Halley Bow Shock Research Articles

The structure of mass‐loading shocks: 3. Magnetohydrodynamics

The dissipative, mass‐loading, multifluid model, developed by Zank et al. [1993, 1994] to describe the structurally complex bow shocks observed at comets, has been extended to include the effects of a magnetic field. After describing the model, the shock structure problem associated with the one‐dimensional, steady state conservation equations is solved. The solutions are compared to those obtained from previous cold and warm gasdynamic models. The characteristic speeds of the system are calculated, and it is found that the physically relevant solutions correspond to fast magnetosonic shocks. The extended multifluid model is used to explore a new type of wave, called an “MHD draping shock,” which was proposed by Neubauer et al. [1990] to explain the unusual behavior of the magnetic field across the outbound Halley bow shock. It is found that mass loading induces switch‐on behavior at quasi‐parallel shocks, even in a high plasma beta environment. Across quasi‐parallel shocks we find switch‐on rotations as large as 30° in the cold solar wind case. This value decreases with increasing solar wind plasma beta, to a value of 16° at a value of βsw = 1. We do not find rotations large enough to explain the 69° twist in the field observed by Giotto, nor do we find any cases where the perpendicular component of the field changes sign.

Structure of mass‐loading shocks: 2. Comparison of theory and observation at comet Halley

The multifluid diffusive model of G. P. Zank et al. (1994), which describes the interaction of the solar wind with a cometary plasma in the outer coma, has been used to model the structure of the Halley bow shock. The theoretical results are compared to in situ observations made by Giotto. We compare the solar wind and cometary ion number densities and pressures upstream and through the quasi‐perpendicular and quasi‐parallel shocks (observed on the inbound and outbound legs of the encounter, respectively). In general, good agreement is found between theory and observations in terms of shock structure, strength, and location, especially for the quasi‐parallel shock. The comparison between the quasi‐perpendicular shock observations and theory is complicated by the apparently nonstationary behavior of the shock, a feature which has been remarked upon by other investigators. The cometary bow shock appears to be an excellent example of an energetic‐particle‐mediated shock where the energetic particles comprise less than 10% of the total number density.

Comment on “Comparison of observed and calculated implanted ion distributions outside comet Halley's bow shock” by T. I. Gombosi, M. Neugebauer, A. D. Johnstone, A. J. Coates, and D. E. Huddleston

It is argued that the formulation used by Gombosi (1991) does not distinguish between two fundamental types of resonant interactions (those between cometary pickup ions and LF electromagnetic waves). Two problems arise from using their overly simplified expressions. The wave polarization of the solar wind Alfven wave is not purely right-handed, and values from alpha sub com and alpha sub sw are not well known, nor are the 'polarizations' of the 'backward'-going waves in either case. Gombosi et al. discuss the antisunward vs the sunward propagating solar wind Alfven wave, and assume a reasonable value of 0.2 for alpha sub sw. However, alpha sub com is totally unknown. It is concluded that a more correct analysis of wave polarization can lead to significant changes in the formulation and results from Gombosi et al. In his reply Gombosi argues that his simplified wave-particle interaction model is consistent with Giotto observations and plasma kinetic simulations and it leads to a reasonable approximation of the implanted ion transport coefficients. The more complicated approach suggested by Tsurutani & Thorne (1993) requires the introduction of several ad hoc parameters and it does not lead to any change of the energy diffusion coefficient.

Reply [to “Comparison of observed and calculated implanted ion distributions outside comet Halley's bow shock” by T. I. Gombosi, M. Neugebauer, A. D. Johnstone, A. J. Coates, and D. E. Huddleston

Reply [to “Comparison of observed and calculated implanted ion distributions outside comet Halley's bow shock” by T. I. Gombosi, M. Neugebauer, A. D. Johnstone, A. J. Coates, and D. E. Huddleston

Correction to “Accelerated cometary ions observed downstream of the comet Halley bow shock”

Correction to “Accelerated cometary ions observed downstream of the comet Halley bow shock”

Accelerated cometary ions observed downstream of the comet Halley bow shock

Fluxes of energetic ions with energies exceeding 100 keV were observed upstream of the bow shock of comet Halley by the Tünde instrument which was on board the VEGA 1 spacecraft. Downstream of the shock, ion fluxes in the energy range 100 to 800 keV were observed. Cometary ions, such as O+, newly picked up by the solar wind have energies of about 15 keV in the solar wind frame of reference; hence the measured ion fluxes indicate that acceleration processes must have been operating near comet Halley. The measured ion fluxes were transformed into distribution functions in the solar wind frame using a variety of assumptions concerning the energy dependence of the distribution function and the identity of the ion species. The derived distribution function upstream of the shock falls off steeply with energy between 100 and 150 keV, with an effective temperature of about 7 keV or spectral index about −15. The distribution function increases with decreasing cometocentric distance, on average, reaching a maximum at the bow shock. Downstream of the shock, the spectra can be represented in two ways: (1) one population with a single spectral index based on a power law energy dependence or (2) two exponential function populations with different effective temperatures. In the latter case a soft component exists with an effective temperature of about 30 keV for energies less than about 250 keV and a harder component exists for higher energies with an effective temperature of about 100 keV. Downstream of the shock, the ion fluxes decrease with decreasing cometocentric distance. The measured distribution functions are compared with those obtained by similar instruments on Giotto and the International Cometary Explorer as well as with the predictions of several theoretical models that employ different acceleration mechanisms.

Electron distributions upstream of the comet Halley bow shock: Evidence for adiabatic heating

We report on three‐dimensional plasma electron (22 eV to 30 keV) observations upstream of the comet Halley bow shock, obtained by the RPA‐1 COPERNIC (Rème Plasma Analyzer ‐ Complete Positive Ion, Electron and Ram Negative Ion Measurements near Comet Halley) experiment on the Giotto spacecraft. Besides electron distributions typical of the undisturbed solar wind and backstreaming electrons observed when the magnetic field line intersects the cometary bow shock, we find a new type of distribution characterized by enhanced low energy (<100 eV) flux which peaks at 90° pitch angles. These are most prominent when the spacecraft is on field lines which pass close to but are not connected to the bow shock. The 90° pitch angle electrons appear to have been adiabatically heated by the increase in the magnetic field strength resulting from the compression of the upstream solar wind plasma by the cometary mass loading. We present a model calculation of this effect which agrees qualitatively with the observed 90° flux enhancements.

Alfven wave amplifications and generation at cometary bow shocks

The possible effect of hydromagnetic wave amplification and generation at cometary bow shocks is investigated by means of a planar hydromagnetic shock model. For the inbound crossing of comet Halley's bow shock, it is found that the transmission of the sunward-streaming hydromagnetic waves through the bow shock could lead to the enhancement of its wave amplitude by a factor of 2–3 and the generation of Alfvén waves with the opposite helicity. The plasma observations during inbound crossing of comet Halley's bow shock provide some evidence for such effect.

Comparison of observed and calculated implanted ion distributions outside comet Halley's bow shock

This paper compares calculated and measured energy spectra of implanted H+ and O+ ions on the assumption that the pickup geometry is quasi‐parallel and about 1% of the waves generated by the cometary pickup process propagate backward (toward the comet). The model provides a good description of the implanted O+ and H+ energy distribution near the pickup energies. The thickness of the implanted ion velocity distribution shells was nearly constant between 2.50×106 km and 1.20×106 km (just outside the shock) along the inbound Giotto trajectory. The explanation is that the velocity diffusion coefficient and characteristic diffusion time vary approximately as 1/r and r, respectively, and therefore their product (which determines the velocity shell thickness) remains nearly constant.

Properties of mass‐loading shocks: 1. Hydrodynamic considerations

The one‐dimensional hydrodynamics of flows subjected to mass loading are considered anew, with particular emphasis placed on determining the properties of mass‐loading shocks. This work has been motivated by recent observations of the outbound Halley bow shock (Neubauer et al., 1990), which cannot be understood in terms of simple hydrodynamical or magnetohydrodynamical descriptions. By including mass injection at the shock, we have investigated the properties of the Rankine‐Hugoniot conditions on the basis of a geometric formulation of the entropy condition. Such a condition, which is more powerful than the usual thermodynamical formulation, serves to determine those solutions to the Rankine‐Hugoniot conditions which correspond to a physically realizable downstream state. On this basis a concise theoretical description of hydrodynamic mass‐loading shocks is obtained. We show that mass‐loading shocks have more in common with combustion shocks than with ordinary nonreacting gas dynamical shocks. It is shown that for decelerated solutions to the Rankine‐Hugoniot conditions to exist, the upstream flow speed u0 must satisfy u0 > ucrit > cs, where cs is the sound speed. Besides the usual supersonic‐subsonic transition, mass‐loading fronts can also admit a decelerating supersonic‐supersonic transition, the structure of which consists of a sharp decrease in the flow velocity preceding a recovery and an increase in the final downstream flow speed. We suggest the possibility that such structures may describe the inbound Halley bow shock (Coates et al., 1987a). Both parallel and oblique shocks are considered, the primary difference being that oblique shocks are subjected to a shearing stress due to mass loading. It is conjectured that such a shearing may destabilize the shock.

Cometary ion distributions near the pickup energy outside comet Halley's bow shock

This paper compares calculated and measured energy spectra of implanted H + and O + ions on the assumption that the pick-up geometry is quasi-parallel and about 1% of the waves generated by the cometary pickup process propagates backward (towards the comet). The model provides a good description of the implanted O + and H + energy distribution near the pickup energies. The thickness of the implanted ion velocity distribution shells was nearly constant between 2.50×10 6 km and 1.20×10 6 km (just outside the shock) along the inbound Giotto trajectory. The explanation is that the velocity diffusion coefficient and characteristic diffusion time vary approximately as 1 r and r, respectively, therefore their product (which determines the velocity shell thickness) remains nearly constant.

Plasma parameters near the comet Halley bow shock

We present the plasma data from the Johnstone Plasma Analyser (JPA) instrument on Giotto for the inbound and outbound crossings of the structures which up to now were assumed to be bow shocks at comet Halley. Proton bulk parameters from the Fast Ion Sensor (FIS) inbound have been analyzed taking into account the wider downstream distributions which require a different analysis method from the upstream solar wind. The water group densities from the Implanted Ion Sensor (IIS) are obtained using updated processing procedures. These densities are consistent with the density inferred from the slowdown of the solar wind. The cometary ion pressure dominates in the shock region. The outbound parameters are presented from IIS for the first time. The inbound and outbound data are used to infer the shock normal directions from Rankine‐Hugoniot analyses. We calculate the fast mode Mach numbers of the shock structures moving into the upstream solar wind following the method of Smith et al. (1986), giving values of 1.1–1.8 (inbound) and 1.6–1.7 (outbound). The positions of the shock features are consistent with the inferred critical point in the solar wind flow. In addition, both the solar wind protons and the water group ion populations are observed to thermalize across the shock region, and we therefore conclude that the comet Halley bow shock features were indeed shocks.

Comparison of picked‐up protons and water group ions upstream of comet Halley's bow shock

Data are presented on the properties of picked‐up cometary protons and water group (WG) ions observed upstream of the bow shock of comet Halley by the ion mass spectrometer and Johnstone plasma analyzer experiments on the Giotto spacecraft. The number of WG ions exceeded the number of cometary protons at cometocentric distances r < 1.3×106 km, while the WG mass density exceeded the proton mass density when r < 6×106 km. The small scale variations of proton and WG densities were well correlated, which argues against the "expanding halo" model which has been used to explain the quasi‐periodicity of energetic particles observed by VEGA and Giotto. Two parameters are used to describe the pitch angle distributions of the picked‐up ions: a 10% width, which is the full angular width at 10% of the maximum of the pitch angle distribution, and a mean width. The cometocentric distance profiles of both parameters exhibited a great deal of scatter, and both parameters showed a steeper average radial gradient for WG ions than for protons. The 10% widths of WG ions were consistent with less than 10∶1 anisotropies for r < 2.5×106 km, but the proton anisotropy did not drop below 10∶1 until the spacecraft entered the “foreshock” region at r = 1.4×106 km. After subtraction of the variation in field direction, the mean width of the proton pitch angle distribution was nearly independent of distance everywhere outside the shock. The WG mean width, on the other hand, increased with increasing WG density (as expected) and with increasing angle α between the interplanetary field and the solar wind velocity vector (an unexpected result). No increase in shell radii, due to either adiabatic compression or first‐order Fermi acceleration, could be discerned for either ion species until the spacecraft was very close to the bow shock. The thickness of the picked‐up proton shell slowly increased as r decreased inside 2.5×106 km, whereas the water group shell thickness remained fairly constant until just outside the shock. While some of the differences between the two ion species can be attributed to the greater ionization scale length of cometary H atoms compared to WG atoms and molecules, the very different dependences of their pitch angle and energy diffusion rates on ion densities and on α are difficult to understand in terms of presently available theories and models.

Structure of the Halley bow shock

The similarities between cosmic ray mediated shocks and the bow shock of comet Halley are discussed briefly and a two-fluid model is presented. Since the shock is weak, we use a perturbation scheme to study the shock structure. We show that the shock is smoothed by the pick-up ions and that the length scale of the cometary ion foot is determined by the diffusive length scale of the cometary ions. Our results suggest that the spatial diffusion coefficient of the cometary ions is close to its “Bohm” limit in the vicinity of the shock. In addition, we suggest that small irregularities on the smoothed shock may be explained by means of a cometary ion driven instability.

The velocity distributions of cometary protons picked up by the solar wind

Velocity space distributions of picked up cometary protons were measured by the ion mass spectrometer on the Giotto spacecraft upstream of the Halley bow shock. Large pitch angle anisotropies were observed at all distances >1.2×106 km from the comet. As expected, pitch angle diffusion was much more rapid than energy diffusion. When the field was quasi‐parallel to the solar wind velocity vector, it was possible to discern the effect of pitch angle scattering by sunward propagating, field‐aligned hydromagnetic waves, but there is evidence for other scattering modes as well. For quasi‐perpendicular geometries, the pitch angle distribution was very asymmetric with phase space density peaks near pitch angles of 180°. It is suggested that the asymmetric pitch angle distribution may be caused by global rather than local wave‐particle interactions. Just outside the shock, the pitch angle distribution was nearly isotropic and the radius of the pickup shell increased significantly.

The density of cometary protons upstream of comet Halley's bow shock

Cometary protons picked up by the solar wind were detected by the high energy range spectrometer of the Giotto ion mass spectrometer starting at a cometocentric distance of ∼12×106 km. On the average, the density of cometary protons varied approximately as the inverse square of the cometocentric distance, reaching a value of 0.11 cm−3 just outside the bow shock. The data can be successfully fit to models that include substantial amounts of both slow (∼1 km/s) and fast (≥8 km/s) H atoms beyond the bow shock. Large local variations in the density of picked‐up protons can be explained on the basis of variations in the direction of the interplanetary magnetic field in upstream regions where pitch angle scattering was weak.

Pair of plasma discontinuities inside Halley's bow shock as seen by the plasma wave experiment

Plasma wave experiment APV-N (Vega mission) has detected clear effects correlating with two internal boundaries (at ∼770 000 and ∼350 000 km from the nucleus) of the comet Halley plasma environment. Important signatures of these boundaries were found by some other experiments aboard the Giotto and Vega spacecraft. Taking into account all the effects we have proposed the following interpretation: the charge-exchange cooling of cometary plasma leads to formation of a rarefaction wave (the region between ∼900 and ∼800 000 km) and of a weak shock wave (probably at ∼350 000 km) in the supersonic region inside the bow shock flanks: at the inner edge of the rarefaction wave as well as at the shock front the nonlinear (solitary) waves, with length ∼20 000 km, are generated; reflection of ions at the nonlinear waves gives rise to the cumulation of α-particles, plasma turbulence, electron heating.

The variation of protons, alpha particles, and the magnetic field across the bow shock of comet Halley

Data from the Ion Mass Spectrometer and the magnetometer on the Giotto spacecraft are used to examine the structure of the inbound crossing of the comet Halley bow shock on March 13, 1986. It is found that the velocity decrease, the field strength increase, and the heating of picked up cometary protons occurred over a broad region corresponding to several heavy‐ion gyroradii. The solar‐wind protons and alphas, on the other hand, were compressed and heated at a narrow structure, which might be called a subshock, on the leading edge of the broad shock region. The electrostatic potential difference across the shock was less than 40 V.

Giotto measurements of cometary and solar wind plasma at the Comet Halley bow shock

The interaction of comets with the solar wind depends on the ionization of the heavy cometary neutrals (mostly H2O and its dissociation products O, OH) which flow out from the nucleus, and the coupling of these newly produced cometary ions with the solar wind through its embedded magnetic field. The 'pick-up' of these heavy ions slows the solar wind such that a shock may form. As expected, the structure of such a shock transition is highly complex because the gyroradius of a heavy cometary ion is much larger than that of a solar wind proton. Here we present a comparative study of the solar wind electrons and protons and the cometary pick-up ions measured by Giotto at the inbound crossing of the bow shock at comet Halley. We find a highly structured shock transition starting with a cometary ion 'foot' seen at a distance on the order of the cometary ion gyroradius upstream from a sharp decrease in the solar wind proton speed. The total solar wind thermal and magnetic pressure is dominated by the relatively small population of cometary ions throughout the shock region.

Position and structure of the comet Halley bow shock: Vega‐ 1 and Vega‐2 measurements

The effect of solar wind loading by cometary ions on the position and structure of the comet Halley bow shock is discussed on the basis of simultaneous measurements of plasma, magnetic field and plasma waves aboard the "Vega‐1" and "Vega‐2" spacecraft. Data from the inbound crossings of the bow shock show that both quasiperpendiuclar ("Vega‐1") and quasiparallel ("Vega‐2") shocks were observed. The thickness of these shocks is greater than that of the Earth's bow shock at least by the ratio of the masses of cometary ions and protons. The bow shock position is reasonably well described by the kinetic model of solar wind loading by cometary ions.