Slow Magnetosonic Shocks Research Articles

Implications of High-density, High-temperature Ridges Observed in Some Two-ribbon Flares

Several two-ribbon solar flares observed on the disk, notably including the Bastille flare of 2000 July 14, show an extended ridge of plasma running along the loop tops of the post-reconnection arcade. In that and two more recent examples, the ridge is visible in emission by Fe xxiv at roughly 17 MK, with a high, steadily increasing emission measure suggesting an expanding column of very dense plasma. We find that ridges are consistent with overhead views of long, vertical plasma sheets, such as seen above certain limb flares. Those vertical features show enhanced temperature and density over their entire lengths, making explanations in terms of termination shocks and evaporation collision seem less plausible. We use observations of several ridge events to argue in favor of compression and heating by slow magnetosonic shocks in the reconnection outflow. In this scenario, the ridge is built up as retracting flux piles hot, compressed plasma atop the post-flare arcade. Thanks to the overhead perspective offered by the ridge observations, we are able to measure the reconnection rate and show it to be consistent with the rate of increase in column emission measure across the ridge. This consistency supports the hypothesis that slow shocks and retraction compress the plasma seen in ridges, vertical plasma sheets, and possibly the high-temperature fans through which post-reconnection downflows are observed. Such a unified picture of these diverse features enhances our understanding of the role played by magnetic reconnection in solar flares.

Expansion of a radially symmetric blast shell into a uniformly magnetized plasma

The expansion of a thermal pressure-driven radial blast shell into a dilute ambient plasma is examined with two-dimensional PIC simulations. The purpose is to determine if laminar shocks form in a collisionless plasma which resemble their magnetohydrodynamic counterparts. The ambient plasma is composed of electrons with the temperature of 2 keV and cool fully ionized nitrogen ions. It is permeated by a spatially uniform magnetic field. A forward shock forms between the shocked ambient medium and the pristine ambient medium, which changes from an ion acoustic one through a slow magnetosonic one to a fast magnetosonic shock with increasing shock propagation angles relative to the magnetic field. The slow magnetosonic shock that propagates obliquely to the magnetic field changes into a tangential discontinuity for a perpendicular propagation direction, which is in line with the magnetohydrodynamic model. The expulsion of the magnetic field by the expanding blast shell triggers an electron-cyclotron drift instability.

A RECONNECTION-DRIVEN MODEL OF THE HARD X-RAY LOOP-TOP SOURCE FROM FLARE 2004 FEBRUARY 26

ABSTRACT A compact X-class flare on 2004 February 26 showed a concentrated source of hard X-rays at the tops of the flare’s loops. This was analyzed in previous work and interpreted as plasma heated and compressed by slow magnetosonic shocks (SMSs) generated during post-reconnection retraction of the flux. That work used analytic expressions from a thin flux tube (TFT) model, which neglected many potentially important factors such as thermal conduction and chromospheric evaporation. Here we use a numerical solution of the TFT equations to produce a more comprehensive and accurate model of the same flare, including those effects previously omitted. These simulations corroborate the prior hypothesis that slow-mode shocks persist well after the retraction has ended, thus producing a compact, loop-top source instead of an elongated jet, as steady reconnection models predict. Thermal conduction leads to densities higher than analytic estimates had predicted, and evaporation enhances the density still higher, but at lower temperatures. X-ray light curves and spectra are synthesized by convolving the results from a single TFT simulation with the rate at which flux is reconnected, as measured through motion of flare ribbons, for example. These agree well with light curves observed by RHESSI and GOES and spectra from RHESSI. An image created from a superposition of TFT model runs resembles one produced from RHESSI observations. This suggests that the HXR loop-top source, at least the one observed in this flare, could be the result of SMSs produced in fast reconnection models like Petschek’s.

HOW GAS-DYNAMIC FLARE MODELS POWERED BY PETSCHEK RECONNECTION DIFFER FROM THOSE WITH AD HOC ENERGY SOURCES

Aspects of solar flare dynamics, such as chromospheric evaporation and flare light-curves, have long been studied using one-dimensional models of plasma dynamics inside a static flare loop, subjected to some energy input. While extremely successful at explaining the observed characteristics of flares, all such models so far have specified energy input ad hoc, rather than deriving it self-consistently. There is broad consensus that flares are powered by magnetic energy released through reconnection. Recent work has generalized Petschek's basic reconnection scenario, topological change followed by field line retraction and shock heating, to permit its inclusion into a one-dimensional flare loop model. Here we compare the gas dynamics driven by retraction and shocking to those from more conventional static loop models energized by ad hoc source terms. We find significant differences during the first minute, when retraction leads to larger kinetic energies and produces higher densities at the loop top, while ad hoc heating tends to rarify the loop top. The loop-top density concentration is related to the slow magnetosonic shock, characteristic of Petschek's model, but persists beyond the retraction phase occurring in the outflow jet. This offers an explanation for observed loop-top sources of X-ray and EUV emission, with advantages over that provided by ad hoc heating scenarios. The cooling phases of the two models are, however, notably similar to one another, suggesting observations at that stage will yield little information on the nature of energy input.

THE RETURN OF THE BOW SHOCK

Recently it has been discussed whether a bow shock ahead of the heliospheric stagnation region does exist or not. This discussion was triggered by measurements indicating that the Alfv\'en speed and that of fast magnetosonic waves are higher than the flow speed of the local interstellar medium (LISM) relative to the heliosphere and resulted in the conclusion that there might exist either a bow wave or a slow magnetosonic shock. We demonstrate here that including the He$^{+}$ component of the LISM yields both an Alfv\'en and fast magnetosonic wave speed lower than the LISM flow speed. Consequently, the scenario of a bow shock in front of the heliosphere as modelled in numerous simulations of the interaction of the solar wind with the LISM remains valid.

A slow bow shock ahead of the heliosphere

Current estimates of plasma parameters in the local interstellar medium indicate that the speed of the interstellar wind, i.e., the relative speed of the local interstellar cloud with respect to the Sun, is most likely less than both the fast magnetosonic speed (subfast) and the Alfvén speed (sub‐Alfvénic) but greater than the slow magnetosonic speed (superslow). In this peculiar parameter regime, MHD theory postulates a slow magnetosonic shock ahead of the heliosphere, provided that the angle between the interstellar magnetic field and the interstellar plasma flow velocity is quite small (e.g., 15° to 30°). In this likely scenario, our multifluid MHD model of the heliospheric interface self‐consistently produces a spatially confined quasi‐parallel slow bow shock. Voyager 1 is heading toward the slow bow shock, while Voyager 2 is not, which means that the two spacecraft are expected to encounter different interstellar plasma populations beyond the heliopause. The slow bow shock also affects the density and spatial extent of the neutral hydrogen wall.

A MODEL FOR THE ORIGIN OF HIGH DENSITY IN LOOPTOP X-RAY SOURCES

Super-hot looptop sources, detected in some large solar flares, are compact sources of HXR emission with spectra matching thermal electron populations exceeding 30 megakelvins. High observed emission measure, as well as inference of electron thermalization within the small source region, both provide evidence of high densities at the looptop; typically more than an order of magnitude above ambient. Where some investigators have suggested such density enhancement results from a rapid enhancement in the magnetic field strength, we propose an alternative model, based on Petschek reconnection, whereby looptop plasma is heated and compressed by slow magnetosonic shocks generated self-consistently through flux retraction following reconnection. Under steady conditions such shocks can enhance density by no more than a factor of four. These steady shock relations (Rankine-Hugoniot relations) turn out to be inapplicable to Petschek's model owing to transient effects of thermal conduction. The actual density enhancement can in fact exceed a factor of ten over the entire reconnection outflow. An ensemble of flux tubes retracting following reconnection at an ensemble of distinct sites will have a collective emission measure proportional to the rate of flux tube production. This rate, distinct from the local reconnection rate within a single tube, can be measured separately through flare ribbon motion. Typical flux transfer rates and loop parameters yield emission measures comparable to those observed in super-hot sources.

Fast and slow magnetosonic waves in two-dimensional spin-1/2 quantum plasma

Using the spin-1/2 resistive quantum magnetohydrodynamics model, linear and nonlinear relations for slow and fast magnetosonic modes are derived. Spin effects are incorporated via spin force and macroscopic spin magnetization current. The plasma resistivity is shown to play a role of dissipation in the system. With the aid of tanh method the traveling wave solution of Kadomstev–Petviashvili–Burgers is obtained. The solution shows a general shock wave profile superposed by a perturbative solitary-wave contribution. The dynamics of fast and slow magnetosonic shock and soliton, respectively, in the presence and absence of dissipation is investigated with respect to electron spin magnetization, quantum diffraction, and plasma statistic. It is found that results obtained from the spin quantum plasmas differ significantly from the nonspin quantum plasmas. The relevance of the present work to dense astrophysical plasmas such as pulsar magnetosphere is pointed out.

SLOW SHOCKS AND CONDUCTION FRONTS FROM PETSCHEK RECONNECTION OF SKEWED MAGNETIC FIELDS: TWO-FLUID EFFECTS

In models of fast magnetic reconnection, flux transfer occurs within a small portion of a current sheet triggering stored magnetic energy to be thermalized by shocks. When the initial current sheet separates magnetic fields which are not perfectly anti-parallel, i.e. they are skewed, magnetic energy is first converted to bulk kinetic energy and then thermalized in slow magnetosonic shocks. We show that the latter resemble parallel shocks or hydrodynamic shocks for all skew angles except those very near the anti-parallel limit. As for parallel shocks, the structures of reconnection-driven slow shocks are best studied using two-fluid equations in which ions and electrons have independent temperature. Time-dependent solutions of these equations can be used to predict and understand the shocks from reconnection of skewed magnetic fields. The results differ from those found using a single-fluid model such as magnetohydrodynamics. In the two-fluid model electrons are heated indirectly and thus carry a heat flux always well below the free-streaming limit. The viscous stress of the ions is, however, typically near the fluid-treatable limit. We find that for a wide range of skew angles and small plasma beta an electron conduction front extends ahead of the slow shock but remains within the outflow jet. In such cases conduction will play a more limited role in driving chromospheric evaporation than has been predicted based on single-fluid, anti-parallel models.

GAS-DYNAMIC SHOCK HEATING OF POST-FLARE LOOPS DUE TO RETRACTION FOLLOWING LOCALIZED, IMPULSIVE RECONNECTION

We present a novel model in which shortening of a magnetic flux tube following localized, three-dimensional reconnection generates strong gas-dynamic shocks around its apex. The shortening releases magnetic energy by progressing away from the reconnection site at the Alfven speed. This launches inward flows along the field lines whose collision creates a pair of gas-dynamic shocks. The shocks raise both the mass density and temperature inside the newly shortened flux tube. Reconnecting field lines whose initial directions differ by more that 100 degrees can produce a concentrated knot of plasma hotter that 20 MK, consistent with observations. In spite of these high temperatures, the shocks convert less than 10% of the liberated magnetic energy into heat - the rest remains as kinetic energy of bulk motion. These gas-dynamic shocks arise only when the reconnection is impulsive and localized in all three dimensions; they are distinct from the slow magnetosonic shocks of the Petschek steady-state reconnection model.

Dynamics of equilibrium upset and electromagnetic energy transformation in the geomagnetotail: A theory and simulation using particles. 2. Numerical simulation using particles

The process of rapid geomagnetotail reconfiguration after the equilibrium upset (substorm activation) has been studied using the numerical simulation. The decisive reconfiguration feature consists in the spontaneous formation of nonlinear kinetic small-scale structures in the position of the initial current sheet (CS). Substantially different reconfiguration channels are possible depending on the value of the magnetic field component normal to CS: the dominating process can be the formation of a collisionless slow magnetosonic shock or a forced kinetic current sheet (FKCS). The first option is presented in this part of the work. During the late stages, the process is independent of the type of an initial disturbance; the disturbance intensity is spontaneously formed at a certain final level. Far from CS, the disturbance has the form of a rarefaction wave propagating from CS in background plasma. The reconfiguration results in a large-scale transformation of electromagnetic energy into the energy of plasma flows and heat.

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.

Suppression of the Richtmyer–Meshkov instability in the presence of a magnetic field

We present numerical evidence from two dimensional simulations that the growth of the Richtmyer–Meshkov instability is suppressed in the presence of a magnetic field. A bifurcation occurs during the refraction of the incident shock on the density interface which transports baroclinically generated vorticity away from the interface to a pair of slow or intermediate magnetosonic shocks. Consequently, the density interface is devoid of vorticity and its growth and associated mixing is completely suppressed.

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.

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.

Coronal Heating by Resonant Absorption: The Effects of Chromospheric Coupling

We present the first 2.5 dimensional numerical model calculations of the nonlinear wave dynamics and heating by resonant absorption in coronal loops with thermal structuring of the transition region and higher chromosphere. The numerical calculations were done with the Versatile Advection Code. The transition region can move freely and is transparent for mass motions from chromosphere to corona. The loops are excited at the chromospheric level by linearly polarized monochromatic Alfven waves. We find that the efficiency of resonant absorption can be much lower than in equivalent line-tied coronal loop models. The inefficiency is due to the fast rate at which slow magnetosonic waves are nonlinearly generated in the chromosphere and transition region. This leads to considerable transfer of energy from the Alfven wave to the magnetosonic waves. Consequently, only a relatively small fraction of the Poynting flux that is injected into the loop system at the chromospheric level is available at the coronal level. Cavity leakage and detuning also have a negative impact on the efficiency, but less so than the nonlinear energy transfer. Inclusion of radiative and conductive losses improves the efficiency of resonant absorption. While the efficiency of resonant absorption heating is low, our results indicate that heating by compression and dissipation of the slow magnetosonic waves and shocks can easily lead to a temperature rise of a few percent, and for larger driver amplitudes even to a rise over 10%. Hence, our results support the idea of indirect coronal heating through the nonlinear generation of magnetosonic waves that was put forward more than 20 yr ago. Furthermore, the large transition region and coronal density oscillations that are associated with the slow magnetosonic waves provide an explanation for some observed coronal and transition region loop extreme-ultraviolet intensity variations.

High-Energy Gamma and Radio Variability of Blazars in the Model of Non-Stationary Jets

A model has been developed for impulsive VLBI jet formation and gamma ray outbursts of Blazars. Propagation of newly expelled matter in the old channel of a jet is calculated supposing that the main driving force is the electromagnetic field. The new outflowing matter overtakes the old matter and forms double, fast or slow magnetosonic shock fronts. In the region of the fronts, the number of particles and their energy increase continuously with propagation time from the central object (Romanova and Lovelace, 1995). Accelerated electrons and positrons in the front interact with a diffuse field of UV photons (inverse Compton scattering), with the magnetic field (synchrotron radiation), and with synchrotron photons (SSC processes), thus creating radiation in a very wide range of bands. The self-consistent relativistic equations for the number of particles, the momentum, energy, and magnetic flux in the front are derived and solved numerically (Lovelace and Romanova, 1995). The time-dependent apparent luminosities in the radio to gamma ray bands are calculated taking into account the Doppler boost of the photons. The model predicts a short outburst of radiation in gamma rays (weeks or so) connected with Compton processes, a sharp (less than a day) outburst in the X-rays with a smooth decrease of the luminosity connected with SSC processes, and synchrotron radiation changing from infrared to radio bands (Fig. 1A). The lepton distribution function was taken as fl = K1/γ2 in the main energy containing range, γ1 ≤ γ ≤ γ2, steeper distribution fl = K2/γ3 for γ2 ≤ γ ≤ γ3, and even steeper for γ ≥ γ3. For γ < γ1, fl is assumed negligible as a result of synchrotron self-absorption. The lowest frequency f(syn1), determined by self-absorption, corresponds initially to the infrared band, and later - to the radio band. From Fig.1B, one can see that radio at 3 mm may start to appear after 2 weeks after outburst. But its maximum may correspond to much later times (months), because f(syn1) decreases slowly with time. The appearance of the new VLBI component in QSO 0528+134, which approximately coincides with the strong gamma-ray flash and with the beginning of the strong mm radio outburst (Krichbaum, et al. 1995; Pohl, et al. 1995), supports the proposed model.Both authors were supported in part by NSF grant AST-9320068. MMR is grateful to RFBR and Organizers of the Symposium for the partial support.

The Corrugation Instability in Slow Magnetosonic Shock Waves

The Corrugation Instability in Slow Magnetosonic Shock Waves

Two‐dimensional structure of slow shocks

The two‐dimensional (2‐D) structure of switch‐off slow magnetosonic shocks is investigated using an electromagnetic hybrid (fluid electrons, kinetic ions) code. It is shown that the basic physical processes occurring at 1‐D slow shocks are also operative in 2‐D. Specifically, the interaction between the upstream ions and those streaming away from the shock results in the excitation of Alfvén/ion‐cyclotron (AIC) waves. Depending on the plasma parameters, these waves may either stay in the upstream or convect back into the shock resulting in a non‐steady shock behavior which prevents the formation of a trailing wave train. Despite this similarity, some slow shocks which are steady in 1‐D are found to be non‐steady in 2‐D. Fourier analysis of the waves downstream of non‐steady shocks identifies them as AIC, demonstrating that the waves remain on the same branch as they convect from upstream into the downstream region.

A review of the physics of electron heating at collisionless shocks

The current understanding of the increase of electron temperature across fast and slow magnetosonic collisionless shocks observed in space is reviewed. The concept advanced by Goodrich and Scudder /1/ that the electron temperature increase is essentially caused by the inflation of the phase space in the presence of the DC deHoffmann-Teller (HT) /2/ electric field within the shock layer has achieved wide acceptance. This review reiterates the essential basis of that work: that with their relatively small inertia the electrons remain magnetized while the ions do not. It is this fact that makes the HT frame the relevant one for electron energetics. Subsequent discussions of the electron issues and its corollaries always come back to the same issue: m M ⪡ 1 makes collisionless shocks the way they are observed. The predicted corollaries of this understanding in terms of the diagnostic signatures in the magnetic field within the shock structure have been challenged in the intervening years, but nevertheless confirmed by independent groups. This understanding has also been transferred to the relatively rare slow shocks. These corollaries concern the geometry of magnetic tubes of force that underlie the one-fluid J × B force. This geometry clarifies that the tubes of force that pierce the shock do not lie in a single coplanarity plane, but meander in a staircase-like fashion between distinct asymptotic coplanarity planes perpendicular to the tangential electric field direction, E T . It is also developed that the relative size of the deHoffmann-Teller and Normal Incidence cross shock electrical potential is now established, with the Normal Incidence potential jump bigger (smaller) than the deHoffmann-Teller jump in observed fast (slow) shock waves. A geometrical discussion has been made in this review that these relations are consistent with the required tangential torques needed for the ion deflections required by Hugoniot, being opposite for the fast and slow shocks. Computer simulations with particle electrons have just recently been able to verify the experimental picture summarized above, including the self-consistent generation of the strong shock flat-topped electron distribution functions and the relatively unimportant role of instabilities in electron heating as opposed to assimilation or scattering. The diagnostics of this code have supported the overwhelming importance of the DC effects of the coherent forces in the electron shock heating physics.