Magnetohydrodynamic Shock Research Articles

Generation of shocked hot regions in black hole magnetosphere

AbstractWe study magnetohydrodynamic (MHD) standing shocks in ingoing plasmas in a black hole (BH) magnetosphere. We find that low or mid latitude (non-equatorial) standing MHD shocks are both physically possible, creating very hot and/or magnetized plasma regions close to the event horizon. We also investigate the effects of the poloidal magnetic field and the BH spin on the properties of shocks and show that both effects can quantitatively affect the MHD shock solutions. MHD shock formation can be a plausible mechanism for creating high energy radiation region above an accretion disk in AGNs.

The turbulent environment of low-mass dense cores

AbstractThe signatures of intermittent dissipation of turbulent energy have been sought in the translucent environment of a low-mass dense core. Molecular line observations reveal a network of narrow filamentary structures, found on statistical grounds to be the locus of the largest velocity shears. Three independent properties of these structures make them the plausible sites of intermittent dissipation of turbulence: (1) gas there is warmer and more diluted than average, (2) it bears the signatures of a non-equilibrium chemistry triggered by impulsive heating due to turbulence dissipation, and (3) the power that these structures radiate in the gas cooling lines (mostly H2) is so large that it balances the total energy injection rate of the turbulent cascade, for a volume filling factor of only a few percents, consistent with other observations in the Solar Neighborhood. These filamentary structures may act as tiny seeds of gas condensation in diffuse molecular gas. They do not exhibit the properties of steady-state low-velocity magneto-hydrodynamic (MHD) shocks, as presently modelled.

Standing Shocks in Transmagnetosonic Accretion Flows onto a Black Hole

Fast and slow magnetosonic shock formation is presented for stationary and axisymmetric magnetohydrodynamic (MHD) accretion flows onto a black hole. The shocked black hole accretion solution must pass through magnetosonic points at some locations outside and inside the shock location. We analyze critical conditions at the magnetosonic points and the shock conditions. Then, we show the restrictions on the flow parameters for strong shocks. We also show that a very hot shocked plasma is obtained for a very high energy inflow with a small number density. Such a MHD shock can appear very close to the event horizon and can be expected as a source of high-energy emissions. Examples of shocked MHD accretion flows are presented in the Schwarzschild case.

Envelope expansion with core collapse - III. Similarity isothermal shocks in a magnetofluid

We explore magnetohydrodynamic (MHD) solutions for envelope expansions with core collapse (EECC) with isothermal MHD shocks in a quasi-spherical symmetry, and outline potential astrophysical applications of such magnetized shock flows. By including a random magnetic field in a gas medium, we further extend the recent isothermal shock results of Bian & Lou who have unified earlier similarity isothermal shock solutions of Tsai & Hsu, of Shu et al. and of Shen & Lou in a more general framework. MHD shock solutions are divided into three classes according to the downstream characteristics near the core. Class I solutions are those characterized by free-fall collapses towards the core downstream of an MHD shock, while Class II solutions are those characterized by Larson–Penston (LP) type near the core downstream of an MHD shock. Class III solutions are novel, sharing both features of Class I and II solutions with the presence of a sufficiently strong magnetic field as a prerequisite. Various MHD processes may occur within the regime of these isothermal MHD shock similarity solutions, such as submagnetosonic oscillations, free-fall core collapses, radial contractions and expansions. Both possibilities of perpendicular and oblique MHD shocks are analysed. Under the current approximation of MHD EECC (MEECC) solutions, only perpendicular shocks are systematically calculated. These similar MHD shocks propagate at either submagnetosonic or supermagnetosonic constant speeds. We can construct Class I, II and III MHD shocks matching with an isothermal magnetostatic outer envelope or an MHD breeze. We can also construct families of twin MHD shock solutions as well as an ‘isothermal MHD shock’ separating two magnetofluid regions of two different yet constant temperatures. The versatile behaviours of such MHD shock solutions may be utilized to model a wide range of astrophysical problems, including star formation in magnetized molecular clouds, ‘MHD champagne flows’ in H-ii regions around luminous massive OB stars, MHD link between the asymptotic giant branch (AGB) phase and the protoplanetary nebula (pPN) phase with a hot central magnetized white dwarf, relativistic MHD pulsar winds in supernova remnants (SNRs), radio afterglows of soft gamma-ray repeaters (SGRs) and so forth.

Strong magnetic field in W75N OH maser flare

A flare of OH maser emission was discovered in W75N in 2000. Its location was determined with the Very Long Baseline Array (VLBA) to be within 110 au from one of the ultracompact H II regions, Very Large Array 2 (VLA2). The flare consisted of several maser spots. Four of the spots were found to form Zeeman pairs, all of them with a magnetic field strength of about 40 mG. This is the highest ever magnetic field strength found in OH masers, an order of magnitude higher than in typical OH masers. Three possible sources for the enhanced magnetic field are discussed: (i) the magnetic field of the exciting star dragged out by the stellar wind; (ii) the general interstellar field in the gas compressed by the magnetohydrodynamic shock; and (iii) the magnetic field of planets which orbit the exciting star and produce maser emission in gaseous envelopes.

High-Temperature Coal-Syngas Plasma Characteristics for Advanced MHD Power Generation

Properties of magnetohydrodynamic (MHD) plasma based on syngas (CO, H/sub 2/) combustion products were investigated experimentally with shock tube facility. The experiments were carried out under various MHD generator load and shock tube operation conditions. Important characteristics of syngas plasma such as temperature, electric field, conductivity, and total output power were directly measured and evaluated. Special attention was paid to the influence of syngas composition (CO:H/sub 2/:O/sub 2/ ratio). The results show that syngas combustion can provide high plasma ionization and attainable plasma electrical conductivity has an order of 60-80 S/m at gas temperature 3100-3300 K.

Oscillation of Quasi-Steady Earth's Magnetosphere

A three-dimensional magnetohydrodynamics (MHD) code is designedspecially for global simulations of the solarwind–magnetosphere–ionosphere system. The code possesses a highresolution in capturing MHD shocks and discontinuities and a lownumerical dissipation in examining possible instabilities inherent inthe system. The ionosphere is approximated by a spherical shell withuniform height-integrated conductance. The solar wind is steady, and theinterplanetary magnetic field is either due northward or due southward.The code is then run to find solutions of the whole system. It is foundthat the system has never reached a steady state, but keeps oscillatingwith a period of about one hour in terms of density variation at thegeosynchronous orbit. However, if a certain artificial resistivity isadded either in the whole numerical box or in the reconnection sitesonly, the reconnections change from intermittent to steady regime andthe oscillation disappears accordingly. We conclude that the Earth'smagnetosphere tends to be in a ceaseless oscillation status because ofthe low dissipation property inherent in the magnetospheric plasma, andthe oscillation may be driven by intermittent magnetic reconnectionsthat occur somewhere in the magnetopause and/or the magnetotail.

Magnetohydrodynamic waves within the medium separated by the plane shock wave or rotational discontinuity

Abstract. Characteristics of small amplitude plane waves within the medium separated by the plane discontinuity into two half spaces are analysed. The approximation of the ideal one-fluid magnetohydrodynamics (MHD) is used. The discontinuities with the nonzero mass flux across them are mainly examined. These are fast or slow shock waves and rotational discontinuities. The dispersion equation for MHD waves within each of half space is obtained in the reference frame connected with the discontinuity surface. The solution of this equation permits one to determine the wave vectors versus the parameter cp, which is the phase velocity of surface discontinuity oscillations. This value of cp is common for all MHD waves and determined by an incident wave or by spontaneous oscillations of the discontinuity surface. The main purpose of the study is a detailed analysis of the dispersion equation solution. This analysis let us draw the following conclusions. (I) For a given cp, ahead or behind a discontinuity at most, one diverging wave can transform to a surface wave damping when moving away from the discontinuity. The surface wave can be a fast one or, in rare cases, a slow, magnetoacoustic one. The entropy and Alfvén waves always remain in a usual homogeneous mode. (II) For certain values of cp and parameters of the discontinuity behind the front of the fast shock wave, there can be four slow magnetoacoustic waves, satisfying the dispersion equation, and none of the fast magnetoacoustic waves. In this case, one of the four slow magnetoacoustic waves is incident on the fast shock wave from the side of a compressed medium. It is shown that its existence does not contradict the conditions of the evolutionarity of MHD shock waves. The four slow magnetoacoustic waves, satisfying the dispersion equation, can also exist from either side of a slow shock wave or rotational discontinuity. (III) The expressions determining the polarisation of the MHD waves are derived in the reference frame connected with the discontinuity surface. This form of presentation is much more convenient in investigating the interaction of small perturbations with MHD discontinuities. It is shown that the perturbations of the velocity and magnetic field associated with the surface magnetoacoustic wave have the elliptic polarisation. Usually the planes of polarisation for the perturbations of the velocity and magnetic field are not coincident with each other. Keywords. Space plasma physics (Discontinuities; Shock waves) – Interplanetary physics (Discontinuities; Interplanetary shocks) – Magnetospheric physics (Solar windmagnetosphere interactions)

The brightest OH maser in the sky: A flare of emission in W75 N

A flare of maser radio emission in the 1665-MHz OH line with a flux density of about 1000 Jy was discovered in the star-forming region W75 N in 2003. At the time of its observations, it was the strongest OH maser in the entire history of research since the discovery of cosmic OH masers in 1965. The linear polarization of the flare emission reached 100%. A weaker flare with a flux density of 145 Jy was observed in this source in 2000–2001; this was probably a precursor of the intense flare. The intensity of two other spectral features decreased when the flare emerged. This change in the intensity of the emission from maser condensations (a brightening of some of them and a weakening of others) can be explained by the passage of a magnetohydrodynamic shock through regions of enhanced gas concentration.

Magnetohydrodynamic shock wave formation: Effect of area and density variation

The nonlinear steepening of finite amplitude magnetohydrodynamic (MHD) waves propagating perpendicular to the magnetic field is investigated. The nonlinear evolution of a planar fast magnetosonic wave in a homentropic flow field is understood well through simple waves. However, in situations where the wave is moving through a variable area duct or when the flow field is nonhomentropic, the concept of simple waves cannot be used. In the present paper, the quasi-one-dimensional MHD equations that include the effect of area variation and density gradients are solved using the wave front expansion technique. The analysis is performed for a perfectly conducting fluid and also for a weakly conducting fluid. Closed form solutions are obtained for the nonlinear evolution of the slope of the wave front in the limits of infinitely large and small conductivity. A general criterion for a compression wave to steepen into a shock is obtained. An analytical expression for the location of shock formation is derived. The effect of area variation and density gradient on shock formation is studied and examples highlighting the same are presented.

Warm Molecular Gas Traced with COJ= 7→6 in the Galaxy’s Central 2 Parsecs: Dynamical Heating of the Circumnuclear Disk

We present an 11 resolution map of the central 2 pc of the Galaxy in the CO J = 7 --> 6 rotational transition. The CO emission shows rotation about Sgr A* but also evidence for noncircular turbulent motion and a clumpy morphology. We combine our data set with available CO measurements to model the physical conditions in the disk. We find that the molecular gas in the region is both warm and dense, with T approx. 200-300 K and n(sub H2) approx. (5-7) x 10(exp 4) cm(exp -3). The mass of warm molecular gas we measure in the central 2 pc is at least 2000 M(solar), about 20 times the UV-excited atomic gas mass, ruling out a UV heating scenario for the molecular material. We compare the available spectral tracers with theoretical models and conclude that molecular gas is heated with magnetohydrodynamic shocks with v approx. 10-20 km s(exp -1) and B approx. 0.3- 0.5 mG. Using the conditions derived with the CO analysis, we include the other important coolants, neutral oxygen and molecular hydrogen, to estimate the total cooling budget of the molecular material. We derive a mass-to-luminosity ratio of approx. 2-3 M(solar)(L(solar)exp -1), which is consistent with the total power dissipated via turbulent decay in 0.1 pc cells with v(sub rms) approx. 15 kilometers per second. These size and velocity scales are comparable to the observed clumping scale and the velocity dispersion. At this rate, the material near Sgr A* is dissipating its orbital energy on an orbital timescale and cannot last for more than a few orbits. Our conclusions support a scenario in which the features near Sgr A* such as the circumnuclear disk and northern arm are generated by infalling clouds with low specific angular momentum.

Formation of Compression Shocks in a Nonequilibrium Plasma Flow in a Magnetic Field

Plasma flow in a linearly widening, ideally sectioned, short-circuited magnetohydrodynamic (MHD) channel is studied. MHD flows are classified into two types: continuous flows and flows with a compressional MHD shock in plasmas that are stable and unstable against the onset of ionization instability. Specific features in the evolution of a stationary compression MHD shock are investigated, and its position as a function of the Stewart number is determined. It is found that, in a plasma flow in which ionization instability develops, a compression MHD shock arises at lower values of the MHD interaction parameter than in a stable plasma flow. An unidentified type of instability of MHD discontinuities is revealed.

Regular shock refraction at an oblique planar density interface in magnetohydrodynamics

We consider the problem of regular refraction (where regular implies all waves meet at a single point) of a shock at an oblique planar contact discontinuity separating conducting fluids of different densities in the presence of a magnetic field aligned with the incident shock velocity. Planar ideal magnetohydrodynamic (MHD) simulations indicate that the presence of a magnetic field inhibits the deposition of vorticity on the shocked contact. We show that the shock refraction process produces a system of five to seven plane waves that may include fast, intermediate, and slow MHD shocks, slow compound waves, 180◦ rotational discontinuities, and slow-mode expansion fans that intersect at a point. In all solutions, the shocked contact is vorticity free and hence stable. These solutions are not unique, but differ in the types of waves that participate. The set of equations governing the structure of these multiple-wave solutions is obtained in which fluid property variation is allowed only in the azimuthal direction about the wave-intersection point. Corresponding solutions are referred to as either quintuple-points, sextuple-points, or septuple-points, depending on the number of participating waves. A numerical method of solution is described and examples are compared to the results of numerical simulations for moderate magnetic field strengths. The limit of vanishing magnetic field at fixed permeability and pressure is studied for two solution types. The relevant solutions correspond to the hydrodynamic triple-point with the shocked contact replaced by a singular structure consisting of a wedge, whose angle scales with the applied field magnitude, bounded by either two slow compound waves or two 180◦ rotational discontinuities, each followed by a slow-mode expansion fan. These bracket the MHD contact which itself cannot support a tangential velocity jump in the presence of a non-parallel magnetic field. The magnetic field within the singular wedge is finite and the shock-induced change in tangential velocity across the wedge is supported by the expansion fans that form part of the compound waves or follow the rotational discontinuities. To verify these findings, an approximate leading-order asymptotic solution appropriate for both flow structures was computed. The full and asymptotic solutions are compared quantitatively.

A first step towards proton flux forecasting

We present a preliminary version of a potential tool for real time proton flux prediction which provides proton flux profiles and cumulative fluence profiles at 0.5 and 2 MeV of solar energetic particle events, from their onset up to the arrival of the interplanetary shock at the spacecraft position (located at 1 or 0.4 AU). Based on the proton transportation model by Lario et al. [Lario, D., Sanahuja, B., Heras, A.M. Energetic particle events: efficiency of interplanetary shocks as 50 keV E < 100 MeV proton accelerators. Astrophys. J. 509, 415–434, 1998] and the magnetohydrodynamic shock propagation model of Wu et al. [Wu, S.T., Dryer, M., Han, S.M. Non-planar MHD model for solar flare-generated disturbances in the Heliospheric equatorial plane. Sol. Phys. 84, 395–418, 1983], we have generated a database containing “synthetic” profiles of the proton fluxes and cumulative fluences of 384 solar energetic particle events. We are currently validating the applicability of this code for space weather forecasting by comparing the resulting “synthetic” flux profiles with those of several real events.

Experimental Studies on Characteristics of High-Temperature Syngas Plasma and Magnetohydrodynamic Power Generation

Properties of magnetohydrodynamic (MHD) plasma based on syngas (CO, H2) combustion products were investigated experimentally using a shock tube facility. The experiments were carried out under various MHD generator load and shock tube operation conditions. Important characteristics of syngas plasma such as temperature, conductivity and total output power were directly measured and evaluated. Special attention was paid to the influence of the syngas composition (CO:H2:O2 ratio). The results show that syngas combustion can provide high plasma ionization and the attainable electric plasma conductivity has the order of 60–70 S/m at gas temperatures in the range of 3150–3300 K.

Multifluid, Magnetohydrodynamic Shock Waves with Grain Dynamics. II. Dust and the Critical Speed for C Shocks

This is the second in a series of papers on the effects of dust on multifluid, magnetohydrodynamic shock waves in weakly ionized molecular gas. We investigate the influence of dust on the critical shock speed, vcrit, above which C shocks cease to exist. Chernoff showed that vcrit cannot exceed the grain magnetosound speed, Vgms, if dust grains are dynamically well coupled to the magnetic field. Since Vgms ≃ 5 km s-1 in a dense cloud or core, the potential implications for models of shock emission are profound. We present numerical simulations of steady shocks where the grains may be well or poorly coupled to the field. We use a time-dependent, multifluid MHD code that models the plasma as a system of interacting fluids: neutral particles, ions, electrons, and various "dust fluids" comprised of grains with different sizes and charges. Our simulations include grain inertia and grain charge fluctuations, but to highlight the essential physics we assume adiabatic flow and single-size grains and neglect the effects of chemistry. We show that the existence of a phase speed vϕ does not necessarily mean that C shocks will form for all shock speeds vs less than vϕ. When the grains are weakly coupled to the field, steady, adiabatic shocks resemble shocks with no dust: the transition to J-type flow occurs at vcrit ≈ 2.76VnA, where VnA is the neutral Alfvén speed, and steady shocks with vs > 2.76VnA are J shocks with magnetic precursors in the ion-electron fluid. When the grains are strongly coupled to the field, vcrit = min (2.76VnA,Vgms). Shocks with vcrit < vs < Vgms have magnetic precursors in the ion-electron-dust fluid. Shocks with vs > Vgms have no magnetic precursor in any fluid. We present time-dependent calculations to study the formation of steady, multifluid shocks. The dynamics differ qualitatively, depending on whether or not the grains and field are well coupled.

Coronal heating and acceleration of the high/low-speed solar wind by fast/slow MHD shock trains

We investigate coronal heating and acceleration of the high- and low-speed solar wind in the open field region by dissipation of fast and slow magnetohydrodynamical (MHD) waves through MHD shocks. Linearly polarized Alfven (fast MHD) waves and acoustic (slow MHD) waves travelling upwardly along with a magnetic field line eventually form fast switch-on shock trains and hydrodynamical shock trains (N waves) respectively to heat and accelerate the plasma. We determine the one-dimensional structure of the corona from the bottom of the transition region (TR) out to 1 au under the steady-state condition by solving evolutionary equations for the shock amplitudes simultaneously with the momentum and proton/electron energy equations. Our model reproduces the overall trend of the high-speed wind from the polar holes and the low-speed wind from the mid- to low-latitude streamer except the observed hot corona in the streamer. The heating from the slow waves is effective in the low corona to increase the density there, and plays an important role in the formation of the dense low-speed wind. On the other hand, the fast waves can carry a sizable energy to the upper level to heat the outer corona and accelerate the high-speed wind effectively. We also study dependence on field strength, B 0 , at the bottom of the TR and non-radial expansion of a flow tube, f max , to find that large B 0 /f max ? 2 but small B 0 ≃ 2 G are favourable for the high-speed wind and that small B 0 /f max ≃ 1 is required for the low-speed wind.

Dependence of the magnetohydrodynamic shock thickness on the finite electrical conductivity

The results of MHD plane shock waves with infinite electrical conductivity are generalized for a plasma with a finite conductivity. We derive the adiabatic curves that describe the evolution of the shocked gas as well as the change in the entropy density. For a parallel shock (i.e., in which the magnetic field is parallel to the normal to the shock front) we find an expression for the shock thickness which is a function of the ambient magnetic field and of the finite electrical conductivity of the plasma. We give numerical estimates of the physical parameters for which the shock thickness is of the order of, or greater than, the mean free path of the plasma particles in a strongly magnetized plasma.

On the nature of eclipses in binary pulsar J0737-3039

We consider magnetohydrodynamical interaction between relativistic pulsar wind and static magnetosphere in binary pulsar system PSR J0737-3039. We construct semi-analytical model describing the form of the interface separating the two pulsars. An assumption of vacuum dipole spin down for Pulsar B leads to eclipse duration ten times longer than observed. We discuss possible Pulsar B torque modification and magnetic field estimates due to the interaction with Pulsar A wind. Unless the orbital inclination is $\leq 86 ^\circ$, the duration of eclipses is typically shorter than the one implied by the size of the eclipsing region. We propose that eclipses occur due to synchrotron absorption by mildly relativistic particles in the shocked Pulsar A wind. The corresponding optical depth may be high enough if Pulsar A wind density is at the upper allowed limits. We derive jump conditions at oblique, relativistic, magnetohydrodynamical shocks and discuss the structure of the shocked Pulsar A wind. Finally, we speculate on a possible mechanism of orbital modulation of Pulsar B radio emission.

The Nonlinear Alfvn Wave Model for Solar Coronal Heating and Nanoflares

The mechanism of solar coronal heating has been unknown since the discovery that the coronal plasma temperature is a few million degrees. There are two promising mechanisms, the Alfven wave model and the nanoflare-reconnection model. Recent observations favor the nanoflare model since it readily explains the ubi-quitous small-scale brightenings all over the Sun. We have performed magnetohydrodynamic (MHD) simulations of the nonlinear Alfven wave coronal heating model that include both heat conduction and radiative cooling in an emerging flux loop and found that the corona is episodically heated by fast- and slow-mode MHD shocks generated by nonlinear Alfven waves via nonlinear mode-coupling. We also found that the time variation of the simulated extreme-ultraviolet and X-ray intensities of these loops, on the basis of the Alfven wave model, is quite similar to the observed one, which is usually attributed to nanoflare or picoflare heating. This suggests that the observed nanoflares may not be a result of reconnection but in fact may be due to nonlinear Alfven waves, contrary to current widespread opinion.