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1.
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   

2.
We present a perturbation theory for studying the instabilities of non-axisymmetric gaseous discs. We perturb the dynamical equations of self-gravitating fluids in the vicinity of a non-axisymmetric equilibrium, and expand the perturbed physical quantities in terms of a complete basis set and a small non-axisymmetry parameter ε. We then derive a linear eigenvalue problem in matrix form, and determine the pattern speed, growth rate and mode shapes of the first three unstable modes. In non-axisymmetric discs, the amplitude and the phase angle of travelling waves are functions of both the radius R and the azimuthal angle φ. This is due to the interaction of different wave components in the response spectrum. We demonstrate that wave interaction in unstable discs, with small initial asymmetries, can develop dense clumps during the phase of exponential growth. Local clumps, which occur on the major spiral arms, can constitute seeds of gas giant planets in accretion discs.  相似文献   

3.
We discuss the stability of galactic discs in which the energy of interstellar clouds is gained in encounters with expanding supernova (SN) remnants and lost in inelastic collisions. Energy gain and loss processes introduce a phase difference between the pressure and density perturbations, making discs unstable on small scales for several recipes of star formation. This is in contrast to the standard stability analysis in which small-scale perturbations are stabilized by pressure. In the limit of small scales, the dispersion relation for the growth rate reduces to that of thermal instabilities in a fluid without gravity. If instabilities lead to star formation, then our results imply a secondary mode of star formation that operates on small scales and feeds on the existence of a primary mode on intermediate scales. This may be interpreted as positive feedback. Further, the standard stability criterion on intermediate scales is significantly modified.  相似文献   

4.
We show that the algorithm proposed by Gauss to compute the secular evolution of gravitationally interacting Keplerian rings extends naturally to softened gravitational interactions. The resulting tool is ideal for the study of the secular dynamical evolution of nearly Keplerian systems such as stellar clusters surrounding black holes in galactic nuclei, cometary clouds or planetesimal discs. We illustrate its accuracy, efficiency and versatility on a variety of configurations. In particular, we examine a secularly unstable system of counterrotating discs, and follow the unfolding and saturation of the instability into a global, uniformly precessing, lopsided  ( m = 1)  mode.  相似文献   

5.
We present three-dimensional smoothed particle hydrodynamics calculations of warped accretion discs in X-ray binary systems. Geometrically thin, optically thick accretion discs are illuminated by a central radiation source. This illumination exerts a non-axisymmetric radiation pressure on the surface of the disc, resulting in a torque that acts on the disc to induce a twist or warp. Initially planar discs are unstable to warping driven by the radiation torque and, in general, the warps also precess in a retrograde direction relative to the orbital flow. We simulate a number of X-ray binary systems which have different mass ratios, using a number of different luminosities for each. Radiation-driven warping occurs for all systems simulated. For mass ratios   q ∼ 0.1  a moderate warp occurs in the inner disc while the outer disc remains in the orbital plane (cf. X 1916−053). For less extreme mass ratios, the entire disc tilts out of the orbital plane (cf. Her X–1). For discs that are tilted out of the orbital plane in which the outer edge material of the disc is precessing in a prograde direction, we obtain both positive and negative superhumps simultaneously in the dissipation light curve (cf. V603 Aql).  相似文献   

6.
In the generic CDM cosmogony, dark-matter haloes emerge too lumpy and centrally concentrated to host observed galactic discs. Moreover, discs are predicted to be smaller than those observed. We argue that the resolution of these problems may lie with a combination of the effects of protogalactic discs, which would have had a mass comparable to that of the inner dark halo and be plausibly non-axisymmetric, and of massive galactic winds, which at early times may have carried off as many baryons as a galaxy now contains. A host of observational phenomena, from quasar absorption lines and intracluster gas through the G-dwarf problem, point to the existence of such winds. Dynamical interactions will homogenize and smooth the inner halo, and the observed disc will be the relic of a massive outflow. The inner halo expanded after absorbing energy and angular momentum from the ejected material. Observed discs formed at the very end of the galaxy formation process, after the halo had been reduced to a minor contributor to the central mass budget and strong radial streaming of the gas had died down.  相似文献   

7.
We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height.
We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.  相似文献   

8.
Angular momentum transport within young massive protoplanetary discs may be dominated by self-gravity at radii where the disc is too weakly ionized to allow the development of the magneto-rotational instability. We use time-dependent one-dimensional disc models, based on a local cooling time calculation of the efficiency of transport, to study the radial structure and stability (against fragmentation) of protoplanetary discs in which self-gravity is the sole transport mechanism. We find that self-gravitating discs rapidly attain a quasi-steady state in which the surface density in the inner disc is high and the strength of turbulence very low (  α∼ 10−3  or less inside 5 au). Temperatures high enough to form crystalline silicates may extend out to several astronomical units at early times within these discs. None of our discs spontaneously develop regions that would be unambiguously unstable to fragmentation into substellar objects, though the outer regions (beyond 20 au) of the most massive discs are close enough to the threshold that fragmentation cannot be ruled out. We discuss how the mass accretion rates through such discs may vary with disc mass and with mass of the central star, and note that a determination of the     relation for very young systems may allow a test of the model.  相似文献   

9.
The complex-shift method is applied to the Kuzmin–Toomre family of discs to generate a family of non-axisymmetric flat distributions of matter. These are then superposed to construct non-axisymmetric flat rings. We also consider triaxial potential–density pairs obtained from these non-axisymmetric flat systems by means of suitable transformations. The use of the imaginary part of complex-shifted potential–density pairs is also discussed.  相似文献   

10.
We study how well the complex gas velocity fields induced by massive spiral arms are modelled by the hydrodynamical simulations that we used recently to constrain the dark matter fraction in nearby spiral galaxies. More specifically, we explore the dependence of the positions and amplitudes of features in the gas flow on the temperature of the interstellar medium (assumed to behave as a one-component isothermal fluid), the non-axisymmetric disc contribution to the galactic potential, the pattern speed  Ωp  , and finally the numerical resolution of the simulation. We argue that, after constraining the pattern speed reasonably well by matching the simulations to the observed spiral arm morphology, the amplitude of the non-axisymmetric perturbation (the disc fraction) is left as the primary parameter determining the gas dynamics. However, owing to the sensitivity of the positions of the shocks to modelling parameters, one has to be cautious when quantitatively comparing the simulations to observations. In particular, we show that a global least-squares analysis is not the optimal method for distinguishing different models, as it tends to slightly favour low disc fraction models. Nevertheless, we conclude that, given observational data of reasonably high spatial resolution and an accurate shock-resolving hydro-code, this method tightly constrains the dark matter content within spiral galaxies. We further argue that, even if the perturbations induced by spiral arms are weaker than those of strong bars, they are better suited for this kind of analysis because the spiral arms extend to larger radii where effects like inflows due to numerical viscosity and morphological dependence on gas sound speed are less of a concern than they are in the centres of discs.  相似文献   

11.
A model for gas outflows is proposed which simultaneously explains the correlations between the (i) equivalent widths of low-ionization and Lyα lines, (ii) outflow velocity, and (iii) star formation rate observed in Lyman break galaxies (LBGs). Our interpretation implies that LBGs host short-lived (30 ± 5 Myr) starburst episodes observed at different evolutionary phases. Initially, the starburst powers a hot wind bound by a denser cold shell, which after ≈5 Myr becomes dynamically unstable and fragments; afterwards the fragment evolution is approximately ballistic while the hot bubble continues to expand. As the fragments are gravitationally decelerated, their screening ability of the starlight decreases as the ultraviolet (UV) starburst luminosity progressively dims. LBG observations sample all these evolutionary phases. Finally, the fragments fall back on to the galaxy after ≈60 Myr. This phase cannot be easily probed as it occurs when the starburst UV luminosity has already largely faded; however, galaxies dimmer in the UV than LBGs should show infalling gas.  相似文献   

12.
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   

13.
We examine the local stability of galactic discs against axisymmetric density perturbations with special attention to the different dynamics of the stellar and gaseous components. In particular, the discs of the Milky Way and of NGC 6946 are studied. The Milky Way is shown to be stable, whereas the inner parts of NGC 6946, a typical Sc galaxy from the Kennicutt sample, are dynamically unstable. The ensuing dynamical evolution of the composite disc is studied by numerical simulations. The evolution is so fierce that the stellar disc heats up dynamically on a short time-scale to such a high degree, which seems to contradict the morphological appearance of the galaxy. The star formation rate required to cool the disc dynamically is estimated. Even if the star formation rate in NGC 6946 is at present high enough to meet this requirement, it is argued that the discs of Sc galaxies cannot sustain such a high star formation rate for extended periods.  相似文献   

14.
Fluorescent iron line profiles currently provide the best diagnostic for engine geometries of active galactic nuclei (AGN). Here we construct a method for calculating the relativistic iron line profile from an arbitrarily warped accretion disc, illuminated from above and below by hard X-ray sources. This substantially generalizes previous calculations of reprocessing by accretion discs by including non-axisymmetric effects. We include a relativistic treatment of shadowing by ray-tracing photon paths along Schwarzschild geodesics. We apply this method to two classes of warped discs, and generate a selection of resulting line profiles. New profile features include a time-varying line profile if the warp precesses about the disc, profile differences between 'twisted' and 'twist-free' warps and the possibility of steeper red and softer blue fall-offs than for flat discs. We discuss some qualitative implications of the line profiles in the context of Type I and II Seyfert AGN and other sources.  相似文献   

15.
We present the results of collapse calculations for uniformly rotating, prolate clouds performed using the numerical method: smoothed particle hydrodynamics (SPH). The clouds considered are isothermal, prolate spheroids with different axial ratios ( a/b ), and with different values of β, the ratio of the rotational to gravitational energy. Small density perturbations are added to the clouds, and different initial perturbation spectra are studied. All of the clouds considered are strongly unstable to gravitational contraction, and so collapse to form a spindle configuration. Such a linear structure is unstable to fragmentation, so that the clouds break up into a number of subcondensations. The long-term evolution of the system is then determined by the angular momentum possessed by these fragments.
It is found that a number of the calculations performed result in the formation of orbitally stable binary systems, composed of two rotationally supported discs in orbit about their common centre of mass. Tidal interactions during closest approach, close three-body interactions and the continued accretion of material with high specific angular momentum are all found to increase the orbital separation during these calculations, ensuring that the systems do not merge at later times. The calculations are therefore relevant to the problem of binary star formation, though the systems produced tend to have large orbital separations and periods. One of the strong points of the models presented, however, is their ability to produce systems with a range of mass ratios and orbital eccentricities, without the explicit inclusion of biases in the initial conditions.  相似文献   

16.
《New Astronomy》2007,12(3):246-263
It is difficult to imagine a planet formation model that does not at some stage include a gravitationally unstable disc. Initially unstable gas–dust discs may form planets directly, but the high surface density required has motivated the alternative that gravitational instability occurs in a dust sub-layer only after grains have grown large enough by electrostatic sticking. Although such growth up to the instability stage is efficient for laminar discs, previous research concluded that realistic disc turbulence catastrophically increases the settling time, thereby requiring additional processes to facilitate planet formation on the needed time scales. We develop a different model for the influence of turbulence on the collisional velocity of grains and on the scale height of the dust layer and find that the earlier conclusions must be revisited. The model produces a disc-radius dependent time scale to reach a gravitationally unstable phase of planet formation. For a range of dust sticking and disc parameters, we find that for viscosity parameters α ⩽ 10−3, this time scale is short enough over a significant range in radii R that turbulence does not catastrophically slow the early phases of planet formation, even in the absence of agglomeration enhancement agents like vortices.  相似文献   

17.
Observations of turbulent velocity dispersions in the H  i component of galactic discs show a characteristic floor in galaxies with low star formation rates and within individual galaxies the dispersion profiles decline with radius. We carry out several high-resolution adaptive mesh simulations of gaseous discs embedded within dark matter haloes to explore the roles of cooling, star formation, feedback, shearing motions and baryon fraction in driving turbulent motions. In all simulations the disc slowly cools until gravitational and thermal instabilities give rise to a multiphase medium in which a large population of dense self-gravitating cold clouds are embedded within a warm gaseous phase that forms through shock heating. The diffuse gas is highly turbulent and is an outcome of large-scale driving of global non-axisymmetric modes as well as cloud–cloud tidal interactions and merging. At low star formation rates these processes alone can explain the observed H  i velocity dispersion profiles and the characteristic value of  ∼10 km s−1  observed within a wide range of disc galaxies. Supernovae feedback creates a significant hot gaseous phase and is an important driver of turbulence in galaxies with a star formation rate per unit area  ≳10−3 M⊙ yr−1 kpc−2  .  相似文献   

18.
We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density  Σ0∝ r −α  , a coplanar azimuthal magnetic field   B 0∝ r −γ  , a consistent self-gravity and a power-law rotation curve   v 0∝ r −β  , where v 0 is the linear azimuthal gas rotation speed. The barotropic equation of state  Π∝Σ n   is adopted for both MHD background equilibrium and coplanar MHD perturbations where Π is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among  α, β, γ  and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of  −1/4 < β < 1/2  . As an illustrative example, we discuss specifically the  β= 1/4  case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.  相似文献   

19.
The linear theory and N-body simulations are used to present a new, alternative model of the galaxy A0035-324 (the “Cartwheel”), which is the most striking example of the relatively small class of ring galaxies. The model is based on the gravitational Jeans-type instability of both axisymmetric (radial) and nonaxisymmetric (spiral) small-amplitude gravity perturbations (e.g., those produced by spontaneous disturbances) of a dynamically cold subsystem (identified as the gaseous component) of an isolated disk galaxy. The simplified model of a galaxy is used in which stars (and a dark matter, if it exists at all) do not participate in the disk collective oscillations and just form a background charge. In the theory presented here, a case for both purely radial solutions and purely spiral solutions to the equations of motion of an infinitesimally thin gaseous disk is made, which is associated with both a radial density wave and a dominant spiral density wave which propagate outwards creating a rough ring and a number of spiral arms. Through three-dimensional numerical simulation of a collisionless set of many particles, I associate these gravitationally unstable axisymmetric waves and nonaxisymmetric waves with growing clumps of matter which take on the appearance of a ring and spokes of mass blobs.  相似文献   

20.
The eclipsing nova-like cataclysmic variable star V348 Pup exhibits a persistent luminosity modulation with a period 6 per cent longer than its 2.44-h orbital period ( P orb). This has been interpreted as a 'positive superhump' resulting from a slowly precessing non-axisymmetric accretion disc gravitationally interacting with the secondary. We find a clear modulation of mid-eclipse times on the superhump period, which agrees well with the predictions of a simple precessing eccentric disc model. Our modelling shows that the disc light centre is on the far side of the disc from the donor star when the superhump reaches maximum light. This phasing suggests a link between superhumps in V348 Pup and late superhumps in SU UMa systems. Modelling of the full light curve and maximum entropy eclipse mapping both show that the disc emission is concentrated closer to the white dwarf at superhump maximum than at superhump minimum. We detect additional signals consistent with the beat periods between the implied disc precession period and both and  相似文献   

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