Flux-Transport Solar Dynamos

Large-scale solar dynamo models were first built by Parker (1955). Over the past half a century these models have evolved significantly. We discuss here the development of a class of large-scale dynamo models which include, along with the α-effect and Ω-effect, an important third process, flux transport by meridional circulation. We present the properties of this ‘flux-transport’ dynamo, including the crucial role meridional circulation plays in giving this dynamo predictive power.     

Magnetic Flux Emergence, Activity, Eruptions and Magnetic Clouds: Following Magnetic Field from the Sun to the Heliosphere

We present an overview of how the principal physical properties of magnetic flux which emerges from the toroidal fields in the tachocline through the turbulent convection zone to the solar surface are linked to solar activity events, emphasizing the effects of magnetic field evolution and interaction with other magnetic structures on the latter. We compare the results of different approaches using various magnetic observables to evaluate the probability of flare and coronal mass ejection (CME) activity and forecast eruptive activity on the short term (i.e. days). Then, after a brief overview of the observed properties of CMEs and their theoretical models, we discuss the ejecta properties and describe some typical magnetic and composition characteristics of magnetic clouds (MCs) and interplanetary CMEs (ICMEs). We review some individual examples to clarify the link between eruptions from the Sun and the properties of the resulting ejecta. The importance of a synthetic approach to solar and interplanetary magnetic fields and activity is emphasized.     

Origin of the Solar Wind: Theory

A theory is presented for the origin of the solar wind, which is based on the behavior of the magnetic field of the Sun. The magnetic field of the Sun can be considered as having two distinct components: Open magnetic flux in which the field lines remain attached to the Sun and are dragged outward into the heliosphere with the solar wind. Closed magnetic flux in which the field remains entirely attached to the Sun, and forms loops and active regions in the solar corona. It is argued that the total open flux should tend to be constant in time, since it can be destroyed only if open flux of opposite polarity reconnect, a process that may be unlikely since the open flux is ordered into large-scale regions of uniform polarity. The behavior of open flux is thus governed by its motion on the solar surface. The motion may be due primarily to a diffusive process that results from open field lines reconnecting with randomly oriented closed loops, and also due to the usual convective motions on the solar surface such as differential rotation. The diffusion process needs to be described by a diffusion equation appropriate for transport by an external medium, which is different from the usual diffusion coefficient used in energetic particle transport. The loops required for the diffusion have been identified in recent observations of the Sun, and have properties, both in size and composition, consistent with their use in the model. The diffusive process, in which reconnection occurs between open field lines and loops, is responsible for the input of mass and energy into the solar wind. This revised version was published online in August 2006 with corrections to the Cover Date.     

Solar Magnetism: The State of Our Knowledge and Ignorance

We review some longstanding scientific mysteries related to solar magnetism, with final attention to the mystery of the “turbulent diffusion” essential for the theoretical α ω-dynamo that is believed to be the source of the magnetic fields of the Sun. Fundamental difficulties with the concept of turbulent diffusion of magnetic fields suggest that the solar dynamo problem needs to be reformulated. An alternative dynamo model is proposed, but it remains to be shown that the model can provide the quantitative aspects of the cyclic magnetic fields of the Sun.     

Total Solar Irradiance: What Have We Learned from the Last Three Cycles and the Recent Minimum?

The record of total solar irradiance (TSI) during the past 35 years shows similarities of the three solar cycles, but also important differences. During the recent minimum with an unusually long periods with no sunspots, TSI was also extremely low, namely 25% of a typical cycle amplitude lower than in 1996. Together with the values during the previous minima this points to a long-term change related to the strength of solar activity. On the other hand, activity indices as the 10.7?cm radio flux (F10.7), the CaII and MgII indices and also the Ly-α irradiance, show a much smaller decrease. This means that proxy models for TSI based on the photometric sunspot index (PSI), and on e.g. MgII index to represent faculae and network have to be complemented by a further component for the long-term change. TSI values at minima are correlated with the simultaneous values of the open magnetic field of the Sun at 1 AU and thus, these values may be used as a surrogate for the long-term change component. Such a 4-component model explains almost 85% of the variance of TSI over the three solar cycles available. This result supports also the idea that the long-term change of TSI is not due to manifestations of surface magnetism as the solar cycle modulation, but due to a change of the global temperature of Sun modulated by the strength of activity—being lower during low activity. To explain the difference between the minima in 1996 and 2008 we need a change of only 0.25?K.     

Coronal Holes and Open Magnetic Flux

Coronal holes are low-density regions of the corona which appear dark in X-rays and which contain “open” magnetic flux, along which plasma escapes into the heliosphere. Like the rest of the Sun’s large-scale field, the open flux originates in active regions but is subsequently redistributed over the solar surface by transport processes, eventually forming the polar coronal holes. The total open flux and radial interplanetary field component vary roughly as the Sun’s total dipole strength, which tends to peak a few years after sunspot maximum. An inverse correlation exists between the rate of flux-tube expansion in coronal holes and the solar wind speed at 1 AU. In the rapidly diverging fields present at the polar hole boundaries and near active regions, the bulk of the heating occurs at low heights, leading to an increase in the mass flux density at the Sun and a decrease in the asymptotic wind speed. The quasi-rigid rotation of coronal holes is maintained by continual footpoint exchanges between open and closed field lines, with the reconnection taking place at the streamer cusps. At much lower heights within the hole interiors, “interchange reconnection” between small bipoles and the overlying open flux also gives rise to coronal jets and polar plumes.     

Planetary Dynamos from a Solar Perspective

Direct numerical simulations of the geodynamo and other planetary dynamos have been successful in reproducing the observed magnetic fields. We first give an overview on the fundamental properties of planetary magnetism. We review the concepts and main results of planetary dynamo modeling, contrasting them with the solar dynamo. In planetary dynamos the density stratification plays no major role and the magnetic Reynolds number is low enough to allow a direct simulation of the magnetic induction process using microscopic values of the magnetic diffusivity. The small-scale turbulence of the flow cannot be resolved and is suppressed by assuming a viscosity far in excess of the microscopic value. Systematic parameter studies lead to scaling laws for the magnetic field strength or the flow velocity that are independent of viscosity, indicating that the models are in the same dynamical regime as the flow in planetary cores. Helical flow in convection columns that are aligned with the rotation axis play an important role for magnetic field generation and forms the basis for a macroscopic α-effect. Depending on the importance of inertial forces relative to rotational forces, either dynamos with a dominant axial dipole or with a small-scale multipolar magnetic field are found. Earth is predicted to lie close to the transition point between both classes, which may explain why the dipole undergoes reversals. Some models fit the properties of the geomagnetic field in terms of spatial power spectra, magnetic field morphology and details of the reversal behavior remarkably well. Magnetic field strength in the dipolar dynamo regime is controlled by the available power and found to be independent of rotation rate. Predictions for the dipole moment agree well with the observed field strength of Earth and Jupiter and moderately well for other planets. Dedicated dynamo models for Mercury, Saturn, Uranus and Neptune, which assume stably stratified layers above or below the dynamo region, can explain some of the unusual field properties of these planets.     

Photospheric and Subphotospheric Dynamics of Emerging Magnetic Flux

Magnetic fields emerging from the Sun’s interior carry information about physical processes of magnetic field generation and transport in the convection zone. Soon after appearance on the solar surface the magnetic flux gets concentrated in sunspot regions and causes numerous active phenomena on the Sun. This paper discusses some properties of the emerging magnetic flux observed on the solar surface and in the interior. A statistical analysis of variations of the tilt angle of bipolar magnetic regions during the emergence shows that the systematic tilt with respect to the equator (the Joy’s law) is most likely established below the surface. However, no evidence of the dependence of the tilt angle on the amount of emerging magnetic flux, predicted by the rising magnetic flux rope theories, is found. Analysis of surface plasma flows in a large emerging active region reveals strong localized upflows and downflows at the initial phase of emergence but finds no evidence for large-scale flows indicating future appearance a large-scale magnetic structure. Local helioseismology provides important tools for mapping perturbations of the wave speed and mass flows below the surface. Initial results from SOHO/MDI and GONG reveal strong diverging flows during the flux emergence, and also localized converging flows around stable sunspots. The wave speed images obtained during the process of formation of a large active region, NOAA 10488, indicate that the magnetic flux gets concentrated in strong field structures just below the surface. Further studies of magnetic flux emergence require systematic helioseismic observations from the ground and space, and realistic MHD simulations of the subsurface dynamics.     

Energy release in stellar magnetospheres

The interaction of a stellar magnetosphere with a thin accretion disk is considered. Specifically, I consider a model in which (1) the accretion disk is magnetically linked to the star over a large range of radii and (2) the magnetic diffusivity of the disk is sufficiently small that there is little slippage of field lines within the disk on the rotation time scale. In this case the magnetic energy built up as a result of differential rotation between the star and the disk is released in quasi-periodic reconnection events occuring in the magnetosphere (Aly and Kuijpers 1990). The radial transport of magnetic flux in such an accretion disk is considered. It is show that the magnetic flux distribution is stationary on the accretion time scale, provided the time average of the radial component of the field just above the disk vanishes. A simple model of the time-dependent structure of the magnetosphere is presented. It is shown that energy release in the magnetosphere must take place for (differential) rotation angles less than about 3 radians. The magnetic flux distribution in the disk depends on the precise value of the rotation angle.     

3-D magnetic field and current system in the heliosphere

In this paper a global system of the magnetic field and current from the interaction of the solar wind plasma and the interstellar medium is modeled using a 3-D MHD simulation. The terminal shock, the heliopause and the outer shock are clearly determined in our simulation. In the heliosheath the toroidal magnetic field is found to increase with the distance from the sun. The magnetic field increases rapidly in the upstream region of the heliosheath and becomes maximum between the terminal shock and the heliopause. Hence a shell-type magnetic wall is found to be formed in the heliosheath. Because of this magnetic wall the radially expanding solar wind plasma changes its direction tailward in all latitudes except the equatorial region. Only the equatorial disk-like plasma flow is found to extend to the heliopause through the weak magnetic-field region around the equator. Two kinds of global current loops which sustain the toroidal magnetic field in the heliosphere are found in our simulation.The influence of the 11-year solar cycle variation of the magnetic polarity is also examined. It is found that the polarity of the toroidal magnetic field in the heliosheath switches at every solar cycle change. Hence the heliosheath is found to consist of such magnetized plasma bubbles. The neutral sheets are found to extend between such magnetized plasma bubbles in the 3-D heliosheath in a complicated form. The magnetic-pressure effect on the heliosheath plasma structure is also examined.     

Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles,Cosmic Rays,and Magnetic Fields

This paper summarizes the results obtained by the team “Heliosheath Processes and the Structure of the Heliopause: Modeling Energetic Particles, Cosmic Rays, and Magnetic Fields” supported by the International Space Science Institute (ISSI) in Bern, Switzerland. We focus on the physical processes occurring in the outer heliosphere, especially at its boundary called the heliopause, and in the local interstellar medium. The importance of magnetic field, charge exchange between neutral atoms and ions, and solar cycle on the heliopause topology and observed heliocentric distances to different heliospheric discontinuities are discussed. It is shown that time-dependent, data-driven boundary conditions are necessary to describe the heliospheric asymmetries detected by the Voyager spacecraft. We also discuss the structure of the heliopause, especially due to its instability and magnetic reconnection. It is demonstrated that the Rayleigh–Taylor instability of the nose of the heliopause creates consecutive layers of the interstellar and heliospheric plasma which are magnetically connected to different sources. This may be a possible explanation of abrupt changes in the galactic and anomalous cosmic ray fluxes observed by Voyager 1 when it was crossing the heliopause structure for a period of about one month in the summer of 2012. This paper also discusses the plausibility of fitting simulation results to a number of observational data sets obtained by in situ and remote measurements. The distribution of magnetic field in the vicinity of the heliopause is discussed in the context of Voyager measurements. It is argued that a classical heliospheric current sheet formed due to the Sun’s rotation is not observed by in situ measurements and should not be expected to exist in numerical simulations extending to the boundary of the heliosphere. Furthermore, we discuss the transport of energetic particles in the inner and outer heliosheath, concentrating on the anisotropic spatial diffusion diffusion tensor and the pitch-angle dependence of perpendicular diffusion and demonstrate that the latter can explain the observed pitch-angle anisotropies of both the anomalous and galactic cosmic rays in the outer heliosheath.     

Can Surface Flux Transport Account for the Weak Polar Field in Cycle 23?

To reproduce the weak magnetic field on the polar caps of the Sun observed during the declining phase of cycle 23 poses a challenge to surface flux transport models since this cycle has not been particularly weak. We use a well-calibrated model to evaluate the parameter changes required to obtain simulated polar fields and open flux that are consistent with the observations. We find that the low polar field of cycle 23 could be reproduced by an increase of the meridional flow by 55% in the last cycle. Alternatively, a decrease of the mean tilt angle of sunspot groups by 28% would also lead to a similarly low polar field, but cause a delay of the polar field reversals by 1.5 years in comparison to the observations.     

Source Region of High and Low Speed Wind during the Spartan 201-05 Flight

The large-scale coronal magnetic fields of the Sun are believed to play an important role in organizing the coronal plasma and channeling the high and low speed solar wind along the open magnetic field lines of the polar coronal holes and the rapidly diverging field lines close to the current sheet regions, as has been observed by the instruments aboard the Ulysses spacecraft from March 1992 to March 1997. We have performed a study of this phenomena within the framework of a semi-empirical model of the coronal expansion and solar wind using Spartan, SOHO, and Ulysses observations during the quiescent phase of the solar cycle. Key to this understanding is the demonstration that the white light coronagraph data can be used to trace out the topology of the coronal magnetic field and then using the Ulysses data to fix the strength of the surface magnetic field of the Sun. As a consequence, it is possible to utilize this semi-empirical model with remote sensing observation of the shape and density of the solar corona and in situ data of magnetic field and mass flux to predict values of the solar wind at all latitudes through out the solar system. We have applied this technique to the observations of Spartan 201-05 on 1–2 November, 1998, SOHO and Ulysses during the rising phase of this solar cycle and speculate on what solar wind velocities Ulysses will observe during its polar passes over the south and the north poles during September of 2000 and 2001. In order to do this the model has been generalized to include multiple streamer belts and co-located current sheets. The model shows some interesting new results. This revised version was published online in August 2006 with corrections to the Cover Date.     

A New Morphology of Solar Activity and Recurrent Geomagnetic Disturbances: The Late-Declining Phase of the Sunspot Cycle

Certain aspects of the Sun and resulting geomagnetic disturbances can be studied better on the source surface, an imaginary spherical surface of 3.5 solar radii, than on the photospheric surface. This paper presents evidence that the Sun exhibits one of the most fundamental aspects of activities most clearly during the late-declining phase of the sunspot cycle. It is the period when 27-day average values of the solar wind speed and of geomagnetic disturbances tend to be highest during the sunspot cycle. Important findings of this study on the late-declining phase of the sunspot cycle are the following:

1. By introducing a new coordinate system, modifying the Carrington coordinates, it is shown that various solar activity phenomena, solar flares, the brightest coronal regions, and also the lowest solar wind speed region, tend to concentrate in two quadrants, one around 90^° in longitude in the northern hemisphere (NE) and the other around 270^° in longitude in the southern hemisphere (SW). For this reason, the new coordinate system is referred to as the NESW coordinate system.
2. It is shown that the above results are closely related to the fact that the neutral line exhibits a single wave (sinusoidal or rectangular) in both the Carrington coordinates and the NESW coordinate system during the late-declining phase. The shift of the neutral line configuration during successive solar rotations during the late-declining phase causes longitudinal scatter of the location of solar flares with respect to the neutral line in a statistical study. The NESW coordinate system is designed to suppress the shift, so that the single wave location is fixed and thus a ‘nest’ of solar flares emerges in the NE and SW quadrants.
3. It is also shown that the single wave is the source of the double peak of the solar wind speed and two series of recurrent geomagnetic disturbances in each solar rotation, making the 27-day average solar wind and geomagnetic disturbances highest during the sunspot cycle. The double peak is a basic feature during the late-declining phase, but is obscured by several complexities which we identified in this paper; see item 8.
4. The single wave of the neutral line configuration can be approximated by three dipole fields, one which can be represented by a central dipole (parallel or anti-parallel to the rotation axis) and two hypothetical dipoles on the photosphere. This configuration is referred to as the triple dipole model.
5. The location of the two hypothetical photospheric dipoles coincide with the two active regions (solar flares, the brightest coronal region) and also the lowest solar wind speed region in the NESW coordinate system; the lowest solar wind regions are the cause of the valleys of the double peak of the solar wind speed.
6. The two hypothetical dipole fields actually do exist at the location of the two active regions in a coarse magnetic map (5 × 5^°). The two dipoles follow the Hale–Nicholson polarity law. Thus, they are real physical entities.
7. The apparent meridional rotation of the dipolar field on the source surface during the sunspot cycle results from combined changes of both the central dipole field and of the two photospheric dipoles, although the central dipole remains axially parallel or anti-parallel. Thus, the Sun has a general field that can be represented by an axially aligned dipole located at the center of the Sun throughout the sunspot cycle, except for the sunspot maximum period when the polarization reversal occurs.
8. The complexity of recurrent geomagnetic disturbances can also be understood by having the NESW coordinate system for various solar phenomena and the relative location of the earth with respect to the solar equatorial plane.
9. As the intensity of the two dipoles decreases toward the end of the sunspot cycle, the amplitude of the single wave decreases, and the neutral line tends to align with the heliographic equator.
10. The neutral line shows a double wave structure during certain epochs of the sunspot cycle. In such a situation, it can be considered that two NESW coordinate systems are present in one Carrington coordinate, resulting in four active regions.
11. The so-called classical “sector boundary” arises when the peaks (top and bottom) of the single wave reached 90^° in latitude in both hemispheres.
12. In summary: A study of the late-declining period of the sunspot cycle is very important compared with the sunspot maximum period. In the late-declining period, the Sun shows its activities in the simplest form. It is suggested that some of the basic features of solar activities and recurrent geomagnetic disturbances that have been studied by many researchers in the past can be synthesized in a simplest way by introducing the NESW coordinate system and the triple dipole model. There is a possibility that the basic results we learned during the late phase of the sunspot cycle can be applicable to the rest of the sunspot cycle.

     

Solar flux and its variations

We present data on the solar irradiance as derived from a number of sources. An attempt was made to bring these data onto a uniform scale. The results are presented in Table IV and Figure 6. Summation of fluxes at all wavelengths yields a figure of 1357.826 W m^-2 for the solar constant. Estimates are made of the solar flux variations due to flares, active regions (slowly varying component), solar rotation and the 11-year cycle.Solar activity does not produce a significant variation in the value of the solar constant. Nevertheless, variations in the X-ray and extreme ultraviolet portions of the solar flux may be several orders of magnitude during solar activity, especially at times of major flares. It is well established that these short wavelength flux enhancements cause significant changes in the terrestrial ionosphere.     

Modelling solar irradiance variations: Comparison with observations,including line-ratio variations

Solar irradiance variations show a strong temporal and spectral dependence. The progression of the Sun through its activity cycle as well as solar rotation are mirrored in the irradiance variations. The spectral dependence is such that the variations are several magnitudes larger in the EUV than in the visible or infrared.We present a simple 3-component model that is based on the assumption that changes in the solar flux are exclusively due to changes in spot and facular coverage. We compare our model to observations of the spectral solar irradiance variations.Despite its simplicity, we find that the agreement between our model and the observations is surprisingly good. We also explore the reliability and the limitations of our approach by comparing observations of the solar facular contrast and of the changes in spectral line depths with our calculations.     

Magnetic Fields, Relativistic Particles, and Shock Waves in Cluster Outskirts

It is only now, with low-frequency radio telescopes, long exposures with high-resolution X-ray satellites and γ-ray telescopes, that we are beginning to learn about the physics in the periphery of galaxy clusters. In the coming years, Sunyaev-Zel’dovich telescopes are going to deliver further great insights into the plasma physics of these special regions in the Universe. The last years have already shown tremendous progress with detections of shocks, estimates of magnetic field strengths and constraints on the particle acceleration efficiency. X-ray observations have revealed shock fronts in cluster outskirts which have allowed inferences about the microphysical structure of shocks fronts in such extreme environments. The best indications for magnetic fields and relativistic particles in cluster outskirts come from observations of so-called radio relics, which are megaparsec-sized regions of radio emission from the edges of galaxy clusters. As these are difficult to detect due to their low surface brightness, only few of these objects are known. But they have provided unprecedented evidence for the acceleration of relativistic particles at shock fronts and the existence of μG strength fields as far out as the virial radius of clusters. In this review we summarise the observational and theoretical state of our knowledge of magnetic fields, relativistic particles and shocks in cluster outskirts.     

Planetary Magnetic Fields and Solar Forcing: Implications for Atmospheric Evolution

The solar wind and the solar XUV/EUV radiation constitute a permanent forcing of the upper atmosphere of the planets in our solar system, thereby affecting the habitability and chances for life to emerge on a planet. The forcing is essentially inversely proportional to the square of the distance to the Sun and, therefore, is most important for the innermost planets in our solar system—the Earth-like planets. The effect of these two forcing terms is to ionize, heat, chemically modify, and slowly erode the upper atmosphere throughout the lifetime of a planet. The closer to the Sun, the more efficient are these process. Atmospheric erosion is due to thermal and non-thermal escape. Gravity constitutes the major protection mechanism for thermal escape, while the non-thermal escape caused by the ionizing X-rays and EUV radiation and the solar wind require other means of protection. Ionospheric plasma energization and ion pickup represent two categories of non-thermal escape processes that may bring matter up to high velocities, well beyond escape velocity. These energization processes have now been studied by a number of plasma instruments orbiting Earth, Mars, and Venus for decades. Plasma measurement results therefore constitute the most useful empirical data basis for the subject under discussion. This does not imply that ionospheric plasma energization and ion pickup are the main processes for the atmospheric escape, but they remain processes that can be most easily tested against empirical data. Shielding the upper atmosphere of a planet against solar XUV, EUV, and solar wind forcing requires strong gravity and a strong intrinsic dipole magnetic field. For instance, the strong dipole magnetic field of the Earth provides a “magnetic umbrella”, fending of the solar wind at a distance of 10 Earth radii. Conversely, the lack of a strong intrinsic magnetic field at Mars and Venus means that the solar wind has more direct access to their topside atmosphere, the reason that Mars and Venus, planets lacking strong intrinsic magnetic fields, have so much less water than the Earth? Climatologic and atmospheric loss process over evolutionary timescales of planetary atmospheres can only be understood if one considers the fact that the radiation and plasma environment of the Sun has changed substantially with time. Standard stellar evolutionary models indicate that the Sun after its arrival at the Zero-Age Main Sequence (ZAMS) 4.5 Gyr ago had a total luminosity of ≈70% of the present Sun. This should have led to a much cooler Earth in the past, while geological and fossil evidence indicate otherwise. In addition, observations by various satellites and studies of solar proxies (Sun-like stars with different age) indicate that the young Sun was rotating more than 10 times its present rate and had correspondingly strong dynamo-driven high-energy emissions which resulted in strong X-ray and extreme ultraviolet (XUV) emissions, up to several 100 times stronger than the present Sun. Further, evidence of a much denser early solar wind and the mass loss rate of the young Sun can be determined from collision of ionized stellar winds of the solar proxies, with the partially ionized gas in the interstellar medium. Empirical correlations of stellar mass loss rates with X-ray surface flux values allows one to estimate the solar wind mass flux at earlier times, when the solar wind may have been more than 1000 times more massive. The main conclusions drawn on basis of the Sun-in-time-, and a time-dependent model of plasma energization/escape is that:

1. Solar forcing is effective in removing volatiles, primarily water, from planets,
2. planets orbiting close to the early Sun were subject to a heavy loss of water, the effect being most profound for Venus and Mars, and
3. a persistent planetary magnetic field, like the Earth’s dipole field, provides a shield against solar wind scavenging.