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1.
The power-law discs are a family of infinitesimally thin, axisymmetric stellar discs of infinite extent. The rotation curve can be rising, falling or flat. The self-consistent power-law discs are scale-free, so that all physical quantities vary as a power of radius. They possess simple equilibrium distribution functions depending on the two classical integrals, energy and angular momentum. While maintaining the scale-free equilibrium force law, the power-law discs can be transformed into cut-out discs by preventing stars close to the origin (and sometimes also at large radii) from participating in any disturbance. This paper derives the homogeneous Fredholm integral equation for the in-plane normal modes in the self-consistent and the cut-out power-law discs. This is done by linearizing the collisionless Boltzmann equation to find the response density corresponding to any imposed density and potential. The normal modes — that is, the self-consistent modes of oscillation — are found by requiring the imposed density to equal the response density. In practice, this scheme is implemented in Fourier space, by decomposing both imposed and response densities in logarithmic spirals. The Fredholm integral equation then relates the transform of the imposed density to the transform of the response density. Numerical strategies to solve the integral equation and to isolate the growth rates and the pattern speeds of the normal modes are discussed.  相似文献   

2.
We use three-integral models to infer the distribution function (DF) of the boxy E3–E4 galaxy NGC 1600 from surface brightness and line-profile data on the minor and major axes. We assume axisymmetry and that the mass-to-light ratio is constant in the central ∼1 R e. Stars in the resulting gravitational potential move mainly on regular orbits. We use an approximate third integral K from perturbation theory and write the DF as a sum of basis functions in the three integrals E , L z and K . We then fit the projected moments of these basis functions to the kinematic observables and deprojected density, using a non-parametric algorithm. The deduced dynamical structure is radially anisotropic, with σ θ σ r ≈ σ φ σ r ≈0.7 on the major axis. Both on the minor axis and near the centre the velocity distribution is more isotropic; thus the model is flattened by equatorial radial orbits. The kinematic data are fitted without the need for a central black hole; the central mass determined previously from ground-based data therefore overestimates the actual black-hole mass. The mass-to-light ratio of the stars is M L V =6  h 50. The anisotropy structure of NGC 1600 with a radially anisotropic main body and more nearly isotropic centre is similar to that found recently in NGC 1399, 2434, 3379 and 6703, suggesting that this pattern may be common amongst massive elliptical galaxies. We discuss a possible merger origin of NGC 1600 in the light of these results.  相似文献   

3.
Galaxies acting as gravitational lenses are surrounded by, at most, a handful of images. This apparent paucity of information forces one to make the best possible use of what information is available to invert the lens system. In this paper, we explore the use of a genetic algorithm to invert in a non-parametric way strong lensing systems containing only a small number of images. Perhaps the most important conclusion of this paper is that it is possible to infer the mass distribution of such gravitational lens systems using a non-parametric technique. We show that including information about the null space (i.e. the region where no images are found) is prerequisite to avoid the prediction of a large number of spurious images, and to reliably reconstruct the lens mass density. While the total mass of the lens is usually constrained within a few per cent, the fidelity of the reconstruction of the lens mass distribution depends on the number and position of the images. The technique employed to include null space information can be extended in a straightforward way to add additional constraints, such as weak-lensing data or time-delay information.  相似文献   

4.
A method for inverting the statistical star counts equation, including proper motions, is presented; in order to break the degeneracy in that equation, it uses the supplementary constraints required by dynamical consistency. The inversion gives access to both the kinematics and the luminosity function of each population in three régimes: the singular ellipsoid, the constant ratio Schwarzschild ellipsoid plane-parallel models and the epicyclic model. This more realistic model is tailored to account for the local neighbourhood density and velocity distribution.
The first model is fully investigated, both analytically and by means of a non-parametric inversion technique, while the second model is shown to be formally its equivalent. The effect of noise and incompleteness in apparent magnitude is investigated. The third model is investigated by a     non-parametric inversion technique where positivity of the underlying luminosity function is explicitly accounted for.
It is argued that its future application to data such as the Tycho catalogue (and in the upcoming satellite GAIA ) could lead – provided that the vertical potential and or the asymmetric drift or w ⊙ are known – to a non-parametric determination of the local neighbourhood luminosity function without any reference to stellar evolution tracks. It should also yield the proportion of stars for each kinematic component and a kinematic diagnostic to split the thin disc from the thick disc or the halo.  相似文献   

5.
Photometry and long-slit spectroscopy are presented for a sample of six galaxies with a low surface-brightness stellar disc and a bulge. The characterizing parameters of the bulge and disc components were derived by means of a two-dimensional photometric decomposition of the images of the sample galaxies. Their surface-brightness distribution was assumed to be the sum of the contribution of a Sérsic bulge and an exponential disc, with each component being described by elliptical and concentric isophotes of constant ellipticity and position angle. The stellar and ionized-gas kinematics were measured along the major and minor axes in half of the sample galaxies, whereas the other half was observed only along two diagonal axes. Spectra along two diagonal axes were obtained also for one of the objects with major and minor axis spectra. The kinematic measurements extend in the disc region out to a surface-brightness level  μ R ≈ 24  mag arcsec−2, reaching in all cases the flat part of the rotation curve. The stellar kinematics turns out to be more regular and symmetric than the ionized-gas kinematics, which often shows the presence of non-circular, off-plane and non-ordered motions. This raises the question about the reliability of the use of the ionized gas as the tracer of the circular velocity in the modelling of the mass distribution, in particular in the central regions of low surface-brightness galaxies.  相似文献   

6.
We present a non-parametric technique to infer the projected mass distribution of a gravitational lens system with multiple strong-lensed images. The technique involves a dynamic grid in the lens plane on which the mass distribution of the lens is approximated by a sum of basis functions, one per grid cell. We used the projected mass densities of Plummer spheres as basis functions. A genetic algorithm then determines the mass distribution of the lens by forcing images of a single source, projected back on to the source plane, to coincide as well as possible. Averaging several tens of solutions removes the random fluctuations that are introduced by the reproduction process of genomes in the genetic algorithm and highlights those features common to all solutions. Given the positions of the images and the redshifts of the sources and the lens, we show that the mass of a gravitational lens can be retrieved with an accuracy of a few percent and that, if the sources sufficiently cover the caustics, the mass distribution of the gravitational lens can also be reliably retrieved. A major advantage of the algorithm is that it makes full use of the information contained in the radial images, unlike methods that minimize the residuals of the lens equation, and is thus able to accurately reconstruct also the inner parts of the lens.  相似文献   

7.
A new method is presented to obtain a non-parametric maximum likelihood estimate of the luminosity function and the selection function of a flux-limited redshift survey. The method parametrizes the selection function as a series of stepwise power laws and allows possible evolution of the luminosity function. We also propose a new technique to estimate the rate of evolution of the luminosity function. This is based on a minimization of the observed large-scale power with respect to the evolutionary model. We use an ensemble of mock surveys extracted from an N -body simulation to verify the power of this method. We apply our estimators to the 1.2-Jy survey of IRAS galaxies. We find a far-infrared luminosity function in good agreement with previously published results and evidence for rather strong evolution. If the comoving number density of IRAS galaxies is assumed to scale ∝ (1 +  z ) P , we estimate P  = 4.3 ± 1.4.  相似文献   

8.
We present a method for recovering the distribution functions of edge-on thin axisymmetric discs directly from their observable kinematic properties. The most generally observable properties of such a stellar system are the line-of-sight velocity distributions of the stars at different projected radii along the galaxy. If the gravitational potential is known, then the general two-integral distribution function can be reconstructed using the shapes of the high-velocity tails of these line-of-sight distributions. If the wrong gravitational potential is adopted, then a distribution function can still be constructed using this technique, but the low-velocity parts of the observed velocity distributions will not be reproduced by the derived dynamical model. Thus, the gravitational potential is also tightly constrained by the observed kinematics.  相似文献   

9.
We present the results of new radio interferometer H  i line observations for the merging galaxy pair NGC 4038/9 ('The Antennae'), obtained using the Australia Telescope Compact Array. The results improve substantially with respect to those of van der Hulst and show in detail the two merging galactic discs and the two tidal tails produced by their interaction. The small edge-on spiral dwarf galaxy ESO 572–G045 is also seen near the tip of the southern tail, but distinct from it. It shows no signs of tidal interaction. The northern tidal tail of the Antennae shows no H  i connection to the discs and has an extension towards the west. The southern tidal tail is continuous, with a prominent H  i concentration at its tip, roughly at the location of the tidal dwarf galaxy observed optically by Mirabel, Dottori & Lutz. Clear velocity structure is seen along the tidal tails and in the galactic discs. Radio continuum images at 20 and 13 cm are also presented, showing the discs in detail.  相似文献   

10.
We investigate the properties of satellite galaxies formed in N -body/SPH simulations of galaxy formation in the ΛCDM cosmology. The simulations include the main physical effects thought to be important in galaxy formation and, in several cases, produce realistic spiral discs. In total, a sample of nine galaxies of luminosity comparable to the Milky Way was obtained. At magnitudes brighter than the resolution limit,   MV =−12  , the luminosity function of the satellite galaxies in the simulations is in excellent agreement with data for the Local Group. The radial number density profile of the model satellites, as well as their gas fractions also match observations very well. In agreement with previous N -body studies, we find that the satellites tend to be distributed in highly flattened configurations whose major axis is aligned with the major axis of the (generally triaxial) dark halo. In two out of three systems with sufficiently large satellite populations, the satellite system is nearly perpendicular to the plane of the galactic disc, a configuration analogous to that observed in the Milk Way. The discs themselves are perpendicular to the minor axis of their host haloes in the inner parts, and the correlation between the orientation of the galaxy and the shape of the halo persists even out to the virial radius. However, in one case the disc's minor axis ends up, at the virial radius, perpendicular to the minor axis of the halo. The angular momenta of the galaxies and their host halo tend to be well aligned.  相似文献   

11.
The frequency of barred spiral galaxies as a function of redshift contains important information on the gravitational influence of stellar discs in their dark matter haloes and may also distinguish between contemporary theories for the origin of galactic bulges. In this paper we present a new quantitative method for determining the strength of barred spiral structure, and verify its robustness to redshift-dependent effects. By combining galaxy samples from the Hubble Deep Field North with newly available data from the Hubble Deep Field South, we are able to define a statistical sample of 46 low-inclination spiral systems with I 814 W<23.2 mag. Analysing the proportion of barred spiral galaxies seen as a function of redshift, we find a significant decline in the fraction of barred spirals with redshift. The redshift distribution of 22 barred and 24 non-barred spirals with suitable inclinations is inconsistent with their being drawn from the same distribution at the 99 per cent confidence level. The physical significance of this effect remains unclear, but several possibilities include dynamically hotter (or increasingly dark-matter-dominated) high-redshift discs, or an enhanced efficiency in bar destruction at high redshifts. By investigating the formation of the 'orthogonal' axis of Hubble's classification tuning fork, our result complements studies of evolution in the early–late sequence, and pushes to later epochs the redshift at which the Hubble classification sequence is observed to be in place.  相似文献   

12.
A new approach of the initial orbit determination for too-short-arc with angular measurements is implemented by building the probabilistic model in the solution space with the estimation of distribution algorithm. Without any assumption about distribution, the non-parametric kernel density estimation is employed in the model building. The method, unlike other evolutionary algorithms, such as the genetic algorithm and particle swarm optimization, considers the fitness as well as the characteristics of the solution space. Numerical experiments with real observations indicate that without any constraints, the proposed technique has a good performance for the observations of usual accuracy.  相似文献   

13.
We study the distribution of dark matter in dwarf spheroidal galaxies by modelling the moments of their line-of-sight velocity distributions. We discuss different dark matter density profiles, both cuspy and possessing flat density cores. The predictions are made in the framework of standard dynamical theory of two-component (stars and dark matter) spherical systems with different velocity distributions. We compare the predicted velocity dispersion profiles to observations in the case of Fornax and Draco dwarfs. For isotropic models the dark haloes with cores are found to fit the data better than those with cusps. Anisotropic models are studied by fitting two parameters, dark mass and velocity anisotropy, to the data. In this case all profiles yield good fits, but the steeper the cusp of the profile, the more tangential is the velocity distribution required to fit the data. To resolve this well-known degeneracy of density profile versus velocity anisotropy, we obtain predictions for the kurtosis of the line-of-sight velocity distribution for models found to provide best fits to the velocity dispersion profiles. It turns out that profiles with cores typically yield higher values of kurtosis which decrease more steeply with distance than the cuspy profiles, which will allow us to discriminate between the profiles once the kurtosis measurements become available. We also show that with present quality of the data the alternative explanation of velocity dispersions in terms of Modified Newtonian Dynamics cannot yet be ruled out.  相似文献   

14.
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   

15.
We investigate the dynamical response, in terms of disc size and rotation velocity, to mass loss by supernovae in the evolution of spiral galaxies. A thin baryonic disc having the Kuzmin density profile embedded in a spherical dark matter halo having a density profile proposed by Navarro, Frenk & White is considered. For the purpose of comparison, we also consider the homogeneous and   r −1  profiles for dark matter in a truncated spherical halo. Assuming for simplicity that the dark matter distribution is not affected by mass-loss from discs and the change of baryonic disc matter distribution is homologous, we evaluate the effects of dynamical response in the resulting discs. We found that the dynamical response only for an adiabatic approximation of mass-loss can simultaneously account for the rotation velocity and disc size as observed particularly in dwarf spiral galaxies, thus reproducing the Tully–Fisher relation and the size versus magnitude relation over the full range of magnitude. Furthermore, we found that the mean specific angular momentum in discs after the mass-loss becomes larger than that before the mass-loss, suggesting that the mass-loss would most likely occur from the central disc region where the specific angular momentum is low.  相似文献   

16.
We obtain a robust, non-parametric, estimate of the Hubble constant from the linear diameters and rotation velocities of galaxies in the recent KLUN sample, calibrated using Cepheid distances to Hubble Space Telescope Key Project galaxies. There are two key features that make our analysis considerably more robust than previous work. First, the method is independent of the spatial distribution of galaxies and is insensitive to Malmquist bias. It may, therefore, be applied to more distant samples than so-called 'plateau' methods – making it much less vulnerable to the impact of peculiar motions in the Local Supercluster. Secondly, we include information on the galaxy rotation velocities in a fully non-parametric manner: unlike the conventional Tully–Fisher relation we reconstruct a robust estimate of the cumulative distribution function of galaxy diameter at given rotation velocity, without requiring the assumption of, for example, a linear Tully–Fisher relation with symmetric Gaussian residuals.
Using this robust method we find H 0=65±6 km s−1 Mpc−1 from our analysis – in excellent agreement with many recent determinations of the Hubble parameter, although somewhat larger than previous results using galaxy diameters.  相似文献   

17.
We consider the sensitivity of the circular-orbit adiabatic contraction approximation to the baryon condensation rate and the orbital structure of dark matter haloes in the Λ cold dark matter (ΛCDM) paradigm. Using one-dimensional hydrodynamic simulations including the dark matter halo mass accretion history and gas cooling, we demonstrate that the adiabatic approximation is approximately valid even though haloes and discs may assemble simultaneously. We further demonstrate the validity of the simple approximation for ΛCDM haloes with isotropic velocity distributions using three-dimensional N -body simulations. This result is easily understood: an isotropic velocity distribution in a cuspy halo requires more circular orbits than radial orbits. Conversely, the approximation is poor in the extreme case of a radial orbit halo. It overestimates the response of a core dark matter halo, where radial orbit fraction is larger. Because no astronomically relevant models are dominated by low angular momentum orbits in the vicinity of the disc and the growth time-scale is never shorter than a dynamical time, we conclude that the adiabatic contraction approximation is useful in modelling the response of dark matter haloes to the growth of a disc.  相似文献   

18.
In order to test the basic equations believed to dictate the dynamics of disc galaxies, we present and analyse deep two-dimensional spectral data obtained using the PPAK integral field unit for the early-type spiral systems NGC 2273, NGC 2985, NGC 3898 and NGC 5533. We describe the care needed to obtain and process such data to a point where reliable kinematic measurements can be obtained from these observations, and a new more optimal method for deriving the rotational motion and velocity dispersions in such disc systems. The data from NGC 2273 and NGC 2985 show systematic variations in velocity dispersion with azimuth, as one would expect if the shapes of their velocity ellipsoids are significantly anisotropic, while the hotter discs in NGC 3898 and NGC 5533 appear to have fairly isotropic velocity dispersions. Correcting the rotational motion for asymmetric drift using the derived velocity dispersions reproduces the rotation curves inferred from emission lines reasonably well, implying that this correction is quite robust, and that the use of the asymmetric drift equation is valid. NGC 2985 is sufficiently close to face on for the data, combined with the asymmetric drift equation, to determine all three components of the velocity ellipsoid. The principal axes of this velocity ellipsoid are found to be in the ratio  σ z : σφ : σ R ≈ 0.7 : 0.7 : 1  , which shows unequivocally that this disc distribution function respects a third integral of motion. The ratio is also consistent with the predictions of epicyclic theory, giving some confidence in the application of this approximation to even fairly early-type disc galaxies.  相似文献   

19.
In this paper, we investigate the star formation and chemical evolution of damped Lyman α systems (DLAs) based on the disc galaxy formation model developed by Mo, Mao & White. We propose that the DLAs are the central galaxies of less-massive dark haloes present at redshifts z ∼3, and they should inhabit haloes of moderately low circular velocity. The empirical Schmidt law of star formation rates, and closed box model of chemical evolution that an approximation known as instantaneous recycling is assumed, are adopted. In our models, when the predicted distribution of metallicity for DLAs is calculated, two cases are considered. One is that, using the closed-box model, empirical Schmidt law and star formation time, the distribution of metallicity can be directly calculated. The other is that, when the simple gravitational instability of a thin isothermal gas disc as first discussed by Toomre is considered, the star formation occurs only in the region where the surface density of gas satisfies the critical value, not everywhere of a gas disc. In this case, we first obtain the region where the star formation can occur by assuming that the disc has a flat rotation curve and rotational velocity is equal to the circular velocity of the surrounding dark matter halo, and then calculate the metallicity distribution as in case one. We assume that star formation in each DLA lasts for a period of 1 Gyr from redshifts z =3. There is only one output parameter in our models, i.e. the stellar yield, which relates to the time of star formation history and is obtained by normalizing the predicted distribution of metallicity to the mean value of 1/13 Z⊙ as presented by Pettini et al.. The predicted metallicity distribution is consistent with the current (rather limited) observational data. A random distribution of galactic discs is taken into account.  相似文献   

20.
The shape of a galaxy is constrained both by mechanisms of formation (dissipational versus dissipationless) and by the available orbit families (the shape and amount of regular and stochastic orbits). It is shown that, despite the often very flattened shapes of banana and fish orbits, these boxlet orbits generally do not fit a triaxial galaxy in detail because, similar to loop orbits, they spend too little time at the major axis of the model density distribution. This constraint from the shape of fish orbits is relaxed at (large) radii where the density profile of a galaxy is steep.  相似文献   

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