37 research outputs found
Two-integral Schwarzschild models
We describe a practical method for constructing axisymmetric two-integral
galaxy models (with distribution functions of the form f(E,L_z), in which E is
the orbital energy, and L_z is the vertical component of the angular momentum),
based on Schwarzschild's orbit superposition method. Other f(E,L_z)-methods are
mostly based on solving the Jeans equations or on finding the distribution
function directly from the density, which often places restrictions on the
shape of the galaxy. Here, no assumptions are made and any axisymmetric density
distribution is possible. The observables are calculated (semi-)analytically,
so that our method is faster than most previous, fully numerical
implementations. Various aspects are tested extensively, the results of which
apply directly to three-integral Schwarzschild methods. We show that a given
distribution function can be reproduced with high accuracy and investigate the
behaviour of the parameter that is used to measure the goodness-of-fit.
Furthermore, we show that the method correctly identifies the range of cusp
clopes for which axisymmetric two-integral models with a central black hole do
not exist.Comment: 10 pages, 9 figures, Accepted for publication in MNRA
The dynamical distance and intrinsic structure of the globular cluster omega Centauri
We determine the dynamical distance D, inclination i, mass-to-light ratio M/L
and the intrinsic orbital structure of the globular cluster omega Cen, by
fitting axisymmetric dynamical models to the ground-based proper motions of van
Leeuwen et al. and line-of-sight velocities from four independent data-sets. We
correct the observed velocities for perspective rotation caused by the space
motion of the cluster, and show that the residual solid-body rotation component
in the proper motions can be taken out without any modelling other than
assuming axisymmetry. This also provides a tight constraint on D tan i.
Application of our axisymmetric implementation of Schwarzschild's orbit
superposition method to omega Cen reveals no dynamical evidence for a
significant radial dependence of M/L. The best-fit dynamical model has a
stellar V-band mass-to-light ratio M/L_V = 2.5 +/- 0.1 M_sun/L_sun and an
inclination i = 50 +/- 4 degrees, which corresponds to an average intrinsic
axial ratio of 0.78 +/- 0.03. The best-fit dynamical distance D = 4.8 +/- 0.3
kpc (distance modulus 13.75 +/- 0.13 mag) is significantly larger than obtained
by means of simple spherical or constant-anisotropy axisymmetric dynamical
models, and is consistent with the canonical value 5.0 +/- 0.2 kpc obtained by
photometric methods. The total mass of the cluster is (2.5 +/- 0.3) x 10^6
M_sun. The best-fit model is close to isotropic inside a radius of about 10
arcmin and becomes increasingly tangentially anisotropic in the outer region,
which displays significant mean rotation. This phase-space structure may well
be caused by the effects of the tidal field of the Milky Way. The cluster
contains a separate disk-like component in the radial range between 1 and 3
arcmin, contributing about 4% to the total mass.Comment: 37 pages (23 figures), accepted for publication in A&A, abstract
abridged, for PS and PDF file with full resolution figures, see
http://www.strw.leidenuniv.nl/~vdven/oc
General solution of the Jeans equations for triaxial galaxies with separable potentials
The Jeans equations relate the second-order velocity moments to the density
and potential of a stellar system. For general three-dimensional stellar
systems, there are three equations and six independent moments. By assuming
that the potential is triaxial and of separable Staeckel form, the mixed
moments vanish in confocal ellipsoidal coordinates. Consequently, the three
Jeans equations and three remaining non-vanishing moments form a closed system
of three highly-symmetric coupled first-order partial differential equations in
three variables. These equations were first derived by Lynden-Bell, over 40
years ago, but have resisted solution by standard methods. We present the
general solution here.
We consider the two-dimensional limiting cases first. We solve their Jeans
equations by a new method which superposes singular solutions. The singular
solutions, which are new, are standard Riemann-Green functions. The
two-dimensional solutions are applied to non-axisymmetric discs, oblate and
prolate spheroids, and also to the scale-free triaxial limit. We then extend
the method of singular solutions to the triaxial case, and obtain a full
solution. The general solution can be expressed in terms of complete
(hyper)elliptic integrals which can be evaluated in a straightforward way, and
provides the full set of second moments which can support a triaxial density
distribution in a separable triaxial potential. (abridged)Comment: 28 pages (7 figures), LaTeX MN2e, accepted for publication in MNRA
SAURON Observations of Disks in Spheroids
The panoramic integral-field spectrograph SAURON is currently being used to
map the stellar kinematics, gaseous kinematics, and stellar populations of a
large number of early-type galaxies and bulges. Here, we describe SAURON
observations of cold stellar disks embedded in spheroids (NGC3384, NGC4459,
NGC4526), we illustrate the kinematics and ionization state of large-scale
gaseous disks (NGC4278, NGC7742), and we show preliminary comparisons of SAURON
data with barred galaxy N-body simulations (NGC3623).Comment: 8 pages including 5 figures. To appear in Galaxies: The Third
Dimension, eds. M. Rosado, L. Binnette, & L. Arias (ASP: San Francisco
SAURON: An Innovative Look at Early-Type Galaxies
A summary of the SAURON project and its current status is presented. SAURON
is a panoramic integral-field spectrograph designed to study the stellar
kinematics, gaseous kinematics, and stellar populations of spheroids. Here, the
sample of galaxies and its properties are described. The instrument is detailed
and its capabilities illustrated through observational examples. These includes
results on the structure of central stellar disks, the kinematics and
ionization state of gaseous disks, and the stellar populations of galaxies with
decoupled cores.Comment: 10 pages, 6 figures. To appear in "The Dynamics, Structure & History
of Galaxies", eds. G. S. Da Costa & E. M. Sadler (San Francisco: ASP).
Version with full resolution images available at
http://www.strw.leidenuniv.nl/~dynamics/Instruments/Sauron/pub_list.htm
SAURON Observations of Disks in Early-Type Galaxies
We briefly describe the SAURON project, aimed at determining the intrinsic
shape and internal dynamics of spheroids. We focus here on the ability of
SAURON to identify gaseous and stellar disks and to measure their morphology
and kinematics. We illustrate some of our results with complete maps of
NGC3377, NGC3623, and NGC4365.Comment: 4 pages, 4 figures (newpasp.sty). To appear in ASP Conf. Series
"Galaxy Disks and Disk Galaxies", eds. J.G. Funes S.J. & E.M. Corsini.
Version with full resolution images available at
http://www.strw.leidenuniv.nl/~bureau/pub_list.htm
A SAURON view of galaxies
We have measured the two-dimensional kinematics and line-strength
distributions of 72 representative nearby early-type galaxies, out to
approximately one effective radius, with our panoramic integral-field
spectrograph SAURON. The resulting maps reveal a rich variety in kinematical
structures and linestrength distributions, indicating that early-type galaxies
are more complex systems than often assumed. We are building detailed dynamical
models for these galaxies, to derive their intrinsic shape and dynamical
structure, and to determine the mass of the supermassive central black hole.
Here we focus on two examples, the compact elliptical M32 and the E3 galaxy
NGC4365. These objects represent two extreme cases: M32 has very regular
kinematics which can be represented accurately by an axisymmetric model in
which all stars rotate around the short axis, while NGC4365 is a triaxial
galaxy with a prominent kinematically decoupled core, with an inner core that
rotates about an axis that is nearly perpendicular to the rotation axis of the
main body of the galaxy. Our dynamical models for these objects demonstrate
that two-dimensional observations are essential for deriving the intrinsic
orbital structure and dark matter content of galaxies.Comment: 7 pages (3 figures, full resolution Fig. 1 available at
http://www.strw.leidenuniv.nl/~verolme/M32.ps). Contributed talk to the
Athens Workshop on Galaxies and Chaos, Theory and Observations; Proceedings
to appear in "Galaxies and Chaos", eds. G. Contopoulos and N. Vogli
Dynamical Modeling of SAURON Galaxies
We describe our program for the dynamical modeling of early-type galaxies
observed with the panoramic integral-field spectrograph SAURON. We are using
Schwarzschild's numerical orbit superposition method to reproduce in detail all
kinematical and photometric observables, and recover the intrinsic orbital
structure of the galaxies. Since catastrophes are the most prominent features
in the orbital observables, two-dimensional kinematical coverage is essential
to constrain the dynamical models.Comment: 5 pages, 4 figures, LaTeX. Published in 2003, Carnegie Observatories
Astrophysics Series, Vol. 1: Coevolution of Black Holes and Galaxies, ed. L.
C. Ho (Pasadena: Carnegie Observatories,
http://www.ociw.edu/ociw/symposia/series/symposium1/proceedings.html
Regularized orbit models unveiling the stellar structure and dark matter halo of the Coma elliptical NGC 4807
This is the second in a series of papers dedicated to unveil the mass
structure and orbital content of a sample of flattened early-type galaxies in
the Coma cluster. The ability of our orbit libraries to reconstruct internal
stellar motions and the mass composition of a typical elliptical in the sample
is investigated by means of Monte-Carlo simulations of isotropic rotator
models. The simulations allow a determination of the optimal amount of
regularization needed in the orbit superpositions. It is shown that under
realistic observational conditions and with the appropriate regularization
internal velocity moments can be reconstructed to an accuracy of about 15 per
cent; the same accuracy can be achieved for the circular velocity and dark
matter fraction. In contrast, the flattening of the halo remains unconstrained.
Regularized orbit superpositions are applied to a first galaxy in our sample,
NGC 4807, for which stellar kinematical observations extend to 3 Reff. The
galaxy seems dark matter dominated outside 2 Reff. Logarithmic dark matter
potentials are consistent with the data, as well as NFW-profiles, mimicking
logarithmic potentials over the observationally sampled radial range. In both
cases, the derived stellar mass-to-light ratio agrees well with independently
obtained mass-to-light ratios from stellar population analysis. Kinematically,
NGC 4807 is characterized by mild radial anisotropy outside r>0.5 Reff,
becoming isotropic towards the center. Our orbit models hint at either a
distinct stellar component or weak triaxiality in the outer parts of the
galaxy.Comment: 20 pages, 25 figures, accepted for publication in MNRA
The counterrotating core and the black hole mass of IC1459
The E3 giant elliptical galaxy IC1459 is the prototypical galaxy with a fast
counterrotating stellar core. We obtained one HST/STIS long-slit spectrum along
the major axis of this galaxy and CTIO spectra along five position angles. We
present self-consistent three-integral axisymmetric models of the stellar
kinematics, obtained with Schwarzschild's numerical orbit superposition method.
We study the dynamics of the kinematically decoupled core (KDC) in IC1459 and
we find it consists of stars that are well-separated from the rest of the
galaxy in phase space. The stars in the KDC counterrotate in a disk on orbits
that are close to circular. We estimate that the KDC mass is ~0.5% of the total
galaxy mass or ~3*10^9 Msun. We estimate the central black hole mass M_BH of
IC1459 independently from both its stellar and its gaseous kinematics. Some
complications probably explain why we find rather discrepant BH masses with the
different methods. The stellar kinematics suggest that M_BH = (2.6 +/-
1.1)*10^9 Msun (3 sigma error). The gas kinematics suggests that M_BH ~
3.5*10^8 Msun if the gas is assumed to rotate at the circular velocity in a
thin disk. If the observed velocity dispersion of the gas is assumed to be
gravitational, then M_BH could be as high as ~1.0*10^9 Msun. These different
estimates bracket the value M_BH = (1.1 +/- 0.3)*10^9 Msun predicted by the
M_BH-sigma relation. It will be an important goal for future studies to assess
the reliability of black hole mass determinations with either technique. This
is essential if one wants to interpret the correlation between the BH mass and
other global galaxy parameters (e.g. velocity dispersion) and in particular the
scatter in these correlations (believed to be only ~0.3 dex). [Abridged]Comment: 51 pages, LaTeX with 19 PostScript figures. Revised version, with
three new figures and data tables. To appear in The Astrophysical Journal,
578, 2002 October 2