Impulses of activity and the Solar cycle

Extreme-ultraviolet data from EIT/SOHO (1996–2002), soft X-ray data from Yohkoh (1991–2001), and magnetic field data from MDI/SOHO (1996–2002) and Kitt Peak Observatory, NSO/NOAO (1991–2002) are analyzed together in the form of synoptic maps for the investigation of solar cycle variations of the corona and their relation to the magnetic field. These results show new interesting relations between the evolution of the topological structure of the corona, coronal heating and the large-scale magnetic field. The long-lived coronal structures are related to complexes of solar activity and display quasi-periodic behavior (in the form of impulses of coronal activity) with periods of 1.0–1.5 year, in the axisymmetric distribution of EUV and X-ray fluxes during the current solar cycle 23. In particular, during the second maximum of this cycle the solar corona became somewhat hotter than it was in the period of the first maximum.     

2D Feature Recognition And 3d Reconstruction In Solar Euv Images

EUV images show the solar corona in a typical temperature range of T >rsim 1 MK, which encompasses the most common coronal structures: loops, filaments, and other magnetic structures in active regions, the quiet Sun, and coronal holes. Quantitative analysis increasingly demands automated 2D feature recognition and 3D reconstruction, in order to localize, track, and monitor the evolution of such coronal structures. We discuss numerical tools that “fingerprint” curvi-linear 1D features (e.g., loops and filaments). We discuss existing finger-printing algorithms, such as the brightness-gradient method, the oriented-connectivity method, stereoscopic methods, time-differencing, and space–time feature recognition. We discuss improved 2D feature recognition and 3D reconstruction techniques that make use of additional a priori constraints, using guidance from magnetic field extrapolations, curvature radii constraints, and acceleration and velocity constraints in time-dependent image sequences. Applications of these algorithms aid the analysis of SOHO/EIT, TRACE, and STEREO/SECCHI data, such as disentangling, 3D reconstruction, and hydrodynamic modeling of coronal loops, postflare loops, filaments, prominences, and 3D reconstruction of the coronal magnetic field in general.     

Understanding the Physical Nature of Coronal “EIT Waves”

For almost 20 years the physical nature of globally propagating waves in the solar corona (commonly called “EIT waves”) has been controversial and subject to debate. Additional theories have been proposed over the years to explain observations that did not agree with the originally proposed fast-mode wave interpretation. However, the incompatibility of observations made using the Extreme-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory with the fast-mode wave interpretation was challenged by differing viewpoints from the twin Solar Terrestrial Relations Observatory spacecraft and data with higher spatial and temporal resolution from the Solar Dynamics Observatory. In this article, we reexamine the theories proposed to explain EIT waves to identify measurable properties and behaviours that can be compared to current and future observations. Most of us conclude that the so-called EIT waves are best described as fast-mode large-amplitude waves or shocks that are initially driven by the impulsive expansion of an erupting coronal mass ejection in the low corona.     

What Is the Nature of EUV Waves? First STEREO 3D Observations and Comparison with Theoretical Models

One of the major discoveries of the Extreme ultraviolet Imaging Telescope (EIT) on SOHO was the intensity enhancements propagating over a large fraction of the solar surface. The physical origin(s) of the so-called EIT waves is still strongly debated with either wave (primarily fast-mode MHD waves) or nonwave (pseudo-wave) interpretations. The difficulty in understanding the nature of EUV waves lies in the limitations of the EIT observations that have been used almost exclusively for their study. They suffer from low cadence and single temperature and viewpoint coverage. These limitations are largely overcome by the SECCHI/EUVI observations onboard the STEREO mission. The EUVI telescopes provide high-cadence, simultaneous multitemperature coverage and two well-separated viewpoints. We present here the first detailed analysis of an EUV wave observed by the EUVI disk imagers on 7 December 2007 when the STEREO spacecraft separation was ≈?45°. Both a small flare and a coronal mass ejection (CME) were associated with the wave. We also offer the first comprehensive comparison of the various wave interpretations against the observations. Our major findings are as follows: (1) High-cadence (2.5-minute) 171 Å? images showed a strong association between expanding loops and the wave onset and significant differences in the wave appearance between the two STEREO viewpoints during its early stages; these differences largely disappeared later; (2) the wave appears at the active region periphery when an abrupt disappearance of the expanding loops occurs within an interval of 2.5 minutes; (3) almost simultaneous images at different temperatures showed that the wave was most visible in the 1?–?2 MK range and almost invisible in chromospheric/transition region temperatures; (4) triangulations of the wave indicate it was rather low lying (≈?90 Mm above the surface); (5) forward-fitting of the corresponding CME as seen by the COR1 coronagraphs showed that the projection of the best-fit model on the solar surface was inconsistent with the location and size of the co-temporal EUV wave; and (6) simulations of a fast-mode wave were found in good agreement with the overall shape and location of the observed wave. Our findings give significant support for a fast-mode interpretation of EUV waves and indicate that they are probably triggered by the rapid expansion of the loops associated with the CME.     

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.     

The Recovery of CME-Related Dimmings and the ICME’s Enduring Magnetic Connection to the Sun

It is generally accepted that transient coronal holes (TCHs, dimmings) correspond to the magnetic footpoints of CMEs that remain rooted in the Sun as the CME expands out into the interplanetary space. However, the observation that the average intensity of the 12 May 1997 dimmings recover to their pre-eruption intensity in SOHO/EIT data within 48 hours, whilst suprathermal unidirectional electron heat fluxes are observed at 1 AU in the related ICME more than 70 hours after the eruption, leads us to question why and how the dimmings disappear whilst the magnetic connectivity is maintained. We also examine two other CME-related dimming events: 13 May 2005 and 6 July 2006. We study the morphology of the dimmings and how they recover. We find that, far from exhibiting a uniform intensity, dimmings observed in SOHO/EIT data have a deep central core and a more shallow extended dimming area. The dimmings recover not only by shrinking of their outer boundaries but also by internal brightenings. We quantitatively demonstrate that the model developed by Fisk and Schwadron (Astrophys. J. 560, 425, 2001) of interchange reconnections between “open” magnetic field and small coronal loops is a strong candidate for the mechanism facilitating the recovery of the dimmings. This process disperses the concentration of  “open” magnetic field (forming the dimming) out into the surrounding quiet Sun, thus recovering the intensity of the dimmings whilst still maintaining the magnetic connectivity to the Sun. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Advances in Observing Various Coronal EUV Waves in the SDO Era and Their Seismological Applications (Invited Review)

Global extreme-ultraviolet (EUV) waves are spectacular traveling disturbances in the solar corona associated with energetic eruptions such as coronal mass ejections (CMEs) and flares. Over the past 15 years, observations from three generations of space-borne EUV telescopes have shaped our understanding of this phenomenon and at the same time led to controversy about its physical nature. Since its launch in 2010, the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) has observed more than 210 global EUV waves in exquisite detail, thanks to its high spatio–temporal resolution and full-disk, wide-temperature coverage. A combination of statistical analysis of this large sample, more than 30 detailed case studies, and data-driven MHD modeling, has been leading their physical interpretations to a convergence, favoring a bimodal composition of an outer, fast-mode magnetosonic wave component and an inner, non-wave CME component. Adding to this multifaceted picture, AIA has also discovered new EUV wave and wave-like phenomena associated with various eruptions, including quasi-periodic fast propagating (QFP) wave trains, magnetic Kelvin–Helmholtz instabilities (KHI) in the corona and associated nonlinear waves, and a variety of mini-EUV waves. Seismological applications using such waves are now being actively pursued, especially for the global corona. We review such advances in EUV wave research focusing on recent SDO/AIA observations, their seismological applications, related data-analysis techniques, and numerical and analytical models.     

A New Model for Propagating Parts of EIT Waves: A Current Shell in a CME

EIT waves are observed in EUV as bright fronts. Some of these bright fronts propagate across the solar disk. EIT waves are all associated with a flare and a CME and are commonly interpreted as fast-mode magnetosonic waves. Propagating EIT waves could also be the direct signature of the gradual opening of magnetic field lines during a CME. We quantitatively addressed this alternative interpretation. Using two independent 3D MHD codes, we performed nondimensional numerical simulations of a slowly rotating magnetic bipole, which progressively result in the formation of a twisted magnetic flux tube and its fast expansion, as during a CME. We analyse the origins, the development, and the observability in EUV of the narrow electric currents sheets that appear in the simulations. Both codes give similar results, which we confront with two well-known SOHO/EIT observations of propagating EIT waves (7 April and 12 May 1997), by scaling the vertical magnetic field components of the simulated bipole to the line of sight magnetic field observed by SOHO/MDI and the sign of helicity to the orientation of the soft X-ray sigmoids observed by Yohkoh/SXT. A large-scale and narrow current shell appears around the twisted flux tube in the dynamic phase of its expansion. This current shell is formed by the return currents of the system, which separate the twisted flux tube from the surrounding fields. It intensifies as the flux tube accelerates and it is co-spatial with weak plasma compression. The current density integrated over the altitude has the shape of an ellipse, which expands and rotates when viewed from above, reproducing the generic properties of propagating EIT waves. The timing, orientation, and location of bright and faint patches observed in the two EIT waves are remarkably well reproduced. We conjecture that propagating EIT waves are the observational signature of Joule heating in electric current shells, which separate expanding flux tubes from their surrounding fields during CMEs or plasma compression inside this current shell. We also conjecture that the bright edges of halo CMEs show the plasma compression in these current shells.     

Flare-produced coronal MHD-fast-mode wavefronts and Moreton's wave phenomenon

The propagation characteristics of MHD fast-mode disturbances, which can emanate from flare regions, are computed for realistic conditions of the solar corona at the times of particular flares. The path of a fast-mode disturbance is determined by the large-scale (global) coronal distributions of magnetic field and density, and can be computed by a general raytracing procedure (eikonal equation) adapted to MHD. We use the coronal (electron) density distribution calculated from daily K-coronameter data, and the coronal magnetic field calculated under the current-free approximation from magnetograph measurements of the photospheric magnetic field. We compare the path and time-development of an MHD fast-mode wavefront emitted from the flare region (as calculated from a realistic model corona for the day of the observed Moreton wave event) with actual observations of the Moreton wave event, and find that the Moreton wave can be identified with the rapidly moving intersection of the coronal fast-mode wavefront and the chromosphere (as hypothesized in our previous paper); the directivity (anisotropic propagation), as well as other characteristics of the propagation of the Moreton wave can be successfully explained.sponsored by the National Science Foundation.     

Automated Detection Of Eit Waves And Dimmings

Studies of the onset of Earth-directed coronal mass ejections (CMEs) rely on solar disk observations where CME structures are difficult to disentangle because of the diversity and transient character of the phenomena involved. Dimmings and coronal waves are among the best evidence of the large-scale reorganization of coronal magnetic fields associated with the onset of CMEs. The physical mechanism behind EIT waves is still unclear: they are considered as MHD waves and/or as a consequence of plasma compression on the extending border of a dimming. In this paper, we address the problem of automatically detecting and analyzing EIT waves and dimmings in EUV images. This paper presents a “proof of principle” that automated detection of EIT wave and dimmings is indeed possible. At the current stage of work, the method can unambiguously detect dimmings and EIT waves when applied on a typical test-case event. Moreover, we propose a way to extract these events from the data, and determine such parameters as life time, depth, area and volume of dimmings for future catalogs. For EIT waves we unambiguously define, in near solar minimum conditions, the eruption center, the front of EIT wave and its propagation velocity. In addition, we show that the presented methods yield new insights about the geometrical shape of dimmings and the connection with the EIT wave front properties, and the apparent angular rotation of the EIT wave under study.     

Coronal Shock Waves,EUV Waves,and Their Relation to CMEs. III. Shock-Associated CME/EUV Wave in an Event with a Two-Component EUV Transient

On 17 January 2010, STEREO-B observed in extreme ultraviolet (EUV) and white light a large-scale dome-shaped expanding coronal transient with perfectly connected off-limb and on-disk signatures. Veronig et al. (Astrophys. J. Lett. 716, L57, 2010) concluded that the dome was formed by a weak shock wave. We have revealed two EUV components, one of which corresponded to this transient. All of its properties found from EUV, white light, and a metric type II burst match expectations for a freely expanding coronal shock wave, including correspondence with the fast-mode speed distribution, while the transient sweeping over the solar surface had a speed typical of EUV waves. The shock wave was presumably excited by an abrupt filament eruption. Both a weak shock approximation and a power-law fit match kinematics of the transient near the Sun. Moreover, the power-law fit matches the expansion of the CME leading edge up to 24 solar radii. The second, quasi-stationary EUV component near the dimming was presumably associated with a stretched CME structure; no indications of opening magnetic fields have been detected far from the eruption region.     

Nine Years Of Euv Bright Points

We discuss early results derived from an algorithm that automates the detection, cataloging, and analysis of extreme-ultraviolet (EUV) “bright points” (BP) from 9 years of data acquired by the Extreme-ultraviolet Imaging Telescope (EIT) on the Solar and Heliospheric Observatory (SOHO). The algorithm relies upon the computation of a map of “intensity significance”; this then contains the location of the EUV BPs. By mapping the location of BPs in each image and linking them through long sequences of EIT images we can describe the temporal and spatial variations of the 1.3× 10⁸ EUV BPs observed by SOHO to date. We suggest that there is a considerable amount of physical information about the solar coronal plasma that can be readily gleamed from the BP detection database. In this paper we discuss only a small portion of the possible correlations, but we point to the possibility of BP lifetime distributions that are well described by modified power-laws; the components of which vary with the different temperature filters and with time over the present solar cycle. Dedicated to the memory of John (Ian) Hamilton (1938–2004).     

Location and parameters of a microwave millisecond spike event

A typical microwave millisecond spike event on November 2, 1997 was observed by the radio spectrograph of National Astronomical Observatories (NAOs) at 2.6–3.8 GHz with high time and frequency resolution. This event was also recorded by Nobeyama Radio Polarimeters (NoRP) at 1–35 GHz and Radio Heliograph (NoRH) at 17 GHz. The source at 17 GHz is located in one foot-point of a small bright coronal loop of YOHKOH SXT and SOHO EIT images with strong photospheric magnetic field in SOHO MDI magnetograph. It is assumed that the electron cyclotron maser instability and gyro-resonance absorption dominate, respectively, the rising and decay phase of the spike event. For different harmonic number of gyro-frequency or magnetic field strength, a fitting program with free plasma parameters is used to minimize the difference between the observational and theoretical values of the exponential growth and decay rates for a given spike. The plasma parameters at third harmonic number are more comparable to their typical values in solar corona. Hence, it is able to provide a diagnosis for the source parameters (magnetic field, density, and temperature), the properties of radiations (wave vector and propagation angle), and the properties of non-thermal electrons (density, pitch angle, and energy). The results are also comparable with the diagnosis of the gyro-synchrotron radiation model, the frequency drift rates and a dipole magnetic field model, as well as the YOHKOH SXT and SOHO MDI data. This study is supported by the NFSC project nos. 10333030 and 10273025, and “973” program with no. G2000078403.     

On the Coronal Mass Ejection onset and Coronal Dimming

A comprehensive case and statistical study of CME onsets has been conducted on the solar limb using the CDS, LASCO and EIT instruments aboard the SOHO spacecraft. This is the first dedicated campaign to establish firmly the EUV signatures of CME onsets and is based on a series of low-corona observing campaigns made in 2002. The event database consisted of 36 multiple emission line sequences observed with CDS and the study builds, in particular, on studies of EUV coronal dimming which have been associated with CME onsets. We witness a range of dimming events in EUV coronal emission line data. Shorter events, commonly of duration < 4 hours, we find are indirectly associated with CME onsets whereas longer-duration dimmings (> 4 hours) appear to be either due to coronal evolution or rotational effects. However, for some CME onsets, where the CDS pointing was appropriate, no dimming was observed. Dimming observed in EIT typically occurred immediately after the launch of a loop or prominence, and in 5 out of 9 events there is evidence of a matter buildup within the loop before launch. A total of 10 events occurred where CDS was used to directly observe the CME footprint, but no relationship between these events was found. The results suggest that the response of the corona to a CME launch differs between the low (1.0 R _⊙≤R≤1.2 R _⊙) and middle (1.2 R _⊙<R≤2.0 R _⊙) corona regions, hence implying a difference between dimming observations conducted with different instruments.     

EUV and Magnetic Activities Associated with Type-I Solar Radio Bursts

Type-I bursts (i.e. noise storms) are the earliest-known type of solar radio emission at the meter wavelength. They are believed to be excited by non-thermal energetic electrons accelerated in the corona. The underlying dynamic process and exact emission mechanism still remain unresolved. Here, with a combined analysis of extreme ultraviolet (EUV), radio and photospheric magnetic field data of unprecedented quality recorded during a type-I storm on 30 July 2011, we identify a good correlation between the radio bursts and the co-spatial EUV and magnetic activities. The EUV activities manifest themselves as three major brightening stripes above a region adjacent to a compact sunspot, while the magnetic field there presents multiple moving magnetic features (MMFs) with persistent coalescence or cancelation and a morphologically similar three-part distribution. We find that the type-I intensities are correlated with those of the EUV emissions at various wavelengths with a correlation coefficient of 0.7?–?0.8. In addition, in the region between the brightening EUV stripes and the radio sources there appear consistent dynamic motions with a series of bi-directional flows, suggesting ongoing small-scale reconnection there. Mainly based on the induced connection between the magnetic motion at the photosphere and the EUV and radio activities in the corona, we suggest that the observed type-I noise storms and the EUV brightening activities are the consequence of small-scale magnetic reconnection driven by MMFs. This is in support of the original proposal made by Bentley et al. (Solar Phys. 193, 227, 2000).     

How to Reach Superequipartition Field Strengths in Solar Magnetic Flux Tubes

A number of independent arguments indicate that the toroidal flux system responsible for the sunspot cycle is stored at the base of the convection zone in the form of flux tubes with field strength close to 10⁵ G. Although the evidence for such strong fields is quite compelling, how such field strength can be reached is still a topic of debate. Flux expulsion by convection should lead to about the equipartition field strength, but the magnetic energy density of a 10⁵-G field is two orders of magnitude larger than the mean kinetic energy density of convective motions. Line stretching by differential rotation (i.e., the “Ω effect” in the classical mean-field dynamo approach) probably plays an important role, but arguments based on energy considerations show that it does not seem feasible that a 10⁵-G field can be produced in this way. An alternative scenario for the intensification of the toroidal flux system in the overshoot layer is related to the explosion of rising, buoyantly unstable magnetic flux tubes, which opens a complementary mechanism for magnetic-field intensification. A parallelism is pointed out with the mechanism of “convective collapse” for the intensification of photospheric magnetic flux tubes up to field strengths well above equipartition; both mechanisms, which are fundamentally thermal processes, are reviewed.     

VLA,SOHO and TRACE Observations of Nonthermal Burst Activity,Coronal Mass Ejections,and EUV Transient Events

Very Large Array (VLA) observations of the Sun at 91 and 400 cm wavelength have been used to investigate the radio signatures of EUV heating events and coronal mass ejections (CMEs) detected by SOHO and TRACE. Our 91 cm observations show the onset of Type I noise storm emission about an hour after an EUV ejection event was detected by EIT and TRACE. The EUV event also coincided with the estimated start time of a CME detected by the LASCO C2 coronagraph, suggesting an association between the production of nonthermal particles and evolving plasma-magnetic field structures at different heights in the corona. On another day, our VLA 400 cm observations reveal weak, impulsive microbursts that occurred sporadically throughout the middle corona. These low-brightness-temperature (T _b=0.7–22×10⁶ K) events may be weak Type III bursts produced by beams of nonthermal electrons which excite plasma emission at a height where the local plasma frequency or its first harmonic equals the observing frequency of 74 MHz. For one microburst, the emission was contained in two sources separated by 0.7 R ₀, indicating that the electron beams had access to widely-divergent magnetic field lines originating at a common site of particle acceleration. Another 400 cm microburst occurred in an arc-like source lying at the edge of EUV loops that appeared to open outward into the corona, possibly signaling the start of a CME. In most instances the 400 cm microbursts were not accompanied by detectable EUV activity, suggesting that particles that produce the microbursts were independently accelerated in the middle corona, perhaps as the result of some quasi-continuous, large-scale process of energy release.     

Combined Analysis of Ultraviolet and Radio Observations of the 7 May 2004 CME/Shock Event

We report results from the combined analysis of UV and radio observations of a CME-driven shock observed on 7 May 2004 above the southeast limb of the Sun at 1.86 R _⊙ with the Ultraviolet Coronagraph Spectrometer (UVCS) on board the Solar and Heliospheric Observatory (SOHO). The coronal mass ejection (CME) was first detected in white-light by the SOHO’s Large Angle and Spectrometric Coronagraph (LASCO) C2 telescope and shock-associated type II metric emission was recorded simultaneously by ground-based radio spectrographs. The shock speed (∼ 690 km s⁻¹), as deduced from the analysis of the type II emission drift in the radio spectra and the pre-shock local electron density estimated with the diagnostics provided by UVCS observations of the O vi λλ 1031.9, 1037.6 doublet line intensities, is just a factor ∼ 0.1 higher than the CME speed inferred by means of the white-light (and EUV) data in the middle corona. The local magnetosonic speed, computed from a standard magnetic field model, was estimated as high as ∼ 600 km s⁻¹, implying that the CME speed was probably just sufficient to drive a weak fast-mode MHD shock ahead of the front. Simultaneously with the type II radio emission, significant changes in the O vi doublet line intensities and profiles were recorded in the UVCS spectra and found compatible with abrupt post-shock plasma acceleration and modest ion heating. This work provides further evidence for the CME-driven origin of the shocks observed in the middle corona.     

On the Nature and Genesis of EUV Waves: A Synthesis of Observations from SOHO, STEREO, SDO, and Hinode (Invited Review)

A major, albeit serendipitous, discovery of the SOlar and Heliospheric Observatory mission was the observation by the Extreme Ultraviolet Telescope (EIT) of large-scale extreme ultraviolet (EUV) intensity fronts propagating over a significant fraction of the Sun??s surface. These so-called EIT or EUV waves are associated with eruptive phenomena and have been studied intensely. However, their wave nature has been challenged by non-wave (or pseudo-wave) interpretations and the subject remains under debate. A string of recent solar missions has provided a wealth of detailed EUV observations of these waves bringing us closer to resolving the question of their nature. With this review, we gather the current state-of-the-art knowledge in the field and synthesize it into a picture of an EUV wave driven by the lateral expansion of the CME. This picture can account for both wave and pseudo-wave interpretations of the observations, thus resolving the controversy over the nature of EUV waves to a large degree but not completely. We close with a discussion on several remaining open questions in the field of EUV waves research.     

Polar Coronal Structures and the Global Magnetic Field Evolution Through the Cycle

We compare the shape and position of some plasma formations visible in the polar corona with the cyclic evolution of the global magnetic field. The first type of object is polar crown prominences. A two-fold decrease of the height of polar crown prominences was found during their poleward migration from the middle latitudes to the poles before a polar magnetic field reversal. The effect could be assigned to a decrease of the magnetic field scale. The second type of object is the polar plumes, ray like structures that follow magnetic field lines. Tangents to polar ray structures are usually crossed near some point, “a magnetic focus,” below the surface. The distance q between the focus and the center of the solar disk changes from the maximum value about 0.65 R _⊙ at solar minimum activity to the minimum value about 0.45 R _⊙ at solar maximum. At first glance this behaviour seems to be contrary to the dynamics of spherical harmonics of the global magnetic field throughout a cycle. We believe that the problem could be resolved if one takes into account not only scale changes in the global magnetic field but also the phase difference in the cyclic variations of large-scale and small-scale components of the global field.