Self-Consistent, Axisymmetric Two_Integral Models of Elliptical Galaxies with embedded Nuclear Discs

Recently, observations with the Hubble Space Telescope have revealed small stellar discs embedded in the nuclei of a number of ellipticals and S0s. In this paper we construct two-integral axisymmetric models for such systems. We calculate the even part of the phase-space distribution function, and specify the odd part by means of a simple parameterization. We investigate the photometric as well as the kinematic signatures of nuclear discs, including their velocity profiles (VPs), and study the influence of seeing convolution. The rotation curve of a nuclear disc gives an excellent measure of the central mass-to-light ratio whenever the VPs clearly reveal the narrow, rapidly rotating component associated with the nuclear disc. Steep cusps and seeing convolution both result in central VPs that are dominated by the bulge light, and these VPs barely show the presence of the nuclear disc, impeding measurements of the central rotation velocities of the disc stars. However, if a massive BH is present, the disc component of the VP can be seen in the wing of the bulge part, and measurements of its mean rotation provide a clear signature of the presence of the BH. This signature is insensitive to the uncertainties in the velocity anisotropy, which often lead to ambiguity in the interpretation of a central rise in velocity dispersion as due to a central BH.Comment: 13 pages, uses mn.tex (included). MNRAS accepted. The 17 PS figures (not enclosed) can be retrieved from ftp://strw.leidenuniv.nl/pub/vdbosch/diskpaper

In search of an appropriate abstraction level for motif annotations

In: Proceedings of the 2012 Workshop on Computational Models of Narrative, (pp. 22-28).

Evidence for a 3 x 10^8 solar mass black hole in NGC 7052 from HST observations of the nuclear gas disk

We present an HST study of the nuclear region of the E4 radio galaxy NGC 7052, which has a nuclear disk of dust and gas. The WFPC2 was used to obtain B, V and I broad-band images and an H_alpha+[NII] narrow-band image. The FOS was used to obtain H_alpha+[NII] spectra along the major axis, using a 0.26 arcsec diameter circular aperture. The observed rotation velocity of the ionized gas is V = 155 +/- 17 km/s at r = 0.2 arcsec from the nucleus. The Gaussian dispersion of the emission lines increases from sigma = 70 km/s at r=1 arcsec, to sigma = 400 km/s on the nucleus. To interpret the gas kinematics we construct axisymmetric models in which the gas and dust reside in a disk in the equatorial plane of the stellar body. It is assumed that the gas moves on circular orbits, with an intrinsic velocity dispersion due to turbulence. The circular velocity is calculated from the combined gravitational potential of the stars and a possible nuclear black hole (BH). Models without a BH predict a rotation curve that is shallower than observed (V_pred = 92 km/s at r = 0.2 arcsec), and are ruled out at > 99% confidence. Models with a BH of 3.3^{+2.3}_{-1.3} x 10^8 solar masses provide an acceptable fit. NGC 7052 can be added to the list of active galaxies for which HST spectra of a nuclear gas disk provide evidence for the presence of a central BH. The BH masses inferred for M87, M84, NGC 6251, NGC 4261 and NGC 7052 span a range of a factor 10, with NGC 7052 falling on the low end. By contrast, the luminosities of these galaxies are identical to within 25%. Any relation between BH mass and luminosity, as suggested by independent arguments, must therefore have a scatter of at least a factor 10.Comment: 39 pages, LaTeX, with 16 PostScript figures. Submitted to the Astronomical Journal. Postscript version with higher resolution figures available from http://sol.stsci.edu/~marel/abstracts/abs_R22.htm

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

Dynamics of the nuclear gas & dust disc in the E4 radio galaxy NGC 7052

We present high spatial resolution ground-based broad-band imaging, H-alpha +[NII] narrow-band imaging and long-slit spectroscopy for the E4 radio galaxy NGC 7052, which has a nuclear dust disc. We detect ionized gas with a LINER spectrum, residing also in a nuclear disc. The gas rotates rapidly and the emission line widths increase towards the nucleus. The images are well fit by an axisymmetric model with the gas and dust in a disc of 1.5" radius (340 pc) in the equatorial plane of the stellar body, viewed at an inclination of 70 degrees. We assume the gas to be on circular orbits in the equatorial plane, with in addition a local turbulent velocity dispersion. The circular velocity is calculated from the combined gravitational potential of the stars and a possible nuclear black hole. The observed gas rotation curve is well fit, either with or without a black hole. Turbulent velocities >300 km/s must be present at radii <0.5" to fit the observed nuclear line widths. Models with a black hole and no turbulence can also fit the line widths, but these models cannot fit the observed nuclear line shapes. Models with both a black hole and gas turbulence can fit the data well, but the black hole is not required by the data, and if present, its mass must be < 5 x 10^8 solar masses. This upper limit is 5 times smaller than the black hole mass inferred for M87 from HST data. Our modelling and analysis techniques will be useful also for the study of the kinematics of nuclear gas discs in other galaxies. Such data will yield important information on the presence of massive black holes.Comment: 15 pages, uuencoded compressed PostScript, without the figures. Figures at ftp://eku.ias.edu/pub/marel/ngc7052fig.u