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.     

Particle acceleration by ultrarelativistic shocks: theory and simulations

We consider the acceleration of charged particles near ultrarelativistic shocks, with Lorentz factor     . We present simulations of the acceleration process and compare these with results from semi-analytical calculations. We show that the spectrum that results from acceleration near ultrarelativistic shocks is a power law,     , with a nearly universal value     for the slope of this power law.
We confirm that the ultrarelativistic equivalent of the Fermi acceleration at a shock differs from its non-relativistic counterpart by the occurrence of large anisotropies in the distribution of the accelerated particles near the shock. In the rest frame of the upstream fluid, particles can only outrun the shock when their direction of motion lies within a small loss cone of opening angle     around the shock normal.
We also show that all physically plausible deflection or scattering mechanisms can change the upstream flight direction of relativistic particles originating from downstream by only a small amount:     . This limits the energy change per shock crossing cycle to     , except for the first cycle where particles originate upstream. In that case the upstream energy is boosted by a factor     for those particles that are scattered back across the shock into the upstream region.     

The Plasma and Magnetic Field Characteristics of a Double Discontinuity in Interplanetary Space

A double discontinuity is a rarely observed compound structure composed of a slow shock layer and an adjoining rotational discontinuity layer in the downstream region. In this paper, we report the observations of a double discontinuity detected by Wind on May 15, 1997. This double discontinuity is found to be the front boundary of a magnetic cloud boundary layer. We strictly identify the shock layer and the rotational discontinuity layer by using the high-resolution plasma and magnetic field data from Wind. The observed jump conditions of the upstream and downstream region of the slow shock layer are in good agreement with the Rankine – Hugoniot relations. The flow speeds in the shock frame U _n <V _Acos θ _Bn on both sides of the slow shock layer. In the upstream region, the slow Mach number M _s1=U _n1/V _s1 is 1.95 (above unity), and in the downstream region, the slow Mach number M _s2=U _n2/V _s2 is 0.31 (below unity). Here V _A and V _s represent the Alfvén speed and the local slow magnetosonic speed, respectively, and θ _Bn is the angle between the direction of the magnetic field and the shock normal. The magnetic cloud boundary layer observed by Wind was also detected by Geotail 48 min later when the spacecraft was located outside the bow shock of the magnetosphere. However, Geotail observations showed that its front boundary was no longer a double discontinuity and the rotational discontinuity layer disappeared, indicating that this double discontinuity was unstable when propagating from Wind to Geotail.     

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.     

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.     

Variable synchrotron emission from BL Lacertae objects. II. Optical and X-ray flares in HBL source 1ES 1959+650

This paper presents the results of the optical R band and 1.5–12 keV band X-ray monitoring of the high-energy peaked BL Lacertae source 1ES 1959+650 performed during 2002–2007 with the 70 cm Meniscus Telescope of Abastumani Astrophysical Observatory (Georgia) and the All-Sky Monitor on board the Rossi X-ray Time Explorer, respectively. The observed long- and short-term outbursts are fitted with the lightcurves obtained by means of the modeling of synchrotron flares that are assumed to be the result of a propagation of the relativistic shock waves through the jet of 1ES 1959+650, pointed to the observer. Different values of the input parameters (shock velocity, particles’ spectral index, sizes of emission region, minimum and maximum Lorentz factors of the particles etc.) are used in order to fit the simulated lightcurves whose constructed by means of observational data. This investigation shows that both shock velocity and physical conditions in the jet of 1ES 1959+650 should be variable from flare to flare. The shocks are found to be mildly relativistic with the apparent speeds β=0.46–0.85, expressed in the units of c. Spectral index of the particle energy distribution varied from 2.10 to 2.17 for the long-term flares while it is higher in the case of short-term outbursts: s=2.32–2.45 that is suggested to be a result of the deceleration of shock front during its passage through the shell situated downstream the Mach disc. The average strength of a turbulent magnetic field ranged from 0.025 gauss to 0.04 gauss for different long-term flares while the values of 0.07–0.14 gauss were adopted for the different short-term outbursts. The lengths of variable jet area found to be of 0.13–0.47 pc with the transverse extents of (0.5–1.0)×10¹⁷ cm in the case of long-term flares. The same characteristics for short-term outbursts were (2.74–5.5)×10¹⁶ cm and (0.2–04)×10¹⁷ cm, respectively. We conclude that both shock velocity and properties of pre-shocked plasma were not the same in 1ES 1959+650 for the different flaring epochs.     

The physics of particle acceleration by collisionless shocks

Using analytic theory, test-particle simulations, and self-consistent hybrid simulations, we show that quasi-perpendicular shocks—those which propagate nearly perpendicular to the upstream magnetic field—accelerate particles directly out of the incident thermal population to energies much higher than the upstream ram energy of the plasma. It has already been established that quasi-parallel shocks—those which propagate nearly in the same direction as the upstream magnetic field—efficiently accelerate particles directly out of the incident thermal population; however, this has not yet been established for quasi-perpendicular shocks. Our results can be understood within the framework of the diffusive shock acceleration theory. We find that the accelerated-particle spectrum obtained from a more-general self-consistent hybrid plasma simulation are quantitatively consistent with a less-sophisticated test-particle simulation. The implications of this are discussed.     

Observations of a 2→3 Type Interplanetary Intermediate Shock

An intermediate shock-like event was observed by Voyager 2 on 9 January 1979. The discontinuity structure is well identified to be a 2→3 type intermediate shock by fitting the Rankine – Hugoniot relations. The shock satisfies the following conditions: i) the plasma density increases from the upstream region to the downstream region, ii) The normal Alfvén Mach number (M _AN) is greater than unity in the preshock state and less than unity in the postshock state, iii) The fast-mode Mach numbers in the upstream and downstream regions are less than unity and both the slow-mode Mach numbers are greater than unity, iv) The tangential component of the magnetic field changes sign across the shock front.     

Long-wavelength MHD instability in the prefront of collisionless shocks with accelerated particles

Collisionless shocks in turbulent space plasmas accelerate particles by the Fermi mechanism to ultrarelativistic energies. The interaction of accelerated particles with the plasma inflow produces extended supersonic MHD flows of multicomponent plasma. We investigate the instabilities of a flow of three-component turbulent plasma with relativistic particles against long-wavelength perturbations with scales larger than the accelerated particle transport mean free path and the initial turbulence scales. The presence of turbulence allows us to formulate the system of single-fluid equations, the equation of motion for the medium as a whole, and the induction equation for the magnetic field with turbulent magnetic and kinematic viscosities. The current of accelerated particles enters into the induction equation with an effective magnetic diffusion coefficient. We have calculated the local growth rates of the perturbations related to the nonresonant long-wavelength instability of the current of accelerated particles for MHD perturbations in the WKB approximation. The amplification of long-wavelength magnetic field perturbations in the flow upstream of the shock front can affect significantly the maximum energies of the particles accelerated by a collisionless shock and can lead to the observed peculiarities of the synchrotron X-ray radiation in supernova remnants.     

The influence of the Mach number on the stability of radiative shocks

We study the stability properties of hydrodynamic shocks with finite Mach numbers. The linear analysis supplements previous analyses which took the strong shock limit. We derive the linearized equations for a general specific heat ratio as well as temperature and density power-law cooling functions, corresponding to a range of conditions relevant to interstellar atomic and molecular cooling processes. Boundary conditions corresponding to a return to the upstream temperature  ( R = 1)  and to a cold wall  ( R = 0)  are investigated. We find that for Mach number   M > 5  , the strong shock overstability limits are not significantly modified. For   M < 3  , however, shocks are considerably more stable for most cases. In general, as the shock weakens, the critical values of the temperature power-law index (below which shocks are overstable) are reduced for the overtones more than for the fundamental, which signifies a change in basic behaviour. In the   R = 0  scenario, however, we find that the overstability regime and growth rate of the fundamental mode are increased when cooling is under local thermodynamic equilibrium. We provide a possible explanation for the results in terms of a stabilizing influence provided downstream but a destabilizing effect associated with the shock front. We conclude that the regime of overstability for interstellar atomic shocks is well represented by the strong shock limit unless the upstream gas is hot. Although molecular shocks can be overstable to overtones, the magnetic field provides a significant stabilizing influence.     

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.     

Particle acceleration at multiple internal relativistic shocks

Relativistic shocks provide an efficient method for high-energy particle acceleration in many astrophysical sources. Multiple shock systems are even more effective and of importance, for example, in the internal shock model of gamma-ray bursts. We investigate the reacceleration of pre-existing energetic particles at such relativistic internal shocks by the first order Fermi process of pitch angle scattering. We use a well established eigenfunction method to calculate the resulting spectra for infinitely thin shocks. Implications for GRBs and relativistic jets are discussed. Paul Dempsey would like to thank IRCSET for their financial support.     

Electron surfing acceleration in oblique magnetic fields

Initially, inhomogeneous plasma jets, ejected by active galactic nuclei and associated with gamma-ray bursts, are thermalized by the formation of internal shocks. Jet subpopulations can hereby collide at Lorentz factors of a few. As the resulting relativistic shock expands into the upstream plasma, a significant fraction of the upstream ions is reflected. These ions, together with downstream ions that leak through the shock, form relativistic beams of ions that outrun the shock. The thermalization of these beams via the two-stream instability is thought to contribute significantly to plasma heating and particle acceleration by the shock. Here, the capability of a two-stream instability to generate relativistic field-aligned and cross-field electron flow, is examined for a magnetized plasma by means of a particle-in-cell (PIC) simulation. The electrons interact with the developing quasi-electrostatic waves and oblique magnetic fields. The simulation results bring forward evidence that such waves, by their non-linear interactions with the plasma, produce a highly relativistic field-aligned electron flow and electron energies, which could contribute to the radio synchrotron emissions from astrophysical jets, to ultrarelativistic leptonic subpopulations propagating with the jet and to the halo particles surrounding the accretion disc of the black hole.     

Radio signature of cosmological structure formation shocks

In the course of the formation of cosmological structures, large shock waves are generated in the intracluster medium (ICM). In analogy to processes in supernova remnants, these shock waves may generate a significant population of relativistic electrons which, in turn, produce observable synchrotron emission. The extended radio relics found at the periphery of several clusters and possibly also a fraction of radio halo emission may have this origin. Here, we derive an analytic expression for (i) the total radio power in the downstream region of a cosmological shock wave, and (ii) the width of the radio-emitting region. These expressions predict a spectral slope close to −1 for strong shocks. Moderate shocks, such as those produced in mergers between clusters of galaxies, lead to a somewhat steeper spectrum. Moreover, we predict an upper limit for the radio power of cosmological shocks. Comparing our results to the radio relics in Abell 115, 2256 and 3667, we conclude that the magnetic field in these relics is typically at a level of 0.1 μG. Magnetic fields in the ICM are presumably generated by the shocks themselves; this allows us to calculate the radio emission as a function of the cluster temperature. The resulting emissions agree very well with the radio power–temperature relation found for cluster haloes. Finally, we show that cosmic accretion shocks generate less radio emission than merger shock waves. The latter may, however, be detected with upcoming radio telescopes.     

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.     

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.     

Variable synchrotron emission from BL Lacertae objects. I. Shock-in-jet scenario

This paper presents a modeling of the variable synchrotron emission in the BL Lacertae sources (BLLs). Flux variability is assumed to be a result of the interaction between a relativistic shock wave with a magnetized jet material. Long-term flares (of months to years durations) are modeled via the propagation of a plane relativistic shock wave though the emission zone of a cylindrical form with the radius R and length H. As for short-term bursts (lasting from days to weeks), they may result from shock passage through the jet inhomogeneities such as a shell of enhanced density downstream to a Mach disc, originated due to pressure imbalance between the jet and its ambient medium. Emitting particles (electrons) gain the energies, sufficient to produce synchrotron photons at optical—X-ray frequencies, via the first-order Fermi mechanism. Observation’s frequency is the main parameter determining a rate of the increase/ decay of the emission via the characteristic decay time of emitting electrons. The magnetic field, assumed to be turbulent with an average field constant throughout the entire emission zone, is another key parameter determining the slope of a lightcurve corresponding to the flare—the higher strength the magnetic field has, the steeper the lightcurve is. The rest input parameters (shock speed, jet viewing angle, maximum/minimum energies of the electrons, particles’ density etc.), as well the strength of average magnetic field, influence the energy output from a flare.     

3-D Rpic Simulations of Relativistic Jets: Particle Acceleration, Magnetic Field Generation, and Emission

We have applied numerical simulations and modeling to the particle acceleration, magnetic field generation, and emission from relativistic shocks. We investigate the nonlinear stage of theWeibel instability and compare our simulations with the observed gamma-ray burst emission. In collisionless shocks, plasma waves and their associated instabilities (e.g., the Weibel, Buneman and other two-stream instabilities) are responsible for particle (electron, positron, and ion) acceleration and magnetic field generation. 3-D relativistic electromagnetic particle (REMP) simulations with three different electron-positron jet velocity distributions and also with an electron-ion plasma have been performed and show shock processes including spatial and temporal evolution of shocks in unmagnetized ambient plasmas. The growth time and nonlinear saturation levels depend on the initial jet parallel velocity distributions. Simulations show that the Weibel instability created in the collisionless shocks accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. The nonlinear fluctuation amplitude of densities, currents, electric, and magnetic fields in the electron-positron shocks are larger for smaller jet Lorentz factor. This comes from the fact that the growth time of the Weibel instability is proportional to the square of the jet Lorentz factor. We have performed simulations with broad Lorentz factor distribution of jet electrons and positrons, which is assumed to be created by photon annihilation. Simulation results with this broad distribution show that the Weibel instability is excited continuously by the wide-range of jet Lorentz factor from lower to higher values. In all simulations the Weibel instability is responsible for generating and amplifying magnetic fields perpendicular to the jet propagation direction, and contributes to the electron’s (positron’s) transverse deflection behind the jet head. This small scale magnetic field structure contributes to the generation of “jitter” radiation from deflected electrons (positrons), which is different from synchrotron radiation in uniform magnetic fields. The jitter radiation resulting from small scale magnetic field structures may be important for understanding the complex time structure and spectral evolution observed in gamma-ray bursts or other astrophysical sources containing relativistic jets and relativistic collisionless shocks. The detailed studies of shock microscopic process evolution may provide some insights into early and later GRB afterglows.     

Heavy ion reflection and heating by collisionless shocks in polar solar corona

We propose a new model for explaining the observations of preferential heating of heavy ions in the polar solar corona. We consider that a large number of small scale shock waves can be present in the solar corona, as suggested by recent observations of polar coronal jets by the Hinode and STEREO spacecraft. The heavy ion energization mechanism is, essentially, the ion reflection off supercritical quasi-perpendicular collisionless shocks in the corona and the subsequent acceleration by the motional electric field E=−(1/c)V ×B. The acceleration due to E is perpendicular to the magnetic field, giving rise to large temperature anisotropy with T_⊥?T_∥, which can excite ion cyclotron waves. Also, heating is more than mass proportional with respect to protons, because the heavy ion orbit is mostly upstream of the quasi-perpendicular shock foot. The observed temperature ratios between O⁵⁺ ions and protons in the polar corona, and between α particles and protons in the solar wind are easily recovered. We also discuss the mechanism of heavy ion reflection, which is based on ion gyration in the magnetic overshoot of the shock.