Bow Shock Crossings Research Articles

STEREO and Wind observations of intense cyclotron harmonic waves at the Earth's bow shock and inside the magnetosheath

We present the first observations of electron cyclotron harmonic waves at the Earth's bow shock from STEREO and Wind burst waveform captures. These waves are observed at magnetic field gradients at a variety of shock geometries ranging from quasi‐parallel to nearly perpendicular along with whistler mode waves, ion acoustic waves, and electrostatic solitary waves. Large amplitude cyclotron harmonic waveforms are also observed in the magnetosheath in association with magnetic field gradients convected past the bow shock. Amplitudes of the cyclotron harmonic waves range from a few tens to more than 500 mV/m peak‐peak. A comparison between the short (15 m) and long (100 m) Wind spin plane antennas shows a similar response at low harmonics and a stronger response on the short antenna at higher harmonics. This indicates that wavelengths are not significantly larger than 100 m, consistent with the electron cyclotron radius. Waveforms are broadband and polarizations are distinctively comma‐shaped with significant power both perpendicular and parallel to the magnetic field. Harmonics tend to be more prominent in the perpendicular directions. These observations indicate that the waves consist of a combination of perpendicular Bernstein waves and field‐aligned waves without harmonics. A likely source is the electron cyclotron drift instability which is a coupling between Bernstein and ion acoustic waves. These waves are the most common type of high‐frequency wave seen by STEREO during bow shock crossings and magnetosheath traversals and our observations suggest that they are an important component of the high‐frequency turbulent spectrum in these regions.

Electron demagnetization and heating in quasi‐perpendicular shocks

Field and plasma measurements made during a quasi‐perpendicular terrestrial bow shock crossing by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) E spacecraft on 21 August 2010 show that the measured electric field, being as great as 300 mV/m in the ramp, produced potential fluctuations over an electron gyrodiameter, which were as much as 15 times greater than the electron temperature. This fact requires that the electrons were unmagnetized in the ramp as a result of being scattered many times in a single gyroperiod by the fluctuating electric field. Supporting observations include the facts that the perpendicular electron heating and the parallel electron heating were equal in magnitude and simultaneous in time within experimental uncertainties and a factor of about five smaller than expected for perpendicular adiabatic heating of magnetized electrons. The conclusion that the electrons were unmagnetized is generalized through observations of 70 bow shock crossings on THEMIS and 140 shock crossings on Cluster to conclude that electrons are at least frequently unmagnetized in shock ramps such that their trajectories are more random than adiabatic and that they are energized during their chaotic traversal of the shock by the cross‐shock quasi‐DC electric field in the Normal Incidence Frame.

A comparison of bow shock models with Cluster observations during low Alfvén Mach number magnetic clouds

Abstract. Magnetic clouds (MCs) are very geoeffective solar wind structures. Their properties in the interplanetary medium have been extensively studied, yet little is known about their characteristics in the Earth's magnetosheath. The Cluster spacecraft offer the opportunity to observe MCs in the magnetosheath, but before MCs reach the magnetosphere, their structure is altered when they interact with the terrestrial bow shock (BS). The physics taking place at the BS strongly depends on ΘBn, the angle between the shock normal and the interplanetary magnetic field. However, in situ observations of the BS during an MC's crossing are seldom available. In order to relate magnetosheath observations to solar wind conditions, we need to rely on a model to determine the shock's position and normal direction. Yet during MCs, the models tend to be less accurate, because the Alfvén Mach number (MA) is often significantly lower than in regular solar wind. On the contrary, the models are generally optimised for high MA conditions. In this study, we compare the predictions of four widely used models available in the literature (Wu et al., 2000; Chapman and Cairns, 2003; Jeřáb et al., 2005; Měrka et al., 2005b) to Cluster's dayside BS crossings observed during five MC events. Our analysis shows that the ΘBn angle is well predicted by all four models. On the other hand, the Jeřáb et al. (2005) model yields the best estimates of the BS position during low MA MCs. The other models locate the BS either too far from or too close to Earth. The results of this paper can be directly used to estimate the BS parameters in all studies of MC interaction with Earth's magnetosphere.

Multispacecraft observations of the terrestrial bow shock and magnetopause during extreme solar wind disturbances

Abstract. Three events are discussed from the declining phase of the last solar cycle when the magnetopause and/or the bow shock were observed unusually close to the Earth due to major interplanetary disturbances. The observed extreme locations of the discontinuities are compared with the predictions of three magnetopause and four bow shock models which describe them in considerably different ways using statistical methods based on observations. A new 2-D magnetopause model is introduced (based on Verigin et al., 2009) which takes into account the pressure of the compressed magnetosheath field raised by the interplanetary magnetic field (IMF) component transverse to the solar wind flow. The observed magnetopause crossings could be predicted with a reasonable accuracy (0.1–0.2 RE) by one of the presented models at least. For geosynchronous magnetopause crossings observed by the GOES satellites, (1) the new model provided the best predictions when the IMF was extremely large having a large negative Bz component, and (2) the predictions of the model of Shue et al. (1998) agreed best with the observations when the solar wind dynamic pressure was extremely large. The magnetopause crossings close to the cusp observed by the Cluster spacecraft were best predicted by the 3-D model of Lin et al. (2010). The applied empirical bow shock models and the 3-D semi-empiric bow shock model combined with magnetohydrodynamic (MHD) solution proved to be insufficient for predicting the observed unusual bow shock locations during large interplanetary disturbances. The results of a global 3-D MHD model were in good agreement with the Cluster observations on 17 January 2005, but they did not predict the bow shock crossings on 31 October 2003.

Deep Solar Activity Minimum 2007 – 2009: Solar Wind Properties and Major Effects on the Terrestrial Magnetosphere

We discuss the temporal variations and frequency distributions of solar wind and interplanetary magnetic field parameters during the solar minimum of 2007 – 2009 from measurements returned by the IMPACT and PLASTIC instruments on STEREO-A. We find that the density and total field strength were significantly weaker than in the previous minimum. The Alfvén Mach number was higher than typical. This reflects the weakness of magnetohydrodynamic (MHD) forces, and has a direct effect on the solar wind–magnetosphere interactions. We then discuss two major aspects that this weak solar activity had on the magnetosphere, using data from Wind and ground-based observations: i) the dayside contribution to the cross-polar cap potential (CPCP), and ii) the shapes of the magnetopause and bow shock. For i) we find a low interplanetary electric field of 1.3±0.9 mV m−1 and a CPCP of 37.3±20.2 kV. The auroral activity is closely correlated to the prevalent stream–stream interactions. We suggest that the Alfvén wave trains in the fast streams and Kelvin–Helmholtz instability were the predominant agents mediating the transfer of solar wind momentum and energy to the magnetosphere during this three-year period. For ii) we determine 328 magnetopause and 271 bow shock crossings made by Geotail, Cluster 1, and the THEMIS B and C spacecraft during a three-month interval when the daily averages of the magnetic and kinetic energy densities attained their lowest value during the three years under survey. We use the same numerical approach as in Fairfield’s (J. Geophys. Res. 76, 7600, 1971) empirical model and compare our findings with three magnetopause models. The stand-off distance of the subsolar magnetopause and bow shock were 11.8 R E and 14.35 R E, respectively. When comparing with Fairfield’s (1971) classic result, we find that the subsolar magnetosheath is thinner by ∼1 R E. This is mainly due to the low dynamic pressure which results in a sunward shift of the magnetopause. The magnetopause is more flared than in Fairfield’s model. By contrast the bow shock is less flared, and the latter is the result of weaker MHD forces.

A new approach to magnetopause and bow shock modeling based on automated region identification

The present empirical models describing a location and shape of the magnetopause and bow shock are based on a statistical evaluation of magnetopause and bow shock crossings. The crossings are usually identified by a visual inspection of the plots or by automatic methods which are less reliable. We present a new method of determination of the most probable boundary locations. The method is based on continuous plasma and magnetic field measurements in the regions visited by a sounding spacecraft (the solar wind, magnetosheath, and magnetosphere) and on the determination of ratios of these parameters to simultaneously monitored upstream parameters. The regions identified by this method are then used for development of simple models of the magnetopause and bow shock locations parameterized by the upstream pressure. The performance of the models is tested with corresponding boundary crossings based mainly on the THEMIS observations. Both developed models are in a good agreement with the results obtained from identification of crossings.

A statistical study of the cross‐shock electric potential at low Mach number, quasi‐perpendicular bow shock crossings using Cluster data

The cross‐shock electrostatic potential at the front of collision‐less shocks plays a key role in the distribution of energy at the shock front. Multipoint measurements such as those provided by the Cluster II mission provide an ideal framework for the study of the cross‐shock potential because of their ability to distinguish between temporal and spacial variations at the shock front. We present a statistical study of the cross‐shock potential calculated for around 50 crossings of the terrestrial bow shock. The statistical dependency of the normalized (with resect to upstream ion kinetic energy) cross‐shock potential (ΦK) on the upstream Alfvén Mach number is in good agreement with analytical results that predict decrease of Φk with increasing Mach number.

Electron heating at Saturn's bow shock

Collisionless shock waves are a widespread phenomenon in both solar system and astrophysical contexts. The nature of energy dissipation at such shocks is of particular interest, especially at high Mach numbers. We use data taken by the Cassini spacecraft to investigate electron heating at Saturn's bow shock, one of the strongest collisionless shocks encountered by spacecraft to date. Measurements of the upstream solar wind ion parameters are scarce due to spacecraft pointing constraints and the absence of an upstream monitor. To address this, we use solar wind speed predictions from the Michigan Solar Wind Model. Since these model predictions are based on near-Earth solar wind measurements, we restrict our analysis to bow shock crossings made by Cassini within ±75 days of apparent opposition of Earth and Saturn. An analysis of the resulting set of 94 crossings made in 2005 and 2007 reveals a positive correlation between the electron temperature increase across the shock and the kinetic energy of an incident proton, where electron heating accounts for between ∼3% and ∼7% of this incident ram energy. This percentage decreases with increasing Alfven Mach number, a trend that we confirm continues into the hitherto poorly explored high–Mach number regime, up to an Alfven Mach number of ∼150. This work reveals that further studies of the Saturnian bow shock will bridge the gap between the more modest Mach numbers encountered in near-Earth space and more exotic astrophysical regimes where shock processes play central roles.

A new semiempirical model of Saturn's bow shock based on propagated solar wind parameters

[1] A new semiempirical model of Saturn’s dayside bow shock is presented. The model uses observations made during the Pioneer 11, Voyager 1, and Voyager 2 flybys as well as data from the first 6 years of the Cassini mission (2004–2010) to derive the average shape of the shock surface and the variation of shock subsolar distance with solar wind dynamic pressure. The 574 bow shock crossings used to construct the model provide good local time coverage of the dayside shock surface up to latitudes of roughly 45°, allowing the three‐dimensional shape of the shock surface to be investigated for the first time. Narrowband Langmuir waves observed by the Radio and Plasma Wave Science instrument are combined with propagated solar wind velocities in order to estimate the solar wind dynamic pressure associated with each of the Cassini crossings. An axisymmetric second‐order surface is then fit to the resulting crossing distribution, self‐consistently accounting for solar wind dynamic pressure variations. The new semiempirical model is compared with existing models of Saturn’s bow shock and magnetopause, and the physical implications of the model are discussed. On the basis of these comparisons, it is proposed that the new semiempirical model is the most accurate representation of Saturn’s bow shock surface to date.

Slow-mode shock candidate in the Jovian magnetosheath

We discuss some interesting plasma observations in the Jovian magnetosheath by the onboard plasma instruments of the Cassini spacecraft during the 2000–2001 Jupiter flyby. We propose that the observations are consistent with a slow-mode shock transition. In the terrestrial magnetosheath, a number of observations have been made that are consistent with slow-mode waves or shocks. In addition, a number of observations have established that, at least occasionally, slow-mode structures form at the plasma sheet-lobe boundary in the terrestrial magnetotail, related to X lines associated with reconnection. There has been only one previously reported observation of a slow-mode shock-like transition in the Jovian plasma environment. This observation was made in the dayside magnetosheath. The observation we report here was made well downstream of the magnetosphere in Jupiter’s magnetosheath, at local time ∼19:10. For our analysis we have used the data from the Cassini Plasma Spectrometer (CAPS) the Magnetospheric Imaging Instrument (MIMI) and the Magnetometer (MAG). The bow shock crossings observed by Cassini ranged downstream to −600 R J from the planet

Simultaneous measurements of Martian plasma boundaries by Rosetta and Mars Express

We present the first two-spacecraft near-simultaneous observations of the Martian bow shock (BS), magnetic pileup boundary (MPB) and photo-electron boundary (PEB) obtained by the plasma instruments onboard Rosetta and Mars Express during the Rosetta Mars flyby on February 25, 2007. Our observations are compared with shape models for the BS and MPB derived from previous statistical studies. The MPB is found at its expected position but the BS for this event is found significantly closer to the planet than expected for the rather slow and moderately dense solar wind. Cross-calibration of the density measurements on the two spacecraft gives a density profile through the magnetosheath, indicating an increasing solar wind flux during the Rosetta passage which is consistent with the multiple BS crossings at the Rosetta exit.

Statistical analysis of the location of the Martian magnetic pileup boundary and bow shock and the influence of crustal magnetic fields

We use the data set from the magnetometer and electron reflectometer instruments on board the Mars Global Surveyor spacecraft to show that the crustal magnetic fields of Mars affect the location of the magnetic pileup boundary (MPB) and bow shock (BS) globally. We search for crossings of the MPB and BS in the data that were observed over the first 16 months of the mission. To identify the influence of the crustal magnetic fields, all crossings are extrapolated to the terminator plane in order to remove the solar zenith angle (SZA) dependence, and to make it possible to compare crossings independently of location. The MPB crossings that were observed over regions on Mars, which contain strong crustal magnetic fields, are on average located further out than crossings observed over regions with weak crustal fields. This is shown in three separate longitude intervals. We also find that the dayside BS crossings observed over the southern hemisphere of Mars are on average located further out than the BS crossings observed over the northern hemisphere, possibly because of the influence of the crustal fields. We also study the magnetic field strength and its variation at the inside of the MPB and their dependence on the SZA and altitude. We find that the magnitude of the magnetic field in the MPB is closely linked to the altitude of the MPB, with the magnitude increasing as the MPB is observed closer to the planet.

Influence of the tilt angle on the bow shock shape and location

The bow shock is created in front of an obstacle immersed into a supersonic flow and its location depends on the size and shape of the obstacle. It was found that the obstacle (magnetopause) is scaled with the solar wind dynamic pressure and changes its dimensions and shape with the dipole tilt angle and interplanetary magnetic field orientation. Similar functional dependencies would be expected for the bow shock position, however, none of the bow shock models considers the parametrization of bow shock properties with the tilt angle. The present study employs a set of bow shock crossings registered during 1994–2002 by different spacecraft and demonstrates the tilt angle influence on the bow shock location. The study is based on a comparison of a recent bow shock model with observations and shows that the night–side bow shock moves in the direction of the positive ZGSM axis for positive tilt angles. The magnitude of the displacement can reach ≈3 RE. The analysis reveals that the high–latitude bow shock surface is significantly distorted near the dawn–dusk meridian. This effect was identified as a counterpart of the magnetopause indentation in the cusp region.

The Quasi-Perpendicular Bow Shock as a Temporal Trapping Barrier and Accelerator of Magnetospheric Particles

The bow shock has been studied so far, mostly as a boundary that influences the particles that are incident from the upstream region (of solar origin). In this paper, we provide, for the first time, observational evidence from the energetic-particle-experiment and the charged-particle-measurement-experiment instruments onboard the IMP-8 spacecraft, showing that ions leaking from the magnetosphere, during storms or substorms, are affected by the quasi-perpendicular (Q-P) bow shock and can be temporally trapped just downstream from the shock in a magnetic configuration opposite to the magnetic mirror. The observations from three representative event periods examined in this paper suggest that magnetospheric energetic ( keV) ions show general flows along the field lines in the direction from the magnetosheath toward the interplanetary space, in both sides of the shock (up- and downstream), and characteristic cross-field anisotropic distributions just downstream from the shock, consistent with a ldquotrapped population.rdquo In a series of successive bow-shock crossings within several hours, the IMP-8 spacecraft observed intensity gradients toward the magnetosheath, which strongly suggest a spatial modulation of magnetospheric ion fluxes at the Q-P bow shock. Highest peaks of ion intensities and a very hard spectrum in the energy range between 100 and 400 keV were observed just at the shock front, which suggest acceleration of magnetospheric particles during their temporal trapping at the bow shock. The observations near the Earth's bow shock examined in this paper are well explained in terms of the shock drift acceleration (SDA) theory for magnetospheric particles reaching the bow shock. The phenomenon discussed here, an apparent temporal trapping-and acceleration-of escaped magnetospheric ions at the Earth's bow shock, appears to be an important mechanism that influences the particle distributions near the Earth's bow shock and may have important applications to other shocks in our solar system (planetary, heliospheric, interplanetary, and corotating shock waves) and the interstellar medium (supernova shocks).

Electron dynamics and cross‐shock potential at the quasi‐perpendicular Earth's bow shock

The evolution of the electron distribution function through quasi‐perpendicular collisionless shocks is believed to be dominated by the electron dynamics in the large‐scale coherent and quasi‐stationary magnetic and electric fields. We investigate the electron distributions measured on board Cluster by the Plasma Electron and Current Experiment (PEACE) instrument during three quasi‐perpendicular bow shock crossings. Observed distributions are compared with those predicted by electron dynamics resulting from conservation of the first adiabatic invariant and energy in the de Hoffmann‐Teller frame, for all pitch angles and all types of trajectories (passing and, for the first time, reflected or trapped). The predicted downstream velocity distributions are mapped from upstream measurements using an improved Liouville mapping technique taking into account the overshoots. Furthermore, for one of these crossings we could take advantage of the configuration of the Cluster quartet to compare mapped upstream velocity distributions with those simultaneously measured at a relatively well magnetically connected downstream location. Consequences of energy and adiabatic invariant conservation are found to be compatible with the observed electron distributions, confirming the validity of electron “heating” theories based on DC fields as zeroth‐order approximations, but some systematic deviations are found between the dynamics of low‐ and high‐adiabatic invariant electrons. Our approach also provides a way to estimate the cross‐shock electric potential profile making full use of the electron measurements, and the results are compared to other estimates relying on the steady state dissipationless electron fluid equations. At the temporal resolution of the instruments, the scales associated to the change of the potential generally appear to be comparable to those of the magnetic field, but some differences between the methods appear within the shock transition. It is argued that potentials evaluated from Liouville mapping rely on less restrictive hypotheses and are therefore more reliable. Finally, we show how, in contrast to methods using electron velocity moments, the technique can be used to produce high‐time‐resolution electric potentials and discuss the electric potential profiles through the shock.

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.

Orientation, location, and velocity of Saturn's bow shock: Initial results from the Cassini spacecraft

The Cassini spacecraft commenced its tour of the planet Saturn on 1 July 2004 (GMT). During the insertion orbit, the Cassini magnetometer (MAG), radio/plasma wave experiment (RPWS), and plasma spectrometer (CAPS) obtained in situ measurements of the magnetic field and plasma conditions associated with Saturn's environment. Analysis of the magnetic field data indicate that Cassini repeatedly crossed a mainly quasi‐perpendicular bow shock boundary on both the inbound (post‐dawn) and outbound (predawn) legs. Modeling of the bow shock and magnetopause crossing positions shows evidence for a magnetospheric compression during Cassini's immersion in the magnetosphere. The magnetic signatures of the bow shock crossings show the clearly defined “overshoot” and “foot” regions associated with the quasi‐perpendicular geometry. The duration of the shock foot, considered in combination with the RPWS and CAPS solar wind electron parameters upstream of the bow shock crossings, indicates that the length scale for the bow shock ramp at Saturn is about an ion inertial length. This is consistent with multispacecraft observations of the spatial scale of the Earth's shock foot region. The data are generally consistent with Saturn bow shock velocities up to ∼400 km s−1 and shock structures governed by ion dynamics.

Martian shock and magnetic pile-up boundary positions and shapes determined from the Phobos 2 and Mars Global Surveyor data sets

A great many Martian bow shock and magnetic pile-up boundary crossings have been identified in the Phobos 2 and Mars Global Surveyor, MGS, data. From these observations the positions and shapes of the bow shock and magnetic pile-up boundary, MPB, have been derived and modelled, using curve-fitting techniques. The models thus derived separately from the Phobos 2 and MGS data sets do not differ drastically, despite the different time and space data coverages. The purpose of the paper is therefore to show the results obtained from the mixing of the Phobos 2 and MGS data bases and to compare the derived bow shock and MPB models with the ones obtained previously. The underlying objective was to see whether it was possible to determine improved bow shock and MPB models or not. The answer is definitely yes, and particularly for the MPB, thanks to the complementary nature of the observations. The boundaries crossed close to the subsolar direction or mostly far downstream by Phobos 2 indeed allow a better coverage of the Martian space environment to be considered. Nevertheless, in order to reduce the domination of the overabundant MGS data set and/or the crossings that are close to Mars ( x>−4 R M, i.e. x>−13 562 km) weighting factors have been introduced.

Global MHD simulations of Saturn's magnetosphere at the time of Cassini approach

We present the results of a 3D global magnetohydrodynamic simulation of the magnetosphere of Saturn for the period of Cassini's initial approach and entry into the magnetosphere. We compare calculated bow shock and magnetopause locations with the Cassini measurements. In order to match the measured locations we use a substantial mass source due to the icy satellites (∼1 × 1028 s−1 of water product ions). We find that the location of bow shock and magnetopause crossings are consistent with previous spacecraft measurements, although Cassini encountered the surfaces further from Saturn than the previously determined average location. In addition, we find that the shape of the model bow shock and magnetopause have smaller flaring angles than previous models and are asymmetric dawn‐to‐dusk. Finally, we find that tilt of Saturn's dipole and rotation axes results in asymmetries in the bow shock and magnetopause and in the magnetotail being hinged near Titan's orbit (∼20 RS).

Three‐dimensional position and shape of the bow shock and their variation with upstream Mach numbers and interplanetary magnetic field orientation

Peredo et al. (1995) derived a frequently used three‐dimensional bow shock model parameterized by the upstream Alfvénic Mach number from the set of approximately 550 bow shock crossings provided by 17 distinct spacecraft over the period of 1963–1980. However, several studies reported some systematic biases in the bow shock model predictions. Therefore we have attempted to improve upon the bow shock model of Peredo et al. (1995) using their original data set and methodology in an effort to better understand these effects. We have performed three‐dimensional best fits to the bow shock crossings binned by the upstream Mach numbers MA, MS, and MMS and found that the best fitting surfaces were best ordered with the MA. In agreement with predictions from the magnetohydrodynamic theory, the results show that the bow shock surface expands when the MA decreases. The found dawn‐dusk asymmetry in the bow wave is consistent with previous studies only in the Geocentric Plasma Ecliptic System (GPE) coordinates but not in the Geocentric Interplanetary Medium (GIPM) coordinates which suggests that the employed data set is not comprehensive enough for resolving this asymmetry. Nor is the Mach cone asymmetry resolved in our data set (not even in the GIPM frame). We have derived two models predicting the statistical position and shape of the bow shock in the GPE or GIPM coordinates. Error analysis shows that the GPE‐based model is more accurate and applicable for MA = 3–20 except the nose region where the model underestimates the bow shock position for MA < 5. A direct comparison of the model predictions with 5870 IMP 8 bow shock crossings demonstrated high accuracy of predictions and, for the GPE‐based model, an exceptional stability of predictions even under extreme upstream conditions. Indeed, the new GPE‐based bow shock model is more accurate and equally or more stable than the Formisano (1979), Němeček and Šafránková (1991), Farris and Russell (1994), Cairns and Lyon (1995), Peredo et al. (1995), or Verigin et al. (2001) models.