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.     

Helioseismology and the solar cycle

Helioseismic measurements stretching back for about three decades have clearly shown that the acoustic modes are sensitive to solar-cycle changes. 2006 marks the first full 11-year cycle of continuous observations from the Global Oscillation Network Group (GONG), and 10 years of observations with the Michelson Doppler Imager (MDI) aboard the SOHO spacecraft. For the first time, global helioseismology has traced the migrating zonal flow pattern of the torsional oscillation deep within the convection zone, while local helioseismology has revealed the changing pattern of meridional flows over the cycle. The frequencies, lifetimes, and amplitudes of acoustic modes all show variations that closely track the surface distribution of magnetic activity and may provide insight into the excitation and damping of the oscillations. Efforts to trace magnetic field and sound speed or density changes in the solar interior have proved more challenging.     

Probing solar and stellar interior dynamics and dynamo

Solar and stellar activity is a result of complex interaction between magnetic field, turbulent convection and differential rotation in a star’s interior. Magnetic field is believed to be generated by a dynamo process in the convection zone. It emerges on the surface forming sunspots and starspots. Localization of the magnetic spots and their evolution with the activity cycle is determined by large-scale interior flows. Thus, the internal dynamics of the Sun and other stars hold the key to understanding the dynamo mechanism and activity cycles. Recently, significant progress has been made for modeling magnetohydrodynamics of the stellar interiors and probing the internal rotation and large-scale dynamics of the Sun by helioseismology. Also, asteroseismology is beginning to probe interiors of distant stars. I review key achievements and challenges in our quest to understand the basic mechanisms of solar and stellar activity.     

Coupling of earth’s magnetosphere,solar wind and lunar plasma environment

The Moon does not have significant atmosphere and magnetic field. So it was considered like a passive absorber of incoming plasma. The latest observation revealed that the significant deflected proton fluxes exist over magnetic anomalies at lunar surface. Such deflection implies that the magnetic anomalies may act as magnetosphere-like obstacles (mini-magnetospheres), modifying the upstream plasma.     

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.     

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.     

Modeling of the outer heliosphere with the realistic solar cycle

Time-dependent kinetic-continuum model of the solar wind interaction with the two-component local interstellar cloud (LIC) has been developed recently [Izmodenov, V., Malama, Y.G., Ruderman, M.S. Solar cycle influence on the interaction of the solar wind with local interstellar cloud. Astron. Astrophys. 429, 1069–1080, 2005a.]. Here, we adopted this model to the realistic solar cycle, when the solar wind parameters at the Earth’s orbit are taken from space data. This paper focuses on the results related to the termination shock (TS) excursion with the solar cycle that may help to understand Voyager 1 data obtained at and after the crossing of the termination shock and to predict the time of the TS crossing by Voyager 2.     

Model of a fluxtube with a twisted magnetic field in the stratified solar atmosphere

We build a single vertical straight magnetic fluxtube spanning the solar photosphere and the transition region which does not expand with height. We assume that the fluxtube containing twisted magnetic fields is in magnetohydrostatic equilibrium within a realistic stratified atmosphere subject to solar gravity. Incorporating specific forms of current density and gas pressure in the Grad–Shafranov equation, we solve the magnetic flux function, and find it to be separable with a Coulomb wave function in radial direction while the vertical part of the solution decreases exponentially. We employ improved fluxtube boundary conditions and take a realistic ambient external pressure for the photosphere to transition region, to derive a family of solutions for reasonable values of the fluxtube radius and magnetic field strength at the base of the axis that are the free parameters in our model. We find that our model estimates are consistent with the magnetic field strength and the radii of Magnetic bright points (MBPs) as estimated from observations. We also derive thermodynamic quantities inside the fluxtube.     

The characteristics of sharp (small-scale) boundaries of solar wind plasma and magnetic field structures

We investigate properties of large (>20%) and sharp (<10 min) solar wind ion flux changes using INTERBALL-1 and WIND plasma and magnetic field measurements from 1996 to 1999. These ion flux changes are the boundaries of small-scale and middle-scale solar wind structures. We describe the behavior of the solar wind velocity, temperature and interplanetary magnetic field (IMF) during these sudden flux changes. Many of the largest ion flux changes occur during periods when the solar wind velocity is nearly constant, so these are mainly plasma density changes. The IMF magnitude and direction changes at these events can be either large or small. For about 55% of the ion flux changes, the sum of the thermal and magnetic pressure are in balance across the boundary. In many of the other cases, the thermal pressure change is significantly more than the magnetic pressure change. We also attempted to classify the types of discontinuities observed.     

Gnevyshev gap, Forbush decreases, ICMEs and solar wind electric field: relationships

We have studied annual frequency distribution of the Forbush decreases for three solar cycles (20, 21, 22); most are associated with the fast ICMEs and SSCs. The frequency varies in step with the solar cycle but the distribution has a notable gap embedded in it, near the maximum of the cycle leading to two peaks in Forbush decreases per cycle. We show that the gap coincides with the epoch of solar polar field reversal. There is an indication of an odd/even cycle effect in the frequency distribution of Forbush decreases and the associated SSCs. We find that two peaks in Forbush decrease and SSC distributions are separated by the Gnevyshev gap; second peaks occur well before the onset of the high-speed streams in the descending phase of a cycle which do not cause Forbush decreases but do contribute to a peak in the geomagnetic activity index Ap. We compare Forbush decrease and SSC distributions with the corresponding distribution of the solar wind electric field and find that a large amplitude of the electric field of itself does not cause a Forbush decrease to occur unless it is also associated with a fast ICME/SSC.     

Characterization of the slow wind in the outer corona

The study concerns the streamer belt observed at high spectral resolution during the minimum of solar cycle 23 with the Ultraviolet Coronagraph Spectrometer (UVCS) onboard SOHO. On the basis of a spectroscopic analysis of the O VI doublet, the solar wind plasma parameters are inferred in the extended corona. The analysis accounts for the coronal magnetic topology, extrapolated through a 3D magneto-hydrodynamic model, in order to define the streamer boundary and to analyse the edges of coronal holes. The results of the analysis allow an accurate identification of the source regions of the slow coronal wind that are confirmed to be along the streamer boundary in the open magnetic field region.     

Solar wind origins in coronal holes and in the quiet Sun

Coronal hole (CH) and the quiet Sun (QS) are considered to account for sources of fast and slow solar wind streams, respectively. The differences between the solar wind streams flowing out from the CH and the QS are thought to be related with different plasma generation and acceleration mechanisms in the respective source regions. Here we review recent studies on the solar wind origin in the CH and the QS, compare the possible flow geometries and magnetic structures in these two kinds of solar regions, and summarize the physics associated with two different origin scenarios.     

The characteristics of valley phase as predictor of the forthcoming solar cycle

Is Solar Cycle 24 anomalous? How do we predict the main features of a forthcoming cycle? In order to reply such questions, this work partitions quantitatively each cycle into valley, ascend, peak, and descend phases, statistically investigate the correlations between valley phase and the forthcoming cycle. We find that the preceding valley phase may dominate and can be predictor of the forthcoming cycle: (1) The growth rate in ascend phase strongly negatively correlates to valley length and strongly positively correlates to cycle maximum. (2) The cycle maximum strongly negatively correlates to valley length, and strongly positively correlates to cycle minimum. (3) The cycle period strongly negatively correlates to the valley variation. Based on these correlations, we conclude that the solar cycle 24 is a relatively weak and long cycle which is obviously weaker than Cycle 23. The similarity analysis also presents the similar result. The Cycle 25 is also inferred possibly to be a weak cycle. These results can help us understanding the physical processes of solar cycles.     

Predicting indices of the ionosphere response to solar activity for the ascending phase of the 25th solar cycle

The international reference ionosphere, IRI, and its extension to plasmasphere, IRI-Plas, models require reliable prediction of solar and ionospheric proxy indices of solar activity for nowcasting and forecasting of the ionosphere parameters. It is shown that IRI prediction errors could increase for the F2 layer critical frequency foF2 and the peak height hmF2 due to erroneous predictions of the ionospheric global IG index and the international sunspot number SSN1 index on which IRI and IRI-Plas models are built. Regression relation is introduced to produce daily SSN1 proxy index from new time series SSN2 index provided from June 2015, after recalibration of sunspots data. To avoid extra errors of the ionosphere model a new solar activity prediction (SAP) model for the ascending part of the solar cycle SC25 is proposed which expresses analytically the SSN1 proxy index and the 10.7-cm radio flux F10.7 index in terms of the phase of the solar cycle, Φ. SAP model is based on monthly indices observed during the descending part of SC24 complemented with forecast of time and amplitude for SC25 peak. The strength of SC25 is predicted to be less than that of SC24 as shown with their amplitudes for eight types of indices driving IRI-Plas model.     

Effect of current sheets on the power spectrum of the solar wind magnetic field using a cell model

A puzzling observation of solar wind MHD turbulence is the often seen Kolmogorov scaling of k^-5/3$k^{-5/3}$, even though the solar wind MHD turbulence is dominated by Alfvénic fluctuations. Recently Li et al. (2011) proposed that the presence of current sheets may be the cause of the Kolmogorov scaling. Here, using a cell model of the solar wind we examine the effect of current sheets on the power spectrum of the solar wind magnetic field. We model the solar wind as multiple cells separated by current sheets. We prescribe the spectra of turbulent magnetic field in individual cells as IK-like and examine the spectra along trajectories that cross multiple boundaries. We find that these spectra become softer and are consistent with the Kolmogorov-scaling. Our finding supports our recent proposal of Li et al. (2011).     

Real-time global MHD simulation of the solar wind interaction with the earth’s magnetosphere

We have developed a real-time global MHD (magnetohydrodynamics) simulation of the solar wind interaction with the earth’s magnetosphere. By adopting the real-time solar wind parameters and interplanetary magnetic field (IMF) observed routinely by the ACE (Advanced Composition Explorer) spacecraft, responses of the magnetosphere are calculated with MHD code. The simulation is carried out routinely on the super computer system at National Institute of Information and Communications Technology (NICT), Japan. The visualized images of the magnetic field lines around the earth, pressure distribution on the meridian plane, and the conductivity of the polar ionosphere, can be referred to on the web site (http://www2.nict.go.jp/y/y223/simulation/realtime/).The results show that various magnetospheric activities are almost reproduced qualitatively. They also give us information how geomagnetic disturbances develop in the magnetosphere in relation with the ionosphere. From the viewpoint of space weather, the real-time simulation helps us to understand the whole image in the current condition of the magnetosphere. To evaluate the simulation results, we compare the AE indices derived from the simulation and observations. The simulation and observation agree well for quiet days and isolated substorm cases in general.     

Statistical properties of the IMF clock angle in the solar wind with northward and southward interplanetary magnetic field based on ACE observation from 1998 to 2009: Dependence on the temporal scale of the solar wind

Utilizing ACE satellite observations from 1998 to 2009, we performed the elaborate study on the properties of the clock angle θ_CA (arctan(By/Bz) (?90° to 90°) of the interplanetary magnetic field (IMF) in the solar wind at 1?AU. The solar wind with northward IMF (NW-IMF) and southward IMF (SW-IMF) are analyzed, independently. Statistical analysis shows that the solar wind with SW-IMF and NW-IMF has similar properties in general, including their durations, the IMF Bz and By components, and the IMF θ_CA. Then, the solar wind with NW-IMF (SW-IMF) is classified into five different temporal scales according to the duration of the NW-IMF (SW-IMF), i.e., very-short wind of 10–30?min, short-scale wind of 0.5–1?h, moderate-scale wind of 1–3?h, long-scale wind of 3–5?h, and super-long wind >5?h. Our analysis reveals that the IMF θ_CA has a distinct decrease with increase of the temporal scale of the solar wind. Next, the solar wind is classified into two groups, i.e., the high-speed solar wind (>450?km/s) and the low-speed solar wind (<450?km/s). Our analysis indicates that the IMF θ_CA depends highly on the solar wind speed. Statistically, high-speed solar wind tends to have larger IMF θ_CA than low-speed solar wind. The evolutions of the solar wind and IMF with the solar activity are further studied, revealing no clear solar variation of the IMF θ_CA. Finally, we analyze the monthly variation of the IMF θ_CA. Superposed epoch result strongly suggests the seasonal variation of the IMF θ_CA.     

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.     

Statistical properties of the most powerful solar and heliospheric disturbances

We present and discuss here the first version of a data base of extreme solar and heliospheric events. The data base contains now 87 extreme events mostly since 1940. An event is classified as extreme if one of the three critical parameters passed a lower limit. The critical parameters were the X-ray flux (parameter R), solar proton flux (parameter S) and geomagnetic disturbance level (parameter G). We find that the five strongest extreme events based on four variables (X-rays SEP, Dst, Ap) are completely separate except for the October 2003 event which is one the five most extreme events according to SEP, Dst and Ap. This underlines the special character of the October 2003 event, making it unique within 35 years. We also find that the events based on R and G are rather separate, indicating that the location of even extreme flares on the solar disk is important for geomagnetic effects. We also find that S = 3 events are not extreme in the same sense as R > 3 and G > 3 events, while S = 5 events are missing so far. This suggests that it might be useful to rescale the classification of SEP fluxes.