Numerical calculation of linear modes in stellar disks

We present a method for solving the two-dimensional linearized collisionless Boltzmann equation using Fourier expansion along the orbits. It resembles very much solutions present in the literature, but it differs by the fact that everything is performed in coordinate space instead of using action-angle variables. We show that this approach, though less elegant, is both feasible and straightforward. This approach is then incorporated in a matrix method in order to calculate self-consistent modes, using a set of potential-density pairs which is obtained numerically. We investigated the stability of some unperturbed disks having an almost flat rotation curve, an exponential disk and a non-zero velocity dispersion. The influence of the velocity dispersion, halo mass and anisotropy on the stability is further discussed.Comment: 12 pages LaTeX format, uses laa.tex (enclosed), 16 PostScript figures. tarred, gzipped, uuencoded. Postscript version available at ftp://naos.rug.ac.be/pub/LINMOD2.ps.Z Accepted for publication in A &

On the deprojection of triaxial galaxies with St\"ackel potentials

A family of triaxial St\"ackel potential-density pairs is introduced. With the help of a Quadratic Programming method, a linear combination of potential-density pairs of this family which fits a given projected density distribution can be built. This deprojection strategy can be used to model the potentials of triaxial elliptical galaxies with or without dark halos. Besides, we show that the expressions for the St\"ackel triaxial density and potential are considerably simplified when expressed in terms of divided differences, which are convenient numerically. We present an example of triaxial deprojection for the galaxy NGC~5128 whose photometry follows the de Vaucouleurs law.Comment: 8 pages, to appear in A&A, postscript file with figures available at ftp://naos.rug.ac.be/pub/deprojection.ps.

A method for solving the linearized Boltzmann equation for almost uniformly rotating stellar disks.

We construct analytical phase-space solutions for perturbations of flat disks by performing a power series expansion for the radius and the velocity coordinates. We show that this approach translates into an elegant mathematical formulation which is easy to use for a wide variety of distribution functions, for as far as resonances do not play a role, such as is the case for potentials which are close to quadratic. As a testcase, the method is applied on the Kalnajs disks. The results obtained are in full agreement with the analytical solutions of the mode analysis. The strongest advantages of this method are its independence of the mathematical complexity of the unperturbed distribution, the degree of detail with which the solutions can be calculated and its computational straightforwardness. On the contrary, power series solutions are not suitable for describing regions where resonant orbits occur, which we therefore exclude in this paper. We used the technique to analyse perturbations in the central regions of a galaxy, tracking the dynamical consequences of a Galactic bar on the kinematics of the solar neighbourhood (Hipparcos). We showed how the orientation and strength of the bar is related to the properties of the velocity ellipsoid in our model.Comment: 10 pages, PostScript file including figures, to appear in Astronomy and Astrophysic

Determination of the dynamical structure of galaxies using optical spectra

Galaxy spectra are a rich source of kinematical information since the shapes of the absorption lines reflect the movement of stars along the line-of-sight. We present a technique to directly build a dynamical model for a galaxy by fitting model spectra, calculated from a dynamical model, to the observed galaxy spectra. Using synthetic spectra from a known galaxy model we demonstrate that this technique indeed recovers the essential dynamical characteristics of the galaxy model. Moreover, the method allows a statistically meaningful error analysis on the resulting dynamical quantities.Comment: 14 pages, 14 figures, Latexfile, MNRAS, in pres

Probing the halo of Centaurus A: a merger dynamical model for the PN population

Photometry and kinematics of the giant elliptical galaxy NGC~5128 (Centaurus~A) based on planetary nebulae observations (Hui~\etal 1995) are used to build dynamical models which allow us to infer the presence of a dark matter halo. To this end, we apply a Quadratic Programming method. Constant mass-to-light ratio models fail to reproduce the major axis velocity dispersion measurements at large radii: the profile of this kind of models falls off too steeply when compared to the observations, clearly suggesting the necessity of including a dark component in the halo. By assuming a mass-to-light ratio which is increasing with radius, the model satisfactorily matches the observations. The total mass for the best fit model is $\sim4\times10^{11}M_\odot$ of which about 50\% is dark matter. However, models with different total masses and dark halos are also consistent with the data; we estimate that the total mass of Cen~A within 50~kpc may vary between $3\times10^{11}M_\odot$ and $5\times10^{11}M_\odot$. The best fit model consists of 75\% of stars rotating around the short axis $z$ and 25\% of stars rotating around the long axis $x$. Finally, the morphology of the projected velocity field is analyzed using Statler's classification criteria (Statler 1991). We find that the appearance of our velocity field is compatible with a type 'Nn' or 'Nd'.Comment: 13 pages, uuencoded compressed postscript, without figures. The full postscript version, including all 14 figures, is available via anonymous ftp at ftp://naos.rug.ac.be/pub/cena.ps.

Simulations of the formation and evolution of isolated dwarf galaxies

We present new fully self-consistent models of the formation and evolution of isolated dwarf galaxies. We have used the publicly available N-body/SPH code HYDRA, to which we have added a set of star formation criteria, and prescriptions for chemical enrichment (taking into account contributions from both SNIa and SNII), supernova feedback, and gas cooling. The models follow the evolution of an initially homogeneous gas cloud collapsing in a pre-existing dark-matter halo. These simplified initial conditions are supported by the merger trees of isolated dwarf galaxies extracted from the milli-Millennium Simulation. The star-formation histories of the model galaxies exhibit burst-like behaviour. These bursts are a consequence of the blow-out and subsequent in-fall of gas. The amount of gas that leaves the galaxy for good is found to be small, in absolute numbers, ranging between 3x10^7 Msol and 6x10^7 Msol . For the least massive models, however, this is over 80 per cent of their initial gas mass. The local fluctuations in gas density are strong enough to trigger star-bursts in the massive models, or to inhibit anything more than small residual star formation for the less massive models. Between these star-bursts there can be time intervals of several Gyrs. We have compared model predictions with available data for the relations between luminosity and surface brightness profile, half-light radius, central velocity dispersion, broad band colour (B-V) and metallicity, as well as the location relative to the fundamental plane. The properties of the model dwarf galaxies agree quite well with those of observed dwarf galaxies.Comment: 16 pages, 20 figures, accepted for publication in MNRA

A genetic algorithm for the non-parametric inversion of strong lensing systems

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 onto 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 minimise the residuals of the lens equation, and is thus able to accurately reconstruct also the inner parts of the lens.Comment: 11 pages, accepted for publication by MNRA

The stability of uniformly rotating stellar disks

We explore a series expansion method to calculate the modes of oscillations for a variety of uniformly rotating finite disks, either with or without a dark halo. Since all models have the same potential, this survey focuses on the role of the distribution function in stability analyses. We show that the stability behaviour is greatly influenced by the structure of the unperturbed distribution, particularly by its energy dependence. In addition we find that uniformly rotating disks with a halo in general can feature spiral-like instabilities

Three-component Stackel potentials satisfying recent estimates of Milky Way parameters

We present a set of three-component Stackel potentials defined by five parameters and designed to model the Milky Way. We review the fundamental constraints that any model of the Milky Way must satisfy, including the most recent ones derived from Hipparcos data, and we study how the parameters of the presented potentials can vary in order to match these constraints. Five different valid potentials are presented and analyzed in detail: they are designed to be confronted with kinematical surveys in the future, by the construction of three-integral analytic distribution functions.Comment: 13 pages, 5 figures, accepted for publication in MNRA