Magnetic Field Is Playing Up Again Pch Pl Help

ane. Introduction

Magnetic fields play a key role in the existence and variability of a broad variety of phenomena institute on the Sun. These range from relatively stable, slowly evolving objects such every bit sunspots, coronal loops and solar prominences, to highly dynamic phenomena such every bit solar flares and coronal mass ejections (CMEs). Solar magnetic fields may straight or indirectly touch on the Earth through the Lord's day'due south open flux, solar wind and irradiance variations.

Our nowadays-day understanding of solar magnetic fields dates from 1908 when Unhurt made the outset magnetic field observations of sunspots [1]. However, it was not until the systematic mapping of the Sun's magnetic field that its true circadian nature became apparent [2]. While significant advances in observations take been fabricated over the last 50 years, just the forcefulness and distribution of the line-of-sight magnetic field component at the level of the photosphere have been regularly measured over solar bike time scales. Since many important phenomena occur in the solar corona, a fundamental component in our understanding of solar magnetic fields is the utilise of theoretical models to construct (or extrapolate) coronal magnetic fields from photospheric information.

In recent years, the technique of Zeeman Doppler imaging (ZDI) [3] has led to a significant advance in our understanding of magnetic fields on other stars. Results show a broad range of magnetic morphologies across stars of varying mass and spectral type [4]. With the accurate measurement of stellar magnetic fields, techniques adult to model solar magnetic fields are at present widely applied in the stellar context.

In this review, we primarily focus on our present-twenty-four hour period understanding of global solar photospheric and coronal magnetic fields. Where appropriate, we expand this word into stellar magnetic fields to summarize new results. In §2, observations of both solar and stellar magnetic fields are discussed. Following this, magnetic flux transport models used to model the evolution of photospheric magnetic fields are described (§3), along with techniques used to construct coronal magnetic fields (§four). The application of these models to the Dominicus's open magnetic flux (§five), hemispheric pattern of solar filaments and CMEs (§six) are then described. In §7, recent advances in global magnetohydrodynamics (MHD) models are discussed. Finally in §8, outstanding problems are outlined.

two. Observations

Presently, three solar cycles of continuous data have been collected past a variety of observatories (Kitt Peak, Solar Heliospheric Observatory/Magnetic Doppler Imager, Synoptic Optical Long-term Investigations of the Sun) showing the distribution and evolution of the Sun's normal magnetic field component at the level of the photosphere. An illustration of this can be seen in effigy anea (from Hathaway [5]). The image known as the magnetic butterfly diagram illustrates the radial magnetic field equally a function of time (averaged in longitude, horizontal axis) versus sine-latitude (vertical axis). The main features in the development of the global magnetic field are as follows.

	— At the start of each solar cycle (cf. 1975, 1986, 1996), the majority of magnetic flux sits in reverse polarity polar regions. New magnetic flux and so emerges in the class of sunspots or big bipoles in 2 latitude bands between ±30^° [7]. As the wheel progresses, these bands approach the equator.
	— The new magnetic bipoles lie mainly in an east–west orientation. The leading polarity (in the direction of rotation) has the same sign as the polar field of the hemisphere in which information technology lies, the following polarity has the opposite sign (Unhurt'southward polarity constabulary). In addition, the majority of bipoles emerge subject to Joy's law, where the leading polarity lies equator-ward of the following. The effect of Joy's law can be conspicuously seen in effigy anea past the latitudinal separation of flux between ±30^°.
	— Owing to this latitudinal separation, the following polarity may be preferentially transported poleward by meridional flow [8,ix]. In contrast, the leading polarity, which lies at lower latitudes, may partially escape the outcome of meridional flow to disperse and cancel beyond the equator. In each hemisphere, more than post-obit, than leading polarity, flux is transported poleward, where it cancels with the existing polar field and then builds up a new polar field of the following polarity.
	— The reversal in sign of the polar field typically occurs but after cycle maximum. A 22 year magnetic bicycle overlies the xi yr activity bicycle.

Figure 1. — Effigy 1. (a) The solar magnetic butterfly diagram (from Hathaway [v]). Yellow represents positive flux and blue represents negative flux, where the field saturates at ±5 Grand. (b) Example of a typical radial magnetic field distribution for AB Dor taken through ZDI [6], where the image saturates at ±300G. White/black denotes positive/negative flux. Owing to the tilt angle of AB Dor, measurements can only be made in the Northern Hemisphere. (Online version in colour.)

While continuous global measurements of magnetic action just be from effectually 1975, observations of the numbers of sunspots may be used to provide a long-running dataset of solar activity back to 1611 [10,11]. These show that on meridian of the approximate 11 or 22 year activity bicycle, there are strong modulations in the number of sunspots (or flux emergence rate) over periods of centuries. It is possible also for large-scale magnetic activity to disappear. Such an consequence occurred between 1645 and 1715, where it is known equally the Maunder minimum [12,13]. Before 1611, indicators of magnetic activity on the Sun may be found through the use of proxies such equally ¹⁴C and ¹⁰Exist isotopes. Through this, reconstructions of the level of magnetic activeness over the by x 000 years may be made [14].

The majority of our present-mean solar day knowledge of solar magnetic fields comes from observing the line-of-sight component at the level of the photosphere. To gain a much fuller understanding of the Sun'due south magnetic field, vector field measurements are required [15]. These measurements are complicated to make, and in the past, such measurements have only been routinely made for localized areas of the Sunday. However, with the new space mission of the Solar Dynamics Observatory (SDO), such measurements should now be made regularly over the full solar disc. This should significantly enhance our understanding of the solar magnetic field.

The typical distribution of magnetic flux on the Lord's day when averaged over large spatial scales shows strong fields at low latitudes and weak unipolar polar caps. For immature, rapidly rotating solar-like stars, very dissimilar magnetic field distributions may be found. An example of this tin be seen in figure 1b, where a typical radial magnetic field distribution for AB Dor taken through ZDI is shown. Compared with the Sun, key differences include: kilogauss polar fields and the mixing of both positive and negative polarities in the poles. While this is an illustration of a single star at a single time, many such observations have been made beyond a broad range of spectral classes. In fig. iii of Donati et al. [4], the varying grade of magnetic morphology and strength of the magnetic fields compared with those of the Sun, for a number of stars, can be seen as a part of stellar rotation menses and mass. While ZDI magnetic field datasets are generally too short to bear witness cyclic variations, contempo observations of the planet-hosting star, τ Bootis, accept shown that it may take a magnetic bike with a menstruum of only two years [xvi]. Indirect evidence for cyclic magnetic field variations on other stars can be seen from the Mt Wilson CaII H+1000 observations, which utilise chromospheric observations as a proxy for photospheric magnetic activeness [17] and through observations of stellar spots [xviii]. In the adjacent section, magnetic flux transport models used to simulate the evolution of the radial magnetic field at the level of the photosphere on the Lord's day and stars are discussed.

three. Magnetic flux transport simulations

Magnetic flux transport simulations [xix] model the big-scale, long-time evolution of the radial magnetic field across the solar photosphere. On the Sun, in one case new magnetic flux emerges, it evolves via big-scale flows such every bit differential rotation [20] and meridional menstruation [9]. In addition, convective cells such as super-granulation leads to a random walk of magnetic elements. Over large scales, this random walk may be modelled equally a diffusive process. Taking these effects into business relationship, the evolution of the radial magnetic field, B _r, at the solar surface (R _⊙=1) is governed by

where Ω(θ), u(θ) and D=200–450 km² s⁻¹ [21] are the differential rotation profile, meridional flow profile and diffusion coefficient. On the Sun, these iii effects human action on time scales of 0.25 year, ii years and finally 34 years.

Magnetic flux transport models have been highly successful in reproducing many features of the evolution of the radial magnetic field. These include the forcefulness of mid-latitude fields and the reversal of the polar fields. Full details of this can be establish in the review paper by Sheeley [19]. Since the early flux transport models were produced [21], new variations have been developed. These include:

	— describing the evolution of the magnetic field through a particle tracking concept, along with including emergence of small-calibration fields (ephemerial regions) and magneto-convective coupling [22];
	— reformulating the flux transport equation into a 'synoptic' send equation that evolves synoptic magnetic field observations from one rotation to the adjacent [23];
	— including a linear decay term for the radial field [24]; and
	— coupling the flux send model with a coronal evolution model so that both the photospheric and coronal magnetic fields are evolved together (see §4c [25,26]).

Owing to advances in measuring stellar magnetic fields, magnetic flux transport models have recently been applied in the stellar context. By increasing the flux emergence rate to 30 times that of the Lord's day, Schrijver & Title [27] showed how unipolar spots could exist produced in the poles of absurd solar-like stars. In contrast, Mackay et al. [28] showed that in social club to produce stiff intermingled polarities inside the polar regions of AB Dor (figure 1b), more meaning changes are required. These include increasing the emergence latitude of new bipoles from 40^° to 70^° and increasing the charge per unit of meridional flow from xi to 100 m s⁻ⁱ. This result suggests that on AB Dor, the meridional flow time calibration is comparable to that of its differential rotation.

4. Coronal magnetic field models

While the distribution and strength of magnetic fields are routinely measured in the solar photosphere, the aforementioned is not truthful for the solar corona, where such measurements are non presently possible owing to low coronal densities. To report coronal magnetic fields, theoretical models are required. In this department, we restrict the discussion of these models to global ones and in particular to those that utilize the force-free field approximation. The current state of global MHD models volition exist discussed in §seven.

Within the coronae of stars, the plasma beta is usually small (β=2μ _o p/B ²≪one). When this condition holds and length scales are smaller than the pressure scale height and velocities much less than the Alfven speed, the Lorentz force is dominant and whatsoever magnetic field that is in equilibrium satisfies the forcefulness-free field equation, j×B=0. The electric current, j=1/μ _o∇×B, can be written as j=α(r)B. The two most useful class of solution occur when α=0 (a potential magnetic field) and α=α(r) (a nonlinear force field). In the following subsections, we talk over the techniques used to construct both global potential and nonlinear force-free models. The first two techniques depict extrapolation techniques where there is no explicit human relationship between the coronal fields from one extrapolation to the next. In contrast, the third technique couples the evolution of both photospheric and coronal fields and produces continuous sequences of related forcefulness-costless fields.

(a) Potential field source surface models

The most mutual technique for modelling the global coronal magnetic field is through potential field source surface (PFSS) models [29]. Such models only require the radial magnetic field at the photosphere to exist specified, either from observations or theoretical models. The central assumption of a PFSS model is that there is zero electric current in the corona. The construction then reduces to solving Laplace'south equation where an outer purlieus condition of B _θ=B _ϕ=0 at a source surface (R _ss=2.5R _⊙) is commonly applied. In figure 2a, an example of a potential field extrapolation tin exist seen. This technique has been used to written report a wide diverseness of phenomena ranging from coronal holes [32], open up flux (see §5), coronal null points [33] and magnetic fields in the coronae of other stars [34].

Figure 2. (a) Example of a PFSS extrapolation. (b) Example of a non-potential coronal field produced past the global coronal evolution model of Mackay & van Ballegooijen [26] and Yeates *et al.* [30]. The images are taken from Yeates *et al.* [31], where the grey-scale image shows the radial field at the photosphere and the thin lines the coronal field lines.

(b) Current sheet source surface models

As an improvement to the PFSS model, Zhao & Hoeksema [35] have adult the current sheet source surface (CSSS) model. In contrast to the PFSS model, which has only i outer boundary, in the CSSS model, two boundaries are applied. Between the photosphere and an inner boundary, the 'cusp surface', the coronal field is assumed to be potential. However, betwixt this cusp surface and an outer boundary, electric currents may exist that redistribute the coronal field so that it is purely radial and uniformly distributed at this purlieus. Such uniform distribution of the radial field has been observed by the Ulysses mission [36], but is not produced by the PFSS models. In contempo years, the CSSS model has been used as an alternative to the PFSS model in describing the origin and variation of the Lord's day'south open magnetic flux (this will exist discussed in §5).

(c) Nonlinear strength-free global coronal models

Recently, van Ballegooijen et al. [25] and Mackay & van Ballegooijen [26] developed a new technique to study the global, long-term evolution of coronal magnetic fields. The technique couples together two distinct models. The first is a information-driven magnetic flux send model [37]. This uses observations of newly emerging magnetic bipoles to produce a continuous evolution of the observed photospheric magnetic flux over long periods of fourth dimension. Coupled to this is a quasi-static coronal evolution model [26,30], which evolves the coronal magnetic field through the sequences of nonlinear force-free fields in response to the observed photospheric evolution and flux emergence. Through this technique, the long-term continuous build-upward of free magnetic energy and electrical currents in the corona tin be followed. Such an evolution of the field is significantly different from extrapolation approaches that do not retain a memory of magnetic flux or connectivity from i extrapolation to the next. Such a memory is required to explain the slow build upward of free energy needed for many eruptive phenomena establish on the Sunday. In figure iib, an instance of a nonlinear strength-gratuitous global coronal field can be seen after 100 days of evolution. Figure iia illustrates a PFSS approximation corresponding to the same photospheric distribution of magnetic flux. The coronal field in the not-potential model is significantly different and is made upwards of highly twisted flux ropes, slightly sheared coronal arcades and well-nigh-potential open field lines. This technique has been applied to consider the long-term helicity transport across the solar surface from low to high latitudes [37]. In contrast to the technique described above, which constructs nonlinear force-gratuitous fields, Ruan et al. [38] accept recently adult a technique for the global extrapolation of magneto-hydrostatic fields from fixed radial boundary conditions.

Application of these 3 coronal modelling techniques to the Sunday's open up magnetic flux, solar filaments and finally CMEs is discussed over the next ii sections.

five. Open flux

The Dominicus's open up magnetic flux is office of the Sun'south big-calibration magnetic field that extends from the solar surface out into interplanetary space. In interplanetary space, information technology forms what is known every bit the interplanetary magnetic field (IMF). Understanding the origin and variation of the open flux is of import as

	— information technology is the origin of the high-speed solar air current and
	— the IMF straight interacts with the World'southward magnetosphere and the irregularities or curvatures in the Imf besides modulate the flux of high-energy catholic rays that impact the Earth's upper atmosphere; such impacts produce ¹⁴C [39] and ¹⁰Be [xl] isotopes, and therefore these isotopes, may exist used as historical datasets of solar activity.

Our present-day understanding of the Lord's day's open magnetic flux mainly comes from an important outcome from the Ulysses mission. Namely, that the magnitude of the radial IMF component in the heliosphere is independent of latitude [36]. This ways that magnetometer measurements at a single location at 1 AU (ane.v×10¹¹ m) may exist used to deduce the total open flux. In effigy 3, the variation of open flux relative to sunspot number can be seen for the final 3.five cycles. Over a solar bike, the open up flux varies at most by a factor of 2. Notwithstanding, this variation is not regular from one wheel to the next. A cardinal property of the open up flux is that it slightly lags behind the variation in sunspot number and peaks i–ii years afterward cycle maximum.

Figure 3. — Effigy 3. Graph of (a) open flux variation and (b) sunspot number for cycles xx–23 (from Lockwood *et al.* [41]).

While both directly and indirect observations exist for the Sun'south open flux, such measurements cannot exist fabricated for other stars. Attributable to this, theoretical models that predict the magnitude and spatial distribution of open flux are used. Inside the stellar context, the distribution of open flux with latitude [42] plays a key part in determining the mass and angular momentum loss and subsequently the spin down of stars [43–45].

(a) Theoretical models

Over the last xx years, a wide diversity of techniques have been adult to model the origin and variation of the Sunday'southward open flux. These may be split into ii wide categories: magnitude variation models and spatial distribution models.

(i) Magnitude variation models

The two most successful magnitude variation models are by Lockwood et al. [46] and Solanki et al. [47,48]. A key feature of these models is that they drive the variation of open flux through the direct input of observational data. However, the type of observational data used in each case is very different: ane originates from the Sun, the other from the Earth. In the instance of Lockwood et al. [46], they employ the geomagnetic aa-index [49], which provides a long-running measure out of geomagnetic action at the World. The aa-index is combined with a physics-based model of the solar air current and Parker spiral theory. The authors then deduce the magnitude of the open flux back to 1860 and conclude that the open up flux has doubled over the final 100 years.

In contrast, Solanki et al. [47] construct a semi-empirical model to decide the rate of change of open up flux. A key characteristic of this model is that the variation of open up flux is driven by observed sunspot numbers. In add-on, the model includes a linear decay term that contains a best-fit fourth dimension constant (τ _o). The all-time fit to observed IMF data occurs with τ _o=three.half dozen years. Using observed sunspot numbers, the model computes the open flux back to 1610. The linear decay term allows for secular variations of the open flux and explains why the open flux increases/decreases during short/long cycles. Later extensions of the model included the effect of ephemeral regions [48].

(two) Spatial distribution models

These models consider the spatial distribution of open flux on the Sunday. To do then, they couple together the two components. The first is a description of B _r at the photosphere, specified either through synoptic magnetic field observations or from magnetic flux ship simulations (§3). Secondly, a coronal field model is applied. A broad multifariousness of coronal models, each applying different approximations have been used. These range from PFSS models to CSSS models and more recently to non-potential coronal models. In all of these coronal models, field lines reaching the upper purlieus are deemed to be open.

In the written report past Wang & Sheeley [l], a combination of synoptic magnetograms and PFSS models were used to compute the open flux from 1971 to 1998. The synoptic magnetograms originated from either Wilcox Solar Observatory (WSO 1976–1995) or Mount Wilson Observatory (MWO 1971–1976, 1995–1998). The authors constitute that to reproduce a good understanding to Imf field measurements at 1 AU, they had to multiply the magnetograms by a strong breadth-dependent correction cistron ( Inline Formula ).

The use of such a latitude-dependent correction factor was recently questioned by Riley [51]. The writer pointed out that the correction gene used by Wang & Sheeley [fifty] was only correct for the utilize on MWO data and did not utilise to WSO data. It has its own correction factor of 1.85 52. On applying the correct correction cistron, Riley [51] showed that PFSS models gave a poor fit to observed IMF data (see fig. 4 of Riley [51]). To resolve the difference, Riley [51] put forward an alternative caption. He assumed that the open flux has two contributions, the first a variable groundwork contribution, such every bit that obtained from the PFSS model and secondly a short-term enhancement attributable to interplanetary CMEs, which he computed using a simple club of magnitude calculation. Through combining the two, a skilful agreement to IMF field observations was institute.

As an culling to using synoptic magnetic field observations, magnetic flux transport models take been widely used to provide the lower boundary condition in the report of the origin and variation of the Sun'due south open magnetic flux. Initial studies that combined the magnetic flux transport model with a PFSS coronal model plant conflicting results. Mackay et al. [53,54] found that commonly used input parameters of the magnetic flux send model failed to reproduce the master features of the open flux. However, Wang et al. [55] found that the correct behaviour could be institute if the rate of meridional catamenia was increased to 25ms ^−one and the flux of input bipoles multiplied past a factor of 3. Opposing such a stiff variation in the input parameters, Schussler & Baumann [56] put frontwards another possibility. Through using a variation of the magnetic flux transport model, which included a radial improvidence term for B _r, and irresolute the coronal model to a CSSS model, they plant that the correct variation of the open flux could be obtained. But only if new bipole tilt angles were decreased from 0.5λ to 0.15λ. Later studies by Cameron et al. [57] using the same technique showed that the radial improvidence term was not required if the tilt angles of the bipoles varied from i cycle to the next, such that stronger cycles have weaker tilt angles.

The word above shows that the correct variation of the Sun'south open flux may exist obtained through a variety of methods. More than recently, Yeates et al. [31] showed that, by assuasive electric currents to form in the corona, a improve agreement to the Imf measurements can be plant compared with those from PFSS models. Figure 4a compares various PFSS extrapolations using different magnetogram data (coloured lines) to the measured IMF field (greyness line). In this graph, the discrepancy between all potential field models and the IMF is specially credible around bicycle maximum. To resolve this, Yeates et al. [31] ran the global non-potential model described in §3.3 over four distinct, 6 calendar month periods (labelled A–D in figure 4a). The results of the simulation for catamenia B can be seen in figure 4b. In the plot, the dashed lines denote open flux from various PFSS extrapolations, the gray line the observed International monetary fund field strength and the black solid line the open flux from the non-potential global simulation. This conspicuously gives a much better agreement compared with the PFSS models. Yeates et al. [31] deduced that the open flux has iii main contributions. The first is a background level owing to the location of the flux sources. The 2d is an enhancement owing to electric currents, which results in an inflation of the magnetic field. This inflation can be seen as the steady increase of the open flux curve over the first rotation to a higher base level. The aggrandizement is the result of big-scale flows such as differential rotation and meridional flows, along with flux emergence, reconfiguring the coronal field. Finally, there is a desultory component to the open flux equally a upshot of CMEs.

Figure 4. — Figure iv. (a) Graph of IMF field variation (grey line) and PFSS approximations to the Imf field (coloured lines). (b) Not-potential open up flux estimate (thick black line) along with IMF field variation (grayness line) and PFSS approximations to the Imf field (coloured lines) over a 6 month period (from Yeates *et al*. [31]). (Online version in colour.)

vi. Long-term not-potential simulations of the solar corona

Recently, Yeates et al. [xxx,58] tested the validity of the non-potential coronal model described in §fourc by carrying out a series of detailed comparisons with observations. These comparisons compare output from the model with observational features for both solar filaments and CMEs.

To carry out the comparisons, the authors simulated the coupled development of both photospheric and coronal fields over a 6 calendar month catamenia from April to September 1999. To maintain the accuracy of the simulation over the six calendar month period, the emergence of new bipoles as determined from observations was also included. In the electronic supplementary cloth, movie1.mpg, a picture show of the simulation tin be seen where the photospheric field distribution is given past the gray-scale paradigm (white is positive flux and black is negative flux) and the lines denote the field lines of the nonlinear force-complimentary coronal field equally seen in the plane of the sky.

(a) Comparison with solar filament chirality

The first exam of the model considers the origin of the hemispheric design of solar filaments [59,lx], and in doing and so determines if the model fairly describes the build-up and transport of helicity from low to loftier latitudes on the Sun. In recent years, solar filaments take been classified in terms of their chirality [61]. This chirality may take 1 of two forms: dextral or sinistral. Dextral/sinistral filaments accept an axial magnetic field that points to the correct/left when the master axis of the filament is viewed from the positive polarity side of the polarity inversion line (PIL). A surprising feature of the chirality of filaments is that it displays an unusual big-calibration hemispheric pattern: dextral/sinistral filaments dominate in the Northern/Southern Hemispheres, although exceptions to this pattern do occur. Since filament chirality is straight related to magnetic helicity (dextral ∼ negative, sinistral ∼ positive), the formation and transport of filaments are an indication of the large-scale pattern of magnetic helicity on the Sunday, a key characteristic in explaining many eruptive phenomena. PFSS models cannot study the generation or transport of this helicity across the surface of the Sun. This tin only exist achieved with models that couple the evolution of both photospheric and coronal fields over long periods of time.

Using the global not-potential simulations, the origin of this hemispheric blueprint was considered through a directly comparison between theory and observations [62,63]. To carry out the comparing, Yeates et al. [37] first used Hα observations from the Large Bear Solar Observatory (BBSO) to determine the location and chirality of 109 filaments.

In the 2nd phase, a direct ane-to-one comparison [xxx] of the chirality produced by the model with the observed chirality of the filaments was carried out at the exact location that the filaments were observed. An example of this can be seen in figure 5a, the global field distribution can exist seen after 108 days of evolution. A zoomed in area along with false flux rope can exist seen in figure 5b, where the axial field is of dextral chirality. For comparison, the observed Hα filament that formed at this location tin be seen in figure vc. The filament was determined to be of dextral chirality, so the chirality formed in the simulation matches that of the observed filament.

Figure 5. — Effigy 5. Case of the comparison of theory and observations performed past Yeates *et al.* [30]. (a) Magnetic field distribution in the global simulation after 108 days of evolution, showing highly twisted flux ropes, weakly sheared arcades and near-potential open up fields. On the central image, white/blackness represents positive/negative flux. (b) Close up view of a dextral flux rope lying in a higher place a PIL inside the simulation. (c) BBSO Hα prototype of the dextral filament observed at this location. (Online version in colour.)

Through varying the sign and amount of helicity emerging inside new bipoles, Yeates et al. [30] (see their fig. 5b) showed that past emerging dominantly negative helicity in the Northern Hemisphere and positive in the Southern, a 96 per cent agreement can exist found between the chirality in the observations and simulations. An important feature is that the agreement is equally good for minority chirality filaments as well equally for dominant ones [64]. Another feature is the longer the simulations are run, the better the understanding. This indicates that the Sun has a long-term memory of the transport of helicity from low to high latitudes and that the model has the right physical furnishings to describe the build-upward and transport of this helicity across the surface of the Sun.

(b) Comparison with coronal mass ejection sites

For the second test, Yeates & Mackay [65] and Yeates et al. [58] considered the formation of flux ropes and their subsequent loss of equilibrium. Over the years, a wide variety of mechanisms take been proposed for the initiation of CMEs [66]. Ane such mechanism is the flux rope ejection model [67], where surface motions and flux cancellation produce a flux rope that subsequently loses equilibrium. Inside the global simulations of Yeates & Mackay [65], the formation of flux ropes is a natural upshot as flux cancels. Every bit these flux ropes become larger, local losses of equilibrium may occur [26]. In the paper of Yeates et al. [58], these losses of equilibrium are compared with the observed sites of CMEs. Kickoff, CMEs are identified from Lasco C2 observations and their initiation location in the low corona determined from cross correlation with Extreme Ultraviolet Imaging Telescope (EIT) 195 Å images. Of 330 CMEs identified, only 98 had a articulate low-coronal signature in the EIT images.

These 98 events were and then cross correlated with the sites of flux rope ejections from the global model. Agreement could be found in some, but not all cases. Overall, the all-time correlation between the model and CMEs was 0.49. The authors, however, identified two split up classes of CME. The first are those that exercise identify with flux rope ejection locations. These account for half of the sample. The other half were those located within the centres of active regions and frequently re-occur over short time scales. The global model was unsuccessful in re-producing these as information technology does not consider the internal structure or dynamics of agile regions. While the comparison was only partially successful, information technology shows that flux rope formation and loss of equilibrium are important models for CME initiation.

seven. Global magnetohydrodynamics models

In recent years, a significant advance has been made in the structure of realistic three-dimensional global MHD models [68,69]. Such models are required to give a self-consequent clarification between the interaction of the magnetic field and the plasma in the Sun'due south atmosphere. Although they requite a cocky-consistent description, these models are at the present time restricted by computational requirements to static photospheric purlieus conditions and steady-state coronal solutions.

A fundamental emphasis of this expanse of inquiry is on the straight comparison of the steady-land solutions with either white-lite [seventy] or multi-spectral extreme ultraviolet (EUV) and X-ray observations [68,69]. Early on global MHD models that used a simplified polytropic free energy equation were able to produce a proficient representation of the Sun's large-scale magnetic field [71], but they were unable to reproduce realistic emission profiles in EUV and X-rays. This was attributed to the fact that they did non produce a sufficiently high density and temperature contrast between open up- and closed-field regions. To improve the models, a more realistic energy equation has been incorporated, which included the effects of thermal conduction, radiative losses and coronal heating, along with modelling the upper chromosphere and transition region [68,69].

In effigy 6, the results of a comparison of the global MHD model of Lionello et al. [68] with observations tin be seen. In the left-hand column, three EUV laissez passer bands (171, 195, 284 Å) along with a Soft Ten-ray Telescope image can be seen. In the 3 other columns, synthetic emission profiles synthetic from the density and temperature distributions plant in the global MHD simulation are shown. Each cavalcade uses exactly the same MHD model with the only difference being the form of the coronal heating applied. While each solution produces roughly the same magnetic structure, the well-nigh important factor in reproducing the emissions is the coronal heating. The second column that uses an exponential form, which falls off with height gives the worst comparing. When spatially varying heating is applied, where the heating depends on the strength of the magnetic field at the loop's footpoint along with the loop's length [68,72], then the simulation captures many of the features of the observed emission. Similar results to those shown in figure 6 were too institute in the recent paper of Downs et al. [69].

Figure 6. — Figure vi. Comparison of observations and simulated emissions from a global steady-state MHD model. The observations are shown in the get-go column, while the emissions owing to different coronal heating profiles are shown in the other columns. The image is taken from fig. viii of Lionello *et al.* [68]. (Online version in colour.)

8. Conclusions

In this review, our nowadays-mean solar day understanding of global magnetic fields on the Dominicus and other stars has been discussed from both an observational and a theoretical viewpoint. For the case of the Sunday, we now have long-running datasets of global magnetic activity. For other stars, nosotros are just outset to larn of the wide variety of magnetic topologies that be. In terms of theoretical models, recent years have seen a significant advance in global modelling techniques. Global magnetic fields may be modelled nether the nonlinear forcefulness-free approximation for long periods of time or for short periods of time using highly detailed MHD models. A primal characteristic of these models is that they take been validated through diverse comparisons with observations. While our agreement has significantly increased over the concluding decade, in that location are several immediate outstanding issues. Four of these are discussed below, where the order in no way reflects their importance.

	— While we have a detailed understanding of the normal magnetic field component on the Dominicus, the aforementioned is not true for the vector field. With the SDO, we now have daily full disc vector magnetograms. Assay of these volition gain u.s.a. an understanding of the emergence and ship of vector fields across the Sun. This will allow us to study the origin and evolution of magnetic helicity, a key component in eruptive phenomena.
	— While our understanding of stellar magnetic fields has profoundly increased, observations are all the same sporadic. Long-term datasets of private stars across dissimilar spectral types are required. From this, we may deduce different magnetic flux emergence and transport parameters that are critical for the next generation of dynamo models.
	— For theoretical models, regular observations of the vector fields mean that more than constraints may be practical to input data that are used to specify the emergence of magnetic flux in models. New techniques must exist developed for the incorporation of vector data into simulations.
	— Global fourth dimension-dependent MHD models with evolving lower purlieus weather condition must be adult to provide a self-consistent model for the development and interaction of magnetic fields with plasma.

These issues may be addressed with the current suite of ground- and space-based observatories, along with developing new theoretical techniques. A key element in achieving this goal is the increasing computing power available for both existent-time data reduction and theoretical modelling.

Acknowledgements

The author would like to thank STFC and the Imperial Club for their financial back up and Alan Hood and Anthony Yeates for reading the review.

Footnotes

1 contribution of xi to a Theme Outcome 'Astrophysical processes on the Sun'.

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