Coronal Shock Waves,EUV Waves,and Their Relation to CMEs. III. Shock-Associated CME/EUV Wave in an Event with a Two-Component EUV Transient

On 17 January 2010, STEREO-B observed in extreme ultraviolet (EUV) and white light a large-scale dome-shaped expanding coronal transient with perfectly connected off-limb and on-disk signatures. Veronig et al. (Astrophys. J. Lett. 716, L57, 2010) concluded that the dome was formed by a weak shock wave. We have revealed two EUV components, one of which corresponded to this transient. All of its properties found from EUV, white light, and a metric type II burst match expectations for a freely expanding coronal shock wave, including correspondence with the fast-mode speed distribution, while the transient sweeping over the solar surface had a speed typical of EUV waves. The shock wave was presumably excited by an abrupt filament eruption. Both a weak shock approximation and a power-law fit match kinematics of the transient near the Sun. Moreover, the power-law fit matches the expansion of the CME leading edge up to 24 solar radii. The second, quasi-stationary EUV component near the dimming was presumably associated with a stretched CME structure; no indications of opening magnetic fields have been detected far from the eruption region.     

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.     

Evidence of Traveling Waves in Filament Threads

High-resolution Hα filtergrams (0.2″) obtained with the Swedish 1-m Solar Telescope resolve numerous very thin, thread-like structures in solar filaments. The threads are believed to represent thin magnetic flux tubes that must be longer than the observable threads. We report on evidence for small-amplitude (1 – 2 km s⁻¹) waves propagating along a number of threads with an average phase velocity of 12 km s⁻¹ and a wavelength of 4″. The oscillatory period of individual threads vary from 3 to 9 minutes. Temporal variation of the Doppler velocities averaged over a small area containing a number of individual threads shows a short-period (3.6 minutes) wave pattern. These short-period oscillations could possibly represent fast modes in accordance with numerical fibril models proposed by Díaz et al. (Astron. Astrophys. 379, 1083, 2001). In some cases, it is clear that the propagating waves are moving in the same direction as the mass flows.     

A Coherence-Based Approach for Tracking Waves in the Solar Corona

We consider the problem of automatically (and robustly) isolating and extracting information about waves and oscillations observed in EUV image sequences of the solar corona with a view to near real-time application to data from the Atmospheric Imaging Array (AIA) on the Solar Dynamics Observatory (SDO). We find that a simple coherence/travel-time based approach detects and provides a wealth of information on transverse and longitudinal wave phenomena in the test sequences provided by the Transition Region and Coronal Explorer (TRACE). The results of the search are pruned (based on diagnostic errors) to minimize false-detections such that the remainder provides robust measurements of waves in the solar corona, with the calculated propagation speed allowing automated distinction between various wave modes. In this paper we discuss the technique, present results on the TRACE test sequences, and describe how our method can be used to automatically process the enormous flow of data (≈1 Tb day⁻¹) that will be provided by SDO/AIA. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward and downward traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an α-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.     

Dissipative cylindrical fast magnetoacoustic waves in planetary magnetospheres

Nonlinear cylindrical fast magnetoacoustic waves are investigated in a dissipative magnetoplasma comprising of electrons, positrons, and ions. In this regard, cylindrical Kadomtsev-Petviashvili-Burgers (CKPB) equation is derived using the small amplitude perturbation expansion method. Furthermore, cylindrical Burgers-Kadomtsev-Petviashvili (Cyl Burgers-KP) for a fast magnetoacoustic wave is derived, for the first time, for spatial scales larger than the electron/positron skin depths, c/ω _p(e,p). Using the tangent hyperbolic method, the solutions of both planar KPB and Burgers-KP equations are obtained and then subsequently used as an initial profile to solve their respective counterparts in the cylindrical geometry. The effect of positron concentration, kinematic viscosity, and plasma β are explored both for the KPB and the Burgers-KP shock waves and the differences between the two are highlighted. The temporal evolution of the cylindrical fast magnetoacoustic wave is also numerically investigated. The present study may be beneficial to study the propagation characteristics of nonlinear electromagnetic shock waves in planetary magnetospheres.     

Propagation of Fast Coronal Mass Ejections and Shock Waves Associated with Type II Radio-Burst Emission: An Analytic Study

Coronal mass ejections (CMEs) are large-scale eruptive events in the solar corona. Once they are expelled into the interplanetary (IP) medium, they propagate outwards and “evolve” interacting with the solar wind. Fast CMEs associated with IP shocks are a critical subject for space weather investigations. We present an analytic model to study the heliocentric evolution of fast CME/shock events and their association with type II radio-burst emissions. The propagation model assumes an early stage where the CME acts as a piston driving a shock wave; beyond this point the CME decelerates, tending to match the ambient solar wind speed and its shock decays. We use the shock speed evolution to reproduce type II radio-burst emissions. We analyse four fast CME halo events that were associated with kilometric type II radio bursts, and in-situ measurements of IP shock and CME signatures. The results show good agreement with the dynamic spectra of the type II frequency drifts and the in-situ measurements. This suggests that, in general, IP shocks associated with fast CMEs evolve as blast waves approaching 1 AU, implying that the CMEs do not drive their shocks any further at this heliocentric range.     

Structure of Radiative Shock Waves in Stellar Atmospheres

A global iteration method to determine the self-consistent structure of steady plane-parallel radiative shock waves is shown to converge to the stable solution with upstream front velocities of 15 km/s ≤ U ₁≤ 60 km/s and for hydrogen gas of unperturbed temperature T= 3000 K and density ρ = 10⁻¹⁰gcm⁻³. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of <Emphasis Type="Italic">q</Emphasis>-nonextensive distribution of electrons on electron acoustic solitons

Ion acoustic shock waves (IASWs) are studied in a plasma consisting of electrons, positrons and ions. Boltzmann distributed positrons and superthermal electrons are considered in the plasma. The dissipation is taken into account the kinematic viscosity among the plasma constituents. The Korteweg–de Vries–Burgers (KdV–Burgers) equation is derived by reductive perturbation method. Shock waves are solutions of KdV–Burgers equation. It is observed that an increasing positron concentration decreases the amplitude of the waves. Furthermore, in the existence of the kinematic viscosity among the plasma, the shock wave structure appears. The effects of ion kinematic viscosity (η ₀) and the superthermal parameter (k) on the ion acoustic waves are found.     

Propagation of the Bastille Day 2000 CME Shock in the Outer Heliosphere

The Bastille Day (14 July) 2000 CME is a fast, halo coronal mass ejection event headed earthward. The ejection reached Earth on 15 July 2000 and produced a very significant magnetic storm and widespread aurora. At 1 AU the Wind spacecraft recorded a strong forward shock with a speed jump from ∼ 600 to over 1000 km s⁻¹. About 6 months later, this CME-driven shock arrived at Voyager 2 (∼ 63 AU) on 12 January 2001 with a speed jump of ∼ 60 km s⁻¹. This provides a good opportunity to study the shock propagation in the outer heliosphere. In this study, we employ a 2.5-D MHD numerical model, which takes the interaction of solar wind protons and interstellar neutrals into account, to investigate the shock propagation in detail and compare the model predictions with the Voyager 2 observations. The Bastille Day CME shock undergoes a dramatic change in character from the inner to outer heliosphere. Its strength and propagation speed decay significantly with distance. The model results at the location of Voyager 2 are in good agreement with in-situ observations. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014293527951     

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.     

Oscillatory Response of the 3D Solar Atmosphere to the Leakage of Photospheric Motion

The direct propagation of acoustic waves, driven harmonically at the solar photosphere, into the three-dimensional solar atmosphere is examined numerically in the framework of ideal magnetohydrodynamics. It is of particular interest to study the leakage of 5-minute global solar acoustic oscillations into the upper, gravitationally stratified and magnetised atmosphere, where the modelled solar atmosphere possesses realistic temperature and density stratification. This work aims to complement and bring further into the 3D domain our previous efforts (by Erdélyi et al., 2007, Astron. Astrophys. 467, 1299) on the leakage of photospheric motions and running magnetic-field-aligned waves excited by these global oscillations. The constructed model atmosphere, most suitable perhaps for quiet Sun regions, is a VAL IIIC derivative in which a uniform magnetic field is embedded. The response of the atmosphere to a range of periodic velocity drivers is numerically investigated in the hydrodynamic and magnetohydrodynamic approximations. Among others the following results are discussed in detail: i) High-frequency waves are shown to propagate from the lower atmosphere across the transition region, experiencing relatively low reflection, and transmitting most of their energy into the corona; ii) the thin transition region becomes a wave guide for horizontally propagating surface waves for a wide range of driver periods, and particularly at those periods that support chromospheric standing waves; iii) the magnetic field acts as a waveguide for both high- and low-frequency waves originating from the photosphere and propagating through the transition region into the solar corona. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Perpendicular Transport in the Inner Heliosphere: A Quick and Dirty Approach

In previous studies, transport of solar energetic particles in the inner heliosphere was regarded as one-dimensional along the Archimedean field spiral; i.e., any perpendicular transport is neglected. We extend Roelof’s equation of focused transport for solar energetic particles to accommodate perpendicular transport in the plane of the ecliptic. Numerically, this additional term is solved with an implicit Laasonen scheme. In this first approximation, it is solved for azimuthal instead of perpendicular transport – these are similar in the inner heliosphere where the Archimedean field is almost radial. The intent of the study is to estimate the possible influence of perpendicular transport, but not to fit energetic particle events; thus, the particle source stays fixed on the Sun. For typical ratios κ _⊥ /κ _‖ between 0.02 and 0.1 at 1 AU scaled with r ² as suggested in nonlinear guiding-center theory, we find that i) an azimuthal spread over some 10° occurs within a few hours, ii) the variation of maximum intensities with longitude is comparable to the ones inferred from multispacecraft observations, and iii) on a given field line, intensity and anisotropy-time profiles are modified such that fits with the two-dimensional transport model give different combinations of injection profiles and mean free paths. Implications for the interpretation of intensity and anisotropy-time profiles observed in interplanetary space and consequences for our understanding of particle propagation and acceleration in space are discussed.     

Acoustic-Gravity Waves from Bolide Sources

We have developed a new approach to modeling the acoustic-gravity wave (AGW) radiation from bolide sources. This first effort involves entry modeling of bolide sources that have available satellite data through procedures developed in ReVelle (Earth Moon Planets 95, 441–476, 2004a; in: A. Milani, G. Valsecchi, D. Vokrouhlicky (eds) NEO Fireball Diversity: Energetics-based Entry Modeling and Analysis Techniques, Near-earth Objects: Our Celestial Neighbors (IAU S236), 2007b). Results from the entry modeling are directly coupled to AGW production through line source blast wave theory for the initial wave amplitude and period at (at 10 blast wave radii and perpendicular to the trajectory). The second effort involves the prediction of the formation and or dominance of the propagation of the atmospheric Lamb, edge-wave composite mode in a viscous fluid (Pierce, J. Acoust. Soc. Amer. 35, 1798–1807, 1963) as a function of the source energy, horizontal range and source altitude using the Lamb wave frequency that was deduced directly during the entry modeling and that is used as a surrogate for the source energy. We have also determined that Lamb wave production by bolides at close range decreases dramatically as either the source energy decreases or the source altitude increases. Finally using procedures in Gill (Atmospheric-Ocean Dynamics, 1982) and in Tolstoy (Wave Propagation, 1973), we have analyzed two simple dispersion relationships and have calculated the expected dispersion for the Lamb edge-wave mode and for the excited, propagating internal acoustic waves. Finally, we have used the above formalism to fully evaluate these techniques for four large bolides, namely: the Tunguska bolide of June 30, 1908; the Revelstoke bolide of March 31, 1965; the Crete bolide of June 6, 2002 and the Antarctic bolide of September 3, 2004. Due to page limitations, we will only present results in detail for the Revelstoke bolide.     

Energy Flux of Alfvén Waves in Weakly Ionized Plasma and Coronal Heating of the Sun

The influence of collisions between neutrals and ions on the energy flux of Alfvén-type waves in partially ionized plasma based on the three-fluid equations is considered. It has been shown that amplitudes of Alfvén waves that are generated or propagating in the solar photosphere do not depend on the ionization ratio, if the wave periods are much larger than 10⁻⁴ s. This contradicts results of Vranjes et al. (Astron. Astrophys. 478, 553, 2008) and is explained by the strong coupling due to ion–neutral collisions. Alfvén waves can be effectively excited in the photosphere of the Sun by convective motions, providing the required energy for coronal heating.     

Two dimensional electromagnetic shock structures in dense electron-positron-ion magnetoplasmas

Linear and nonlinear analysis of low frequency magnetoacoustic waves propagating at an angle θ with the ambient magnetic field are investigated in dense electron-positron-ion (e-p-i) plasmas using the quantum magnetohydrodynamic (QMHD) model. In this regard, a quantum Kadomtsev-Petviashvili-Burgers (KPB) equation is derived in the small amplitude limit. The stability of KPB equation is also presented. The variation of the nonlinear fast and slow magnetoacoustic shock waves with the positron concentration, kinematic viscosity, obliqueness parameter θ, and the magnetic field, are also investigated. It is observed that the aforementioned plasma parameters significantly modify the propagation characteristics of two dimensional nonlinear magnetoacoustic shock waves in dissipative quantum magnetoplasmas. The relevance of the present investigation with regard to dense astrophysical environments is also pointed out.     

Umbral Three-Minute Oscillations and Running Penumbral Waves

We present results of investigations into chromospheric velocity oscillations in sunspots, carried out at the Sayan Solar Observatory. It is shown that the “chevron” structures in the space-time diagrams demonstrate wavetrain properties. Such structures are indicators of a propagating wave process and they are typical of many sunspots. In the authors’ opinion, three-minute umbral oscillations are not the source of running penumbral waves (RPW). It is very likely that umbral oscillations and RPW initially propagate along different magnetic field lines. We explain the decrease in RPW propagation velocity and frequency in the outer penumbra, as compared with the inner, by the combined action of different frequency modes. To better reveal the properties of these modes, frequency filtering was used. Our measurements of the RPW (five-minute mode) wavelength and RPW propagation velocity in different sunspots vary from 12^″ to 30^″ and from 28 to 60 – 70 km s⁻¹ correspondingly.     

Cavitation by Nonlinear Interaction Between Inertial Alfvén Waves and Magnetosonic Waves in Low Beta Plasmas

This paper presents the model equations governing the nonlinear interaction between dispersive Alfvén wave (DAW) and magnetosonic wave in the low-β plasmas (β≪m _e/m _i; known as inertial Alfvén waves (IAWs); here \upbeta = 8pn₀T /B₀²\upbeta = 8\pi n_{0}T /B_{0}^{2} is thermal to magnetic pressure, n ₀ is unperturbed plasma number density, T(=T _e≈T _i) represents the plasma temperature, and m _e(m _i) is the mass of electron (ion)). This nonlinear dynamical system may be considered as the modified Zakharov system of equations (MZSE). These model equations are solved numerically by using a pseudo-spectral method to study the nonlinear evolution of density cavities driven by IAW. We observed the nonlinear evolution of IAW magnetic field structures having chaotic behavior accompanied by density cavities associated with the magnetosonic wave. The relevance of these investigations to low-β plasmas in solar corona and auroral ionospheric plasmas has been pointed out. For the auroral ionosphere, we observed the density fluctuations of ∼ 0.07n ₀, consistent with the FAST observation reported by Chaston et al. (Phys. Scr. T84, 64, 2000). The heating of the solar corona observed by Yohkoh and SOHO may be produced by the coupling of IAW and magnetosonic wave via filamentation process as discussed here.     

The role of solar-wind velocity-waves in comet outburst activity

Comet outburst activity and the structure of solar wind streams were compared on the basis of Pioneer 10, 11, Vela 3 and IMP 7, 8 measurements at the heliocentric distance r ≈ 1–6 AU. It is shown that the solar wind velocity waves which are evolving into corotating shock waves beyond the Earth orbit may be responsible for comet outburst activity. The correlation between variations of comet outburst activity with heliocentric distance and the behavior of the solar wind velocity waves is established. The closeness of the characteristic times for the velocity waves and comet outburst activity (7–8 days at r = 1 AU) as well as the simultaneous growth of both the characteristic times with r are noted. The observed distribution of the comet outburst activity parameters during the 11-year cycle is also in good agreement with the phase distributions during the 11-year cycle of variations of the coronal hole areas and the rate of change of the sunspot area δS _p.     

Nonlinear excitation of small-scale Alfvén waves by fast waves and plasma heating in the solar atmosphere

We study a nonlinear mechanism for the excitation of kinetic Alfvén waves (KAWs) by fast magneto-acoustic waves (FWs) in the solar atmosphere. Our focus is on the excitation of KAWs that have very small wavelengths in the direction perpendicular to the background magnetic field. Because of their small perpendicular length scales, these waves are very efficient in the energy exchange with plasmas and other waves. We show that the nonlinear coupling of the energy of the finite-amplitude FWs to the small-scale KAWs can be much faster than other dissipation mechanisms for fast wave, such as electron viscous damping, Landau damping, and modulational instability. The nonlinear damping of the FWs due to decay FW = KAW + KAW places a limit on the amplitude of the magnetic field in the fast waves in the solar corona and solar-wind at the level B/B ₀∼10⁻². In turn, the nonlinearly excited small-scale KAWs undergo strong dissipation due to resistive or Landau damping and can provide coronal and solar-wind heating. The transient coronal heating observed by Yohkoh and SOHO may be produced by the kinetic Alfvén waves that are excited by parametric decay of fast waves propagating from the reconnection sites.