Martian bow shocks, the solar wind interacting with an unmagnetized planet, are studied. We theoretically investigated how solar parameters, such as the solar wind dynamic pressure and the solar extreme ultraviolet (EUV) flux, influence the bow shock location, which is still currently not well understood. We present the formula for the location of the bow shock nose of the unmagnetized planet. The bow shock location, the sum of the ionopause location and bow shock standoff distance, is calculated in the gasdynamics approach. The ionopause location is determined using thermal pressure continuity, i.e., the solar wind thermal pressure equal to the ionospheric pressure, according to tangential discontinuity. The analytical formula of the ionopause nose location and the ionopause profile around the nose are obtained. The standoff distance is calculated using the empirical model. Our derived formula shows that the shock nose location is a function of the scale height of ionosphere, the dynamic pressure of the solar wind and the peak ionospheric pressure. The theoretical model implies that the shock nose location is more sensitive to the solar EUV flux than solar wind dynamics pressure. Further, we theoretically show that the bow shock location is proportional to the solar wind dynamic pressure to the power of negative C, where C is about the ratio of the ionospheric scale height to the distance between bow shock nose and the planet center. This theory matches the gasdynamics simulation and is consistent with the spacecraft measurement result by Mars Express [Hall, et al. (2016) J. Geophys. Res. Space Physics, 121, 11,474-11,494].
We study relativistic unmagnetized collisionless shocks using unprecedentedly large particle-in-cell simulations of two-dimensional pair plasma. High energy particles accelerated by the shock are found to drive magnetic field evolution on a timescale >10^4 plasma times. Progressively stronger magnetic fields are generated on larger scales in a growing region around the shock. Shock-generated magnetic fields and accelerated particles carry >1% and >10% of the downstream energy flux, respectively. Our results suggest limits on the magnetization of relativistic astrophysical flows.
We present fast algorithms to automatically estimate the statistical position of the bow shock from spacecraft data, using existing analytical two-dimensional (2D) and three-dimensional (3D) models of the shock surface. We derive expressions of the standoff distances in 2D and 3D and of the normal to the bow shock at any given point on it. Two simple bow shock detection algorithms are constructed, one solely based on a geometrical predictor from existing models, the other using this predicted position to further refine it with the help of magnetometer data, an instrument flown on many planetar…
We present Magnetospheric Multiscale observations of electrostatic double layers in quasi-perpendicular Earth's bow shock. These double layers have predominantly parallel electric field with amplitudes up to 100 mV/m, spatial widths of 50-700 m, and plasma frame speeds within 100 km/s. The potential drop across a single double layer is 2-7% of the cross-shock potential in the de Hoffmann-Teller frame and occurs over the spatial scale of ten Debye lengths or one tenth of electron inertial length. Some double layers can have spatial width of 70 Debye lengths and potential drop up to 30% of the c…
Solar Wind Reflected Ion Properties at Earth's Bow Shock: Dependence on Upstream Conditions and Shock Geometry
University of California, Los Angeles（加州大学洛杉矶分校）；Shandong University（山东大学）；Embry-Riddle Aeronautical University（埃默里·莱德航空大学）；University of Potsdam（波茨坦大学）
Shock parameters at Earth's bow shock in rare instances can approach the Mach numbers predicted at supernova remnants. We present our analysis of a high Alfvén Mach number ($M_A= 27$) shock utilizing multipoint measurements from the Magnetospheric Multiscale (MMS) spacecraft during a crossing of Earth's quasi-perpendicular bow shock. We find that the shock dynamics are mostly driven by reflected ions, perturbations that they generate, and nonlinear amplification of the perturbations. Our analyses show that reflected ions create modest magnetic enhancements upstream of the shock which evolve in…
We know that it is the front of the bow shock where the solar wind kinetic energy flux is transformed into the other kinds the most intensively. In our previous studies, we obtained important relationships that enable calculating the key parameters at transition through the bow shock front. One of the most important sources of information on physical processes at the heliosphere boundary are the Voyager 1 and 2 spacecrafts. Since both the solar wind and interstellar medium are supersonic streams, two shocks are formed when flowing around the heliopause. The internal shock, in which the solar w…
We use the Cluster EFW experiment to measure the cross-shock electric field at ten low $β$, quasi-perpendicular supercritical bow shock crossings on March 31, 2001. The electric field data are Lorentz-tranformed to a Normal Incidence frame (NIF), in which the incoming solar wind velocity is aligned with the shock normal. In a boundary normal coordinate system, the cross-shock (normal) electric field is integrated to obtain the cross shock potential. Using this technique, we measure the cross-shock potential at each of the four Cluster satellites and using an electric field profile averaged bet…
We propose a new method to estimate ion escape from unmagnetized planets that combines observations and models. Assuming that upstream solar wind conditions are known, a computer model of the interaction between the solar wind and the planet is executed for different ionospheric ion production rates. This results in different amounts of mass loading of the solar wind. Then we obtain the ion escape rate from the model run that best fit observations of the bow shock location. As an example of the method we estimate the heavy ion escape from Mars on 2015-03-01 to be $2\cdot 10^{24}$ ions per seco…
Solar wind plasma at the Earth's orbit carries transient magnetic field structures including discontinuities. Their interaction with the Earth's bow shock can significantly alter discontinuity configuration and stability. We investigate such an interaction for the most widespread type of solar wind discontinuities - rotational discontinuities (RDs). We use a set of in situ multispacecraft observations and perform kinetic hybrid simulations. We focus on the RD current density amplification that may lead to magnetic reconnection. We show that the amplification can be as high as two orders of mag…
Collisionless shocks vary drastically from terrestrial to astrophysical regimes resulting in radically different characteristics. This poses two complexities. Firstly, separating the influences of these parameters on physical mechanisms such as energy dissipation. Secondly, correlating observations of shock waves over a wide range of each parameter, enough to span across different regimes. Investigating the latter has been restricted since the majority of studies on shocks at exotic regimes (such as supernova remnants) have been achieved either remotely or via simulations, but rarely by means …
We carry out two-dimensional global particle-in-cell simulations of the interaction between the solar wind and a dipole field to study the formation of the bow shock and magnetosphere. A self-reforming bow shock ahead of a dipole field is presented by using relatively high temporal-spatial resolutions. We find that (1) the bow shock and the magnetosphere are formed and reach a quasi-stable state after several ion cyclotron periods, and (2) under the Bz southward solar wind condition the bow shock undergoes a self-reformation for low \b{eta}i and high MA. Simultaneously, a magnetic reconnection…
The first-order Fermi acceleration of electrons requires an injection of electrons into a mildly relativistic energy range. However, the mechanism of injection has remained a puzzle both in theory and observation. We present direct evidence for a novel stochastic shock drift acceleration theory for the injection obtained with Magnetospheric Multiscale (MMS) observations at Earth's bow shock. The theoretical model can explain electron acceleration to mildly relativistic energies at high-speed astrophysical shocks, which may provide a solution to the long-standing issue of electron injection.
When a magnetosheath jet (localized dynamic pressure enhancements) compresses ambient magnetosheath at a (relative) speed faster than the local magnetosonic speed, a bow wave or shock can form ahead of the jet. Such bow waves or shocks were recently observed to accelerate particles, thus contributing to magnetosheath heating and particle acceleration in the extended environment of Earth bow shock. To further understand the characteristics of jet-driven bow waves, we perform a statistical study to examine which solar wind conditions favor their formation and whether it is common for them to acc…
We present a statistical analysis of 132 dayside (LT 0700-1700) bow shock crossings of the AMPTE/IRM spacecraft. We perform a superposed epoch analysis of plasma and magnetic field parameters as well as of low frequency magnetic power spectra some minutes upstream and downstream of the bow shock by dividing the events into categories depending on the angle between bow shock normal and interplanetary magnetic field and on the plasma-beta, i.e., the ratio of plasma to magnetic pressure. Downstream of the quasi-perpendicular low-beta (beta < 0.5) bow shock we find a dominance of the left-hand pol…
Collisionless shocks and plasma turbulence are crucial ingredients for a broad range of astrophysical systems. The shock-turbulence interaction, and in particular the transmission of fully developed turbulence across the quasi-perpendicular Earth's bow shock, is here addressed using a combination of spacecraft observations and local numerical simulations. An alignment between the Wind (upstream) and MMS (downstream) spacecraft is used to study the transmission of turbulent structures across the shock, revealing an increase of their magnetic helicity content in its downstream. Local kinetic sim…
For stars, the bow shock is typically the boundary between their stellar wind and the interstellar medium. Named for the wave made by a ship as it moves through water, the bow shock wave can be created in the space when two streams of gas collide. The space is actually filled with the interstellar medium consisting of tenuous gas and dust. Stars are emitting a flow called stellar wind. Stellar wind eventually bumps into the interstellar medium, creating an interface where the physical conditions such as density and pressure change dramatically, possibly giving rise to a shock wave. Here we dis…
This paper contains a presentation of analytical solution of the problem of calculating the places and moments of intersection of satellite trajectories with elements of the Earth's magnetosphere (bow shock and magnetopause). The satellite motion is presented in a Kepler's approximation. Magnetopause and bow shock are described by second-order surfaces- elliptic paraboloides. These surfaces are employed as situational conditions for determining the points of intersection they have (if any) with the satellite trajectory. The situational condition is herein transformed into the plane of Kepler's…
We report evidence of magnetic reconnection in the transition region of the terrestrial bow shock when the angle between the shock normal and the immediate upstream magnetic field is 65 degrees. An ion-skin-depth-scale current sheet exhibits the Hall current and field pattern, electron outflow jet, and enhanced energy conversion rate through the nonideal electric field, all consistent with a reconnection diffusion region close to the X-line. In the diffusion region, electrons are modulated by electromagnetic waves. An ion exhaust with energized field-aligned ions and electron parallel heating …
Recent observations in the quasi-parallel bow shock by the MMS spacecraft show rapid heating and acceleration of ions up to an energy of about 100 keV. It is demonstrated that a prominent acceleration mechanism is the nonlinear interaction with a spectrum of waves produced by gradient driven instabilities, including the lower hybrid drift (LHD) instability, modified two-stream (MTS) instability and electron cyclotron drift (ECD) instability. Test-particle simulations show that the observed spectrum of waves can rapidly accelerate protons up to a few hundreds keV by the ExB mechanism. The ExB w…
Stellar bow shocks are observed in a variety of interstellar environments and are shaped by the conditions of gas in the interstellar medium (ISM). In situ measurements of turbulent density fluctuations near stellar bow shocks are only achievable with a few observational probes, including H$α$ emitting bow shocks and the Voyager Interstellar Mission (VIM). In this paper, we examine density variations around the Guitar Nebula, an H$α$ bow shock associated with PSR B2224$+$65, in tandem with density variations probed by VIM near the boundary of the solar wind and ISM. High-resolution Hubble Spac…
Identifying collisionless shock crossings in data sent from spacecraft has so far been done manually. It is a tedious job that shock physicists have to go through if they want to conduct case studies or perform statistical studies. We use a machine learning approach to automatically identify shock crossings from the Magnetospheric Multiscale (MMS) spacecraft. We compile a database of those crossings including various spacecraft related and shock related parameters for each event. Furthermore, we show that the shocks in the database have properties that are spread out both in real space and par…
Magnetosheath jets are localized fast flows with enhanced dynamic pressure. When they supermagnetosonically compress the ambient magnetosheath plasma, a bow wave or shock can form ahead of them. Such a bow wave was recently observed to accelerate ions and possibly electrons. The ion acceleration process was previously analyzed, but the electron acceleration process remains largely unexplored. Here we use multi-point observations by Time History of Events and Macroscale during Substorms from three events to determine whether and how magnetosheath jet-driven bow waves can accelerate electrons. W…
Large parallel ($\leq$ 100 mV/m) and perpendicular ($\leq$ 600 mV/m) electric fields were measured in the Earth's bow shock by the vector electric field experiment on the Polar satellite. These are the first reported direct measurements of parallel electric fields in a collisionless shock. These fields exist on spatial scales comparable to or less than the electron skin depth (a few kilometers) and correspond to magnetic field-aligned potentials of tens of volts and perpendicular potentials up to a kilovolt. The perpendicular fields are amongst the largest ever measured in space, with energy d…
Hot flow anomalies (HFAs) represent a subset of solar wind discontinuities interacting with collisionless bow shocks. They are typically formed when the normal component of motional (convective) electric field points toward the embedded current sheet on at least one of its sides. The core region of an HFA contains hot and highly deflected ion flows and rather low and turbulent magnetic field. In this paper, we report first observations of HFA-like events at Mercury identified over a course of two planetary years. Using data from the orbital phase of the MErcury Surface, Space ENvironment, GEoc…
Experimental investigations of the fine plasma structure of interplanetary shocks are extremely difficult to conduct due to their small thickness and high speed relative to the spacecraft. We study the variations in the parameters of twice-ionized helium ions (4He++ ions or α-particles) in the solar wind plasma during the passage of interplanetary shocks and Earth's bow shock. We use data with high time resolution gathered by the BMSW (Bright Monitor of Solar Wind) instrument installed on the SPEKTR-R satellite, which operated between August 2011 and 2019. The MHD parameters of He++ ions (the …
Collisionless shocks are efficient particle accelerators. At Earth, ions with energies exceeding 100 keV are seen upstream of the bow shock when the magnetic geometry is quasi-parallel, and large-scale supernova remnant shocks can accelerate ions into cosmic rays energies. This energization is attributed to diffusive shock acceleration, however, for this process to become active the ions must first be sufficiently energized. How and where this initial acceleration takes place has been one of the key unresolved issues in shock acceleration theory. Using Cluster spacecraft observations, we study…
We present measurements from the ESA/NASA Cluster mission that show in situ acceleration of ions to energies of 1 MeV outside the bow shock. The observed heating can be associated with the presence of electromagnetic structures with strong spatial gradients of the electric field that lead to ion gyro-phase breaking and to the onset of chaos in ion trajectories. It results in rapid, stochastic acceleration of ions in the direction perpendicular to the ambient magnetic field. The electric potential of the structures can be compared to a field of moguls on a ski slope, capable of accelerating and…
The leading explanation for the origin of galactic cosmic rays is particle acceleration at the shocks surrounding young supernova remnants (SNRs), although crucial aspects of the acceleration process are unclear. The similar collisionless plasma shocks frequently encountered by spacecraft in the solar wind are generally far weaker (lower Mach number) than these SNR shocks. However, the Cassini spacecraft has shown that the shock standing in the solar wind sunward of Saturn (Saturn's bow shock) can occasionally reach this high-Mach number astrophysical regime. In this regime Cassini has provide…
