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1.
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2.
A rotating disc galaxy is modelled as a composite system consisting of thin stellar and gaseous discs, which are described by a two-fluid modal formalism. The composite disc system is assumed to retain axisymmetry in the background equilibrium. General density-wave perturbations in the two discs are coupled through the mutual gravitational interaction. We study the basic properties of open and tight spiral density-wave modes in such a composite disc system. Within the Lindblad resonances, perturbation enhancements of surface mass density in stellar and gaseous discs are in phase; this is also true during the initial growth phase of density-wave perturbations. Outside the Lindblad resonances, there exists a possible spiral density-wave branch for which perturbation enhancements of surface mass density in stellar and gaseous discs are out of phase. We discuss implications of these results on the critical parameters for global star formation in barred and normal spiral galaxies and on magnetohydrodynamic density waves within the Lindblad resonances.  相似文献   

3.
We consider a differentially rotating, 2D stellar disc perturbed by two steady-state spiral density waves moving at different pattern speeds. Our investigation is based on direct numerical integration of initially circular test-particle orbits. We examine a range of spiral strengths and spiral speeds and show that stars in this time-dependent gravitational field can be heated (their random motions increased). This is particularly noticeable in the simultaneous propagation of a two-armed spiral density wave near the corotation resonance (CR), and a weak four-armed one near the inner and outer 4:1 Lindblad resonances. In simulations with two spiral waves moving at different pattern speeds, we find: (i) the variance of the radial velocity,  σ2 R   , exceeds the sum of the variances measured from simulations with each individual pattern; (ii)  σ2 R   can grow with time throughout the entire simulation; (iii)  σ2 R   is increased over a wider range of radii compared to that seen with one spiral pattern; and (iv) particles diffuse radially in real space, whereas they do not when only one spiral density wave is present. Near the CR with the stronger, two-armed pattern, test-particles are observed to migrate radially. These effects take place at or near resonances of both spirals, so we interpret them as the result of stochastic motions. This provides a possible new mechanism for increasing the stellar velocity dispersion in galactic discs. If multiple spiral patterns are present in the Galaxy, we predict that there should be large variations in the stellar velocity dispersion as a function of radius.  相似文献   

4.
The kinematics of the Sagittarius (R = 5.7 kpc),Carina (R = 6.5 kpc), Cygnus (R = 6.8 kpc), and Perseus (R = 8.2 kpc) arms suggests the existence of two spiral patterns in the Galaxy that rotate with different speeds. The inner spiral pattern that is represented by the Sagittarius arm rotates with the speed of the bar, Ωb = 60 ± 5 km s−1 kpc−1, while the outer spiral pattern that includes the Carina, Cygnus, and Perseus arms rotates with a lower speed, Ωs = 12–22 km s−1 kpc−1.The existence of an outer slow tightly wound spiral pattern and an inner fast spiral pattern can be explained by numerically simulating the dynamics of outer pseudorings. The outer Lindblad resonance of the bar must be located between the Sagittarius and Carina arms. The Cygnus arm appears as a connecting link between the fast and slow spiral patterns.  相似文献   

5.
It is shown in the present paper that properties of the spiral wave in the Galaxy are determined by the mass distribution of its flat subsystem rather than by the full mass distribution. Then it turns out that better agreement with the observed spiral pattern furnish the ‘long’ waves in contrast to the ‘short’ waves in the Linet al. (1969) theory. With the surface density σI=40M ⊙ /ps 2 which is taken in the first approximation as independent on the galacto-centric distance, and the pattern velocityΩ p=23 km/s kps, the evaluated spiral pattern fits surprisingly well with the Weaver (1970) map of the HI-distribution in the Galaxy, and is in good agreement with the Kerr (1969) map. The inner Lindblad resonance occurs at 2 kps from the Galaxy center, where Weaver has placed the ring condensation of the gas, and the outer resonance lies close by 14 kps. At the outer resonance the nonlinear phenomena are expected, which lead to chaotization of the regular structure. This seems to be consistent with the Weaver (1970) and Kerr (1969) maps. The hypothesis is suggested which associates the generating mechanism of spiral waves with the rotating bar of old stars in the center of the Galaxy. Depending on the velocity of the bar rotation and the bar length, different combinations of the normal wave pattern and bar-like structure may occur, which possibly explains the great variety of transition forms between normal and barred spirals. In the proposed theory the packet of spiral waves moves from the inner Lindblad resonance outwards and could be permanently maintained by the ‘generator’ in the center of the Galaxy. Therefore, the difficulty associated with the rapid obliteration of the packet (Toomre, 1969) does not arise.  相似文献   

6.
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.  相似文献   

7.
This paper reports on the in-plane normal modes in the self-consistent and the cut-out power-law discs. Although the cut-out discs are remarkably stable to bisymmetric perturbations, they are very susceptible to one-armed modes. For this harmonic, there is no inner Lindblad resonance, thus removing a powerful stabilizing influence. A physical mechanism for the generation of the one-armed instabilities is put forward. Incoming trailing waves are reflected as leading waves at the inner cut-out, thus completing the feedback for the swing-amplifier. Growing three-armed and four-armed modes occur only at very low temperatures. However, neutral m  = 3 and m  = 4 modes are possible at higher temperatures for some discs. The rotation curve index β has a marked effect on stability. For all azimuthal wavenumbers, any unstable modes persist to higher temperatures and grow more vigorously if the rotation curve is rising (β < 0) than if the rotation curve is falling (β > 0). If the central regions or outer parts of the disc are carved out more abruptly, any instabilities become more virulent. The self-consistent power-law discs possess a number of unusual stability properties. There is no natural time-scale in the self-consistent disc. If a mode is admitted at some pattern speed and growth rate, then it must be present at all pattern speeds and growth rates. Our analysis — although falling short of a complete proof — suggests that such a two-dimensional continuum of non-axisymmetric modes does not occur and that the self-consistent power-law discs admit no global non-axisymmetric normal modes whatsoever. Without reflecting boundaries or cut-outs, there is no resonant cavity and no possibility of unstable growing modes. The self-consistent power-law discs certainly admit equi-angular spirals as neutral modes, together with a one-dimensional continuum of growing axisymmetric modes.  相似文献   

8.
We present Very Large Array H  i observations of the gas-rich, interacting spiral galaxies, NGC 1253/1253A (Arp 279). The larger of the two galaxies, NGC 1253, has a very pronounced H  i ring and well-defined spiral structure. The velocity structure of the H  i data shows a sudden change at the position of the spiral arms; we identify this change as evidence of a strong spiral shock and hence proceed to estimate the pattern speed, Ωp, of the spiral arms in NGC 1253. Assuming that the pattern speed is constant across the disc our derived value places the outer Lindblad resonance (OLR) at the position of the observed H  i ring. As an accumulation of gas is expected at the OLR when this falls within the disc of a galaxy this agreement provides independent support for the derived value of Ωp.  相似文献   

9.
We study the excitation of density and bending waves and the associated angular momentum transfer in gaseous discs with finite thickness by a rotating external potential. The disc is assumed to be isothermal in the vertical direction and has no self-gravity. The disc perturbations are decomposed into different modes, each characterized by the azimuthal index m and the vertical index n , which specifies the nodal number of the density perturbation along the disc normal direction. The   n = 0  modes correspond to the two-dimensional density waves previously studied by Goldreich & Tremaine and others. In a three-dimensional disc, waves can be excited at both Lindblad resonances (LRs; for modes with   n = 0, 1, 2, …  ) and vertical resonances (VRs; for the   n ≥ 1  modes only). The torque on the disc is positive for waves excited at outer Lindblad/vertical resonances and negative at inner Lindblad/vertical resonances. While the   n = 0  modes are evanescent around corotation, the   n ≥ 1  modes can propagate into the corotation region where they are damped and deposit their angular momenta. We have derived analytical expressions for the amplitudes of different wave modes excited at LRs and/or VRs and the resulting torques on the disc. It is found that for   n ≥ 1  , angular momentum transfer through VRs is much more efficient than LRs. This implies that in some situations (e.g. a circumstellar disc perturbed by a planet in an inclined orbit), VRs may be an important channel of angular momentum transfer between the disc and the external potential. We have also derived new formulae for the angular momentum deposition at corotation and studied wave excitations at disc boundaries.  相似文献   

10.
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.  相似文献   

11.
Linear transient phenomena induced by flow non-normality in thin self-gravitating astrophysical discs are studied using the shearing sheet approximation. The considered system includes two modes of perturbations: vortex and (spiral density) wave. It is shown that self-gravity considerably alters the vortex mode dynamics; its transient (swing) growth may be several orders of magnitude stronger than in the non-self-gravitating case and two to three times larger than the transient growth of the wave mode. Based on this finding, we comment on the role of vortex mode perturbations in a gravitoturbulent state. We also describe the linear coupling of the perturbation modes, caused by the differential character of disc rotation. The coupling is asymmetric: vortex mode perturbations are able to excite wave mode perturbations, but not vice versa. This asymmetric coupling lends additional significance to the vortex mode as a participant in spiral density waves and shock manifestations in astrophysical discs.  相似文献   

12.
When a supermassive black hole exists in the centre of a galaxy, an additional inner Lindblad resonance (ILR) exists inside the usual ILRs. We study gas dynamics in a weakly barred potential with a central supermassive black hole by using 2D numerical simulations, and we investigate the effect of the additional ILR on the fuelling of gas into nuclear starburst regions or active galactic nuclei (AGNs). Our numerical results show that strong trailing spiral shocks are formed at the resonance region, and that the gas in the shock region is rapidly fuelled into a central region and makes a nuclear gas ring. As a result, a large amount of gas is concentrated in the nuclear region beyond the ILR in a dynamical time-scale.  相似文献   

13.
We have investigated the gas and stellar kinematics and the stellar population properties at the center of the early-type galaxy NGC 4245 with a large-scale bar by the method of two-dimensional spectroscopy. The galaxy has been found to possess a pronounced chemically decoupled compact stellar nucleus, which is at least a factor of 2.5 richer in metals than the stellar population of the bulge, and a ring of young stars with a radius of 300 pc. Star formation goes on in the ring even now; its location corresponds to the inner Lindblad resonance of the large-scale bar. According to Hubble Space Telescope data, the mean stellar age in the chemically decoupled nucleus is significantly younger than that within 0″.25 of the center. It may be concluded that we take the former ultracompact star formation ring with a radius of no more than 100 pc located at the inner Lindblad resonance of the now disappeared nuclear bar as the chemically decoupled nucleus. On the whole, the picture of star formation at the center of this gas-poor galaxy is consistent with theoretical predictions of the consequences of the secular evolution of a stellar-gaseous disk under the action of a bar or bars.  相似文献   

14.
Using the method of two-dimensional spectroscopy, we have investigated the kinematics and distribution of the gas and stars at the center of the early-type spiral galaxy NGC 7177 with a mediumscale bar as well as the change in the mean age of the stellar population along the radius. A classical picture of radial gas inflow to the galactic center along the shock fronts delineated by dust concentration at the leading edges of the bar has been revealed. The gas inflow is observed down to a radius R = 1″.5−2″, where the gas flows at the inner Lindblad resonance concentrate in an azimuthally highly inhomogeneous nuclear star formation ring. The bar in NGC 7177 is shown to be thick in z coordinate—basically, it has already turned into a pseudo-bulge as a result of secular dynamical evolution. The mean stellar age inside the star formation ring, in the galactic nucleus, is old, ∼10 Gyr.Outside, at a distance R = 6″−8″ from the nucleus, the mean age of the stellar population is ∼2 Gyr. If we agree that the bar in NGC 7177 is old, then, obviously, the star formation ring has migrated radially inward in the last 1–2 Gyr, in accordance with the predictions of some dynamical models.  相似文献   

15.
We investigate the MHD waves in a double magnetic flux tube embedded in a uniform external magnetic field. The tube consists of a dense hot cylindrical cord surrounded by a co-axial shell. The plasma and the magnetic field are taken to be uniform inside the cord and also inside the shell. Two slow and two fast magnetosonic modes can exist in the thin double tube. The first slow mode is trapped by the cord, the other is trapped by the shell. The oscillations of the second mode have opposite phases inside the cord and shell. The speeds of the slow modes propagating along the tube are close to the tube speeds inside the cord and the shell. The behavior of the fast modes depends on the magnitude of Alfvén speed inside the shell. If it is less than the Alfvén speed inside the cord and in the environment, then the fast mode is trapped by the shell and the other may be trapped under the certain conditions. In the opposite case when the Alfvén speed in the shell is greater than those inside the cord and in the environment, then the fast mode is radiated by the tube and the other may also be radiated under certain conditions. The oscillation of the cord and the shell with opposite phases is the distinctive feature of the process. The proposed model allows to explain the basic phenomena connected to the coronal oscillations: i) the damping of oscillations stipulated in the double tube model by the radiative loss, ii) the presence of two different modes of perturbations propagating along the loop with close speeds, iii) the opposite phases of oscillations of modulated radio emission, coming from the near coronal sources having sharply different densities.  相似文献   

16.
W. Dziembowski 《Solar physics》1983,82(1-2):259-266
It is shown that in consequence of the parametric resonance, g modes of low spherical harmonic degree l are strongly coupled to the modes of high degree. The coupling limits the growth of low l modes to very small amplitudes. For g 1, l = 1 mode, the final amplitude of the radial velocity is of the order of 10 cm s-1. A mixing of solar core as a result of a finite-amplitude development of linear instability of this mode is thus highly unlikely.  相似文献   

17.
An important and widely neglected aspect of the interaction between an accretion disc and a massive companion with a coplanar orbit is the vertical component of the tidal force. As shown by Lubow, the response of the disc to vertical forcing is resonant at certain radii, at which a localized torque is exerted, and from which a compressive wave (p mode) may be emitted. Although these vertical resonances are weaker than the corresponding Lindblad resonances, the   m =2  inner vertical resonance in a binary star is typically located within the tidal truncation radius of a circumstellar disc.
In this paper I develop a general theory of vertical resonances, allowing for non-linearity of the response, and dissipation by radiative damping and turbulent viscosity. The problem is reduced to a universal, non-linear ordinary differential equation with two real parameters. Solutions of the complex non-linear Airy equation are presented to illustrate the non-linear saturation of the resonance and the effects of dissipation. It is argued that the   m =2  inner vertical resonance is unlikely to truncate the disc in cataclysmic variable stars, but contributes to angular momentum transport and produces a potentially observable non-axisymmetric structure.  相似文献   

18.
This paper presents an analytical study of the longitudinal dynamics of a thrusting, lifting, orbital vehicle in a nearly circular orbit. The translational motion is composed of a nonlinear oscillation, or phugoid, and a spiral mode which results in either decay or dilatation of the orbit depending on the perturbed initial conditions. The nonlinear effects on the phugoid period and damping are small in the altitude range considered. Elements of the orbit such as radial distance, velocity, and flight path angle were obtained explicitly as functions of time. The behavior of the variations of these elements is correctly predicted. Explicit expressions for period and damping of the angle-of-attack mode were derived. It is shown that a critical altitude may exist at which the phugoid mode and the angle-of-attack mode have nearly equal periods. Near this resonance altitude linearized solutions are no longer valid and a study of the nonlinear equations shows that there is a strong interactions between the translational and the rotational modes resulting in a switching of the two frequencies of oscillations.This work was supported by NASA Contract No. NASr 54(06).  相似文献   

19.
We study global non-axisymmetric oscillation modes trapped near the inner boundary of an accretion disc. Observations indicate that some of the quasi-periodic oscillations (QPOs) observed in the luminosities of accreting compact objects (neutron stars, black holes and white dwarfs) are produced in the innermost regions of accretion discs or boundary layers. Two simple models are considered in this paper. The magnetosphere–disc model consists of a thin Keplerian disc in contact with a uniformly rotating magnetosphere with and low plasma density, while the star–disc model involves a Keplerian disc terminated at the stellar atmosphere with high density and small density scaleheight. We find that the interface modes at the magnetosphere–disc boundary are generally unstable due to Rayleigh–Taylor and/or Kelvin–Helmholtz instabilities. However, differential rotation of the disc tends to suppress Rayleigh–Taylor instability, and a sufficiently high disc sound speed (or temperature) is needed to overcome this suppression and to attain net mode growth. On the other hand, Kelvin–Helmholtz instability may be active at low disc sound speeds. We also find that the interface modes trapped at the boundary between a thin disc and an unmagnetized star do not suffer Rayleigh–Taylor or Kelvin–Helmholtz instability, but can become unstable due to wave leakage to large disc radii and, for sufficiently steep disc density distributions, due to wave absorption at the corotation resonance in the disc. The non-axisymmetric interface modes studied in this paper may be relevant to the high-frequency QPOs observed in some X-ray binaries and in cataclysmic variables.  相似文献   

20.
The study of standing accretion shock instability (SASI) in core-collapse supernova cores has been done with three-dimensional (3D) computer simulations. Rotations with various perturbations were introduced from outer boundary of an initial steady accreting flow. We found that one or two armed spiral accreting flow onto the proto-neutron star (PNS) is formed inside the shock wave depending on perturbations. The linear growth of spiral modes are clearly diagnosed by the mode analysis of the shock surface, and the lower m modes grow quickly in the linear regime.  相似文献   

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