Small-scale deformation of the bow shock

The prediction of the bow shock location is a proof of our understanding of the processes governing the solar wind – magnetosphere interaction. However, the models describing the bow shock location as a function of upstream parameters are based on a statistical processing of bow shock crossings observed by a single spacecraft. Such crossings locate the bow shock in motion, i.e., in a non-equilibrium state and this fact can be a source of significant errors. We have carefully analyzed a long interval of simultaneous observations of the bow shock and magnetopause and another interval of bow shock observations at two well-separated points. Our results suggest that often a small-scale deformation of the bow shock front due to magnetosheath fluctuations is the most appropriate interpretation of observations. Since the low-frequency magnetosheath variations exhibit largest amplitudes, a simultaneous bow shock displacement over a distance of 10–15 R_E can be observed. We suggest that bow shock models can be probably improved if the tilt angle would be implemented as a parameter influencing the bow shock location in high latitudes.     

Rapid and Asymmetric Response of the Earth's Bow Shock:Multipoint Observations

We analyze observations of three bow shock crossings which occurred during 2007, using upstream data from STEREO A/B, ACE and WIND, combined with multi-point THEMIS and Cluster data, and TC-1 data located near noon. During the crossing of 7 May 2007, we find that following a rapid reduction in solar wind ram pressure and subsequent pressure pulse seen by ACE and WIND upstream, the bow shock responds asymmetrically from dawn to dusk. Cluster data on the dawn-side suggest the bow shock is significantly flared and responds rapidly to the pulse arrival, while TC-1 at noon, and THEMIS on the dusk-side, are well matched to the model bow shock, but show a delayed response. The crossings observed on 21 May and 2 June show contrasting response matching the model boundary for northward Interplanetary Magnetic Field (IMF). The IMF and solar wind plasma data suggest that the bow shock crossing at dawn-dusk side and subsolar point were mainly caused by large and smaller scale features of the solar wind ram pressure rise rather than the influence of IMF.     

Bow shock: Power aspects

It is clear that the primary energy source for magnetospheric processes is the solar wind, but the process of energy transfer from the solar wind into the magnetosphere, or rather, to convecting magnetospheric plasma, appears to be rather complicated. Bow shock is a powerful transformer of the solar wind kinetic energy into the gas dynamic and electromagnetic energy. A jump of the magnetic field tangential component at front crossing means that the front carries an electric current. The solar wind kinetic energy partly transforms to gas kinetic and electromagnetic energy during its passage through the bow shock front. The transition layer (magnetosheath) can use part of this energy for accelerating of plasma, but can conversely spend part its kinetic energy on the electric power generation, which afterwards may be used by the magnetosphere. Thereby, transition layer can be both consumer (sink) and generator (source) of electric power depending upon special conditions. The direction of the current behind the bow shock front depends on the sign of the IMF Bz-component. It is this electric current which sets convection of plasma in motion.     

A stationary bow shock model for plasmas: The spherical blunt obstacle problem

We present an analytic model of a stationary bow shock which describes the interaction between a supermagnetosonic ambient wind and an obstacle with spherical-like frontal shape. We develop expressions for the bow shock’s geometry and the physical properties of the plasma sheath as functions of the upstream conditions. The solution is limited to magnetic fields parallel to the upstream velocity. The model allows to use any value of the upstream alfvenic and sonic Mach numbers and the polytropic index (γ$\gamma$), pointing out the influence of γ$\gamma$ for the magnetosheath compression and the bow shock shape. When both Mach numbers are small, the upstream magnetic field intensity affects also the bow shock shape. We compare our results with other models finding important consistencies. We also compare our results with in-situ data, we fund a reasonable qualitative agreement; however, it seems that our model underestimates the magnetosheath size.     

弓激波模型的对比

使用Cluster卫星的弓激波穿越数据,比较了Peredo弓激波模型、Merka弓激波模型、Chao弓激波模型和Lu弓激波模型在极端太阳风条件、偶极倾角较大和平静太阳风条件下的预测精度.结果表明:Peredo模型在极端太阳风条件和平静太阳风条件下的预测误差均较大;Merka模型在极端太阳风条件下的预测误差较大;Chao模型可以较为准确地描述平静太阳风条件下的弓激波位型,但不能准确描述偶极倾角较大时的弓激波位型;Lu模型可以同时准确描述极端太阳风条件和平静太阳风条件下的弓激波位型.     

Effects of the position of the solar wind termination shock and the heliopause on the heliospheric modulation of cosmic rays

The effects of changing the position of the solar wind termination shock and the position of the heliopause, and therefore the extent of the heliosheath, on the modulation of cosmic ray protons are illustrated. An improved numerical model with diffusive termination shock acceleration, a heliosheath and drifts is used. The modulation is computed in the equatorial plane and at 35 heliolatitude using recently derived diffusion coefficients applicable to a number of cosmic ray species during both magnetic polarity cycles of the Sun. It was found that qualitatively the modulation results for the different heliopause positions are similar although they differ quantitatively, e.g., clearly different radial gradients are predicted for the regions beyond the termination shock compared to inside the shock. The difference between the modulation for the two solar polarity cycles are less significant at a heliolatitude of 35° than in the equatorial plane. We found that moving the termination shock from 90 to 100 AU, with the heliopause fixed at 120 AU, caused only quantitative differences so that the exact position of the TS in the outer heliosphere seems not crucially important to global modulation. Moving the heliopause outwards, to represent the modulation in the tail region of the heliosphere, causes overall decreases in the cosmic ray intensities but not linearly as a function of energy, e.g., at 1 GeV the effect is insignificant. We conclude from this modelling that the modulation of protons in the heliospheric nose and tail regions are qualitatively similar although, clear quantitative and interesting differences occur.     

Plasma flow variations and energetic protons upstream of the earth’s bow shock: A statistical study

Foreshock is a special region located upstream of the Earth’s bow shock characterized by the presence of various plasma waves and fluctuations caused by the interaction of the solar wind plasma with particles reflected from the bow shock or escaping from the magnetosphere. On the other hand, foreshock fluctuations may modify the bow shock structure and, being carried through the magnetosheath, influence the magnetopause. During the years 1995–2000, the INTERBALL-1 satellite made over 10,000 hours of plasma and energetic particles measurements in the solar wind upstream of the Earth’s bow shock. We have sorted intervals according to the level of solar wind ion flux fluctuations and/or according to the flux of back-streaming energetic protons. An analysis of connection between a level of ion flux fluctuations and fluxes of high-energy protons and their relation to the IMF orientation is presented.     

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.     

The heliospheric modulation of cosmic rays: Effects of a latitude dependent solar wind termination shock

Observations made with the two Voyager spacecraft confirmed that the solar wind decelerates to form the heliospheric termination shock and that it has begun its merger with the local interstellar medium. The compression ratio of this shock affects galactic cosmic rays when they enter the heliosphere. Hydrodynamic (HD) models show that the compression ratio can have a significant latitude dependence; with the largest value in the nose direction of the heliosphere, becoming significantly less towards the polar regions. The modulation effects of such large latitude dependence are studied, using a well-established numerical drift and shock modulation model. We focus on computing the modulated spectra for galactic protons with emphasis on the radial and polar gradients in the equatorial plane and at a polar angle of θ = 55°, corresponding to the heliolatitude of Voyager 1. Two sets of solutions are computed and compared each time; with and without a latitude dependence for the compression ratio. All computations are done for the two magnetic field polarity cycles assuming solar minimum conditions. Including the termination shock in the model allows the study of the re-acceleration of galactic protons in the outer heliosphere. We find that for the A < 0 polarity cycle the intensity between ∼200 MeV and ∼1 GeV in the vicinity of the shock in the heliospheric equatorial plane may exceed the local interstellar value specified at the heliopause. Unfortunately, at θ = 55°, the effect is reduced. This seems not possible during an A > 0 cycle because significant modulation is then predicted between the heliopause and the termination shock, depending on how strong global gradient and curvature drifts are in the heliosheath. The overall effect of the shock on galactic protons in the equatorial plane is to reduce the total modulation as a function of radial distance with respect to the interstellar spectrum. Making the compression ratio latitude dependent enhances these effects at energies E < 200 MeV in the equatorial plane. At larger heliolatitudes these effects are even more significant. The differences in the modulation between the two drift cycles are compelling when the compression ratio is made latitude dependent but at Earth this effect is insignificant. A general result is that the computed radial gradient changes for galactic protons at and close to the TS and that these changes are polarity dependent. In line with previous work, large polarity dependent effects are predicted for the inner heliosphere and also close to the shock’s position in the equatorial plane. In contrast, at θ = 55°, the largest polarity effect occurs in the middle heliosphere (50 AU), enhanced by the latitude dependence of the compression ratio. At this latitude, the amount of proton modulation between the heliopause and the termination shock is much reduced. If galactic cosmic rays were to experience some diffusive shock acceleration over the 100–1000 MeV range at the shock, the radial gradient should change its sign in the vicinity of the shock, how large, depends on the compression ratio and the amount of drifts taking place in the outer heliosphere. The effective polar gradient shows a strong polarity dependence at Earth but this dissipates at θ = 55°, especially with increasing radial distance. This tendency is enhanced by making the compression ratio latitude dependent.     

Universal scaling laws for fully-developed magnetic field turbulence near and far upstream of the Earth’s bow shock

We analyze the multifractal scaling of the modulus of the interplanetary magnetic field near and far upstream of the Earth’s bow shock, measured by Cluster and ACE, respectively, from 1 to 3 February 2002. The maximum order of the structure function is carefully estimated for each time series using two different techniques, to ensure the validity of our high-order statistics. The first technique consists of plotting the integrand of the pth order structure function, and the second technique is a quantitative method which relies on the power-law scaling of the extreme events. We compare the scaling exponents computed from the structure functions of magnetic field differences with the predictions obtained by the She–Lévêque model of intermittency in anisotropic magnetohydrodynamic turbulence. Our results show a good agreement between the model and the observations near and far upstream of the Earth’s bow shock, rendering support for the modelling of universal scaling laws based on the Kolmogorov phenomenology in the presence of sheet-like dissipative structures.     

The role of radial perpendicular diffusion and latitude dependent acceleration along the solar wind termination shock

A numerical model, based on Parker’s transport equation, describing the modulation of anomalous cosmic rays and containing diffusive shock acceleration is applied. The role of radial perpendicular diffusion at the solar wind termination shock, and as the dominant diffusion coefficient in the outer heliosphere, is studied, in particular the role it plays in the effectiveness of the acceleration of anomalous protons and helium when its latitude dependence is changed. It is found that the latitudinal enhancement of radial perpendicular diffusion towards the heliospheric poles and along the termination shock has a prominent effect on the acceleration of these particles. It results in a ‘break’ in the energy spectrum for anomalous protons at ∼6.0 MeV, causing the spectral index to change from E^−1.38 to E^−2.23, but for anomalous helium at ∼3.0 MeV, changing the spectral index from E^−1.38 to E^−2.30. When approaching the simulated TS, the changes in the modulated spectra as they unfold to a ‘steady’ power law shape at energies below 50 MeV are much less prominent as a function of radial distances when radial perpendicular diffusion is increased with heliolatitude.     

MHD modeling of the outer heliosphere: Achievements and challenges

An overview is presented of magnetic-field-related effects in the solar wind (SW) interaction with the local interstellar medium (LISM) and the different theoretical approaches used in their investigation. We discuss the possibility that the interstellar magnetic field (ISMF) introduces north–south and east–west asymmetries of the heliosphere, which might explain observational data obtained by the Voyager 1 and Voyager 2 spacecraft. The SW–LISM interaction parameters that are responsible for the deflection of the interstellar neutral hydrogen flow from the direction of propagation of neutral helium in the inner heliosheath are outlined. The possibility of a strong ISMF, which increases the heliospheric asymmetry and the H–He flow deflection, is discussed. The effect of the combination of a slow-fast solar wind during solar minimum over the Sun’s 11-year activity cycle is illustrated. The consequences of a tilt between the Sun’s magnetic and rotational axes are analyzed. Band-like areas of an increased magnetic field distribution in the outer heliosheath are sought in order to discover regions of possible 2–3 kHz radio emission.