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 overtaking interaction of typical shock waves in the solar wind flow

The interaction of traveling fast solar shock waves with other fast shock waves generated previously is considered in terms of magnetohydrodynamics for various solar wind parameters. The shocks are not piston ones and move freely in the flow. The magnetic structure in the interplanetary magnetic field emerging after the shock interaction is shown to correspond to the well-known magnetic configuration commonly observed on spacecraft or the classical Hundhausen R model. A head-on collision of solar shock waves with the boundary of a magnetic cloud is considered. It is pointed out that a slow shockwave refracted into the magnetic cloud can appear at an oblique collision of the shock with the cloud boundary. The results clarify our understanding of the available spacecraft data.     

Numerical simulation of slow shocks in the solar wind

The evolutionary state of slow forward shock waves is examined with the use of two MHD numerical codes. Our study is intended to be exploratory rather than a detailed parametric one. The first code is one-dimensional (with three components of velocity and magnetic field) which is used to follow a slow shock that propagates into a positive gradient of density versus distance. It is found that the slow shock evolves into an extraneous (intermediate) shock wave. The second code has a spherical, one-dimensional, planar geometry (with two velocity and magnetic field components) which is used to follow a spiral interplanetary magnetic field. It is found that a slow shock type perturbation can generate a forward slow shock; a fast forward shock is generated in the front of the slow shock; a contact discontinuity is formed behind the slow shock, and a compound nonlinear MHD wave is formed behind the contact discontinuity with a fast reverse shock formed further behind. Thus, we demonstrate that the evolution of a slow shock into (solely) a fast shock, as suggested by Whang (1987), is much more complicated.     

Geoeffectiveness of interplanetary shocks during solar minimum (1995–1996) and solar maximum (2000)

Plasma and magnetic field parameter variations across fast forward interplanetary shocks are analyzed during the last solar cycle minimum (1995–1996, 15 shocks), and maximum year 2000 (50 shocks). It was observed that the solar wind velocity and magnetic field strength variation across the shocks were the parameters better correlated with Dst. Superposed epoch analysis centered on the shock showed that, during solar minimum, B _z profiles had a southward, long-duration variation superposed with fluctuations, whereas in solar maximum the B _z profile presented 2 peaks. The first peak occurred 4 hr after the shock, and seems to be associated with the magnetic field disturbed by the shock in the sheath region. The second peak occurred 19 hr after the shock, and seems to be associated with the ejecta fields. The difference in shape and peak in solar maximum (Dst peak =−50 nT, moderate activity) and minimum (Dst peak =−30 nT, weak activity) in average Dst profiles after shocks are, probably, a consequence of the energy injection in the magnetosphere being driven by different interplanetary southward magnetic structures. A statistical distribution of geomagnetic activity levels following interplanetary shocks was also obtained. It was observed that during solar maximum, 36% of interplanetary shocks were followed by intense (Dst≤−100 nT) and 28% by moderate (−50≤Dst <−100 nT) geomagnetic activity. During solar minimum, 13% and 33% of the shocks were followed by intense and moderate geomagnetic activity, respectively. Thus, during solar maximum a higher relative number of interplanetary shocks might be followed by intense geomagnetic activity than during solar minimum. One can extrapolate, for forecasting goals, that during a whole solar cycle a shock has a probability of around 50–60% to be followed by intense/moderate geomagnetic activity.     

Low density drivers of strong interplanetary shocks

The theory that most, if not all, interplanetary shocks are caused by coronal mass ejections (CMEs) faces serious problems in accounting for the strongest shocks. The difficulties include (i) a remarkable absence of very strong shocks during solar maximum 1980 when CMEs were prolific, (ii) unrealistic initial speeds near the Sun for impulsive models, (iii) the absence of rarefaction zones behind the shocks and (iv) sustained high speed flows following shocks which are not easily explained as consequences of CME eruptions. Observations of the proton temperature near 1 AU indicate that strong shock drivers have properties similar to high speed streams emitted by coronal holes. Eruptions of fast solar wind from coronal holes influenced by solar activity can explain the occurrence of the strongest interplanetary shocks.     

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.     

Properties of Stream Interactions at One AU During 1995 – 2004

A stream interaction region (SIR) forms when a fast solar stream overtakes a slow stream, leading to structure that evolves as an SIR moves away from the Sun. Based on Wind (1995 – 2004) and ACE (1998 – 2004) in situ observations, we have conducted a comprehensive survey of SIRs at one AU, including a separate assessment of the longer-lasting corotating interaction regions (CIRs) that recur on more than one solar rotation. In all there are 196 CIRs, accounting for about 54% of the 365 SIRs. The largest proportion of CIRs to SIRs (64%) appears in 1999, and the smallest proportion (49%) is in 2002. Over the ten years, the annual number of SIR events varies little, from 32 up to 45. On average, the occurrence rate of shocks at SIRs at one AU is about 24%. Seventy percent of the SIRs with shocks have only forward shocks, more than twice the percentage of SIRs with only reverse shocks. This preponderance of forward shocks is consistent with the deflections of forward and reverse shocks relative to the ecliptic plane. In order to help address the effect of SIRs and CIRs on geomagnetic activity, we determine the solar-cycle variation of the event duration, scale size, the change in velocity from slow stream to fast stream, and the solar-cycle variation of the maximum magnetic field, peak total perpendicular pressure, and other properties. These statistics also provide a baseline for future studies at other heliocentric distances and for validating heliospheric models. Electronic Supplementary Material Supplementary material is available for this article at     

Structure and stationarity of quasi-perpendicular shocks: Numerical simulations

This paper presents an overview of numerical simulation studies of fast collisionless shocks and compares these simulation results with observations of the Earth's bow shock and theoretical works. Especially, we review the structure and stationarity of the supercritical quasi-perpendicular shocks. In situ observations indicate that these shocks are generally quasi-stationary whereas full particle simulations as well as hybrid simulations often present a strong nonstationary behavior, a shock self-reformation. The simulation results, along with theoretical and observational works, suggest that the classical models of the quasi-stationary structure generated by reflected protons or by dispersive whistlers are not generally applicable for the supercritical quasi-perpendicular shocks and other phenomena are to be included into the model to ensure the observed quasi-stationarity: The role of a small scale turbulence and shock ripples is investigated. The downstream turbulence and the electron dynamics in the quasi-perpendicular shocks are also discussed.     

Alfvén-magnetosonic waves interaction in the solar corona

The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the fast wave itself is governed by Burgers type equations possessing both expansion and compression shock solutions. Numerical simulations show that both parallely and perpendicularly propagating fast waves can steepen into shocks if their amplitudes are in excess of some sizeable fraction of the Alfvén velocity. However, if the magnetic field changes linearly in the perpendicular direction, then formation of perpendicular shocks can be hindered. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves whose propagation is described by linearized Boussinesq type equations with ponderomotive terms due to the Alfvén wave. The limits of the slow and fast waves are investigated.     

Solar Cycle Variation of the Interplanetary Forward Shock Drivers Observed at 1 AU

Forecasting space weather more accurately from solar observations requires an understanding of the variations in physical properties of interplanetary (IP) shocks as solar activity changes. We examined the characteristics (occurrence rate, physical parameters, and types of shock driver) of IP shocks. During the period of 1995 – 2001, a total of 249 forward IP shocks were observed. In calculating the shock parameters, we used the solar wind data from Wind at the solar minimum period (1995 – 1997) and from ACE since 1998 including the solar maximum period (1999 – 2001). Most of IP shocks (68%) are concentrated in the solar maximum period. The values of physical quantities of IP shocks, such as the shock speed, the sonic Mach number, and the ratio of plasma density compression, are larger at solar maximum than at solar minimum. However, the ratio of IMF compression is larger at solar minimum. The IP shock drivers are classified into four groups: magnetic clouds (MCs), ejecta, high speed streams (HSSs), and unidentified drivers. The MC is the most dominant and strong shock driver and 150 out of total 249 IP shocks are driven by MCs. The MC is a principal and very effective shock driver not only at solar maximum but also at solar minimum, in contrast to results from previous studies, where the HSS is considered as the dominant IP shock driver.     

Energetic protons associated with a forward-reverse interplanetary shock pair at 1 A.U.

A forward-reverse interplanetary shock was observed on 25 March 1969 by the magnetometer and plasma detector on the HEOS-1 satellite. This relatively rare event was described by Chao et al (1972) who concluded that the shock pair was formed at a distance 0.10–0.13 A.U. upstream of the Earth as a result of the interaction between a fast and a slow solar wind streams. Simultaneous observations of 1 MeV solar proton fluxes were also performed on HEOS-1. A characteristic intensity peak was observed as the forward shock passed by the spacecraft. The evolution of the proton intensity, together with a detailed analysis of anisotropies and pitch angle distributions show a complex dynamic picture of the effect of the forward shock on the ambient proton population. Significant changes in particle fluxes are seen to be correlated with fluctuations in the magnetic field. It is suggested that simple geometrical models of shock-associated acceleration should be expanded to include the effect of magnetic fluctuations on particle fluxes. The interaction region limited by the forward and reverse shocks contained a large variety of magnetic fluctuations. Following the tangential discontinuity separating the fast solar wind stream from the preceding slow stream, a sunward flow was observed in the proton data, followed by a small but significant drop in intensity prior to the reverse shock.     

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.     

Shock surfing acceleration

Analytical and numerical analysis identify shock surfing acceleration as an ideal pre-energization mechanism for the slow pick-up ions at quasiperpendicular shocks. After gaining sufficient energy by shock surfing, pick-up ions undergo diffusive acceleration to reach their observed energies. Energetic ions upstream of the cometary bow shock, acceleration of solar energetic particles by magnetosonic waves in corona, ion enhancement in interplanetary shocks, generation of anomalous cosmic rays from interstellar pick-up ions at the termination shock are some of the cases where shock surfing acceleration apply. Inclusion of the lower-hybrid wave turbulence into the laminar model of shock surfing can explain the preferential acceleration of heavier particles as observed by Voyager at the termination shock. At relativistic energies, unlimited acceleration of ions is theoretically possible; because for sufficiently strong shocks main limitation of the mechanism, caused by the escape of accelerated particles downstream of the shock during acceleration no longer exists.     

Limit shocks of relativistic magnetohydrodynamics

In this paper we show that switch-on and switch-off shocks are allowed by the shock equations of relativistic MHD and have similar properties to their Newtonian counterparts. Just like in Newtonian MHD they are limits of fast and slow shock solutions and as such they may be classified as weakly evolutionary shocks.     

Fundamentals of collisionless shocks for astrophysical application, 2. Relativistic shocks

In this concise review of the recent developments in relativistic shock theory in the Universe we restrict ourselves to shocks that do not exhibit quantum effects. On the other hand, emphasis is given to the formation of shocks under both non-magnetised and magnetised conditions. We only briefly discuss particle acceleration in relativistic shocks where much of the results are still preliminary. Analytical theory is rather limited in predicting the real shock structure. Kinetic instability theory is briefed including its predictions and limitations. A recent self-similar relativistic shock theory is described which predicts the average long-term shock behaviour to be magnetised and to cause reasonable power-law distributions for energetic particles. The main focus in this review is on numerical experiments on highly relativistic shocks in (i) pair and (ii) electron-nucleon plasmas and their limitations. These simulations do not validate all predictions of analytic and self-similar theory and so far they do not solve the injection problem and the self-modification by self-generated cosmic rays. The main results of the numerical experiments discussed in this review are: (i) a confirmation of shock evolution in non-magnetised relativistic plasma in 3D due to either the lepton-Weibel instability (in pair plasmas) or to the ion-Weibel instability; (ii) the sensitive dependence of shock formation on upstream magnetisation which causes suppression of Weibel modes for large upstream magnetisation ratios σ>10⁻³; (iii) the sensitive dependence of particle dynamics on the upstream magnetic inclination angle θ _Bn , where particles of θ _Bn >34° cannot escape upstream, leading to the distinction between ‘subluminal’ and ‘superluminal’ shocks; (iv) particles in ultra-relativistic shocks can hardly overturn the shock and escape to upstream; they may oscillate around the shock ramp for a long time, so to speak ‘surfing it’ and thereby becoming accelerated by a kind of SDA; (v) these particles form a power-law tail on the downstream distribution; their limitations are pointed out; (vi) recently developed methods permit the calculation of the radiation spectra emitted by the downstream high-energy particles; (vii) the Weibel-generated downstream magnetic fields form large-amplitude vortices which could be advected by the downstream flow to large distances from the shock and possibly contribute to an extended strong field region; (viii) if cosmic rays are included, Bell-like modes can generate upstream magnetic turbulence at short and, by diffusive re-coupling, also long wavelengths in nearly parallel magnetic field shocks; (ix) advection of such large-amplitude waves should cause periodic reformation of the quasi-parallel shock and eject large-amplitude magnetic field vortices downstream where they contribute to turbulence and to maintaining an extended region of large magnetic fields.     

The structure of radiative slow-mode shocks

We investigate the structure of slow-mode MHD shocks in a plasma where both radiation and thermal conduction are important. In such a plasma a slow shock dissociates into an extended foreshock, an isothermal subshock, and a downstream radiative cooling region. Our analysis, which is both numerical and analytical, focuses on the nearly switch-off shocks which are generated by magnetic reconnection in a strong magnetic field. These shocks convert magnetic energy into kinetic energy and heat, and we find that for typical flare conditions about f of the conversion occurs in the subshock while the remaining 1/3 occurs in the foreshock. We also find that no stable, steady-state solutions exist for radiative slow shocks unless the temperature in the radiative region downstream of the subshock falls below 10⁵ K. These results suggest that about 2/3 of the magnetic energy released in flare loops is released at the top of the loop, while the remaining 1/3 is released in the legs of the loop.     

Simulations of the wardle instability of c-type shock waves

C-type shocks in the partially ionized ISM are modelled by numerical simulations. Under certain conditions the shocks are subject to the Wardle instability, which initially makes the shock front rippled, then in the non-linear stage can produce density variations in both the ion and neutral fluids. A systematic search in the numerically accessible parameter space is done to determine the wave vector k_max and the growth rates _max of the fastest growing modes. The neutral Alfvén number, and the angle _sbetween the shock normal and the upstream magnetic field determine the strength and obliqueness of the shock, as well as the dimensionless parameters of the fastest growing mode. The results confirm and extend Wardle's linear analysis.The non-linear evolution shows saturation of the instability and the formation of high density regions that detach from the shock front with the downstream flow. Numerical difficulties are partially solved by an implicit treatment of the ion-neutral friction terms, but strong shocks still can not be modelled efficiently. A fully implicit method for the ions and the magnetic field is used to model C-type shocks with low fractional ionization and high ion Alfvén speed.     

Synchrotron emission in the fast cooling regime: which spectra can be explained?

We consider the synchrotron emission from relativistic shocks assuming that the radiating electrons cool rapidly (either through synchrotron or any other radiation mechanism). It is shown that the theory of synchrotron emission in the fast cooling regime can account for a wide range of spectral shapes. In particular, the magnetic field, which decays behind the shock front, brings enough flexibility to the theory to explain the majority of gamma-ray burst spectra even in the parameter-free fast cooling regime. Also, we discuss whether location of the peak in observed spectral energy distributions of gamma-ray bursts and active galactic nuclei can be made consistent with predictions of diffusive shock acceleration theory, and find that the answer is negative. This result is a strong indication that a particle injection mechanism, other than the standard shock acceleration, works in relativistic shocks.     

The Radial Variation of Interplanetary Shocks in the Inner Heliosphere: Observations by <Emphasis Type="Italic">Helios</Emphasis>, MESSENGER,and STEREO

The two major sources of collisionless shocks in the solar wind are interplanetary coronal mass ejections (ICMEs) and stream interaction regions (SIRs). Previous studies show that some SIR-associated shocks form between Venus and Earth while most form beyond 1 AU. Here we examine the high-resolution magnetometer records from Helios 1 and 2 obtained between 0.28 and 1 AU and from MESSENGER obtained between 0.3 and 0.7 AU to further refine our understanding as to where, and in what context, shocks are formed in the inner solar system. From Helios data (Helios 1 from 1974 to 1981 and Helios 2 from 1976 to 1980), we find there were only a few shocks observed inside the orbit of Venus with the closest shock to the Sun at 0.29 AU. We find that there is a strong correlation between shock occurrence and solar activity as measured by the sunspot number. Most of the shocks inside of the orbit of Venus appear to be associated with ICMEs. Even the ICME-associated shocks are quite weak inside the orbit of Venus. By comparing MESSENGER and STEREO results, from 2007 to 2009, we find that in the deep solar minimum, SIR-driven shocks began to form at about 0.4 AU and increased in number with heliocentric distance.     

The Bastille day Shocks and Merged Interaction Region

Near 1 AU the solar wind structure associated with the solar flare of 14 July 2000 (Bastille Day) consisted of a large high-speed stream of 15 July and five nearby small streams during a 10-day period. At the leading edge of the large high-speed stream, in less than 6 hours, the flow speed increased from 600 km s⁻¹ to 1100 km s⁻¹, the magnetic field intensity increased from 10 nT to 60 nT, and an interaction region was identified. The interaction region was bounded between the pair of a forward shock F and a reverse shock R. Additional forward shocks were also identified at the leading edge of each of the five smaller streams. This paper presents a magnetohydrodynamics (MHD) simulation using ACE plasma and magnetic field data near 1 AU as input to study the radial evolution of the Bastille Day solar wind event. The two shocks, F and R, propagated in opposite directions away from each other in the solar wind frame and interacted with neighboring shocks and streams; the spatial and temporal extent of the interaction region continued to increase with the heliocentric distance. The solar wind was restructured from a series of streams at 1 AU to a huge merged interaction region (MIR) extending over a period of 12 days at 5.5 AU. Throughout the interior of the MIR bounded by the shock pair F and R the magnetic field intensity was a few times stronger than that outside the MIR. The simulation shows how merging of shocks, collision of shocks, and formation of new shocks contributed to the evolution process.