301 research outputs found
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.
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 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 and
. The best fit model consists of 75\% of stars rotating
around the short axis and 25\% of stars rotating around the long axis .
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.
The dynamics of planetary nebulae in the Galaxy: evidence for a third integral
We present a dynamical analysis of 673 galactic Planetary Nebulae, using a
two-integral axisymmetric model with a Kuzmin-Kutuzov St\"{a}ckel potential.
The method fits the kinematics to the projected moments of a distribution
function, by means of Quadratic Programming. The 2.2 m COBE brightness map
has been used after correction for the interstellar extinction as a projected
star counts map in the modeling, because it constitutes a galactic distribution
view of evolved red populations which are considered to be the progenitors of
PNe. The model we have obtained provides a 2-integral distribution function for
the COBE 2.2 m map, and thus {\it a fortiori} a deprojection of it, which
allows moreover the identification of all the major Galactic components. We
derive the density laws for them. The projected velocity dispersions are not
well fitted though, especially in the disk, which points at the likely presence
of a third integral. If this result can be confirmed by additional data, this
would mean that for the first time the presence and importance of a third
integral on a global scale is demonstrated.Comment: 9 pages, uuencoded gzipped postscript file, 9 figures include
Dynamical streams in the solar neighbourhood
The true nature of the Hyades and Sirius superclusters is still an open
question. In this contribution, we confront Eggen's hypothesis that they are
cluster remnants with the results of a kinematic analysis of more than 6000 K
and M giants in the solar neighbourhood. This analysis includes new radial
velocity data from a large survey performed with the Coravel spectrometer,
complemented by Hipparcos parallaxes and Tycho-2 proper motions (Famaey et al.
2004). A maximum-likelihood method, based on a bayesian approach, has been
applied to the data, in order to make full use of all the available data
(including less precise parallaxes) and to derive the properties of the
different kinematic subgroups. Two such subgroups can be identified with the
Hyades and Sirius superclusters. Stars belonging to them span a very wide range
of age, which is difficult to account for in Eggen's scenario. These groups are
thus most probably "dynamical streams" related to the dynamical perturbation by
spiral waves rather than to cluster remnants.
In this scenario, the Hyades and Ursa Major clusters just happen to be in the
Hyades and Sirius streams, which are purely dynamical features that have
nothing to do with the remnants of more massive primordial clusters. This
mechanism could be the key to understanding the presence of an old metal-rich
population, and of many exoplanetary systems in our neighbourhood. Moreover, a
strong spiral pattern seems to be needed in order to yield such prominent
streams. Since spiral structure is usually baryonic, this would leave very
little room for dark matter. This may be an indication that the era of the
dark-matter paradigm explaining the dynamics of the Galaxy may come to an end,
and is being superseded by modified gravity.Comment: 5 pages, 1 figure, to appear in The Three Dimensional Universe with
GAIA, eds M. Perryman & C. Turo
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
The Compression of Dark Matter Halos by Baryonic Infall
The initial radial density profiles of dark matter halos are laid down by
gravitational collapse in hierarchical structure formation scenarios and are
subject to further compression as baryons cool and settle to the halo centers.
We here describe an explicit implementation of the algorithm, originally
developed by Young, to calculate changes to the density profile as the result
of adiabatic infall in a spherical halo model. Halos with random motion are
more resistant to compression than are those in which random motions are
neglected, which is a key weakness of the simple method widely employed.
Young's algorithm results in density profiles in excellent agreement with those
from N-body simulations. We show how the algorithm may be applied to determine
the original uncompressed halos of real galaxies, a step which must be computed
with care in order to enable a confrontation with theoretical predictions from
theories such as LCDM.Comment: Revised version for ApJ. 8 pages, 8 figures, latex uses emulateap
Kinematic deprojection and mass inversion of spherical systems of known velocity anisotropy
Traditionally, the mass / velocity anisotropy degeneracy (MAD) inherent in
the spherical, stationary, non-streaming Jeans equation has been handled by
assuming a mass profile and fitting models to the observed kinematical data.
Here, the opposite approach is considered: the equation of anisotropic
kinematic projection is inverted for known arbitrary anisotropy to yield the
space radial velocity dispersion profile in terms of an integral involving the
radial profiles of anisotropy and isotropic dynamical pressure. Then, through
the Jeans equation, the mass profile is derived in terms of double integrals of
observable quantities. Single integral formulas for both deprojection and mass
inversion are provided for several simple anisotropy models (isotropic, radial,
circular, general constant, Osipkov-Merritt, Mamon-Lokas and
Diemand-Moore-Stadel). Tests of the mass inversion on NFW models with these
anisotropy models yield accurate results in the case of perfect observational
data, and typically better than 70% (in 4 cases out of 5) accurate mass
profiles for the sampling errors expected from current observational data on
clusters of galaxies. For the NFW model with mildly increasing radial
anisotropy, the mass is found to be insensitive to the adopted anisotropy
profile at 7 scale radii and to the adopted anisotropy radius at 3 scale radii.
This anisotropic mass inversion method is a useful complementary tool to
analyze the mass and anisotropy profiles of spherical systems. It provides the
practical means to lift the MAD in quasi-spherical systems such as globular
clusters, round dwarf spheroidal and elliptical galaxies, as well as groups and
clusters of galaxies, when the anisotropy of the tracer is expected to be
linearly related to the slope of its density.Comment: Accepted in MNRAS. 19 pages. Minor changes from previous version:
Table 1 of nomenclature, some math simplifications, paragraph in Discussion
on alternative deprojection method by deconvolution. 19 pages. 6 figure
On the kinematic deconvolution of the local neighbourhood luminosity function
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 r\'egimes: the singular ellipsoid, the constant ratio
Schwarzschild ellipsoid plane parallel models and the epicyclic model. This
more realistic model is taylored to account for local neighbourhood density and
velocity distribution.
The first model is fully investigated both analytically and via 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 via a 5D+2D
non-parametric inversion technique where positivity of the underlying
luminosity function is explicitely 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 the vertical
potential, and/or the asymmetric drift or w_0 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
disk from the thick disk or the halo.Comment: 18 pages, LateX (or Latex, etc), mnras, accepted for publicatio
Triaxial orbit based galaxy models with an application to the (apparent) decoupled core galaxy NGC 4365
We present a flexible and efficient method to construct triaxial dynamical
models of galaxies with a central black hole, using Schwarzschild's orbital
superposition approach. Our method is general and can deal with realistic
luminosity distributions, which project to surface brightness distributions
that may show position angle twists and ellipticity variations. The models are
fit to measurements of the full line-of-sight velocity distribution (wherever
available). We verify that our method is able to reproduce theoretical
predictions of a three-integral triaxial Abel model. In a companion paper (van
de Ven, de Zeeuw & van den Bosch), we demonstrate that the method recovers the
phase-space distribution function. We apply our method to two-dimensional
observations of the E3 galaxy NGC 4365, obtained with the integral-field
spectrograph SAURON, and study its internal structure, showing that the
observed kinematically decoupled core is not physically distinct from the main
body and the inner region is close to oblate axisymmetric.Comment: 21 Pages, 14 (Colour) Figures, Companion paper is arXiv:0712.0309
Accepted to MNRAS. Full resolution version at
http://www.strw.leidenuniv.nl/~bosch/papers/RvdBosch_triaxmethod.pd
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