Interaction of interplanetary shocks with the bow shock

Fast forward interplanetary (IP) shocks have been identified as a source of large geomagnetic disturbances. However, the shocks can evolve in the solar wind, they are modified by interaction with the bow shock and during their propagation through the magnetosheath. A few previous papers refer the inclination and deceleration of the IP shock front in this region. Our contribution continues this effort and presents the study of an IP shock interaction with the bow shock. Since the bow shock is a reversed fast shock, the interaction of the IP shock and bow shock is a problem of interaction of two fast MHD shocks.

We compare profiles of magnetic field and plasma parameters observed by several spacecraft in the solar wind and magnetosheath with the profiles of the same parameters resulting from the MHD numerical model. The MHD model suggests that the interaction of an IP shock with the bow shock results in an inward bow shock displacement that is followed by its outward motion. Such motion will result in an indentation propagating along the bow shock surface. This scenario is confirmed by multipoint observations. Moreover, the model confirms also previous suggestions on the IP shock deceleration in the magnetosheath.     

Oscillatory cosmic-ray shock structures

A multiple scales analysis is used to derive a mixed Burgers-Korteweg-de Vries (BKdV) equation in the long wavelength regime for a two-fluid MHD model used to describe cosmic-ray acceleration by the first-order Fermi process in astrophysical shocks. The BKdV equation describes the time evolution of weak shocks in the theory of diffusive shock acceleration for all possible cosmic-ray pressures. Previous work on weak shocks in the cosmic-ray MHD model has assumed that dissipation alone is sufficient to balance nonlinearity, but, as cosmic-ray pressures become small, the weak shock becomes discontinous. By including Hall current effects into the MHD model, the low cosmic-ray pressure limit leads smoothly into solitary wave behaviour. For low cosmic-ray pressures, the shock has a downstream oscillatory precursor which is smoothed into the standard Taylor shock profile with increasing cosmic-ray pressure. As a by-product of the perturbation analysis, a dissipative KdV equation is derived. In conclusion, dispersive effects on Alfvén waves are discussed and a modulational stability analysis is presented.     

Nonplanar magnetic reconnection associated with conical slow shocks

We study a nonplanar model of magnetic reconnection associated with conical slow shocks, assuming that the shock surfaces are two identical cones with circular cross sections symmetrical about the ±x-axis. In the inflow region upstream of the shocks, two oppositely directed magnetic fields are separated by a current sheet. The model treats the current sheet as a tangential discontinuity and treats shocks and tangential discontinuity as surfaces of zero thickness. The dynamical structure of the global magnetic field in the continuous regions is studied using compressible, non-resistive MHD equations. In the inflow region, nonplanar magnetic field lines first move toward the current sheet. Near the sheet, the middle sections of the field lines become highly flattened, almost parallel to the sheet. Eventually, then oppositely directed field lines merge across the tangential discontinuity between the two shocks, and the magnetic lines are reconnected at the intersection of the shock and the tangential discontinuity. Reconnected magnetic lines are carried away at high speeds by the MHD flow in the outflow region, downstream of the shocks.     

Jump relations for magnetohydrodynamic shock waves in non-ideal gas flow

The generalized jump relations across the magnetohydrodynamic (MHD) shock front in non-ideal gas are derived considering the equation of state for non-ideal gas as given by Landau and Lifshitz. The jump relations for pressure, density, and particle velocity have been derived, respectively in terms of a compression ratio. Further, the simplified forms of the MHD shock jump relations have been obtained in terms of non-idealness parameter, simultaneously for the two cases viz., (i) when the shock is weak and, (ii) when it is strong. Finally, the cases of strong and weak shocks are explored under two distinct conditions viz., (i) when the applied magnetic field is strong and, (ii) when the field is weak. The aim of this paper is to contribute to the understanding of how shock waves behave in magnetized environment of non-ideal gases.     

Grain destruction in interstellar shock waves

Interstellar shock waves can erode and destroy grains present in the shocked gas, primarily as the result of sputtering and grain-grain collisions. Uncertainties in current estimates of sputtering yields are reviewed. Results are presented for the simple case of sputtering of fast grains being stopped in cold gas. An upper limit is derived for sputtering of refractory grains in C-type MHD shocks: shock speedsv _s 50 km s^–1 are required for return of more than 30% of the silicate to the gas phase. Sputtering can also be important for removing molecular ice mantles from grains in two-fluid MHD shock waves in molecular gas. Recent estimates of refractory grain lifetimes against destruction in shock waves are summarized, and the implications of these short lifetimes are discussed.     

Evolution of fast and slow shock interactions in the inner heliosphere

We use a one-dimensional, time-dependent adaptive grid MHD code to study the interaction between fast and slow shocks in the solar wind. Our results show that: (1) a forward slow shock (FSS) can be destroyed by a forward fast shock (FFS) that overtakes it from behind; (2) two propagating FSSs can merge into a stronger FSS; (3) a strong FSS can survive by following a strong forward fast shock; and (4) the strength of a FSS is decreased by following an FFS. These simulation results reproduce an important feature of the Helios observations (Richter, 1987) where transient fast shocks were more frequently followed within a few hours by slow shock ype discontinuities rather than by fast reverse shocks.     

On the possibility of radio emission from quasi-parallel and quasi-perpendicular propagation of shocks

A set of 21 solar type II radio bursts observed using Hiraiso radio spectrograph have been analysed to study the direction of propagation of coronal shocks. A simple analysis is carried out to find the approximate angle between the shock normal and magnetic field by solving the Rankine-Hugoniot MHD relation with assumption of Alfven speed and plasma beta. From this analysis, it is suggested that both quasi-parallel shocks (favourable) and quasi-perpendicular shocks can generate type II bursts depending upon the circumstances of the corona.     

Evolution of fast and slow shock interactions in the inner heliosphere

We use a one-dimensional, time-dependent adaptive grid MHD code to study the interaction between fast and slow shocks in the solar wind. Our results show that: (1) a forward slow shock (FSS) can be destroyed by a forward fast shock (FFS) that overtakes it from behind; (2) two propagating FSSs can merge into a stronger FSS; (3) a strong FSS can survive by following a strong forward fast shock; and (4) the strength of a FSS is decreased by following an FFS. These simulation results reproduce an important feature of the Helios observations (Richter, 1987) where transient fast shocks were more frequently followed within a few hours by slow shock ype discontinuities rather than by fast reverse shocks.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion–neutral friction. At times much less than the ion–neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.     

Origin of Coronal Shock Waves

The basic idea of the paper is to present transparently and confront two different views on the origin of large-scale coronal shock waves, one favoring coronal mass ejections (CMEs), and the other one preferring flares. For this purpose, we first review the empirical aspects of the relationship between CMEs, flares, and shocks (as manifested by radio type II bursts and Moreton waves). Then, various physical mechanisms capable of launching MHD shocks are presented. In particular, we describe the shock wave formation caused by a three-dimensional piston, driven either by the CME expansion or by a flare-associated pressure pulse. Bearing in mind this theoretical framework, the observational characteristics of CMEs and flares are revisited to specify advantages and drawbacks of the two shock formation scenarios. Finally, we emphasize the need to document clear examples of flare-ignited large-scale waves to give insight on the relative importance of flare and CME generation mechanisms for type II bursts/Moreton waves.     

Predicting the Arrival Time of Shock Passages at Earth

The purpose of this parametric study is to predict the arrival time at Earth of shocks due to disturbances observed on the Sun. A 3D magnetohydrodynamic (MHD) simulation code is used to simulate the evolution of these disturbances as they propagate out to 1 AU. The model in Han, Wu and Dryer (1988) uses solar data for input at 0.08 AU (18 solar radii). The initial shock speed (ISS) is assumed to be constant from the corona to 0.08 AU. We investigate how variations of this ISS affect the arrival times of the shock at Earth. This basic parametric study, however, does not consider inhomogeneous background solar wind structures such as corotating interaction regions and their precursor stream–stream interactions, nor interplanetary manifestations of complex coronal mass ejecta such as magnetic clouds. In the latter case, only their associated shocks are considered. Because the ambient (pre-existing background) solar wind speed is known to affect the shock arrival time at 1 AU, we also simulated events with various background solar wind speeds (BSWS) to investigate this effect. The results show that the shock arrival time at Earth depends on the BSWS, the speed of solar disturbances, their size, and their source location at the Sun. However, it is found that for a sufficiently large momentum input, the shock arrival time at Earth is not significantly affected by the pre-existing solar wind speed.     

Magnetosonic shocks in nonlinear dispersive media

When account is taken of the finite resistivity, energy equation, and generalized Ohm's law, it can be shown that the propagation of nonlinear magnetosonic waves in a warm plasma is described by a KdV-Burgers' equation. The stationary shock solutions for the latter are discussed. It is suggested that shocks may be responsible for the observed discontinuities in MHD fluctuations in the solar atmosphere.     

MHD study of temporal and spatial evolution of simulated interplanetary shocks in the ecliptic plane within 1 AU

We utilize a 21/2-D MHD time-dependent model to perform a parametric study of interplanetary shock propagation to 1 AU. The input conditions are represented by the following variables:(1) initial shock velocity, (2) duration of the driving pulse, and (3) width of the pulse at the near-Sun position (18 solar radii). The total net energy added to the solar wind was calculated for each pulse. The forward shock's travel time to, and the peak dynamic pressure at, 1 AU as a function of location along the shock front have been studied over a range of total input pulse energies from 10²⁹ to 10³² ergs. For input pulses with modest angular width and temporal duration, we find that the propagation of the resulting interplanetary fast forward shock waves depends primarily upon the net input energy. The dependence of the transit time upon energy is a power law with a -1/3 index which corresponds to the classical, piston driven case. Reverse shocks are also formed behind all but the lowest energy shocks. Their properties, although also a function of input energy, depend upon the specific values of the input pulse shock velocity, width and duration. We also briefly discuss the propagation of the shocks out to 1 AU, and the conditions for which the interplanetary shocks depart from being symmetric about the input pulse central meridian due to magnetic and dynamic effects.     

Variation of Alfven fluctuations across a slow shock near the sun

We consider how the Alfven fluctuation varies as it passes through a slow MHD shock, assuming the fluctuation to originate on the Sun and such slow shocks are present between 2 and 6 solar radii. The results are 1) low latitude region in the vicinity of the neutral sheet is where the fluctuation can propagate with no or little distortion; 2) high latitude region far from the neutral sheet is a region of small distortion only for low Alfven-Mach numbers (about 0.3 or lower); 3) the observation of the Alfven fluctuations in space is consistent with, and lends support to their originating in the Sun and the existence of slow shock around the Sun.     

Dynamic evolution of a quasi-spherical general polytropic magnetofluid with self-gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter n in the conventional polytropic self-similar transformation from the constraint of n+γ=2 with γ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.     

Turbulence in fast-mode shocks as a triggering mechanism in a solar flare

If a solar flare originates from the dissipation of magnetic energy, available in abundance in a larger region, this dissipation must take place very rapidly. A local topological change in the magnetic field structure may be sufficient to start the dissipation process. Such a change in topology might be obtained by fast reconnection in a smaller region, such as e.g. in the Sweet-Parker model, as a result of current-driven microinstabilities.Among the candidates satisfying the requirements to obtain large enough currents, such as magnetically neutral or current sheets and MHD shocks, the latter are shown to be most probable. In a fast MHD shock the (thermal) results of turbulence do in fact destroy the conditions for turbulence. However, in this work we show numerically that the nonlinear steepening mechanism of such a shock is able to restore the driving current for a large range of parameters and over a long time. This is still true if the most difficult threshold for turbulence, being that for Langmuir turbulence, is to be achieved. The critical parameter, not only for the occurrence of turbulence but also for the restoration of the driving current, is the shock thickness.     

On determining magnetohydrodynamic shock parameters θBn and MA

In a collisionless plasma, the magnetohydrodynamic shock structure, the associated waves and turbulence depend strongly on the shock parameters θ_Bn and M_A, where θ_Bn is the angle between the upstream magnetic field and the shock normal and M_A is the upstream Alfvén Mach-number. A method is given to determine θ_Bn and M_A and their estimated errors for all types of shocks without knowing the shock normals. The only measured quantities needed to determine θ_Bn and M_A are the plasma density and magnetic field on both sides of the shock. The estimated error of θ_Bn using our method can be obtained in a straightforward manner and is more reliable than that based on the calculated shock normal and the upstream magnetic field. Its simplicity and ability to handle parallel shocks as well as perpendicular and oblique shocks are illustrated by examples. This method should be useful for characterizing the types of shocks from analyzing the copious amount of data on magnetohydrodynamic (MHD) shocks found in space.     

Shock waves in the large-scale structure of the Universe

Cosmological shock waves are induced during hierarchical formation of large-scale structure in the universe. Like most astrophysical shocks, they are collisionless, since they form in the tenuous intergalactic medium through electromagnetic viscosities. The gravitational energy released during structure formation is transferred by these shocks to the intergalactic gas as heat, cosmic-rays, turbulence, and magnetic fields. Here we briefly described the properties and consequences of the shock waves in the context of the large-scale structure of the universe.     

A piston-driven shock in the solar corona

A solar flare that occurred on the west limb at 1981, March 25, 2038 UT generated a massive, rapidly-expanding optical coronal transient, which moved outward with an approximately constant velocity of 800 km s^–1. An associated magnetohydrodynamic shock travelled out ahead of the transient with a velocity estimated to be approximately 1000 km s^–1. The optical and radio data on the transient and shock fit well with general theories concerning piston-driven shocks and with current MHD models for propagation of such shocks through the solar corona.     

Ignition of MHD shocks associated with solar flares

We have selected single frequency recordings of 28 high-frequency type II bursts characterized by a starting frequency greater than 237 MHz to estimate as accurately as possible the launch-time of the flare-associated MHD shocks. We established the time associations between metric type II burst onsets and the time characteristics of the microwave and X-ray fluxes of the associated flares. The associated flares were impulsive events with rise times most often about 1 min in the hard X-ray range and 1–2 min in the microwave wavelength range. The majority of the type II bursts from our sample started about 1 min after the maximum of the microwave burst. Launch times of MHD shocks producing type II bursts were obtained using the 10 × Saito coronal model and shock velocities estimated from burst characteristics at different frequencies. Back-extrapolations of type II recordings indicate that MHD shocks are launched in the time interval prior to the maximum of the first peak in the associated microwave burst, most probably at the beginning of the rapid increase of the microwave burst.