Estimation and assessment of solar wind propagation time from the Lagrange point L1 to Earth’s bow shock

The wave pattern of the flow developed when a solar wind shock wave propagates along the surface of the Earth's bow shock is studied. The investigation is carried out in the three-dimensional non-plane-polarized formulation within the framework of the ideal magneto- hydrodynamic model in which the medium is assumed to be inviscid and non-heat-conducting and to have the infinite conductivity. The global three-dimensional pattern of the interaction which is a function of the latitude and longitude of elements on the surface of the bow shock is constructed as a mosaic of solutions to the problem of breakdown of a discontinuity developed between the states behind the impinging and bow shocks on the moving curve of intersection of their fronts. The investigation is carried out for typical solar wind parameters and interplanetary magnetic field strength in the Earth's orbit and for several Mach numbers of the interplanetary shock wave, which makes it possible to trace the evolution of the flow developed as a function of the intensity of the shock perturbation of the solar wind. The solution obtained is necessary for interpreting measurements carried out by spacecraft located in the neighborhood of the Lagrange point and the Earth's magnetosphere. At present, spacecraft located in the solar wind in the neighborhood of the Lagrange point L1 at distances of approximately 250 Earth's radii RE from the Earth (Wind, SOHO, and ACE) and groups of spacecraft in the neighborhood of the Earth's bow shock, in the magnetosheath, and in the outer magnetosphere (THEMIS, Cluster, and Double Star) are measuring the state of the interplanetary medium and magnetic field and transferring the data to the Earth. The measurements are used to identify sharp jumpwise changes occurring in the solar wind and related to shock waves, rotational and tangential discontinuities, and their manifestations recorded on spacecraft in the neighborhood of the Earth with the aim to forecast the cosmic weather in the form of sudden storm commencements, magnetic substorms, and sudden impulses in the Earth's magnetosphere (1-4). The results of numerical MHD simulations carried out by means of various methods (2-6) are used in analyzing the events. However, the simulations have insufficient spatial resolution, and due to this fact several MHD waves merge with one another and can hardly be identified; for example, slow or Alfven waves are unified with the contact discontinuity (5). For the correct interpretation of measurements it is necessary to use the exact solutions to the problem of interaction between a solar wind discontinuity and the Earth's bow shock Sb (7-11). The quasi-steady-state method of finding them within the framework of magnetohydrodynamics of an ideally conducting medium was first proposed in (7, 8) as the solution to the problem of breakdown of a discontinuity between the states behind the interacting waves on the moving curve of intersection of their fronts. The wave flow pattern and the dependences of the physical parameters of the medium and the magnetic field were first obtained as functions of the angle of inclination of Sb to the solar wind velocity Vsw in the

Modification of small- and middle-scale solar wind structures by the bow shock and magnetosheath: Correlation analysis

Terrestrial low-frequency bursts: Escape paths of radio waves through the bow shock

Revealing the formation, dynamics, and contribution to plasma heating of magnetic field fluctuations in the solar wind is an important task for heliospheric physics and for a general plasma turbulence theory. Spacecraft observations in the solar wind are limited to spatially localized measurements, so that the evolution of fluctuation properties with solar wind propagation is mostly studied via statistical analyses of data sets collected by different spacecraft at various radial distances from the Sun. In this study we investigate the evolution of turbulence in the Earth’s magnetosheath, a plasma system sharing many properties with the solar wind. The near-Earth space environment is being explored by multiple spacecraft missions, which may allow us to trace the evolution of magnetosheath fluctuations with simultaneous measurements at different distances from their origin, the Earth’s bow shock. We compare ARTEMIS and Magnetospheric Multiscale (MMS) Mission measurements in the Earth magnetosheath and Parker Solar Probe measurements of the solar wind at different radial distances. The comparison is supported by three numerical simulations of the magnetosheath magnetic and plasma fluctuations: global hybrid simulation resolving ion kinetic and including effects of Earth’s dipole field and realistic bow shock, hybrid and Hall-MHD simulations in expanding boxes that mimic the magnetosheath volume expansion with the radial distance from the dayside bow shock. The comparison shows that the magnetosheath can be considered as a miniaturized version of the solar wind system with much stronger plasma thermal anisotropy and an almost equal amount of forward and backward propagating Alfvén waves. Thus, many processes, such as turbulence development and kinetic instability contributions to plasma heating, occurring on slow timescales and over large distances in the solar wind, occur more rapidly in the magnetosheath and can be investigated in detail by multiple near-Earth spacecraft.

Having precise knowledge of the near-Earth solar wind (SW) and the embedded interplanetary magnetic field (IMF) is of critical importance to space weather operation due to the usage of SW and IMF in almost all magnetospheric and ionospheric models. The most widely used data source, OMNI, propagates SW properties from Lagrangian point L1 to the Earth’s bow shock by estimating the propagation time of the SW. However, the time difference between OMNI timeshifted IMF and the best match-up of IMF can reach ˜15 min. Firstly, we aim to develop an improved statistical algorithm to contribute to the SW propagation delay problem of space weather prediction. The algorithm focuses on matching SW features around the L1 point and upstream of the bow shock by computing the variance, cross-correlation coefficient, the plateau-shaped magnitude index, and the non-dimensional measure of average error index between the measurements at the two locations. The obtained propagation times are then compared to OMNI. Factors that limit the OMNI accuracy are also examined. Secondly, the automatic algorithm allows us to generate large sets of input and target variables using multiple spacecraft pairs at L1 and near-Earth locations to train, validate, and test machine learning models to specify and forecast near-Earth SW conditions. Finally, we offer a machine learning (ML) approach to specify and predict the propagation time from L1 monitors to a given location upstream or at the bow shock and forecast near-Earth SW conditions with the gradient boosting and random forest prediction models in the form of an ensemble of decision trees.

A large magnetic depression observed in the solar wind close to the Earth's bow shock

A space experiment is proposed to make continuous remote electromagnetic soundings of the solar wind bow shock interaction with the magnetosphere of the Earth. We discuss the feasibility of construction of a system that will allow us to carry out the bow shock sounding and study solar wind local obstacles tens of minutes before their interaction with the bow shock. The sounding system, placed at a distance about 26 RE from the bow shock, with average transmitter active power of 20 W at a maximum antenna length of 3 km and antenna weight of about 100 kg, would provide bow shock‐solar wind monitoring with spatial resolution of 0.25–1 RE in the frequency range 9–225 kHz and a 10% electron density resolution. Such a system, located at the Lagrange point L1, could provide continuous monitoring of the solar wind interaction with the Earth's magnetosphere.

In the magnetohydrodynamic (MHD) perspective, the planet’s bow shock would disappear when the fast-mode Mach number (M F) of the solar wind is less than one. Compared to Earth, Mercury is subject to a lower M F solar wind due to its proximity to the Sun, resulting in a higher possibility of the disappearance of its bow shock. To examine the variability of Mercury’s bow shock in response to the solar wind properties, analyses of the observations by the Helios spacecraft at 0.30–0.50 au during 1975–1983, covering solar cycle 21, together with the theoretical solutions and MHD simulations are conducted in this study. Our observational analyses show that more solar wind data with extremely low fast-mode Mach numbers (say, M F ≤ 1.5) are observed during the rising and maximum phases and are characterized by a significantly low proton number density. It is also found that approximately 35% of the extremely low fast-mode Mach number solar wind events (M F ≤ 1.5) occur within the main body of interplanetary coronal mass ejections (ICMEs), while about 58% of them are unrelated to ICMEs. Three of these events are selected to demonstrate that the occurrences of the solar wind with M F ≤ 1.5 may not be necessarily affected by ICMEs. Our theoretical and numerical results indicate that when Mercury encounters the solar wind with M F ≤ 1.5, its bow shock would move farther away, become flattened, and even disappear. Furthermore, our calculations suggest that Mercury’s bow shock would become a slow-mode shock with a concave-upward structure under such extreme solar wind conditions.

Abstract. Foreshock ions are compared between Venus and Mars at energies of 0.6~20 keV using the same ion instrument, the Ion Mass Analyser, on board both Venus Express and Mars Express. Venus Express often observes accelerated protons (2~6 times the solar wind energy) that travel away from the Venus bow shock when the spacecraft location is magnetically connected to the bow shock. The observed ions have a large field-aligned velocity compared to the perpendicular velocity in the solar wind frame, and are similar to the field-aligned beams and intermediate gyrating component of the foreshock ions in the terrestrial upstream region. Mars Express does not observe similar foreshock ions as does Venus Express, indicating that the Martian foreshock does not possess the intermediate gyrating component in the upstream region on the dayside of the planet. Instead, two types of gyrating protons in the solar wind frame are observed very close to the Martian quasi-perpendicular bow shock within a proton gyroradius distance. The first type is observed only within the region which is about 400 km from the bow shock and flows tailward nearly along the bow shock with a similar velocity as the solar wind. The second type is observed up to about 700 km from the bow shock and has a bundled structure in the energy domain. A traversal on 12 July 2005, in which the energy-bunching came from bundling in the magnetic field direction, is further examined. The observed velocities of the latter population are consistent with multiple specular reflections of the solar wind at the bow shock, and the ions after the second reflection have a field-aligned velocity larger than that of the de Hoffman-Teller velocity frame, i.e., their guiding center has moved toward interplanetary space out from the bow shock. To account for the observed peculiarity of the Martian upstream region, finite gyroradius effects of the solar wind protons compared to the radius of the bow shock curvature and effects of cold ion abundance in the bow shock are discussed.

Some space weather models, such as the Space Weather Modeling Framework (SWMF) used in this study, use solar wind propagated from the first Lagrange point (L1) to the bow shock nose (BSN) to forecast geomagnetic storms. The SWMF is a highly coupled framework of space weather models that include multiple facets of the Geospace environment, such as the magnetosphere and ionosphere. The propagated solar wind measurements are used as a boundary condition for SWMF. The solar wind propagation method is a timeshift based on the calculated phase front normal (PFN) which leads to some uncertainties. For example, the propagated solar wind could have evolved during this timeshift. We use a data set of 123 geomagnetic storms between 2010 and 2019 run by the SWMF Geospace configuration to analyze the impact solar wind propagation and solar wind driving has on the geomagnetic indices. We look at the probability distributions of errors in SYM‐H, cross polar cap potential (CPCP), and auroral electrojet indices AL and AU. Through studying the median errors (MdE), standard deviations and standardized regression coefficients, we find that the errors depend on the propagation parameters. Among the results, we show that the accuracy of the simulated SYM‐H depends on the spacecraft distance from the Sun‐Earth line. We also quantify the dependence of the standard deviation in SYM‐H errors on the PFN and solar wind pressure. These statistics provide an insight into how the propagation method affects the final product of the simulation, which are the geomagnetic indices.

Earth and its magnetosphere are immersed in the supersonic flow of the solar-wind plasma that fills interplanetary space. As the solar wind slows and deflects to flow around Earth, or any other obstacle, a 'bow shock' forms within the flow. Under almost all solar-wind conditions, planetary bow shocks such as Earth's are collisionless, supercritical shocks, meaning that they reflect and accelerate a fraction of the incident solar-wind ions as an energy dissipation mechanism1,2, which results in the formation of a region called the ion foreshock3. In the foreshock, large-scale, transient phenomena can develop, such as 'hot flow anomalies'4-9, which are concentrations of shock-reflected, suprathermal ions that are channelled and accumulated along certain structures in the upstream magnetic field. Hot flow anomalies evolve explosively, often resulting in the formation of new shocks along their upstream edges5,10, and potentially contribute to particle acceleration11-13, but there have hitherto been no observations to constrain this acceleration or to confirm the underlying mechanism. Here we report observations of a hot flow anomaly accelerating solar-wind ions from roughly 1-10 kiloelectronvolts up to almost 1,000 kiloelectronvolts. The acceleration mechanism depends on the mass and charge state of the ions and is consistent with first-order Fermi acceleration14,15. The acceleration that we observe results from only the interaction of Earth's bow shock with the solar wind, but produces a much, much larger number of energetic particles compared to what would typically be produced in the foreshock from acceleration at the bow shock. Such autogenous and efficient acceleration at quasi-parallel bow shocks (the normal direction of which are within about 45 degrees of the interplanetary magnetic field direction) provides a potential solution to Fermi's 'injection problem', which requires an as-yet-unexplained seed population of energetic particles, and implies that foreshock transients may be important in the generation of cosmic rays at astrophysical shocks throughout the cosmos.

Mercury's magnetosphere is more dynamic than Earth's due to its proximity to the Sun, and it is subject to a lower Mach number solar wind. Regarding the solar wind interaction with Mercury, we are interested in the configurations of Mercury’s magnetosphere and the energy transport under various solar wind conditions. First, this study examines the potential impact of low Mach number solar wind on Mercury's bow shock and the resulting effects on the magnetosphere. To analyze the variability of Mercury's bow shock in response to solar wind properties, this study combines observations by the Helios data with theoretical solutions and MHD simulations. The results show that when Mercury encounters solar wind with an extremely low Mach number, its bow shock is expected to become more flattened, further from the planet, and may even disappear completely. Our other focus is on the Kelvin-Helmholtz instability (KHI) that occurs at the magnetopause, which plays a crucial role in the energy transfer and momentum coupling process between the solar wind and Mercury's magnetospheres. We conducted MHD simulations based on boundary conditions and plasma parameters from a global hybrid simulation of the MESSENGER’s first flyby in 2008. Given the lack of comprehensive plasma observations of Mercury's magnetosphere, we examined two scenarios: one with a heavily mass-loaded magnetosphere and another with a weakly mass-loaded magnetosphere. Our findings show that the KHI in a heavily loaded magnetosphere results in a more turbulent magnetopause, with nonlinear fast-mode plane waves expanding away from the magnetopause. The momentum and energy flux quantified from our simulations reveals that the KHI with a heavily loaded magnetosphere can efficiently transport momentum and energy away from the magnetopause in the presence of the fast-mode plane waves. In such a scenario, observed in the inner magnetosphere, the momentum flux can reach about 0.5 % of the initial solar-wind dynamic pressure; the energy flux can be 10-2 erg/cm2/s, and the energy density is about 1.5 %-3.0 % of the initial solar-wind energy.

Following previous investigations of quasiperiodic plasma density structures in the solar wind at 1 AU, we show using the Helios1 and Helios2 data their first identification in situ in the inner heliosphere at 0.3, 0.4, and 0.6 AU. We present five events of quasiperiodic density structures with time scales ranging from a few minutes to a couple of hours in slow solar wind streams. Where possible, we locate the solar source region of these events using photospheric field maps from the Mount Wilson Observatory as input for the Wang-Sheeley-Arge model. The detailed study of the plasma properties of these structures is fundamental to understanding the physical processes occurring at the origin of the release of solar wind plasma. Temperature changes associated with the density structures are consistent with these periodic structures developing in the solar atmosphere as the solar wind is formed. One event contains a flux rope, suggesting that the solar wind was formed as magnetic reconnection opened up a previously closed flux tube at the Sun. This study highlights the types of structures that Parker Solar Probe and the upcoming Solar Orbiter mission will observe, and the types of data analyses these missions will enable. The data from these spacecrafts will provide additional in situ measurements of the solar wind properties in the inner heliosphere allowing, together with the information of the other interplanetary probes, a more comprehensive study of solar wind formation.

The development of a cometosheath at comet 67P Churyumov-Gerasimenko

During the rise to the maximum phase of solar cycle 23, several periods of extreme solar wind conditions have occurred. During such an example on May 4, 1998, the solar wind monitors observed a period of strong southward interplanetary magnetic field (IMF) accompanied by a solar wind dynamic pressure that was 30 times higher than average. During this period the Polar spacecraft crossed the magnetopause and bow shock and experienced its first solar wind encounter. This case provides a rare opportunity to study the magnetopause, low‐latitude boundary layer, magnetosheath, and bow shock and to test our ability to model the dynamic behavior of these boundary regions under extreme and highly variable solar wind conditions. In this study we use the gas dynamic convected field model to predict the time‐dependent magnetic field and plasma properties upstream from the magnetopause and the location of the Polar spacecraft relative to the magnetopause and bow shock during the event. To test the accuracy of the prediction, model magnetic field characteristics are compared to the fields observed along the satellite track by the magnetometer on Polar. The predicted model plasma characteristics (density, velocity, and temperature) are compared to moments derived from TIDE observations, extrapolated to account for the higher energy portion of the magnetosheath distributions. Where ambiguities occur in identifying the satellite location, plasma distribution functions from two additional ion detectors (TIMAS and HYDRA) are used to resolve the observed location of Polar relative to the boundaries. With this procedure, carried out separately for ACE and Wind and for two different magnetopause models, observed features at Polar can be traced back to drivers in the solar wind, providing a unique opportunity to assess the evolution of the solar wind and its predictability from the solar wind monitors to the magnetopause. When the Polar apogee drifts to low latitudes in the future, it will provide more and more observations in this region. Therefore what we learn from this case can be indicative of what we will see in the future in Polar operations. The high‐level correlation between the predictions and in situ measurements indicates that the solar wind monitors often provide adequate and useful solar wind conditions near the Earth. The tests indicate that in this event the vacuum dipole field magnetosphere model predicts a significantly larger magnetosphere than observed. While the empirical magnetopause model predictions are more consistent with the observations, they overpredict the response of the magnetosphere to transient southward turnings of the IMF, indicating that the magnetosphere does not respond to the southward IMF turnings on small timescales. Sometimes, there are significant differences at relatively small time scales between the measurements from the two solar wind monitors. It is possible for the solar wind conditions near the Earth to be different from the measurements made by at least one of the solar wind monitors. Cautions should be taken when interpreting near‐Earth observations if the observations are inconsistent at small timescales with the predictions based on one solar wind monitor.