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 &

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

The Three-Dimensional Mass Distribution in NGC 1700

A variety of modeling techniques is used with surface photometry from the literature and recently acquired high-accuracy stellar kinematic data to constrain the three-dimensional mass distribution in the luminous cuspy elliptical galaxy NGC 1700. First, we model the radial velocity field and photometry, and, using a Bayesian technique, estimate the triaxiality T and short-to-long axis ratio c in five concentric annuli between approximately 1 and 3 effective radii. The results are completely consistent with T being constant inside about 2.5 r_e (36 arcsec; 6.7/h kpc). Adding an assumption of constant T as prior information gives an upper limit of T < 0.16 (95% confidence); this relaxes to T < 0.22 if it is also assumed that there is perfect alignment between the angular momentum and the galaxy's intrinsic short axis. Near axisymmetry permits us then to use axisymmetric models to constrain the radial mass profile. Using the Jeans (moment) equations, we demonstrate that 2-integral, constant-M/L models cannot fit the data; but a 2-integral model in which the cumulative enclosed M/L increases by a factor of roughly 2 from the center out to 12/h kpc can. Three-integral models constructed by quadratic programming show that, in fact, no constant-M/L model is consistent with the kinematics. Anisotropic 3-integral models with variable M/L, while not uniquely establishing a minimum acceptable halo mass, imply, as do the moment models, a cumulative M/L_B approximately 10 h at 12/h kpc. We conclude that NGC 1700 represents the best stellar dynamical evidence to date for dark matter in elliptical galaxies.Comment: 26 pages, Latex, AASTeX v4.0, with 11 eps figures. To appear in The Astronomical Journal, January 1999. Figures 1 and 3 are color but are readable in b/

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

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

Upper limits on the central black hole masses of 47Tuc and NGC6397

We present upper-limits on the masses of the putative central intermediate-mass black holes in two nearby Galactic globular clusters: 47Tuc (NGC104), the second brightest Galactic globular cluster, and NGC6397, a core-collapse globular cluster and, with a distance of 2.7 kpc, quite possibly the nearest globular cluster, using a technique suggested by T. Maccarone. These mass estimates have been derived from 3sigma upper limits on the radio continuum flux at 1.4 GHz, assuming that the putative central black hole accretes the surrounding matter at a rate between 0.1% and 1% of the Bondi accretion rate. For 47Tuc, we find a 3sigma upper limit of 2060 - 670 solar masses, depending on the actual accretion rate of the black hole and the distance to 47Tuc. For NGC6397, which is closer to us, we derive a 3sigma upper limit of 1290 - 390 solar masses. While estimating mass upper-limits based on radio continuum observations requires making assumptions about the gas density and the accretion rate of the black hole, their derivation does not require complex and time consuming dynamical modeling. Thus, this method offers an independent way of estimating black hole masses in nearby globular clusters. If, generally, central black holes in stellar systems accrete matter faster than 0.1% of the Bondi accretion rate, then these results indicate the absence of black holes in these globular clusters with masses as predicted by the extrapolated M-sigma relation.Comment: 4 pages, 1 figure, accepted for publication by MNRA

Kinematics of elliptical galaxies with a diffuse dust component

Observations show that early-type galaxies contain a considerable amount of interstellar dust, most of which is believed to exist as a diffusely distributed component. We construct a four-parameter elliptical galaxy model in order to investigate the effects of such a smooth absorbing component on the projection of kinematic quantities, such as the line profiles and their moments. We investigate the dependence on the optical depth and on the dust geometry. Our calculations show that both the amplitude and the morphology of these quantities can be significantly affected. Dust effects should therefore be taken in consideration when interpreting photometric and kinematic properties, and correlations that utilize these quantities.Comment: 12 pages, 9 figures, accepted for publication in MNRA