Quantifying Uncertainty in OMNI Solar Wind Measurements Projected from L 1 to the Earth's Bow Shock

In terms of global magnetohydrodynamic (MHD) simulations of the solar wind‐magnetosphere‐ionosphere system, this paper investigates the rotational asymmetry of the Earth's bow shock with respect to the Sun‐Earth line. We are limited to simple cases in which the solar wind is along the Sun‐Earth Line; and both the Earth's magnetic dipole moment and the interplanetary magnetic field (IMF) are perpendicular to the Sun‐Earth line. It is shown that even for the case of vanishing IMF strength the bow shock is not rotationally symmetric with respect to the Sun‐Earth line: the east‐west width of the cross section of the bow shock exceeds the north‐south width by about 9%~11% on the terminator plane (dawn‐dusk meridian plane) and its sunward side, and becomes smaller than the north‐south width by about 8% on the tailward side of the terminator plane. In the presence of the IMF, the configuration of the bow shock is affected by both the shape of the magnetopause and the anisotropy of fast magnetosonic wave speed. The magnetopause expands outward, being stretched along the IMF, and the extent of its expansion and stretch increases when the IMF rotates from north to south. In the magnetosheath, the fast magnetosonic wave speed is higher in the direction perpendicular to the magnetic field than that in the parallel direction. Therefore, the stretch direction of the magnetopause is perpendicular to the maximum direction of the fast magnetosonic wave speed, and their effects on the bow shock position are exactly opposite. The eventual shape of the bow shock depends on which effect dominates. On the tailward side of the terminator plane, the anisotropy of fast magnetosonic wave speed dominates, so the cross section of the bow shock is wider in the direction perpendicular to the IMF. On the terminator plane and its sunward side, the shape of the bow shock cross section depends on the orientation of the IMF: the bow shock cross section is still wider in the direction perpendicular to the IMF under generic northward or dawn‐dusk IMF cases, but it becomes narrower in the direction perpendicular to the IMF instead under generic southward IMF cases. In light of the intimate relationship between the shape of the bow shock and the orientation of the IMF, it is proposed to take the IMF as the datum direction so as to extract the parallel half width Rb// and the perpendicular half width Rb┴ as the scale parameters. In comparison with the commonly used east‐west half width yb and the north‐west half width zb, these parameters provide a more reasonable description of the geometry of the bow shock. Simulation data show that under the assumption of isotropic orientation of the IMF, the statistical averages of yb/zb and Rb‌‌/Rb┴ are both smaller than 1 on the terminator plane, which agrees with relevant observational conclusions.

Given the interplanetary conditions near the Earth's orbit and the geometrical configuration of the Earth's bow shock, this paper discusses the distributions of various parameters of shock strength over the sunward shock front, and the interaction between the bow shock and interplanetary shocks. For the case of axisymmetrical bow shock front with respect to the Sun‐Earth line, we arrive at the following conclusions: (1) The parameters of shock strength are distributed symmetrically with respect to the plane of reference defined by the interplanetary magnetic field (IMF) and the Sun‐Earth line, and their maxima appear in the plane of reference. The ratio of magnetic pressure is larger on the side containing the perpendicular‐shock line, whereas the ratio of gas pressure is larger on the side containing the parallel‐shock point, leading to a distribution of the ratio of total pressure that is largely axisymmetrical with respect to the Sun‐Earth line. (2) When the angle between the IMF and the Sun‐Earth line increases, the maxima of shock strength parameters of the bow shock decrease and the maximum points shift away from the subsolar point, but the distributions of gas‐pressure ratio and total pressure ratio are essentially not affected. (3) After an interplanetary shock is transmitted through the bow shock, the ratio of tangential field strength becomes closer to 1, whereas the jump of total magnetic field strength increases in amplitude. (4) After transmission through the bow shock, the ratio of total magnetic field strength becomes closer to 1 for quasi‐perpendicular interplanetary shocks but farther away from 1 for quasi‐parallel ones.

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

Using global MHD simulations of the solar wind–magnetosphere–ionosphere system, we investigate the dependence of the contribution from the Earth's bow shock (I1bs) to ionospheric region 1 field aligned current (FAC) (I1). It is found that I1bs increases with increasing southward interplanetary magnetic field (IMF) strength Bs, if the Alfvén Mach number MA of the solar wind exceeds 2, a similar result as obtained by previous authors. However, if MA becomes close to or falls below 2, I1bs will decrease with Bs in both magnitude and percentage (i.e., I1bs/I1) because of the resultant reduction of the bow shock strength. Both the surface current density Jbs at the nose of the bow shock and the total bow shock current Ibs share nearly the same relationship with MA, and vary non-monotonically with MA or Bs. The maximum point is found to be located at MA = 2.7. Three conclusions are then made as follows: (1) The surface current density at the nose, which is much easier to be evaluated, may be used to largely describe the behaviour of the bow shock instead of the total bow shock current. (2) The peak of the total bow shock current is reached at about MA = 2.7 when only Bs is adjusted. (3) The non-monotonic variation of the bow shock current with MA causes a similar variation of its contribution to region 1 FAC. The turning point for such contribution is found to be nearly MA = 2. The implication of these conclusions to the saturation of the ionospheric transpolar potential is briefly discussed.

Recent statistical surveys of interplanetary MeV energy nucleon flux anisotropies observed between prompt solar particle events during solar activity minimum have included time blocks of data obtained when the interplanetary magnetic field (IMF) connects the near earth spacecraft to earth's bow shock. The ensemble average nucleon flux anisotropy in the solar wind reference frame <ξD> obtained on these ‘connected’ field lines does not accurately represent the unperturbed <ξD> obtained on field lines free of this magnetic connection. Hourly average observations of interplanetary 0.5‐ to 1.8‐MeV proton fluxes, obtained near earth from 1972 to 1977, are correlated herein with simultaneous measurements of the IMF and solar wind plasma. At moderate flux levels during solar activity minimum, <ξD> indicates that nucleon flow in the solar wind frame is toward the sun and primarily along the IMF, although <ξD> is directed more sunward than strict field‐aligned propagation requires. Cross‐field transport is statistically significant and in the direction expected from the large‐scale MeV energy nucleon flux distributions throughout the heliosphere. The unperturbed nucleon flow direction relative to the IMF is used to demonstrate and characterize the interaction of MeV energy nuclei with the earth's bow shock and magnetosheath. The result of this interaction is that the mean value of <ξD> perpendicular to connected field lines is consistent with zero and therefore is not statistically significant. Obstruction of sunward nucleon flow on connected field lines is indicated by the variation of <ξD> with spacecraft position.

The Earth's bow shock is very efficient in accelerating ions out of the incident solar wind distribution to high energies (≈ 200 keV/e). Fluxes of energetic ions accelerated at the quasi‐parallel bow shock, also known as diffuse ions, are best represented by exponential spectra in energy/charge, which require additional assumptions to be incorporated into these model spectra. One of these assumptions is a so‐called “free escape boundary” along the interplanetary magnetic field into the upstream direction. Locations along the IBEX orbit are ideally suited for in situ measurements to investigate the existence of an upstream free escape boundary for bow shock accelerated ions. In this study we use 2 years of ion measurements from the background monitor on the IBEX spacecraft, supported by ACE solar wind observations. The IBEX Background Monitor is sensitive to protons > 14 keV, which includes the energy of the maximum flux for diffuse ions. With increasing distance from the bow shock along the interplanetary magnetic field, the count rates for diffuse ions stay constant for ions streaming away from the bow shock, while count rates for diffuse ions streaming toward the shock gradually decrease from a maximum value to ~1/e at distances of about 10 RE to 14 RE. These observations of a gradual decrease support the transition to a free escape continuum for ions of energy >14 keV at distances from 10 RE to 14 RE from the bow shock.

In this study we investigate the formation of magnetosheath jets before, during, and after the interaction between Earth's bow shock and a solar wind rotational discontinuity in a 2D ecliptic simulation run of the global magnetospheric hybrid-Vlasov model Vlasiator. Magnetosheath jets are transient enhancements of dynamic pressure downstream of collisionless shocks, and they have been observed in Earth's magnetosheath, the magnetosheaths of other planets, as well as the sheaths of interplanetary shocks. Rotational discontinuities (RD) are boundaries where the components of the magnetic field and velocity tangential to the boundary change abruptly, and they have been observed by spacecraft in the solar wind and in Earth's magnetosheath. Both spacecraft observations and previous simulation studies have shown that RDs interacting with the bow shock can generate dynamic pressure pulses in the magnetosheath.Studying magnetosheath jets is important because they have been shown to potentially have magnetospheric effects if impacting the magnetopause, and while travelling through the magnetosheath they can modify its properties. Statistical studies of simulations and spacecraft observations have shown that jets tend to form mainly at Earth's quasi-parallel bow shock, that is where the interplanetary magnetic field (IMF) direction is nearly parallel to the shock normal, but they have also been observed downstream of the quasi-perpendicular shock. By studying the formation and properties of jets at the quasi-parallel and quasi-perpendicular shock at different times in the simulation, we aim to shed light on the differences between jets forming at different parts of the shock, and during different stages of interaction between an RD and the bow shock.

We investigate the dynamics of Earth's quasi-parallel terrestrial bow shock based on measurements from the Magnetospheric MultiScale (MMS) spacecraft constellation during a period of near-radial interplanetary magnetic conditions, when the interplanetary magnetic field and the solar wind (SW) velocity are nearly anti-parallel. High-speed earthward ion flows with properties that are similar to those of the pristine SW are observed to be embedded within the magnetosheath-like plasma. These flows are accompanied by Interplanetary Magnetic Field (IMF) intensity of less than about 10 nT, compared to nearby magnetosheath intensities of generally greater than 10 nT. The high-speed flow intervals are bounded at their leading and trailing edges by intense fluxes of more energetic ions and large amplitude quasi-sinusoidal magnetic oscillations, similar to ultra-low frequency waves known to steepen and pileup on approach toward Earth to form the quasi-parallel bow shock. The MMS string-of-pearls configuration is aligned with the outbound trajectory and provides inter-spacecraft separations of several hundred km along its near 103 length, allowing sequential observation of the plasma and magnetic field signatures during the event by the four spacecraft. The SW-like interval is most distinct at the outer-most MMS-2 and sequentially less distinct at each of the trailing MMS spacecraft. We discuss the interpretation of this event alternatively as MMS having observed a quasi-rigid bow shock contraction/expansion cycle, ripples or undulations propagating on the bow shock surface, or a more spatially local evolution in the context of either a deeply deformed shock surface or a porous shock surface, as in the three-dimensional patchwork concept of the quasi-parallel bow shock, under the extant near-radial IMF condition.

This work identifies and characterizes magnetic structures, especially in terms of small‐scale magnetic flux ropes (SFRs), in the solar wind and magnetosheath across the Earth's bow shock. We investigate the differences between the properties of SFR structures in these regions immediately upstream and downstream of the bow shock by employing two data analysis methods: one based on wavelet transforms and the other based on the Grad‐Shafranov (GS) detection and reconstruction techniques. In situ magnetic field and plasma data from the Magnetospheric Multiscale and Time History of Events and Macroscale Interactions during Substorms missions are used to identify these coherent structures through the two approaches. We identify thousands of SFR event intervals with a range of variable duration over a total time period of 1,000 hr in each region. We report parameters associated with the SFRs such as scale size, duration, magnetic flux content, and magnetic helicity density, derived from primarily the GS‐based analysis results. These parameters are summarized through statistical analysis, and their changes across the bow shock are shown based on comparisons of their respective distributions. We find that in general, the distributions of various parameters follow power laws. The SFR structures seem to be compressed in the magnetosheath, as compared with their counterparts in the solar wind. A significant rotation in the ‐axis defining the orientation of the structures is also seen across the bow shock. We also discuss the implications for the elongation of the SFRs in the magnetosheath along one spatial dimension.

We have examined AMPTE IRM data obtained in the solar wind near the Earth's bow shock and found 16 well‐defined cases where a region of hot subsonic plasma is embedded in the solar wind. Such structures had been observed first with instruments on ISEE 1 and 2 and later on AMPTE UKS and distinguished from bow shock crossings. Our observations confirm some of the earlier findings, notably the event profile, showing a hot, low‐density core flanked by narrow regions of high density and strong magnetic field. We also find the low (∼200 km/s) flow velocities, strongly deflected from the solar wind, and we substantially strengthen the local time dependence of the flow which invariably is directed dawnward for prenoon events and duskward for postnoon events. Our results differ from the reported ISEE results in two respects. First, the flows we observe tend to have larger angles relative to the solar wind, and they often even have a sunward component. Second, the events we have selected cannot be described as diamagnetic cavities. On the contrary, the magnetic fields are usually significantly enhanced. This apparent discrepancy may simply result from different event selection criteria. A quantitative analysis of the regions flanking the hot core shows they consist of fast, nearly perpendicular, supercritical shocks on the outside and tangential discontinuities on the inside. We find a systematic difference between the orientations of the leading and trailing edge boundary normals. While the former are directed largely transverse to the solar wind flow, the latter are more nearly aligned with the solar wind. Another new finding concerns the presence of enhanced fluxes of >70‐keV electrons which appear to be of magnetospheric origin. The majority of events are associated with directional discontinuities in the interplanetary magnetic field. We have also found events which are not embedded in the solar wind but occur between the solar wind and the magnetosheath, at times replacing the regular bow shock. Among the mechanisms discussed as causes for these events are the formation of sunward directed plasma jets from magnetopause reconnection, or from amplification of magnetic stresses associated with rotational discontinuities in the interplanetary medium; sudden and localized enhancements of bow shock reflection; and the interaction of the bow shock with tangential discontinuities having a specific internal structure.

Magnetosheath jets are localized flows of enhanced dynamic pressure that are frequently observed downstream of the Earth's bow shock. They are significantly more likely to occur downstream of the quasi‐parallel shock than the quasi‐perpendicular shock. However, as the quasi‐perpendicular geometry is a more common configuration at the Earth's subsolar bow shock, quasi‐perpendicular jets comprise a significant fraction of the observed jets. We study the influence of solar wind conditions on jet formation by looking separately at jets during low and high interplanetary magnetic field (IMF) cone angles. According to our results, jet formation commences when Alfvén Mach number MA ≳ 5. We find that during low IMF cone angles (downstream of the quasi‐parallel shock) other solar wind parameters do not influence jet occurrence. However, during high IMF cone angles (downstream of the quasi‐perpendicular shock) jet occurrence is higher during low IMF magnitude, low density, high plasma beta (β), and high MA conditions. The distribution of quasi‐parallel (quasi‐perpendicular) jet sizes parallel to flow peaks at ∼0.3 RE (∼0.1 RE). Some quasi‐perpendicular jets formed during high β and MA are particularly small. We show two examples of high β and MA quasi‐perpendicular shock crossings. Jets were observed in the transition region, but not deeper in the magnetosheath. A more detailed look into one jet revealed signatures of gyrating ions, indicating that gyrobunched ions near the shock may produce jet‐like enhancements. Our results suggest that jets form as part of the quasi‐perpendicular shock dynamics amplified by high solar wind MA and β.

This paper reviews findings since 1966 about the properties of the interplanetary magnetic field; the solar wind plasma; solar wind interactions with the earth, the moon, Mars, and Venus; and the properties and propagation characteristics of energetic solar flare particles. For most purposes the solar wind can be characterized as a fluid that retains some of the properties of its source as it flows outward and that contains an anisotropic temperature distribution and embedded magnetic field. The magnetic field has a sector structure which slowly varies in a manner that resembles the evolution of magnetic features on the solar surface. As the solar wind encounters planetary bodies in its path, the nature of its interaction depends on the size and magnetic properties of the bodies. The solar wind creates a bow shock similar to that at earth as it interacts with Venus, and probably also with Mars. At Venus the plasma is apparently not diverted by a magnetic field, but by the planetary, ionosphere. At Mars the plasma is diverted either by a weak magnetic field or by an ionosphere. Further studies near earth have led to an explanation of the earth's bow shock in terms of hydromagnetic and ion waves. Energetic electrons (>400 kev) have been found in the neutral sheet of the geomagnetotail. The absence of thermal plasma in the earth's outer magnetosphere, beyond the plasmapause, has been explained in terms of a large‐scale convection field. The solar wind interaction with the moon is of an entirely different character. No bow shock is found, and the interplanetary magnetic field appears to convect through the moon. A single‐particle model of the interaction appears adequate to explain the observed phenomena, including the region behind the moon that is void of plasma but contains an enhanced magnetic field. Energetic electrons (20 kev to several Mev), protons (500 kev to 200 Mev), and α particles produced in solar flares have been studied in conjunction with solar X rays and radio bursts. It is now believed that these particles are not necessarily produced in an impulsive event during the flash phase of the flare; proton precursors have been found in some events, and it appears that energetic particles continue to leave the vicinity of the flare for hours or even days. These particles propagate preferentially along interplanetary magnetic field lines. Thus, their velocity distribution is generally anisotropic as long as the injection continues.

The interplay between Earth's magnetic field and the solar wind provides a natural laboratory to study the physics of shock waves in collisionless plasmas. 3D parameterized shape models of Earth's bow shock boundary quantify how this interaction depends on upstream solar wind parameters. Using 2,063 bow shocks observed with the Magnetospheric Multiscale (MMS) mission over 8 years, we investigate the relationship between the observed and parameterized bow shock location with solar wind parameters. We find that the observed bow shock location is strongly correlated with the solar wind density, plasma , and Mach number. In addition, we provide updated fitting parameters to bow shock models from literature derived empirically or using magnetohydrodynamic (MHD) simulations. Models provide a reasonable fit to the data after updating the fit with MMS‐observed bow shocks, with coefficient of determination scores between . However, we find that observed locations can still deviate significantly from model predictions under extreme solar wind conditions. We also explore the models' variability under different interplanetary magnetic field (IMF) clock angles (Northward and Southward) and shock geometries (quasi‐perpendicular and quasi‐parallel). While we observe no discernible difference in the bow shock shape as a function of IMF direction, we find that quasi‐parallel bow shocks are systematically closer to Earth than quasi‐perpendicular, with a disparity of as much as in bow shock stand‐off distance between the two bow shock types.

Interplanetary magnetic field (IMF) observations by ISEE 1 and IMP 8 were correlated to reveal the effects of upstream waves on IMF predictions. Past studies using spacecraft just outside the Earth's bow shock and far upstream at the L1 libration point attributed frequently poor (≤0.5) correlation coefficients to short IMF scale lengths and difficulties in estimating time delays. We find that the correlation coefficients for two near‐Earth spacecraft are actually worse than those for a spacecraft at the L1 point and one just outside the bow shock: 48% of the near‐Earth correlation coefficients for the IMF magnitude are poor (<0.5), and only 17% are good (>0.8). We attribute the poor result to two causes: (1) high‐frequency waves and diamagnetic effects in the foreshock and (2) intervals of low IMF variance. Of these two, high‐frequency waves account for 80% of the cases with poor correlation, and the intervals of nearly constant IMF account for the remaining 20% of the cases. While correlation coefficients do not increase with solar wind density while both spacecraft are in the solar wind, they do increase when one or both spacecraft lie within the foreshock. We argue that foreshock waves and intervals of low IMF variance must also have reduced correlation coefficients in previous IMF correlation studies. While the significance of the foreshock waves on the solar wind input into the magnetosphere deserves further study, there is no obstacle to predicting solar wind input into the magnetosphere during intervals with poor correlation coefficients but low IMF variance.

We report results of our multi‐spacecraft analysis of a solar wind reconnecting current sheet (RCS) and its solar wind magnetic hole (SWMH) observed on November 20, 2018. In the solar wind, the normal vector to the current sheet plane makes an angle of 32° with the Sun‐Earth line. A combination of tilted current sheet plane and foreshock effects cause an asymmetric interaction with the bow shock, in which the structure arrives at the quasi‐perpendicular side of the bow shock before the quasi‐parallel side. The magnetic field strength inside the magnetic hole decreases by ∼69 percent in the solar wind, with a similar depression rate observed inside the magnetosheath due to this structure. The solar wind flow slowdown and deflection during the bow shock crossing significantly disrupt the reconnection exhausts within the RCS. The interaction of the RCS and SWMH with the bow shock creates enhanced fluxes of accelerated electrons and ions. Plasma flow deflection in the magnetosheath also increases with the passage of the RCS. The ion density and temperature both increase within the current sheet to form a roughly pressure balanced structure. Field rotation and change in the dynamic pressure during this event modify the reconnection zones at the magnetopause and cause asymmetric inward motions in portions of the bow shock and the magnetopause boundaries (i.e., deformation). Unlike localized magnetosheath jets, an RCS and its associated SWMH in the solar wind have a global impact on the bow shock and the magnetopause.