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

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

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

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

Solar wind speed and its acceleration inferred using the interplanetary scintillation method in carrington rotation 1753

Solar wind speeds (SWSs) estimated by interplanetary scintillation (IPS) observations during Carrington rotation 1753 are projected onto the so-called source-surface of 2.5 solar radii along magnetic field lines in interplanetary space. The following two working hypotheses are examined from different points of view: (1) The SWS is a weighted mean along the line of sight to a radio source; the weight for the SWS depends on the distance from theP-point, the closest approach to the Sun on the line of sight. (2) The weighting function has a very sharp peak at theP-point, so that the SWS shows a real solar wind speed at theP-point. In both the two cases, the SWSs projected onto the source surface are further projected onto the photosphere along magnetic field lines in the corona. Footpoints of these field lines are inferred as photospheric source regions of the solar wind. The intensity of the Hei (1083 nm) absorption line (HEI) in the chromosphere corresponding to these photospheric sources is interpolated from observational data. The weighted mean of the HEI is calculated in case 1. The HEI corresponding to theP-point is used in case 2. The SWS is compared with the HEI in both the two cases. It is found that the correlation between the SWS and the HEI is better in case 2 than in case 1. It is further inferred by correlation analysis between the SWS and the HEI that the solar wind is accelerated within 27 solar radii on average. Although the data examined in this paper were limited to just one solar rotation, these results suggest that the SWS estimated by the IPS technique corresponds to the solar wind speed near theP-point and the weighting function along the line of sight may have a very sharp peak near theP-point.     

Synoptic Maps of Solar Wind: Comparison of IPS Data and the NOAA/SEC Version of the Wang and Sheeley Model

Since the 1970s, the Solar-Terrestrial Environment Laboratory, Japan, has been publishing synoptic maps of solar wind velocity prepared using the technique of interplanetary scintillation. These maps, known as V-maps, are useful to study the global distribution of solar wind in the heliosphere. As the Earth-orbiting satellites are unable to probe regions outside the ecliptic, it is important to exploit the scope of interplanetary scintillation to study the solar wind properties at these regions and their relation with coronal features. It has been shown by Wang and Sheeley that there exists an inverse correlation between rate of magnetic flux expansion and the solar wind velocity. The NOAA/Space Environment Center daily updated version of the Wang and Sheeley model has been used to produce synoptic maps of solar wind velocity and magnetic field polarity for individual Carrington rotations. The predictions of the model at 1 AU have been found to be in good agreement with the observed values of the same. The present work is a comparison of the synoptic maps on the source surface using the interplanetary scintillation measurements from Japan and the NOAA/SEC version of the Wang and Sheeley model. The two results agree near the equatorial regions and the slow solar wind locations are consistent most of the times. However, at higher latitudes within ±60°, the wind velocities differ considerably. In the Wang and Sheeley model the highest speed obtained is 600 km s^–1 whereas in the IPS results velocities as high as 800 km s^–1 have been detected. The paper discusses the possible causes for this discrepancy and suggestion to improve the agreement between the two results.     

Solar Wind Forecasting with Coronal Holes

An empirical model for forecasting solar wind speed related geomagnetic events is presented here. The model is based on the estimated location and size of solar coronal holes. This method differs from models that are based on photospheric magnetograms (e.g., Wang–Sheeley model) to estimate the open field line configuration. Rather than requiring the use of a full magnetic synoptic map, the method presented here can be used to forecast solar wind velocities and magnetic polarity from a single coronal hole image, along with a single magnetic full-disk image. The coronal hole parameters used in this study are estimated with Kitt Peak Vacuum Telescope He I 1083 nm spectrograms and photospheric magnetograms. Solar wind and coronal hole data for the period between May 1992 and September 2003 are investigated. The new model is found to be accurate to within 10% of observed solar wind measurements for its best 1-month period, and it has a linear correlation coefficient of ∼0.38 for the full 11 years studied. Using a single estimated coronal hole map, the model can forecast the Earth directed solar wind velocity up to 8.5 days in advance. In addition, this method can be used with any source of coronal hole area and location data.     

Interplanetary Signatures of Unipolar Streamers and the Origin of the Slow Solar Wind

Unipolar streamers (also known as pseudo-streamers) are coronal structures that, at least in coronagraph images, and when viewed at the correct orientation, are often indistinguishable from dipolar (or “standard”) streamers. When interpreted with the aid of a coronal magnetic field model, however, they are shown to consist of a pair of loop arcades. Whereas dipolar streamers separate coronal holes of the opposite polarity and whose cusp is the origin of the heliospheric current sheet, unipolar streamers separate coronal holes of the same polarity and are therefore not associated with a current sheet. In this study, we investigate the interplanetary signatures of unipolar streamers. Using a global MHD model of the solar corona driven by the observed photospheric magnetic field for Carrington rotation 2060, we map the ACE trajectory back to the Sun. The results suggest that ACE fortuitously traversed through a large and well-defined unipolar streamer. We also compare heliospheric model results at 1 AU with ACE in-situ measurements for Carrington rotation 2060. The results strongly suggest that the solar wind associated with unipolar streamers is slow. We also compare predictions using the original Wang–Sheeley (WS) empirically determined inverse relationship between solar wind speed and expansion factor. Because of the very low expansion factors associated with unipolar streamers, the WS model predicts high speeds, in disagreement with the observations. We discuss the implications of these results in terms of theories for the origin of the slow solar wind. Specifically, premises relying on the expansion factor of coronal flux tubes to modulate the properties of the plasma (and speed, in particular) must address the issue that while the coronal expansion factors are significantly different at dipolar and unipolar streamers, the properties of the measured solar wind are, at least qualitatively, very similar.     

Solar activity and the variations of the geomagnetic Kp-index

A careful correlation analysis is made between various types of solar activity as observed at photospheric levels and the daily variations of the geomagnetic K_p-index which, in turn, is a measure of the solar wind speed. We find that in no case does a significant enough correlation exist to pin-point a physical relation between some aspect of photospheric activity and the solar wind speed. It is concluded that the physical processes that do determine the wind speed occur at coronal heights.     

Polarity Reversal Time of the Magnetic Dipole Component of the Sun in Solar Cycle 24

The Sun’s general magnetic field has shown polarity reversal three times during the last three solar cycles. We attempt to estimate the upcoming polarity reversal time of the solar magnetic dipole by using the coronal field model and synoptic data of the photospheric magnetic field. The scalar magnetic potential of the coronal magnetic field is expanded into a spherical harmonic series. The long-term variations of the dipole component ( $g^{0}_{1}$ ) calculated from the data of National Solar Observatory/Kitt Peak and Wilcox Solar Observatory are compared with each other. It is found that the two $g^{0}_{1}$ values show a similar tendency and an approximately linear increase between the Carrington rotation periods CR 2070 and CR 2118. The next polarity reversal is estimated by linear extrapolation to be between CR 2132.2 (December 2012) and CR2134.8 (March 2013).     

Solar wind velocity and normalized scintillation index from single-station IPS observations

The recently refurbished Ooty Radio Telescope in southern India was used in a two-month campaign of interplanetary scintillation (IPS) observations in collaboration with the Cambridge IPS array in England during April–May 1992. The unique feature of this campaign was that, for the first time, scintillation enhancements were predicted in real time by observing solar events on 7–8 May, 1992 and then detected at both Ooty and Cambridge. Also, for the first time, high spatial resolution ( 100 sources sr^–1) solar wind all-sky velocity maps were obtained at Ooty. Good consistency is found between the IPS observations from both observatories andin-situ shocks detected at Earth by IMP-8.Yohkoh soft X-ray images were used to infer the generation of a coronal mass ejection on 7 May, 1992.     

Interfacing MHD Single Fluid and Kinetic Exospheric Solar Wind Models and Comparing Their Energetics

An exospheric kinetic solar wind model is interfaced with an observation-driven single-fluid magnetohydrodynamic (MHD) model. Initially, a photospheric magnetogram serves as observational input in the fluid approach to extrapolate the heliospheric magnetic field. Then semi-empirical coronal models are used for estimating the plasma characteristics up to a heliocentric distance of 0.1 AU. From there on, a full MHD model that computes the three-dimensional time-dependent evolution of the solar wind macroscopic variables up to the orbit of Earth is used. After interfacing the density and velocity at the inner MHD boundary, we compare our results with those of a kinetic exospheric solar wind model based on the assumption of Maxwell and Kappa velocity distribution functions for protons and electrons, respectively, as well as with in situ observations at 1 AU. This provides insight into more physically detailed processes, such as coronal heating and solar wind acceleration, which naturally arise from including suprathermal electrons in the model. We are interested in the profile of the solar wind speed and density at 1 AU, in characterizing the slow and fast source regions of the wind, and in comparing MHD with exospheric models in similar conditions. We calculate the energetics of both models from low to high heliocentric distances.     

Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

Solar polar spin-down

An explanation for the solar differential rotation is proposed that makes use of angular momentum transfer in the solar wind and corona. Evidence suggests that for most of the solar cycle, the solar wind is connected by magnetic field lines to high heliographic latitudes on the Sun.Thus the angular momentum lost to the solar wind would present a preferential drag to the photospheric material at high heliographic latitudes. It is shown that this drag is sufficient to offset the restoring forces of the Sun's subsurface magnetic field. In fact, the subsurface magnetic field and differential rotation are thought to grow until the stresses are sufficient to balance the torque induced by the solar wind. The present level of differential rotation and solar activity may be maintained by an intricate feedback mechanism involving the whole solar activity cycle.A power calculation based upon this model suggests the Sun's core rotates with a period of between 0.5 and 5 days. Furthermore, this view requires a major change in present theory of solar magnetic field generation.     

High resolution mapping of the magnetic field of the solar corona

High resolution KPNO magnetograph measurements of the line-of-sight component of the photospheric magnetic field over the entire dynamic range from 0 to 4000 gauss are used as the basic data for a new analysis of the photospheric and coronal magnetic field distributions. The daily magnetograph measurements collected over a solar rotation are averaged onto a 180 × 360 synoptic grid of equal-area elements. With the assumption that there are no electric currents above the photospheric level of measurement, a unique solution is determined for the global solar magnetic field. Because the solution is in terms of an expansion in spherical harmonics to principal index n = 90, the global photospheric magnetic energy distribution can be analyzed in terms of contributions of different scale-size and geometric pattern. This latter procedure is of value (1) in guiding solar dynamo theories, (2) in monitoring the persistence of the photospheric field pattern and its components, (3) in comparing synoptic magnetic data of different observatories, and (4) in estimating data quality. Different types of maps for the coronal magnetic field are constructed (1) to show the strong field at different resolutions, (2) to trace the field lines which open into interplanetary space and to locate their photospheric origins, and (3) to map in detail coronal regions above (specified) limited photospheric areas.The National Center for Atmospheric Research is sponsored by the National Science foundation.Kitt Peak National Observatory is operated by the Association of Universities for Research in Astronomy, Inc. Under contract with the National Science Foundation.     

Magnetic field configurations associated with fast solar wind

In this paper, we consider the implications of the observed inverse correlation between solar wind speed at Earth and the expansion rate of the Sun-Earth flux tube as it passes through the corona. We find that the coronal expansion rate depends critically on the large-scale photospheric field distribution around the footpoint of the flux tube, with the smallest expansions occurring in tubes that are rooted near a local minimum in the field. This suggests that the fastest wind streams originate from regions where large coronal holes are about to break apart and from the facing edges of adjacent like-polarity holes, whose field lines converge as they transit the corona. These ideas lead to the following predictions:

1. Weak holes and fragmentary holes can be sources of very fast wind.
2. Fast wind with steep latitudinal gradients may be generated where the field lines from the polar hole and a lower-latitude hole of like polarity converge to form a mid-latitude ‘apex’.
3. The fastest polar wind should occur shortly after sunspot maximum, when trailing-polarity flux converges onto the poles and begins to establish the new polar fields.

     

Magnetic fields and the structure of the solar corona

Several different mathematical methods are described which use the observed line-of-sight component of the photospheric magnetic field to determine the magnetic field of the solar corona in the current-free (or potential-field) approximation. Discussed are (1) a monopole method, (2) a Legendre polynomial expansion assuming knowledge of the radial photospheric magnetic field, (3) a Legendre polynomial expansion obtained from the line-of-sight photospheric field by a least-meansquare technique, (4) solar wind simulation by zero-potential surfaces in the corona, (5) corrections for the missing flux due to magnetograph saturation. We conclude (1) that the field obtained from the monopole method is not consistent with the given magnetic data because of non-local effects produced by monopoles on a curved surface, (2) that the field given by a Legendre polynomial (which is fitted to the measured line-of-sight magnetic field) is a rigorous and self-consistent solution with respect to the available data, (3) that it is necessary to correct for the saturation of the magnetograph (at about 80 G) because fields exceeding 80 G provide significant flux to the coronal field, and (4) that a zero-potential surface at 2.5 solar radii can simulate the effect of the solar wind on the coronal magnetic field.     

Differential Rotation of the Solar Corona from Magnetic Field Data

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

Global Solar Free Magnetic Energy and Electric Current Density Distribution of Carrington Rotation 2124

Solar eruptive phenomena, like flares and coronal mass ejections (CMEs), are governed by magnetic fields. To describe the structure of these phenomena one needs information on the magnetic flux density and the electric current density vector components in three dimensions throughout the atmosphere. However, current spectro-polarimetric measurements typically limit the determination of the vector magnetic field to only the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field for global solar atmosphere using nonlinear force-free field (NLFFF) extrapolation codes implemented to a synoptic maps of photospheric vector magnetic field synthesized from the Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) as boundary condition. Using the resulting three-dimensional magnetic field, we calculate the three-dimensional electric current density and magnetic energy throughout the solar atmosphere for Carrington rotation 2124 using our global extrapolation code. We found that spatially, the low-lying, current-carrying core field demonstrates a strong concentration of free energy in the active-region core, from the photosphere to the lower corona (about 70 Mm). The free energy density appears largely co-spatial with the electric current distribution.     

On Long-Term Periodicities In The Solar-Wind Ion Density and Speed Measurements During The Period 1973–2000

The ultra-low frequency power spectra (from 1 nHz to 10 Hz) for the solar wind ion density (N) and speed (SWS) measurements taken near 1 AU, have been examined during the period 1973–2000. Although the spectrum shows remarkable peaks at the wavelengths 0.5, 0.7, 1.0, 1.3 years, additional significant peaks of 2.6 yr and 5.6 yr for N and 9.6 yr for SWS are also found. Possible causes are discussed. The 9.6-yr period is not related to the period of the solar activity cycle, but there is some indication of an association with the coronal hole variations in the southern hemisphere of the Sun. The averages of solar wind ion density showed a periodic variation with three nearly equal peaks at intervals of 5.1±0.2 yr. The long-term enhancements in SWS reflect nearly stable variations and a continuously-existing feature in the heliosphere. The observed long periodicities in both N and SWS spectra may be strongly related to, or organized by, the observed variations in the coronal hole areas between northern and southern hemispheres of the Sun. The timing of the maximum peaks in solar ion densities and speeds spectrum is predicted.     

Modeling the Global Coronal Field with Simulated Synoptic Magnetograms from Earth and the Lagrange Points $L_{3}$, L4$L_{4}$, and L5$L_{5}$

The solar photospheric magnetic flux distribution is key to structuring the global solar corona and heliosphere. Regular full-disk photospheric magnetogram data are therefore essential to our ability to model and forecast heliospheric phenomena such as space weather. However, our spatio-temporal coverage of the photospheric field is currently limited by our single vantage point at/near Earth. In particular, the polar fields play a leading role in structuring the large-scale corona and heliosphere, but each pole is unobservable for \({>}\,6\) months per year. Here we model the possible effect of full-disk magnetogram data from the Lagrange points \(L_{4}\) and \(L_{5}\), each extending longitude coverage by \(60^{\circ}\). Adding data also from the more distant point \(L_{3}\) extends the longitudinal coverage much further. The additional vantage points also improve the visibility of the globally influential polar fields. Using a flux-transport model for the solar photospheric field, we model full-disk observations from Earth/\(L_{1}\), \(L_{3}\), \(L_{4}\), and \(L_{5}\) over a solar cycle, construct synoptic maps using a novel weighting scheme adapted for merging magnetogram data from multiple viewpoints, and compute potential-field models for the global coronal field. Each additional viewpoint brings the maps and models into closer agreement with the reference field from the flux-transport simulation, with particular improvement at polar latitudes, the main source of the fast solar wind.     

The Global Context of Solar Activity During the Whole Heliosphere Interval Campaign

The Whole Heliosphere Interval (WHI) was an international observing and modeling effort to characterize the 3-D interconnected ??heliophysical?? system during this solar minimum, centered on Carrington Rotation 2068, March 20??C?April 16, 2008. During the latter half of the WHI period, the Sun presented a sunspot-free, deep solar minimum type face. But during the first half of CR 2068 three solar active regions flanked by two opposite-polarity, low-latitude coronal holes were present. These departures from the quiet Sun led to both eruptive activity and solar wind structure. Most of the eruptive activity, i.e., flares, filament eruptions and coronal mass ejections (CMEs), occurred during this first, active half of the interval. We determined the source locations of the CMEs and the type of associated region, such as active region, or quiet sun or active region prominence. To analyze the evolution of the events in the context of the global solar magnetic field and its evolution during the three rotations centered on CR 2068, we plotted the CME source locations onto synoptic maps of the photospheric magnetic field, of the magnetic and chromospheric structure, of the white light corona, and of helioseismological subsurface flows. Most of the CME sources were associated with the three dominant active regions on CR 2068, particularly AR 10989. Most of the other sources on all three CRs appear to have been associated with either isolated filaments or filaments in the north polar crown filament channel. Although calculations of the flux balance and helicity of the surface magnetic features did not clearly identify a dominance of one region over the others, helioseismological subsurface flows beneath these active regions did reveal a pronounced difference among them. These preliminary results suggest that the ??twistedness?? (i.e., vorticity and helicity) of subsurface flows and its temporal variation might be related to the CME productivity of active regions, similar to the relationship between flares and subsurface flows.