Nonlinear Force-Free and Potential-Field Models of?Active-Region and Global Coronal Fields during?the?Whole Heliosphere Interval

Between 24 March 2008 and 2 April 2008, the three active regions (ARs) NOAA 10987, 10988 and 10989 were observed daily by the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) while they traversed the solar disk. We use these measurements and the nonlinear force-free magnetic field code XTRAPOL to reconstruct the coronal magnetic field for each active region and compare model field lines with images from the Solar Terrestrial RElations Observatory (STEREO) and Hinode X-ray Telescope (XRT) telescopes. Synoptic maps made from continuous, round-the-clock Global Oscillations Network Group (GONG) magnetograms provide information on the global photospheric field and potential-field source-surface models based on these maps describe the global coronal field during the Whole Heliosphere Interval (WHI) and its neighboring rotations. Features of the modeled global field, such as the coronal holes and streamer-belt locations, are discussed in comparison with extreme ultra-violet and coronagraph observations from STEREO. The global field is found to be far from a minimum, dipolar state. From the nonlinear models we compute physical quantities for the active regions such as the photospheric magnetic and electric current fluxes, the free magnetic energy and the relative helicity for each region each day where observations permit. The interconnectivity of the three regions is addressed in the context of the potential-field source-surface model. Using local and global quantities derived from the models, we briefly discuss the different observed activity levels of the regions.     

A comparison of type III metric radio bursts and global solar potential field models

We compare evidence of coronal magnetic fields from polarized metric type III radio bursts with (a) global potential field models, (b) direct averages of the observed photospheric magnetic field, and (c) H synoptic charts. The comparison clearly indicates both that the principal aspects of type III burst radiation are understood and that global potential field models are a significantly more accurate representation of coronal magnetic field structure than either the large-scale photospheric field or H synoptic charts.     

Vector Magnetic Field Synoptic Charts from the <Emphasis Type="Italic">Helioseismic and Magnetic Imager</Emphasis> (HMI)

Vector magnetic field synoptic charts from the Helioseismic and Magnetic Imager (HMI) are now available for each Carrington Rotation (CR) starting from CR 2097 in May 2010. Synoptic charts are produced using 720-second cadence full-disk vector magnetograms remapped to Carrington coordinates. The vector field is derived from the Stokes parameters (\(I, Q, U, V\)) using a Milne–Eddington-based inversion model. The \(180^{\circ}\) azimuth ambiguity is resolved using the minimum energy algorithm for pixels in active regions and for strong-field pixels (the field is greater than about 150 G) in quiet-Sun regions. Three other methods are used for the rest of the pixels: the potential-field method, the radial acute-angle method, and the random method. The vector field synoptic charts computed using these three disambiguation methods are evaluated. The noise in the three components of the vector magnetic field is generally much higher in the potential-field method charts. The component noise levels are significantly different in the radial-acute charts. However, the noise levels in the random-method charts are lower and comparable. The assumptions used in the potential-field and radial-acute methods to disambiguate the weak transverse field introduce bias that propagates differently into the three vector-field components, leading to unreasonable pattern and artifacts, whereas the random method appears not to introduce any systematic bias. The current sheet on the source surface, computed using the potential-field source-surface model applied to random-method charts, agrees with the best solution (the result computed from the synoptic charts with the minimum energy algorithm applied to each and every pixel in the vector magnetograms) much better than the other two. Differences in the synoptic charts determined with the best method and the random method are much smaller than those from the best method and the other two. This comparison indicates that the random method is better for vector field synoptic maps computed from near-central meridian data. The vector field synoptic charts provided by the Joint Science Operations Center (JSOC) are therefore produced with the random method.     

An Evolving Synoptic Magnetic Flux map and Implications for the Distribution of Photospheric Magnetic Flux

We describe a procedure intended to produce accurate daily estimates of the magnetic flux distribution on the entire solar surface. Models of differential rotation, meridional flow, supergranulation, and the random emergence of background flux elements are used to regularly update unobserved or poorly observed portions of an initial traditional magnetic synoptic map that acts as a seed. Fresh observations replace model estimates when available. Application of these surface magnetic transport models gives us new insight into the distribution and evolution of magnetic flux on the Sun, especially at the poles where canopy effects, limited spatial resolution, and foreshortening result in poor measurements. We find that meridional circulation has a considerable effect on the distribution of polar magnetic fields. We present a modeled polar field distribution as well as time series of the difference between the northern and southern polar magnetic flux; this flux imbalance is related to the heliospheric current sheet tilt. We also estimate that the amount of new background magnetic flux needed to sustain the `quiet-Sun' magnetic field is about 1.1×10²³ Mx d^–1 (equivalent to several large active regions) at the spatial resolution and epoch of our maps. We comment on the diffusive properties of supergranules, ephemeral regions, and intranetwork flux. The maps are available on the NSO World Wide Web page.     

Synoptic charts of solar 9.1 cm and coronal hole data

Synoptic charts for Carrington rotations 1601–1605 (May–August, 1973) were prepared using the central meridian column of the daily 9.1 cm Stanford solar radio maps. These charts were especially contoured to emphasize temperatures near the quiet solar disk level. Synoptic charts of coronal holes from the ATM-Skylab were superimposed on the radio data to investigate the ability of the radio charts to show coronal holes. This brief period is unfortunately the only interval for which both sets of data are available. The conclusion reached is that in spite of certain problems due to active regions, side-lobe effects and a rather large beamwidth, the 9.1 cm synoptic charts can be of substantial value in identifying large coronal holes, especially during periods of low solar activity. Such synoptic charts, therefore, for the years 1962–1973 that Stanford data are available, could enhance significantly the meagre data pool for coronal holes prior to the Skylab mission.     

High-Resolution Vector Magnetograms of the Sun’s Poles from Hinode: Flux Distributions and Global Coronal Modeling

The Sun’s polar fields play a leading role in structuring the large-scale solar atmosphere and in determining the interplanetary magnetic field. They are also believed to supply the seed field for the subsequent solar activity cycle. However, present-day synoptic observations do not have sufficient spatial resolution or sensitivity to diagnose accurately the high-latitude magnetic vector field. The high spatial resolution and sensitivity of the full-Stokes observations from the Hinode Solar Optical Telescope Spectro-Polarimeter, observing the poles long-term, allows us to build up a detailed picture of the Cycle 24 polar field reversal, including the changing latitude distribution of the high-latitude flux, and to study the effect on global coronal field models. The Hinode observations provide detailed information on the dominant facular-scale magnetic structure of the polar fields, and their field inclination and flux distribution. Hybrid synoptic magnetograms are constructed from Hinode polar measurements and full-disk magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM), and coronal potential field models are calculated. Loss of effective spatial resolution at the highest latitudes presents complications. Possible improvements to synoptic polar data are discussed.     

Coronal Magnetic Field Context of Simple CMEs Inferred from Global Potential Field Models

Most work on coronal mass ejection (CME) interpretation focuses on the involved active region rather than on the large-scale coronal context. In this paper a global potential-field source-surface model of the coronal magnetic field is used to evaluate the sensitivity of the coronal field configuration to the location, orientation, and strength of a bipolar active region relative to a background polar field distribution. The results suggest that the introduction of antiparallel components between the field of the active region and the background field can cause significant topological changes in the large-scale coronal magnetic field resembling observations during some simple CMEs. Antiparallel components can be introduced in the real corona by the diffusion and convection of photospheric fields, flux emergence, or erupted or shear-induced twist of active-region fields. Global MHD models with time-dependent boundary conditions could easily test the stability of such configurations and the nature of any related transients.     

A coronal magnetic field model with horizontal volume and sheet currents

When globally mapping the observed photospheric magnetic field into the corona, the interaction of the solar wind and magnetic field has been treated either by imposing source surface boundary conditions that tacitly require volume currents outside the source surface (Schatten, Wilcox, and Ness, 1969) or by limiting the interaction to thin current sheets between oppositely directed field regions (Wolfson, 1985). Yet observations and numerical MHD calculations suggest the presence of non-force-free volume currents throughout the corona as well as thin current sheets in the neighborhoods of the interfaces between closed and open field lines or between oppositely directed open field lines surrounding coronal helmet-streamer structures. This work presents a model including both horizontal volume currents and streamer sheet currents. The present model builds on the magnetostatic equilibria developed by Bogdan and Low (1986) and the current-sheet modeling technique developed by Schatten (1971). The calculation uses synoptic charts of the line-of-sight component of the photospheric magnetic field measured at the Wilcox Solar Observatory. Comparison of an MHD model with the calculated model results for the case of a dipole field and comparison of eclipse observations with calculations for CR 1647 (near solar minimum) show that this horizontal current-current-sheet model reproduces polar plumes and axes of corona streamers better than the source-surface model and reproduces coronal helmet structures better than the current-sheet model.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

A method of evolving synoptic maps of the solar magnetic field

The evolution of magnetic flux at the solar surface is widely modeled by the flux transport equation. This describes the distribution of flux from instant to instant over the whole surface but does not describe how the synoptic map for one Carrington rotation evolves into the synoptic map for the next rotation. We derive the correct synoptic evolution equation, show that a simple version yields extremely accurate predictions of synoptic maps and discuss the implications for previous studies of the evolution of surface magnetic structures. We also note that the procedure yields a method of reconstructing an approximate map of the flux over the whole surface at any instant.     

Characteristics of active-region sources of solar wind near solar maximum

Previous studies of the source regions of solar wind sampled by ACE and Ulysses showed that some solar wind originates from open magnetic flux rooted in active regions. These solar wind sources were labeled active-region sources when the open flux was from a strong field region with no corresponding coronal hole in the NSO He 10830 Å synoptic coronal-hole maps. Here, we present a detailed investigation of several of these active-region sources using ACE and Ulysses solar wind data, potential field models of the corona, and solar imaging data. We find that the solar wind from these active-region sources has distinct signatures, e.g., it generally has a higher oxygen charge state than wind associated with helium-10830 Å coronal-hole sources, indicating a hotter source region, consistent with the active region source interpretation. We compare the magnetic topology of the open field lines of these active-region sources with images of the hot corona to search for corresponding features in EUV and soft X-ray images. In most, but not all, cases, a dark area is seen in the EUV and soft X-ray image as for familiar coronal-hole sources. However, in one case no dark area was evident in the soft X-ray images: the magnetic model showed a double dipole coronal structure consistent with the images, both indicating that the footpoints of the open field lines, rooted deep within the active region, lay near the separatrix between loops connecting to two different opposite polarity regions.     

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.     

Comparative Study of MHD Modeling of the Background Solar Wind

Knowledge about the background solar wind plays a crucial role in the framework of space-weather forecasting. In-situ measurements of the background solar wind are only available for a few points in the heliosphere where spacecraft are located, therefore we have to rely on heliospheric models to derive the distribution of solar-wind parameters in interplanetary space. We test the performance of different solar-wind models, namely Magnetohydrodynamic Algorithm outside a Sphere/ENLIL (MAS/ENLIL), Wang–Sheeley–Arge/ENLIL (WSA/ENLIL), and MAS/MAS, by comparing model results with in-situ measurements from spacecraft located at 1 AU distance to the Sun (ACE, Wind). To exclude the influence of interplanetary coronal mass ejections (ICMEs), we chose the year 2007 as a time period with low solar activity for our comparison. We found that the general structure of the background solar wind is well reproduced by all models. The best model results were obtained for the parameter solar-wind speed. However, the predicted arrival times of high-speed solar-wind streams have typical uncertainties of the order of about one day. Comparison of model runs with synoptic magnetic maps from different observatories revealed that the choice of the synoptic map significantly affects the model performance.     

Coronal Field Opens at Lower Height During the Solar Cycles 22 and 23 Minimum Periods: IMF Comparison Suggests the Source Surface Should Be Lowered

The solar cycle 23 minimum period has been characterized by a weaker solar and interplanetary magnetic field. This provides an ideal time to study how the strength of the photospheric field affects the interplanetary magnetic flux and, in particular, how much the observed interplanetary fields of different cycle minima can be understood simply from differences in the areas of the coronal holes, as opposed to differences in the surface fields within them. In this study, we invoke smaller source surface radii in the potential-field source-surface (PFSS) model to construct a consistent picture of the observed coronal holes and the near-Earth interplanetary field strength as well as polarity measurements for the cycles 23 and 22 minimum periods. Although the source surface value of 2.5 R _⊙ is typically used in PFSS applications, earlier studies have shown that using smaller source surface heights generates results that better match observations during low solar activity periods. We use photospheric field synoptic maps from Mount Wilson Observatory (MWO) and find that the values of ≈ 1.9 R _⊙ and ≈ 1.8 R _⊙ for the cycles 22 and 23 minimum periods, respectively, produce the best results. The larger coronal holes obtained for the smaller source surface radius of cycle 23 somewhat offsets the interplanetary consequences of the lower magnetic field at their photospheric footpoints. For comparison, we also use observations from the Michelson Doppler Imager (MDI) and find that the source surface radius of ≈ 1.5 R _⊙ produces better results for cycle 23, rather than ≈ 1.8 R _⊙ as suggested from MWO observations. Despite this difference, our results obtained from MWO and MDI observations show a qualitative consistency regarding the origins of the interplanetary field and suggest that users of PFSS models may want to consider using these smaller values for their source surface heights as long as the solar activity is low.     

Correlation of high latitude coronal holes with solar wind streams far above or below the ecliptic

For the 2.5 year period from January 1, 1977 to June 30, 1979, we have correlated the positions of high latitude coronal holes, obtained from the He 10830 Å synoptic maps, with the velocities of solar wind streams, determined from interplanetary scintillation, that would have originated from these coronal holes. From 24 cases analyzed we find that these high latitude coronal holes are often, but not always, correlated with high speed solar wind streams. The lack of a much stronger correlation may be due to uncertainties in the boundaries of the coronal holes and in the velocities of the solar wind streams. It might also be due to the deflection or attenuation of relatively weak solar wind streams in interplanetary space.     

On the Magnetic Correspondence between the Photosphere and the Heliosphere

The solar magnetic field maps every point in the corona to a corresponding place on the solar surface. Identifying the magnetic connection map is difficult at low latitudes near the heliospheric current sheet, but remarkably simple in coronal hole interiors. We present a simple analytic magnetic model (‘pseudocurrent extrapolation’) that reproduces the global structure of the corona, with significant physical advantages over other nearly analytic models such as source-surface potential field extrapolation. We use the model to demonstrate that local horizontal structure is preserved across altitude in the central portions of solar coronal holes, up to at least 30 R_s, in agreement with observations. We argue that the preserved horizontal structure may be used to track the magnetic footpoint associated with the location of a hypothetical spacecraft traveling through the solar corona, to relate in situ measurements of the young solar wind at ∼10–30 R_s to particular source regions at the solar surface. Further, we discuss the relationship between readily observable geometrical distortions and physical parameters of interest such as the field-aligned current density.     

Evidence linking coronal transients to the evolution of coronal holes

The positions of X-ray coronal transients outside of active regions observed during Skylab were superposed on H synoptic charts and coronal hole boundaries for seven solar rotations. We confirmed a detailed spatial association between the transients and neutral lines. We found that most of the transients were related to large-scale changes in coronal hole area and tended to occur on the borders of evolving equatorial holes.Skylab Solar Workshop Post-Doctoral Appointee, 1975–1977.     

Quiet-Sun emission and local sources at meter and decimeter wavelengths and their relationship with the coronal neutral sheet

We analysed multifrequency 2-dimensional maps of the solar corona obtained with the Nançay radioheliograph during two solar rotations in 1986. We discuss the emission of the quiet Sun, coronal holes and local sources and its association with chromospheric and coronal features as well as with large-scale magnetic fields. The brightness temperature of the quiet Sun was 5 to 5.5 × 10⁵ K at 164 MHz and 4.5 to 5 × 10⁵ K at 408 MHz. A coronal hole, also detected in the 10830 Å He i line, had a brightness temperature of 4.5 × 10⁵ at 164 and 2.5 × 10⁵ at 408 MHz. We give statistics of source brightness temperatures (on the average 8% above the background at 164 MHz and 14% at 408 MHz), as well as distributions in longitude and latitude. Although we found no significant center-to-limb effect in the brightness temperature, the sources were not visible far from the central meridian (apparently a refraction effect). The brightest sources at 164 MHz were near, but not directly above active regions and had characteristics of faint type I continua. At 408 MHz some sources were observed directly above active regions and one was unambiguously a type I continuum. The majority of the fainter sources showed no association with chromospheric features seen on H synoptic charts, including filaments. Most of them were detected at one frequency only. Sources identified at three frequencies (164, 327, and 408 MHz) were located in regions of enhanced large-scale magnetic field, some of them at the same location as decayed active regions visible one rotation before on synoptic H charts. Multifrequency sources are associated with maxima of the green line corona. The comparison with K-corona synoptic charts shows a striking association of the radio sources with dense coronal regions, associated with the coronal neutral sheet. Furthermore, we detected an enhanced brightness region which surrounds the local sources and is stable over at least one solar rotation. We call this feature a coronal plateau and we identify it with the radio counterpart of the coronal neutral sheet.     

Synoptic Solar Cycle 24 in Corona,Chromosphere, and Photosphere Seen by the Solar Dynamics Observatory

The Solar Dynamics Observatory provides multiwavelength imagery from extreme ultraviolet (EUV) to visible light as well as magnetic-field measurements. These data enable us to study the nature of solar activity in different regions of the Sun, from the interior to the corona. For solar-cycle studies, synoptic maps provide a useful way to represent global activity and evolution by extracting a central meridian band from sequences of full-disk images over a full solar Carrington rotation (≈?27.3 days). We present the global evolution during Solar Cycle 24 from 20 May 2010 to 31 August 2013 (CR?2097?–?CR?2140), using synoptic maps constructed from full-disk, line-of-sight magnetic-field imagery and EUV imagery (171 Å, 193 Å, 211 Å, 304 Å, and 335 Å). The synoptic maps have a resolution of 0.1 degree in longitude and steps of 0.001 in sine of latitude. We studied the axisymmetric and non-axisymmetric structures of solar activity using these synoptic maps. To visualize the axisymmetric development of Cycle 24, we generated time–latitude (also called butterfly) images of the solar cycle in all of the wavelengths, by averaging each synoptic map over all longitudes, thus compressing it to a single vertical strip, and then assembling these strips in time order. From these time–latitude images we observe that during the ascending phase of Cycle 24 there is a very good relationship between the integrated magnetic flux and the EUV intensity inside the zone of sunspot activities. We observe a North–South asymmetry of the EUV intensity in high-latitudes. The North–South asymmetry of the emerging magnetic flux developed and resulted in a consequential asymmetry in the timing of the polar magnetic-field reversals.