog…
The infrared solar spectrum contains a wealth of physical data about the Sun and is being explored using modern detectors and technology with new ground-based solar telescopes. One such instrument will be the ground-based Cryogenic Near-IR Spectro-Polarimeter of the Daniel K. Inouye Solar Telescope that will be capable of sensitive imaging of the faint infrared solar coronal spectra with full Stokes I, Q, U, and V polarization states. Highly ionized magnetic dipole emission lines have been observed in galaxies and the solar corona. Quantifying the accuracy of spectral inversion procedures requ…
We propose a new model for explaining the observations of more than mass proportional heating of heavy ions in the polar solar corona. We point out that a large number of small scale intermittent shock waves can be present in the solar corona. The energization mechanism is, essentially, the ion reflection off supercritical quasi-perpendicular collisionless shocks in the corona and the subsequent acceleration by the motional electric field ${\bf E} = - (1/c) {\bf V} \times {\bf B}$. The acceleration due to ${\bf E}$ is perpendicular to the magnetic field, in agreement with observations, and is …
Large coronal loops around one solar radius in altitude are an important connection between the solar wind and the low solar corona. However, their plasma properties are ill-defined as standard X-ray and UV techniques are not suited to these low-density environments. Diagnostics from type J solar radio bursts at frequencies above 10 MHz are ideally suited to understand these coronal loops. Despite this, J-bursts are less frequently studied than their type III cousins, in part because the curvature of the coronal loop makes them unsuited for using standard coronal density models. We used LOw-Fr…
Solar coronal loops are commonly subject to oscillations. Observations of coronal oscillations are used to infer physical properties of the coronal plasma using coronal seismology. Excitation and evolution of oscillations in coronal loops is typically studied using highly idealised models of magnetic flux-tubes. In order to improve our understanding of coronal oscillations, it is necessary to consider the effect of realistic magnetic field topology and evolution. We study excitation and evolution of coronal oscillations in three-dimensional self-consistent simulations of solar atmosphere spann…
Presence of Solar Neutral Atom Corona and Coronal Heating
Yunnan Observatories, CAS（中国科学院云南天文台）；School of Space and Astronomy, Nanjing University（南京大学空间与天文学院）；Institute of Optics and Electronics, CAS（中国科学院光电技术研究所）；Department of Physics, Chinese University of Hong Kong（香港中文大学物理系）；Zhangjiang Laboratory（张江实验室）
The large availability and rich spectral coverage of today's observational data of the solar corona, and the high spatial and temporal resolution of many instruments, has enabled the evolution of three-dimensional (3D) physical models to a great level of detail. However, the 3D information provided by the data is rather limited as every instrument observes from a single angle of vision, or two at the most in the case of the STEREO mission. Two powerful available observational techniques to infer detailed 3D information of the solar corona from empirical data are stereoscopy and tomography. In …
Solar five-minute oscillations have been detected in the power spectra of two six-day time intervals from soft X-ray measurements of the Sun observed as a star using the Extreme Ultraviolet Spectrophotometer (ESP) onboard the Solar Dynamics Observatory (SDO) Extreme Ultraviolet Variability Experiment (EVE). The frequencies of the largest amplitude peaks were found matching within 3.7 microHz the known low-degree (l = 0--3) modes of global acoustic oscillations, and can be explained by a leakage of the global modes into the corona. Due to strong variability of the solar atmosphere between the p…
We study the connections between the sun's convection zone and the evolution of the solar wind and corona. We let the magnetic fields generated by a 2.5D axisymmetric kinematic dynamo code (STELEM) evolve in a 2.5D axisymmetric coronal isothermal MHD code (DIP). The computations cover an 11 year activity cycle. The solar wind's asymptotic velocity varies in latitude and in time in good agreement with the available observations. The magnetic polarity reversal happens at different paces at different coronal heights. Overall sun's mass loss rate, momentum flux and magnetic braking torque vary con…
Understanding how the solar corona is structured is of fundamental importance to determining how the Sun's upper atmosphere is heated to high temperatures. Recent spectroscopic studies have suggested that an instrument with a spatial resolution of 200km or better is necessary to resolve coronal loops. The High Resolution Coronal Imager (Hi-C) achieved this performance on a rocket flight in July 2012. We use Hi-C data to measure the Gaussian widths of 91 loops observed in the solar corona and find a distribution that peaks at about 270km. We also use Atmospheric Imaging Assembly (AIA) data for …
The dynamics of the solar wind depends intrinsically on the structure of the global solar magnetic field, which undergoes fundamental changes over the 11-yr solar cycle. For instance, the wind terminal velocity is thought to be anti-correlated with the expansion factor, a measure of how the magnetic field varies with height in the solar corona, usually computed at a fixed height ($\approx 2.5 R_{\odot}$, the source surface radius which approximates the distance at which all magnetic field lines become open). However, the magnetic field expansion affects the solar wind in a more detailed way, i…
