282 research outputs found
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
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