On the Interaction of Spiral Density Waves with Stars near the Inner Lindblad Resonance in Galactic Disks

The interaction of a spiral wave with stars near the inner Lindblad resonance in a galactic disk has been investigated. The dispersion relation describing the behavior of the complex wave number of the spiral wave as a function of the distance to the resonance has been derived within the framework of a purely linear problem and in the leading orders of the epicyclic and WKB approximations. We also have improved the result of Mark (1971) concerning behavior of the amplitude of leading spiral wave near the resonance circle. We have studied the consequences following from the hypothesis that weak nonlinearity in a narrow resonance region changes the standard rule of bypassing the pole in the complex plane, known as the Landau–Lin bypass rule, to taking the corresponding principal value integral. By analogy with hydrodynamics, where such a problem arises when analyzing the resonant interaction of waves with shear flows, we expect that a small, but finite amplitude can lead to a modification of the bypass rule and, as a consequence, to the elimination of the effect of spiral wave absorption at the resonance and its reflection. We have shown that under some assumptions the presumed picture actually takes place, but the detailed situation looks quite unexpected: near the resonance the regions where stars cause wave attenuation alternate with the regions where the wave is amplified. At the same time, there is no wave absorption effect when integrated over the resonance region.     

Nonlinear dispersive waves on the surface of a self-gravitating fluid layer

The evolution of two dimensional wave packets on the surface of a self-gravitating fluid layer is investigated and shown to be governed by a nonlinear Schrödinger equation. The wave train of finite amplitude is modulationally unstable. Obtained also are the dynamical equations for the second harmonic resonance. The analysis reveals that the general motion consists of both amplitude and phase modulated waves of which the pure phase and amplitude modulated waves, solitary waves, and phase jump are just the special cases.     

Time-fractional KdV equation for electron-acoustic waves in plasma of cold electron and two different temperature isothermal ions

The time fractional KdV equation is derived for small but finite amplitude electron-acoustic solitary waves in plasma of cold electron fluid with two different temperature isothermal ions. The effects of the time fractional parameter on the electrostatic solitary structures are presented. It is shown that the effect of time fractional parameter can be used to modify the amplitude of the electrostatic waves (viz. the amplitude, width and electric field) of the electron-acoustic solitary waves. The model may provide a possible explanation for the low-frequency component of the broadband electrostatic noise in the plasma sheet boundary layer of the Earth’s magnetotail where the electron beams are not present.     

Solar wind interaction with the tail of Comet Kohoutek

Helical waves of large amplitude observed recently in the tail of Comet Kohoutek are interpreted as stable waves arising due to non-linear evolution of Kelvin-Helmholtz instability. The dispersion equation for waves of a finite amplitude shows that the phase velocity of these waves should approximately coincide with the velocity of the plasma outflow in the tail rather than with the Alfvén velocity. This fact is shown to be in agreement with observations. One may estimate the magnetic field in the Comet Kohoutek tail from both the amplitude of observed helical waves and the pressure balance at the tail boundary. The field turns out to be of the order of the interplanetary magnetic field or less, i.e. ?25 γ near ～0.5 AU.     

Critical density solitary waves structures in a hot dusty plasma with vortex-like ion distribution in phase space

The nonlinear properties of solitary waves structure in a hot dusty plasma consisting of isothermal hot electrons, non isothermal ions and high negatively charged massive dust grains, are reported. A modified Korteweg-de Vries equation (modified KdV), which admits a solitary waves solution for small but finite amplitude, is derived using a reductive perturbation theory. A nonisothermal ions distribution provides the possibility of coexistence of amplitude rarefactive as well as compressive solitary waves. On the other hand, consideration of a critical ions density gives a stationary solution of solitary waves and the dynamics of small but finite amplitude of solitary waves is governed by Korteweg-de Vries equation (KdV). The properties of solitary waves in the two cases are discussed.     

星系盘厚度效应的研究

在三维引力Poisson方程严格解基础上，探讨了有限厚星系盘基盘的动力学性质，并进一步讨论了盘的厚度效应对银河系所需晕质量的影响。研究了扰动盘的动力学性质，通过将扰动引力势Poisson方程的严格解与林家翘、徐遐生提出的自维持密度波理论相结合，建立了三维旋涡星系有限厚盘上密度波的色散关系。在此色散关系的基础上讨论了盘的局域稳定性，研究了旋涡星系旋臂的形态、三维盘状星系密度波的群速度。研究表明厚度是星系盘研究中不容忽略的重要参量。另外在有限厚盘星系密度波色散关系的基础上还探讨了一种确定星系厚度的新方法。     

On the role of the magnetic field in a wave theory of the spiral structure of galaxies

The spiral waves in a model galaxy consisting of the differentially rotating interstellar gas and Population I are considered. The instability of spiral waves in the presence of differential rotation and magnetic field is found. This instability may lead as well as the Landau-instability found by Marochnik and Suchkov (1968, 1969) to the formation of an observable spiral pattern in a short time. It may play a definitive role in the spiral structure formation in galaxies with weak Population II.     

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density which travels at a relevant radial group speed C _g. The wave energy surface density and the wave angular momentum surface density are related to by = and = m respectively, where is the angular frequency in an inertial frame of reference and the integer m , proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discussed.     

Expansion of the stellar subsystems of disk galaxies

Based on archival Hubble Space Telescope images, we have performed stellar photometry for eight edge-on spiral and irregular galaxies. We have identified stars with ages of 20, 50, 80, 160, and 500 Myr in the derived Hertzsprung-Russell diagrams and constructed their number density distributions perpendicularly to the plane of the galactic disk. We have determined the sizes of the stellar subsystems and constructed the size-age diagrams for the stars constituting these subsystems. The stellar subsystems have been found to expand in all of the investigated galaxies within the range of ages studied (from 20 to 500 Myr). The expansion velocity of the subsystems decreases as one recedes from the galactic plane. The subsystems with ages of 1.5 and 6 Gyr also exhibit an increase in their sizes with age. The sizes of these subsystems approach those of the thick disk consisting of red giants. Our results confirm the model of thick-disk formation in irregular and low-mass spiral galaxies through thin-disk expansion.     

Effects of dust charge fluctuations and deviations from isothermality of electrons on nonlinear dust ion-acoustic waves

The effects of dust charge fluctuations and deviations from isothermality of electrons are incorporated in the study of nonlinear dust ion-acoustic waves. Deviations from isothermality of electrons are included in this model as a result of nonlinear resonant interaction of the electrostatic wave potential with electrons during its evolution. The basic properties of stationary structures are studied by employing the reductive perturbation method, and conditions for the formation of small but finite amplitude dust ion-acoustic solitary waves in the space dusty plasma situations are clearly explained. It is shown that a more depletion of the background free electrons owing to the attachment of these electrons to the surface of the dust grains during the charging process can lead to the formation of solitary waves with smaller amplitude. Furthermore, effects of the dust charge fluctuation and deviations from isothermality of electrons show a non-uniform behavior for the amplitude of solitary waves in transition from the Boltzmann electron distribution to a trapped electron one. It is also found that the dust charge fluctuation caused by trapped as well as free electrons is a source of dissipation, and is responsible for the formation of the dust ion-acoustic shock waves.     

Ion acoustic solitons of KdV and modified KdV equations in weakly relativistic plasma containing nonthermal electron,positron and warm ion

In this paper, the ion-acoustic solitons in a weakly relativistic electron-positron-ion plasma have been investigated. Relativistic ions, Maxwell-Boltzmann distributed positrons and nonthermal electrons are considered in collisionless warm plasma. Using a reductive perturbation theory, a Korteweg-de Vries (KdV) equation is derived, and the relativistic effect on the solitons is studied. It is found that the amplitude of solitary waves of the KdV equation diverges at the critical values of plasma parameters. Finally, in this situation, the solitons of a modified KdV (mKdV) equation with finite amplitude is derived.     

Non-linear localized ion-acoustic waves in electron–positron–ion plasmas with trapped and non-thermal electrons

For an unmagnetized collisionless electron–positron–ion plasma, the effects of trapped and non-thermal electron distributions are incorporated in the study of arbitrary amplitude ion-acoustic solitary structures. Both highly and weakly analyses are examined by deriving an energy integral equation involving the Sagdeev potential for the large amplitude limit, and obtaining the non-linear partial-differential equations for the small but finite amplitude limit. It is shown that there exist ion-acoustic solitary waves with qualitatively different structures in a way that depend on the population of trapped and non-thermal electrons. In the presence of trapped electrons, fully non-linear analyses show that plasma can support only arbitrary amplitude compressive solitary waves. On the other hand, a consideration of the fast or non-thermal electron distribution provides the possibility of the coexistence of large amplitude compressive and rarefactive solitary waves, whereas both of them are decoupled in the small amplitude limit. It is found that the effects of such electron distributions and positron concentration change the maximum values of the Mach number and the amplitude for which solitary waves can exist. Furthermore, the non-thermally distributed electrons provide a KdV equation in the small amplitude limit, whereas the trapped electrons give rise to a modified KdV equation which exhibits a stronger non-linearity.     

The propagation of Alfvén waves and their directional anisotropy in the solar wind

The propagation of solar Alfvén waves in interplanetary space is studied in the approximation of geometrical optics. Ray paths and the change of wave vectors and amplitudes along the rays are determined assuming an Archimedean-spiral interplanetary magnetic field. In particular, the Alfvénic fluctuations in the 2 directions perpendicular to the magnetic field direction are calculated under the assumption that the Alfvén waves are produced at the Sun and emitted with an isotropic directional distribution from a reference level close to the Sun. It turns out that due to the combined effect of spherical expansion of the solar wind flow and the spiralling of the interplanetary field the magnetic fluctuations in the direction perpendicular both to the unperturbed field and the radial direction have much more power than in the other directions (directional anisotropy).Our results are compared with spacecraft observations made by Belcher and Davis (1971), that show an anisotropy of a similar character. It is argued that under average conditions the physical process leading to an anisotropy is not selective coupling of Alfvén waves into compressional waves, as suggested by Belcher and Davis, but rather the above mentioned dissipationfree effect of geometrical optics. Finally, arguments are presented to explain the discrepancy between the calculated high anisotropy and the measured low anisotropy in terms of finite amplitude effects and wavescattering.     

Parametric coupling between electromagnetic ion-cyclotron and shear Alfvén waves

The nonlinear interaction between finite amplitude electromagnetic ion-cyclotron waves and shear-Alfvén waves is considered. It is shown that this process is governed by three coupled equations. They are here used to study modulational instabilities. The relevance of our investigation to low-frequency electromagnetic fluctuations in space plasmas is pointed out.     

Leading wave as a component of the spiral pattern of the galaxy

The spiral pattern of the Galaxy, identified by analyzing the kinematics of young stars within 3 kpc of the Sun, is Fourier decomposed into spiral harmonics. The spiral pattern of the Galaxy is shown to be representable as a superposition of trailing and leading waves with interarm distances of λ = 1.8 ± 0.4 and 4 ± 2 kpc, respectively. Shock waves are probably present only in the portions of the trailing spiral pattern where it crosses the crest of the leading wave. The small interarm distance of the trailing spiral wave (λ = 1.8 kpc) can be explained by its evolution—by the decrease in the interarmd istance as the wave is displaced toward the inner Lindblad resonance. The Carina arm may be part of this resonance ring.     

On the observability of spiral structures in cataclysmic variable accretion discs

We use the grid of hydrodynamic accretion disc calculations of Stehle to construct orbital phase‐dependent emission‐line profiles of thin discs carrying spiral density waves. The observational signatures of spiral waves are explored to establish the feasibility of detecting spiral waves in cataclysmic variable discs using prominent emission lines in the visible range of the spectrum. For high Mach number accretion discs ( M v _φ c _s≃ 15 – 30), we find that the spiral shock arms are so tightly wound that they leave few obvious fingerprints in the emission lines. Only a minor variation of the double peak separation in the line profile at a level of ∼8 per cent is produced. For accretion discs in outburst ( M ≃ 5 – 20) however, the lines are dominated by the emission from an m =2 spiral pattern in the disc. We show that reliable Doppler tomograms of spiral shock patterns can be reconstructed provided that a signal‐to‐noise ratio of at least 15, a wavelength resolution of ∼80 km s⁻¹ and a time resolution of ∼50 spectra per binary orbit are achieved. We confirm that the observed spiral pattern in the disc of IP Pegasi can be reproduced by tidal density waves in the accretion disc and demands the presence of a large, hot disc, at least in the early outburst stages.     

A new numerical method for simulating the solar wind Alfvén waves: Development of the Vlasov-MHD model

A novel scheme of plasma simulation particularly suited for computing the one-dimensional nonlinear evolution of parallel propagating solar wind Alfvén waves is presented. The scheme is based on the Vlasov and the MHD models, for solving the longitudinal and the transverse components, respectively. As long as the nonlinearity is not very large (so that the longitudinal and transverse components are well separated), our Vlasov-MHD model can correctly describe evolution of finite amplitude parallel Alfvén waves, which are typical in the solar wind, both in the linear and nonlinear stages. The present model can be applied to discussions of phenomena where the parallel Alfvén waves play major roles, for example, the solar coronal heating and solar wind acceleration by the Alfvén waves propagating from the photosphere.     

The Lin–Shu type density–wave structure of the Galaxy: Line-of-sight velocities of selected 37354 RAVE DR5 stars

We exploit information, including velocities from the fifth data release of the RAdial Velocity Experiment (RAVE), to find evidence of the Lin–Shu type tightly wound spiral density waves in the nearby Galactic disk. The Kunder et al. (2017) catalogue of 471117 stars with derived spectrophotometric distances and line-of-sight velocities are explored to find the geometry and parameters of the velocity field in the extended solar neighborhood. Possible existence of noncircular systematic motions of selected 37,354 disk objects within 2 kpc from the Sun and 500 pc from the Galactic mid-plane together with the ordinary differential rotation are assumed. Both the pitch angle of spiral arms and the spatial location of the Sun within the density–wave pattern and the deviations of the motion of objects from the circular motion are calculated by fitting the stellar line-of-sight velocities in RAVE DR5 with the simplest linear perturbation density–wave model. Two radial wavelengths of the wave pattern of about 0.5 kpc and 1.5 kpc in the solar vicinity are found. We argue that the spiral structure of the Galaxy has an oscillating nature corresponding to a concept of the fairly unstable, low amplitude, tightly wound, and rigidly rotating density waves.     

Kepler’s celestial two-body equation: a second attempt to establish a continuous and integrable solution via the <Emphasis Type="Italic">BPES</Emphasis>: Boubaker Polynomials Expansion Scheme

The propagation of nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ions, and nonthermal electrons is studied. By using the reductive perturbation theory, the Kadomtsev–Petviashivili (KP) equation is derived. The energy of the soliton has been calculated. By using standard normal modes analysis a linear dispersion relation has been obtained. The effects of variable dust charge on the energy of the soliton and the angular frequency of the linear wave are also discussed. It is shown that the amplitude of solitary waves of the KP equation diverges at the critical values of plasma parameters. We derive solitons of a modified KP equation with finite amplitude in this situation.     

Filamentation instability of Alfvén waves

The filamentation instability of finite amplitude left-hand circularly polarized Alfvén waves has been investigated taking into account the second-order density and magnetic field perturbations that are created by the Alfvén wave pressure. The minimum scale length and time over which the filamentation occurs, are found. Our results are applied to Alfvén waves that should scatter cosmic rays in the interstellar medium (ISM).