Chaos and multifractals in the solar wind

By using the false-nearest-neighbours method, we have argued that the deterministic component of solar wind plasma dynamics should be low-dimensional. In fact, the results we have obtained using the method of topological embedding indicate that the behaviour of the solar wind can be approximately described by a low-dimensional chaotic attractor in the inertial manifold, which is a subspace of system phase space. We have also shown that the multifractal spectrum of the solar wind attractor is consistent with that for the multifractal measure of the self-similar generalized weighted Cantor set with two different scaling parameters and one probability measure parameter responsible for nonuniform compression in phase space and multifractality. The values of the parameters fitted also demonstrate that the complex solar wind system could only be weakly non-conservative (small dissipation) and quantify nonlinear dynamics; some parts of the attractor in phase space are visited much more frequently than other parts. In addition, to quantify the multifractality of space plasma intermittent turbulence, we consider that generalized Cantor set also in the context of scaling properties of solar wind turbulence. We investigate the resulting multifractal spectrum of a one-dimensional phenomenological model of turbulence cascade depending on its parameters, especially for asymmetric scaling. In particular, we have shown that intermittent pulses are stronger for the cascade model with two different scaling parameters. Even thought solar wind turbulence appears to be rather space filling, a better agreement with the data is obtained, especially for the negative index of generalized dimensions. Therefore we argue that there is a need to use a two-scale asymmetric cascade model. We hope that this generalized multifractal model will be a useful tool for analysis of intermittent turbulence in space plasmas. We thus believe that fractal analysis of chaotic systems could lead us to a deeper understanding of their nature, and maybe even to predict their seemingly unpredictable behaviour.     

Flows and obstacles in the solar wind

Understanding the physics of the various disturbances in the solar wind is critical to successful forecasts of space weather. The STEREO mission promises to bring us new and deeper understanding of these disturbances. As we stand on the threshold of the first results from this mission, it is appropriate to review what we know about solar wind disturbances. Because of their complementary nature we discuss both the disturbances that arise within the solar wind due to the stream structure and coronal mass ejecta and the disturbances that arise when the solar wind collides with planetary obstacles, such as magnetospheres.     

Sharp boundaries of solar wind plasma structures and their relationship to solar wind turbulence

Sharp (<10 min) and large (>20%) solar wind ion flux changes are common phenomena in turbulent solar wind plasma. These changes are the boundaries of small- and middle-scale solar wind plasma structures which can have a significant influence on Earth’s magnetosphere. These solar wind ion flux changes are typically accompanied by only a small change in the bulk solar wind velocity, hence, the flux changes are driven mainly by plasma density variations. We show that these events occur more frequently in high-density solar wind. A characteristic of solar wind turbulence, intermittency, is determined for time periods with and without these flux changes. The probability distribution functions (PDF) of solar wind ion flux variations for different time scales are calculated for each of these periods and compared. For large time scales, the PDFs are Gaussian for both data sets. For small time scales, the PDFs from both data set are more flat than Gaussian, but the degree of flatness is much larger for the data near the sharp flux change boundaries.     

Atmospheric electrodynamics modulated by the solar wind

Variations of stratospheric temperature are connected with changes of the solar wind dynamic pressure. This effect could be explained in the framework of the global electric circuit concept. The energy of the solar wind modulates the energy balance of the global electric circuit where the stratosphere could be one of its other elements. The conductivity of the stratosphere in the polar region is equal to and sometimes more than the conductivity of the ground surface covered by ice or permafrost. Re-distribution of the global electric circuit currents between the stratosphere and the ground surface determines a different relation between solar wind dynamics and variations of the stratospheric temperature during different seasons.     

A polytropic model for the solar wind

The solar wind fills the heliosphere and is the background medium in which coronal mass ejections propagate. A realistic modelling of the solar wind is therefore essential for space weather research and for reliable predictions. Although the solar wind is highly anisotropic, magnetohydrodynamic (MHD) models are able to reproduce the global, average solar wind characteristics rather well. The modern computer power makes it possible to perform full three dimensional (3D) simulations in domains extending beyond the Earth’s orbit, to include observationally driven boundary conditions, and to implement even more realistic physics in the equations. In general, MHD models for the solar wind often make use of additional source and sink terms in order to mimic the observed solar wind parameters and/or they hide the not-explicitly modelled physical processes in a reduced or variable adiabatic index. Even the models that try to take as much as possible physics into account, still need additional source terms and fine tuning of the parameters in order to produce realistic results. In this paper we present a new and simple polytropic model for the solar wind, incorporating data from the ACE spacecraft to set the model parameters. This approach allows to reproduce the different types of solar wind, where the simulated plasma variables are in good correspondence with the observed solar wind plasma near 1 AU.     

Correlations between neutral and ionized solar wind

We report results of a statistical study correlating ionized solar wind (ISW) fluxes observed by ACE during late 2000 and throughout 2001 with neutral solar wind (NSW) fluxes observed by IMAGE/LENA over the same period. The average correlation coefficient between the neutral and ionized solar wind is 0.66 with correlations greater than 0.80 occurring about 29% of the time. Correlations appear to be driven by high solar wind flux variability, similar to results obtained by in situ multi-spacecraft correlation studies. In this study, however, IMAGE remains inside the magnetosphere on over 95% of its orbits. As a function of day of year, or equivalently ecliptic longitude, the slope of the relationship between the neutral solar wind flux and the ionized solar wind flux shows an enhancement near the upstream direction, but the symmetry point appears shifted toward higher ecliptic longitudes than the interstellar neutral (ISN) flow direction by about 20°. The estimated peak interstellar neutral upstream density inside of 1 AU is about 7 × 10⁻³ cm⁻³.     

On the time lag between solar wind dynamic parameters and solar activity UV proxies

The solar activity displays variability and periodic behaviours over a wide range of timescales, with the presence of a most prominent cycle with a mean length of 11 years. Such variability is transported within the heliosphere by solar wind, radiation and other processes, affecting the properties of the interplanetary medium. The presence of solar activity–related periodicities is well visible in different solar wind and geomagnetic indices, although their time lags with respect to the solar cycle lead to hysteresis cycles. Here, we investigate the time lag behaviour between a physical proxy of the solar activity, the Ca II K index, and two solar wind parameters (speed and dynamic pressure), studying how their pairwise relative lags vary over almost five solar cycles. We find that the lag between Ca II K index and solar wind speed is not constant over the whole time interval investigated, with values ranging from 6 years to $～$1 year (average 3.2 years). A similar behaviour is found also for the solar wind dynamic pressure. Then, by using a Lomb-Scargle periodogram analysis we obtain a 10.21-year mean periodicity for the speed and 10.30-year for the dynamic pressure. We speculate that the different periodicities of the solar wind parameters with respect to the solar 11-year cycle may be related to the overall observed temporal evolution of the time lags. Finally, by accounting for them, we obtain empirical relations that link the amplitude of the Ca II K index to the two solar wind parameters.     

Two-velocity structure observed in the inner solar wind

Measurements of the motion of plasma density inhomogeneities in the inner solar wind are presented. The speeds were estimated using a cross-correlation analysis of radio frequency fluctuations of the Galileo spacecraft measured simultaneously at widely spaced ground stations. The radial projections of the correlation baselines on the pattern plane were of the order of several thousand kilometers. For cross-correlation functions calculated with comparatively short averaging times, we find that a pronounced two-velocity configuration is occasionally observed over the range of heliocentric distances 20 R < R < 40 R. The typical mean speed for such observations is about 300–400 km/s and the difference between the two predominant speeds is about 150–200 km/s. These results may indicate that the density fluctuations are associated with slow magnetosonic waves propagating in opposite directions at the local speed of sound in the reference frame moving with the mean solar wind speed. Quite reasonable estimates of the solar wind speed and speed of sound are obtained from this model. Another possible explanation of the two-velocity structures is that two independent solar wind streams are present simultaneously along different segments of the radio ray path.     

Propagation of energetic particles in the solar wind

The characteristics of solar energetic particle events as observed in interplanetary space depend on many physical processes acting at the source and during the transport from the source to the observer. These processes, such as acceleration at the Sun and the propagation near the Sun and in interplanetary space depend, in general, on both the particle velocity and rigidity. Thus, the evaluation of both the nuclear charge and/or atomic mass and the ionic charge of heavy ions turns out to be essential for the interpretation of the physical parameters observed, such as the energy spectra and the compositional variations during individual solar energetic particle events. In this paper recent results on the direct determination of the charge states of He, C, O, and Fe will be summarized. Using these results the compositional variations during individual solar particle events will be discussed. It will be shown that ratio changes by a factor of ～ 10 during the onset phase of solar particle events, as frequently observed, could be explained not only by rigidity dependent interplanetary propagation, but also by rigidity dependent diffusive propagation in the corona. However, there is now increasing experimental evidence that also other processes, such as compositional variations at the source and discontinuities of the interplanetary magnetic field, separating two different particle populations, may be important. Thus the picture emerges that these variations do not have a unique explanation but rather that each event has to be investigated individually.     

Electron densities and temperatures in the Venus ionosphere: Effects of solar EUV,solar wind pressure and magnetic field

The Venus ionosphere is influenced by variations in both solar EUV flux and solar wind conditions. On the dayside the location of the topside of the ionosphere, the ionopause, is controlled by solar wind dynamic pressure. Within the dayside ionosphere, however, electron density is affected mainly by solar EUV variations, and is relatively unaffected by solar wind variations and associated magnetic fields induced within the ionosphere. The existence of a substantial nightside ionosphere of Venus is thought to be due to the rapid nightward transport of dayside ionospheric plasma across the terminator. Typical solar wind conditions do not strongly affect this transport and consequently have little direct influence on nightside ionospheric conditions, except on occasions of extremely high solar wind dynamic pressure. However, both nightside electron density and temperature are affected by the presence of magnetic field, as in the case of ionospheric holes.     

Magnetic reconnection in solar flares and corresponding radio bursts

The 2D MHD model of the flare magnetic reconnection shows that a reconnection activity, changes of the magnetic field topology and generation of waves are connected. It is found that after the phase of a quasi-stationary reconnection in the extended current sheet above the flare arcade the tearing mode instability produces the plasmoids which then can interact and generate MHD waves. Results of particle-in-cell simulations of the tearing processes, which accelerate electrons, are mentioned. Then all these processes are discussed from the point of view of possible radio emissions. While shocks can contribute to the type II radio burst, the superthermal electrons trapped in plasmoids can generate so called drifting pulsating structures. Furthermore, regions with the MHD turbulence may manifest themselves as the lace or dm-spike bursts.     

Space telescope studies of Jupiter and Saturn simulated by Voyager observations

Space Telescope (ST) observations of Jupiter and Saturn will offer a unique opportunity for monitoring their changing meteorological characteristics. They will provide higher spatial and temporal resolution for composition and vertical structure studies than have been available to date. We have simulated the planetary camera observations of Jupiter and Saturn by Voyager images of the appropriate spatial scale. With this data set we have investigated the meteorological properties of these atmospheres which can be studied at these scales. In addition we have considered the advances obtainable with the high resolution spectrometer on ST compared with observations from ground-based and other Earth-orbiting satellites. These studies will provide insight into the scientific gain and possible problems in the use of ST for planetary studies.     

Electron plasma waves in the solar wind: AMPTE/IRM and UKS observations

Selected events of plasma wave and electromagnetic emissions in the earth's electron fore-shock region have been studied. Strong emissions are observed in the plasma-wave band when the site of the satellite is magnetically connected to the bow shock. These emissions are generally highly fluctuating. Under certain conditions one observes electromagnetic radiation at the second harmonic produced locally. Electromagnetic emission generated at a position far away from the site of the spacecraft is occasionally detected giving rise to remote sensing of the bow shock. These emissions are related to energetic electron fluxes.     

Propagation of upstream protons in the near-earth solar wind

The propagation of energetic protons (35–1600 keV) from the Earth's magnetosphere to the ISEE-3 spacecraft located about 240 earth radii (R_E) upstream in the solar wind is used as a tool to study the interaction between these protons and the solar wind. In this preliminary study we present proton pitch angle distributions seen at different times during the development of upstream events that occur in relatively quiet interplanetary conditions. In general a highly anisotropic sunward flow is seen at the beginning of the events. During the course of the events pitch angle distributions may vary between streaming along the field lines (peaked around 0° pitch angle), a uniform intensity between 0° and 90°, and a peaked distribution around a preferred pitch angle that is often near 90°.     

AL index dependence on the solar wind input revisited

Estimates of the geomagnetic indices made with real-time solar wind measurements form the basis of many space weather forecast techniques. We analyze 20 years of hourly AL and OMNI solar wind data to determine geomagnetic importance of various solar wind and IMF parameters. Besides the solar wind driver of primary importance (VB_s), the first-order contributions, significantly increasing the quality of the model are: solar wind velocity, 2 h of solar wind prehistory and 1 h of AL history. The factors of secondary importance, marginally contributing to overall statistical quality, are IMF B_y, solar wind density, and IMF fluctuations. The dynamic pressure is geomagnetically effective only if the pressure is lower than the average. Modelling of the same data set with an artificial neural network (ANN) confirmed our selection of important factors. Statistically the ANN model was just marginally better than our analytic expression . The AU index dependence is principally different from AL in several respects; therefore modelling of the AE composite index is physically misleading.     

Magnetospheric structure and high-energy photon emission of radio pulsars

Some elementary aspects of particle acceleration and flow along the polar field lines of an isolated, rotating magnetized neutron star are described. Semi-quantitaive consequences of these ideas for the emission of high energy gamma rays and their relation to gamma ray observations of radio pulsars are outlined. A global model of the magnetosphere in which these polar flows can occur is described briefly.     

Coronal spectroscopy: Probing sources of slow solar wind in active regions,and the early phases of solar flares

Coronal spectroscopy has pushed forward the understanding of physical processes in all phenomena on the Sun. In this review we concentrate specifically on plasma parameters measured in sources of the slow solar wind in active regions and the early phases of solar flares. These topics are a key part of the science goals of the Solar Orbiter mission (Müller et al., 2020) which has been designed to probe what drives the solar wind and solar transients that fill the heliosphere.Active regions, outside of flaring, have general characteristics that include closed loops showing red-shifted (down-flowing plasma), and the edges of the active regions showing blue-shifted (upflowing plasma). Constraining and understanding the evolution, behaviour and cause of the flows has been developed in the past years and are summarised. Of particular importance is the upflowing plasma which, in some cases, can contribute to the slow solar wind, and this review concentrates on recent results on this topic.The early phases of solar flares and their energy sources are not yet fully understood. For decades, there has been a huge interest in pin-pointing the trigger of a solar flare. Coronal spectroscopy has revealed small-scale dynamics that occurs tens of minutes before the flare begins. The understanding of the trigger is key to improving flare predictions in the future, as well as understanding the physical processes.Finally we look to the future of coronal spectroscopy, with new instruments and methodologies being developed that build on the current knowledge, and will improve significantly our physical understanding of processes at all scales on the Sun.     

Challenges to cosmic ray modeling: From beyond the solar wind termination shock

Voyager 1 crossed the solar wind termination shock on December 16, 2004 at a distance of 94 AU from the Sun, to become the first spacecraft to explore the termination shock region and to enter the heliosheath, the final heliospheric frontier. By the end of 2006, Voyager 1 will be at ∼101 AU, with Voyager 2 at ∼81 AU and still approaching the termination shock. Both spacecraft have been observing the modulation of galactic and anomalous cosmic rays since their launch in 1977. The recent observations close to or inside the heliosheath have provided several interesting ‘surprises’ with subsequent theoretical and modeling challenges. Examples are: what does the modulation of galactic cosmic rays amount to in this region?; how do the anomalous cosmic rays get accelerated and modulated?; why are there ‘breaks’ in the power-law slopes of the spectra of accelerated particles? Several numerical models have been applied to most of these topics over the years and comprehensive global predictions have been made the past decade, thought to be based on reasonable assumptions about the termination shock and the heliosheath. Examples of these predictions and assumptions are concisely discussed within the context of the main observed features of cosmic rays in the vicinity of the termination shock, ending with a discussion of some of the issues and challenges to cosmic ray modeling in particular.     

Simulation of cometary jets in interaction with the solar wind

The influence of cometary jets on the solar wind interaction is studied with a 3D hybrid simulation. Anisotropic outgassing patterns were until recently not considered in cometary simulations, despite strong anisotropies found at observations. Comet 67P Churyumov–Gerasimenko, the target of the ROSETTA mission, was chosen as a case study for a simulation series. The cometary outgassing at 2.7 AU is modeled to originate from a single sun-facing jet with different levels of collimation, from isotropy to extremely thin jets. As no bow shock is present at this distance, solar wind patterns resulting from the anisotropic outgassing become more apparent. We find narrower jets to increase the standoff distance of the plasma interaction structures. Also, the Mach cone is wider and stronger for certain jet profiles. The magnetic field remains unable to propagate through the coma, resulting in strong draping patterns for narrow jets due to the increased standoff distance.     

Impact of the solar wind dynamics on the ozone density variations

The analysis of the baloon and rocket measurement data reveals the changes of temperature in the polar and subpolar middle atmosphere with approaching of the magnetopause of the magnetosphere to the Earth. The data of the most observation points show the notable warming of the middle atmosphere in this situation, but there were some stations (“Vostok” in Antarctica and “Frobisher Bay” in Arctic) where the reverse dependence between these parameters was registered. The experimental data show that the total ozone content (TOC) decreases with approaching of the magnetopause to the Earth under both atmosphere warming or cooling at high altitudes. The drop in the TOC values is closely connected to increase of atmospheric electric field magnitude. The obtained results possibly could be explained in framework of the global electric circuit model.