Slow Shocks Research Articles

Slow and Fast MHD Shocks Associated with a Giant Cusp-Shaped Arcade on 1992 January 24

Abstract We performed magnetohydrodynamic (MHD) simulations of a giant arcade formation with a model of magnetic reconnection coupled with heat conduction, to investigate the dynamical structure of slow and fast MHD shocks associated with reconnection. Based on the numerical results, theoretical soft X-ray images were calculated and compared with the Yohkoh soft X-ray observations of a giant arcade on 1992 January 24. The Y-shaped structure observed in the event was identified to correspond to the slow and fast shocks associated with the magnetic reconnection.

A Numerical Method for General Relativistic Magnetohydrodynamics

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, and Wilson, and uses Evans and Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfv\'en wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and non-relativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-$l$ tori that are subject to the magnetorotational instability.

Evolution of Interplanetary Flow Velocity Enhancement Disturbance

AbstractUsing a two‐dimensional, ideal MHD model, the evolution of a pure flow velocity enhancement disturbance in the solar wind in the heliospheric equatorial plane (2‐D, 2‐component model) and the heliospheric meridional plane (2‐D, 3‐component model) is investigated, respectively. It is shown that the disturbance evolves into a double shock pair, i.e., a shock system that consists of four shocks: a reverse fast shock, a reverse slow shock, a forward slow shock, and a forward fast shock from the close to the distant with respect to the Sun. The double shock pair is nearly symmetrical with respect to the central normal of the disturbance source in the heliospheric meridional plane, whereas it is asymmetrical in the heliospheric equatorial plane. On the western side of the central normal of the disturbance source in the heliospheric equatorial plane, the double shock pair structure is more evident, and the longitudinal span is wider than those on the eastern side. A preliminary analysis shows that the east‐west asymmetry in the heliospheric equatorial plane is mainly attributed to the spiral structure of the interplanetary magnetic field.

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.

Magnetohydrodynamic study of adiabatic supersonic and subsonic expansion accelerations in spontaneous fast magnetic reconnection

The thermodynamic supersonic expansion acceleration mechanism associated with the spontaneous fast magnetic reconnection is studied by two-dimensional magnetohydrodynamic (MHD) simulations and the Rankine–Hugoniot analysis. The reconnection outflow jet can steadily exceed the Alfvén velocity measured in the upstream magnetic field region. Such a high speed jet cannot be explained by the Petschek model. According to previous studies, when supersonic (superfast) plasma jets generated by a pair of slow shocks expand in the direction normal to the jet, the jets can be further accelerated beyond the Alfvén velocity by the adiabatic supersonic expansion process. The expansion process is caused by the swelling of the plasmoid (magnetic loop). In this paper, it is theoretically shown that the sound Mach number of the reconnection jet generated by slow shocks is determined by the plasma density and beta value in the upstream magnetic field region, in which asymmetric reconnection models are also studied. Then, the theoretical prediction of the Mach number is related to the onset of the supersonic expansion acceleration process in MHD simulations. In addition, it is shown that, also when the reconnection jet is subsonic, the jet is further accelerated by the adiabatic subsonic expansion mechanism.

Time-dependent reconnection for anisotropic pressure

An analysis of the reconnection process which extends the famous solution obtained by Petschek for the steady-state case to incorporate the effects of unsteady reconnection in an anisotropic plasma is presented. The case of so-called switch-off shocks, where the Alfvén discontinuity and the slow shock degenerate to one discontinuity and the downstream magnetic field vanishes in lowest order, so that the plasma is isotropic in the field reversal region is studied. It is shown that the plasma anisotropy can essentially modify the plasma acceleration, the magnetic field intensity, and the shape of the moving slow shocks. Characteristics of reconnection in several limits, such as the isotropic limit and extreme pressure anisotropy cases corresponding to the fire hose and the mirror instability are analyzed.

Shock structure for electromagnetic waves in bianisotropic, nonlinear materials

Shock waves are discontinuous solutions to quasi‐linear partial differential equations and can be studied through a singular perturbation known as the vanishing viscosity technique. The vanishing viscosity method is a means of smoothing the shock, which we use to study the case of electromagnetic waves in bianisotropic materials. We derive the conditions arising from this smoothing procedure for a traveling wave, and the waves are classified as fast, slow, or intermediate shock waves.

Computer simulations on three-dimensional magnetic loop dynamics by the spontaneous fast reconnection model

Three-dimensional (3D) dynamics of a large-scale magnetic loop is studied by precise magnetohydrodynamic simulations on the basis of the spontaneous fast reconnection model. Once a (current-driven) anomalous resistivity is ignited, the fast reconnection mechanism drastically evolves by the positive feedback between the (3D) global reconnection flow and the anomalous resistivity; on the nonlinear saturation phase, the global reconnection flow has grown so that the reconnection (diffusion) region shrinks to a small extent, and the fast reconnection mechanism involving a pair of standing slow shocks is established in the finite extent. When the 3D plasmoid, formed ahead of the fast reconnection jet, collides with the mirror plane boundary, the reconnected field lines are piled up, leading to formation of a large-scale 3D magnetic loop. Since the resulting 3D fast reconnection jet becomes supersonic, a definite fast shock builds up at the interface between the magnetic loop top and the fast reconnection jet. The 3D fast reconnection jet is limited in a narrow channel between the pair of slow shocks, so that the resulting fast shock is also limited to a small extent ahead of the magnetic loop top. On the other hand, for the uniform resistivity model the 3D fast reconnection mechanism cannot be realized without any vital positive feedback between the reconnection flow and the local magnetic diffusion; hence, such an effective resistivity that can be self-consistently enhanced locally at the X reconnection point by the global reconnection flow is essential for the fast reconnection mechanism to be realized in actual systems.

Magnetic Reconnection Triggered by the Parker Instability in the Galaxy: Two‐dimensional Numerical Magnetohydrodynamic Simulations and Application to the Origin of X‐Ray Gas in the Galactic Halo

We propose the Galactic flare model for the origin of the X-ray gas in the Galactic halo. For this purpose, we examine the magnetic reconnection triggered by Parker instability (magnetic buoyancy instability), by performing the two-dimensional resistive numerical magnetohydrodynamic simulations. As a result of numerical simulations, the system evolves through the following phases. Parker instability occurs in the Galactic disk. In the nonlinear phase of Parker instability, the magnetic loop inflates from the Galactic disk into the Galactic halo and collides with the antiparallel magnetic field, so that the current sheets are created in the Galactic halo. The tearing instability occurs and creates the plasmoids (magnetic islands). Just after the plasmoid ejection, further current sheet thinning occurs in the sheet, and the anomalous resistivity sets in. Petschek reconnection starts and heats the gas quickly in the Galactic halo. It also creates the slow and fast shock regions in the Galactic halo. The magnetic field (B ~ 3 μG), for example, can heat the gas (n ~ 10-3 cm-3) to a temperature of ~106 K via the reconnection in the Galactic halo. The gas is accelerated to Alfven velocity (~300 km s-1). Such high-velocity jets are the evidence of the Galactic flare model we present in this paper, if the Doppler shift of the bipolar jet is detected in the Galactic halo.

A class of TVD type combined numerical scheme for MHD equations with a survey about numerical methods in solar wind simulations

It has been believed that three-dimensional, numerical, magnetohydrodynamic (MHD) modelling must play a crucial role in a seamless forecasting system. This system refers to space weather originating on the sun; propagation of disturbances through the solar wind and interplanetary magnetic field (IMF), and thence, transmission into the magnetosphere, ionosphere, and thermosphere. This role comes as no surprise to numerical modelers that participate in the numerical modelling of atmospheric environments as well as the meteorological conditions at Earth. Space scientists have paid great attention to operational numerical space weather prediction models. To this purpose practical progress has been made in the past years. Here first is reviewed the progress of the numerical methods in solar wind modelling. Then, based on our discussion, a new numerical scheme of total variation diminishing (TVD) type for magnetohydrodynamic equations in spherical coordinates is proposed by taking into account convergence, stability and resolution. This new MHD model is established by solving the fluid equations of MHD system with a modified Lax-Friedrichs scheme and the magnetic induction equations with MacCormack II scheme for the purpose of developing a combined scheme of quick convergence as well as of TVD property. To verify the validation of the scheme, the propagation of one-dimensional MHD fast and slow shock problem is discussed with the numerical results conforming to the existing results obtained by the piece-wise parabolic method (PPM). Finally, some conclusions are made.

Effect of By in three-dimensional reconnection at the dayside magnetopause

Asymmetric magnetic reconnection with a non-zero By component is studied using a three-dimensional magnetohydrodynamic simulation and the results are interpreted in terms of the dayside reconnection at the magnetopause. The By component is implemented by rotating the magnetosheath field. It is seen that a magnetic bulge is formed in the magnetosheath region but displaced in the y direction due to the tilted magnetic field line geometry of reconnection. The bulge moves away from the reconnection region along the magnetopause with a speed significantly slower than that of the symmetric case. In fact, the reconnection rate is seen much slower than the symmetric case. It is also seen that the reconnection rate decreases as the angle of rotation increases. The discontinuity associated with magnetic reconnection geometry is identified as a slow shock with Alfvén waves attached to it on the magnetospheric side, while on the magnetosheath side an intermediate shock is seen, which evolves into a slow shock and a rotational discontinuity near the center of the bulge and near the y-directional edges of the current disruption region. A large By component is generated on the open field lines, exceeding the initial sheath By near the center of the bulge. The inflow mass flux into the reconnection region from the magnetosheath is seven times larger than that from the magnetosphere in the present study, while the outflow mass flux into the magnetosphere is five times larger than that into the magnetosheath, implying that a significant mass transfer occurs from the magnetosheath into the magnetosphere. The outflow plasmas move mostly along the magnetic field lines in the downstream and transported toward the polar region.

Hall magnetohydrodynamics model of double discontinuities

A double discontinuity is a compound structure composed of a slow shock layer and an adjoining rotational discontinuity layer on the postshock side. Since the Hall current effects become important as the magnetic field rotates by tens of degree over a thin rotational layer, steady state solutions based on the Hall magnetohydrodynamics (MHD) theory can show the merging of a rotational layer and a slow shock layer to form the observed compound structure. This model uses a set of modified Rankine–Hugoniot relations to calculate the jump conditions between the upstream region and the interface between the two layers, and uses the Hall-MHD equations to calculate the variations of the plasma and magnetic field in the rotational layer in the downstream of the interface. Four series of solutions are presented to show the effect for each of four governing parameters on the structure of double discontinuities.

Spicule formation by ion-neutral damping

The possible mechanism of generation of spicules by Alfvenic waves is studied in dissipative MHD where dissipation is mainly caused by ion-neutral collision damping, as suggested by Haerendel ([CITE]). Ion-neutral damping becomes non-negligible at the high cyclic frequencies involved, typically greater than $0.1~{\rm Hz}$, and the potential role played by this effect in both forming and supporting solar spicules is investigated. The propagation of high frequency Alfven waves on vertically open solar magnetic flux tubes is considered. The flux tubes are taken to be axisymmetric and initially untwisted with the field strength declining from $1600~{\rm G}$ in the photosphere to $20~{\rm G}$ in the corona. Their propagation is investigated by numerically solving a set of fully nonlinear, dissipative 1.5D MHD equations with the waves being generated by a continuous sinusoidal driver introduced into the equation of angular momentum in the low atmosphere of the Sun. Spicule-like structures with heights of around $5000{-}6000~{\rm km}$ were formed. The formation was found to be primarily caused by the impact of a series of slow shocks generated by the continuous interaction between the upward propagating driven wave train and the downward propagating train of waves created by reflection off the transition region. At the lower end of frequencies considered the heating due to ion-neutral damping was found to provide only a small benefit due to the increased thermal pressure gradient. At higher frequencies, whilst the heating effect becomes stronger, the much reduced wave amplitude reaching the transition region hinders spicule formation. The adiabatic results suggest that ion-neutral damping may not support spicules as described by Haerendel ([CITE]). However, the effect is highly sensitive to the level of ionisation and therefore the energy balance. Including the effects of thermal conduction and radiation may well lead to different results and thus it would be premature to dismiss the mechanism at this point.

Collapse of Rotating Magnetized Molecular Cloud Cores and Mass Outflows

The collapse of rotating magnetized molecular cloud cores is studied with axisymmetric magnetohydrodynamic (MHD) simulations. Because of the change of the equation of state of the interstellar gas, molecular cloud cores experience several phases during the collapse. In the earliest isothermal runaway collapse (n 1010 H2 cm-3), a pseudodisk is formed, and it continues to contract until an opaque core is formed at the center. In this disk, a number of MHD fast and slow shock pairs appear whose wave fronts are parallel to the disk. We assume that the interstellar gas obeys a polytropic equation of state with the exponent of Γ > 1 above the critical density at which the core becomes optically thick against the thermal radiation from dusts ncr ~ 1010 cm-3. After the equation of state becomes hard, an adiabatic quasi-static core forms at the center (the first core), which is separated from the isothermal contracting pseudodisk by the accretion shock front facing radially outward. By the effect of the magnetic tension, the angular momentum is transferred from the disk midplane to the surface. The gas with an excess angular momentum near the surface is finally ejected, which explains the molecular bipolar outflow. Two types of outflows are found. When the poloidal magnetic field is strong (its energy is comparable to the thermal one), a U-shaped outflow is formed, in which gas is mainly outflowing through a region whose shape looks like a capital letter U at a finite distance from the rotation axis. The gas is accelerated by the centrifugal force and the magnetic pressure gradient of the toroidal component. The other is a turbulent outflow in which magnetic field lines and velocity fields seem to be randomly oriented. In this case, globally the gas moves out almost perpendicularly from the disk, and the outflow looks like a capital letter I. In this case, although the gas is launched by the centrifugal force, the magnetic force working along the poloidal field lines plays an important role in expanding the outflow. The continuous mass accretion leads to a quasi-static contraction of the first core. A second collapse due to the dissociation of H2 occurs in it. Finally, another less massive quasi-static core is formed by atomic hydrogen (the second core). At the same time, it is found that another outflow is ejected around the second atomic core, which seems to correspond to the optical jets or the fast neutral winds.

Magnetohydrodynamic Shock Conditions for Accreting Plasma onto Kerr Black Holes. I.

We extend the work by Appl and Camenzind for special relativistic magnetohydrodynamic (MHD) jets to fully general relativistic studies of standing shock formation for accreting MHD plasma in a rotating, stationary, and axisymmetric black hole magnetosphere. All the postshock physical quantities are expressed in terms of the relativistic compression ratio, which can be obtained in terms of preshock quantities. Then, the downstream state of a shocked plasma is determined by the upstream state of the accreting plasma. In this paper sample solutions are presented for slow magnetosonic shocks for accreting flows in the equatorial plane. We find that some properties of the slow magnetosonic shock for the rotating magnetosphere can behave like a fast magnetosonic shock. In fact, it is confirmed that in the limit of weak gravity for the upstream nonrotating accretion plasma where the magnetic field lines are leading and rotating, our results are very similar to the fast magnetosonic shock solution by Appl and Camenzind. However, we find that the situation becomes far more complicated because of the effects of strong gravity and rotation, such as the frame-dragging effects. We show the tendency that the large spin of the black hole makes the slow magnetosonic shock strong for the accretion solutions with the same energy flux.

Modeling theHubble Space TelescopeUltraviolet and Optical Spectrum of Spot 1 on the Circumstellar Ring of SN 1987A

We report and interpret Hubble Space Telescope (HST) Space Telescope Imaging Spectrograph (STIS) long-slit observations of the optical and ultraviolet (1150-10270 A) emission line spectra of the rapidly brightening spot 1 on the equatorial ring of SN 1987A between 1997 September and 1999 October (days 3869-4606 after outburst). The emission is caused by radiative shocks created where the supernova blast wave strikes dense gas protruding inward from the equatorial ring. We measure and tabulate line identifications, fluxes, and, in some cases, line widths and shifts. We compute flux correction factors to account for substantial interstellar line absorption of several emission lines. Nebular analysis shows that optical emission lines come from a region of cool (Te ≈ 104 K) and dense (ne ≈ 106 cm-3) gas in the compressed photoionized layer behind the radiative shock. The observed line widths indicate that only shocks with shock velocities Vs < 250 km s-1 have become radiative, while line ratios indicate that much of the emission must have come from yet slower (Vs 135 km s-1) shocks. Such slow shocks can be present only if the protrusion has atomic density n 3 × 104 cm-3, somewhat higher than that of the circumstellar ring. We are able to fit the UV fluxes with an idealized radiative shock model consisting of two shocks (Vs = 135 and 250 km s-1). The observed UV flux increase with time can be explained by the increase in shock surface areas as the blast wave overtakes more of the protrusion. The observed flux ratios of optical to highly ionized UV lines are greater by a factor of ~2-3 than predictions from the radiative shock models, and we discuss the possible causes. We also present models for the observed Hα line widths and profiles, which suggest that a chaotic flow exists in the photoionized regions of these shocks. We discuss what can be learned with future observations of all the spots present on the equatorial ring.

Understanding the Nature of Protostellar Jets through Near-Infrared Spectroscopy: The Key Role of the [ITAL]J[/ITAL] Band Proved on HH 43

Spectroscopy in the J band (even at low resolutions of R 103) is a mode commonly available in most near-IR spectrographs but is rarely exploited in star formation studies. We show how it is a crucial tool to tracing the physics (temperature, density, excitation mechanisms) of protostellar jets and Herbig-Haro (HH) objects. In this framework the spectrum of HH 43 is revisited as both a clear demonstration of our statement and a case of slow J-type shock excitation.

Effects of MHD slow shocks propagating along magnetic flux tubes in a dipole magnetic field

Abstract. Variations of the plasma pressure in a magnetic flux tube can produce MHD waves evolving into shocks. In the case of a low plasma beta, plasma pressure pulses in the magnetic flux tube generate MHD slow shocks propagating along the tube. For converging magnetic field lines, such as in a dipole magnetic field, the cross section of the magnetic flux tube decreases enormously with increasing magnetic field strength. In such a case, the propagation of MHD waves along magnetic flux tubes is rather different from that in the case of uniform magnetic fields. In this paper, the propagation of MHD slow shocks is studied numerically using the ideal MHD equations in an approximation suitable for a thin magnetic flux tube with a low plasma beta. The results obtained in the numerical study show that the jumps in the plasma parameters at the MHD slow shock increase greatly while the shock is propagating in the narrowing magnetic flux tube. The results are applied to the case of the interaction between Jupiter and its satellite Io, the latter being considered as a source of plasma pressure pulses.

Flow in the magnetosheath: the legacy of John Spreiter

We review the evolution of our understanding of the processes governing the flow in the magnetosheath from the earliest model of Spreiter to the current outstanding issues. The earlier models can be characterized as single-wave-mode monotonic processes, namely the gasdynamic model for the magnetosonic mode and the plasma depletion models for slow modes. In the 1990s, a slow shock was identified in the magnetosheath from observations and theoretical models were proposed to describe the processes. We are now in an exciting period of reconstructing both our theoretical and observational understanding of the magnetosheath processes.

Magnetic field line reconnection in the frame of anisotropic MHD

Magnetic reconnection is a process which allows topological different magnetic fields to interconnect. Thus, in magnetospheric context, reconnection is strongly associated with substorm phenomena. Because many observations show a difference between the pressure parallel and perpendicular to the magnetic field, it is reasonable to study the reconnection mechanism for the set of equations, involving a pressure tensor. Existing theoretical work for isotropic weak reconnection is extended for anisotropic theory. In particular, the reconnection associated discontinuities as the Alfvén discontinuity, the slow shock, and the contact discontinuity are generalized for anisotropic pressure.