On the kinematic signature of a central Galactic bar in observed star samples

A quasi self-consistent model for a barred structure in the central regions of our Galaxy is used to calculate the signature of such a triaxial structure on the kinematical properties of star samples. We argue that, due to the presence of a velocity dispersion, such effects are much harder to detect in the stellar component than in the gas. It might be almost impossible to detect stellar kinematical evidence for a bar using only l-v diagrams, if there is no a priori knowledge of the potential. Therefore, we propose some test parameters that can easily be applied to observed star samples, and that also incorporate distances or proper motions. We discus the diagnostic power of these tests as a function of the sample size and the bar strength. We conclude that about 1000 stars would be necessary to diagnose triaxiality with some statistical confidence.Comment: 9 pages + 8 PS figures, uses aas2pp4.sty. Accepted by Ap

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

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 &

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

Realistic error estimates on kinematic parameters

Current error estimates on kinematic parameters are based on the assumption that the data points in the spectra follow a Poisson distribution. For realistic data that have undergone several steps in a reduction process, this is generally not the case. Neither is the noise distribution independent in adjacent pixels. Hence, the error estimates on the derived kinematic parameters will (in most cases) be smaller than the real errors. In this paper we propose a method that makes a diagnosis of the characteristics of the observed noise The method also offers the possibility to calculate more realistic error estimates on kinematic parameters. The method was tested on spectroscopic observations of NGC3258. In this particular case, the realistic errors are almost a factor of 2 larger than the errors based on least squares statistics.Comment: 11 pages, 11 figures, accepted for publication by MNRA

The Pattern Speed of the Galactic Bar

Most late-type stars in the solar neighborhood have velocities similar to the local standard of rest (LSR), but there is a clearly separated secondary component corresponding to a slower rotation and a mean outward motion. Detailed simulations of the response of a stellar disk to a central bar show that such a bi-modality is expected from outer-Lindblad resonant scattering. When constraining the run of the rotation curve by the proper motion of Sgr A* and the terminal gas velocities, the value observed for the rotation velocity separating the two components results in a value of (53+/-3)km/s/kpc for the pattern speed of the bar, only weakly dependent on the precise values for Ro and bar angle phi.Comment: 5 pages LaTeX, 2 Figs, accepted for publication in ApJ Letter

Unstable Disk Galaxies. I. Modal Properties

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear eigenvalue problem which is solved using standard numerical methods. I apply the method to the dynamics of a model stellar disk which is embedded in the field of a soft-centered logarithmic potential. The outcome is the full spectrum of eigenfrequencies and their conjugate normal modes for prescribed azimuthal wavenumbers. The results show that the fundamental bar mode is isolated in the frequency space while spiral modes belong to discrete families that bifurcate from the continuous family of van Kampen modes. The population of spiral modes in the bifurcating family increases by cooling the disk and declines by increasing the fraction of dark to luminous matter. It is shown that the variety of unstable modes is controlled by the shape of the dark matter density profile.Comment: Accepted for publication in The Astrophysical Journa

The Effect of the Outer Lindblad Resonance of the Galactic Bar on the Local Stellar Velocity Distribution

Hydro-dynamical modeling of the inner Galaxy suggest that the radius of the outer Lindblad resonance (OLR) of the Galactic bar lies in the vicinity of the Sun. How does this resonance affect the distribution function in the outer parts of a barred disk, and can we identify any effect of the resonance in the velocity distribution f(v) actually observed in the solar neighborhood? To answer these questions, detailed simulations of f(v) in the outer parts of an exponential stellar disks with nearly flat rotation curves and a rotating central bar have been performed. For a model resembling the old stellar disk, the OLR causes a distinct feature in f(v) over a significant fraction of the outer disk. For positions <2kpc outside the OLR radius and at bar angles of \~10-70 degrees, f(v) inhibits a bi-modality between the low-velocity stars moving like the local standard of rest (LSR) and a secondary mode of stars predominantly moving outward and rotating more slowly than the LSR. Such a bi-modality is indeed present in f(v) inferred from the Hipparcos data for late-type stars in the solar neighborhood. If one interpretes this observed bi-modality as induced by the OLR -- and there are hardly any viable alternatives -- then one is forced to deduce that the OLR radius is slightly smaller than Ro. Moreover, by a quantitative comparison of the observed with the simulated distributions one finds that the pattern speed of the bar is 1.85+/-0.15 times the local circular frequency, where the error is dominated by the uncertainty in bar angle and local circular speed. Also other, less prominent but still significant, features in the observed f(v) resemble properties of the simulated velocity distributions, in particular a ripple caused by orbits trapped in the outer 1:1 resonance.Comment: 14 pages, 10 figures (Fig.2 in full resolution available upon request), accepted for publication in A