Three-integral oblate galaxy models

A simple numerical scheme is presented for the construction of three-integral phase-space distribution functions for oblate galaxy models with a gravitational potential of St\"{a}ckel form, and an arbitrary axisymmetric luminous density distribution. The intrinsic velocity moments can be obtained simultaneously with little extra effort. The distribution of the inner and outer turning points of the short-axis tube orbits that are populated can be specified freely, and is chosen in advance. The entire distribution function is then derived from the density by an iterative scheme that starts from the explicitly known distribution function of the thin-orbit (maximum streaming) model, in which only the tubes with equal inner and outer turning points are populated. The versatility and limitations of this scheme are illustrated by the construction of a number of self-consistent three-integral flattened isochrone models of Kuzmin--Kutuzov type, and by investigation of special cases where the scheme is tractable analytically. This includes the behaviour of the distribution functions in the outer regions of the models. The scheme converges rapidly for models containing orbits with ratios of the outer to inner turning point as large as ten, and is particularly suited for the construction of tangentially anisotropic flattened models, self-consistent as well as non-consistent. The algorithm simplifies in the disk and spherical limit, and can be generalized to triaxial models.Comment: uuencoded gziped PostScript, 21 pages without figures. PostScript with figures available from http://www.strw.leidenuniv.nl/dynamics/Papers/ or ftp://ftp.strw.leidenuniv.nl/pub/dynamics/Papers/RobijnDeZeeuw95.tar.Z Accepted by MNRA

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

Kinemetry: a generalisation of photometry to the higher moments of the line-of-sight velocity distribution

We present a generalisation of surface photometry to the higher-order moments of the line-of-sight velocity distribution of galaxies observed with integral-field spectrographs. The generalisation follows the approach of surface photometry by determining the best fitting ellipses along which the profiles of the moments can be extracted and analysed by means of harmonic expansion. The assumption for the odd moments (e.g. mean velocity) is that the profile along an ellipse satisfies a simple cosine law. The assumption for the even moments (e.g velocity dispersion) is that the profile is constant, as it is used in surface photometry. We find that velocity profiles extracted along ellipses of early-type galaxies are well represented by the simple cosine law (with 2% accuracy), while possible deviations are carried in the fifth harmonic term which is sensitive to the existence of multiple kinematic components, and has some analogy to the shape parameter of photometry. We compare the properties of the kinematic and photometric ellipses and find that they are often very similar. Finally, we offer a characterisation of the main velocity structures based only on the kinemetric parameters which can be used to quantify the features in velocity maps (abridged).Comment: 17 pages, 11 figures. MNRAS in press. High resolution version of the paper is available at http://www.strw.leidenuniv.nl/sauron/papers/krajnovic2005_kinemetry.pdf and software implementation of the method is freely available at http://www-astro.physics.ox.ac.uk/~dxk/idl

Separable triaxial potential-density pairs in MOND

We study mass models that correspond to MOND (triaxial) potentials for which the Hamilton-Jacobi equation separates in ellipsoidal coordinates. The problem is first discussed in the simpler case of deep-MOND systems, and then generalized to the full MOND regime. We prove that the Kuzmin property for Newtonian gravity still holds, i.e., that the density distribution of separable potentials is fully determined once the density profile along the minor axis is assigned. At variance with the Newtonian case, the fact that a positive density along the minor axis leads to a positive density everywhere remains unproven. We also prove that (i) all regular separable models in MOND have a vanishing density at the origin, so that they would correspond to centrally dark-matter dominated systems in Newtonian gravity; (ii) triaxial separable potentials regular at large radii and associated with finite total mass leads to density distributions that at large radii are not spherical and decline as ln(r)/r^5; (iii) when the triaxial potentials admit a genuine Frobenius expansion with exponent 0<epsilon<1, the density distributions become spherical at large radii, with the profile ln(r)/r^(3+2epsilon). After presenting a suite of positive density distributions associated with MOND separable potentials, we also consider the important family of (non-separable) triaxial potentials V_1 introduced by de Zeeuw and Pfenniger, and we show that, as already known for Newtonian gravity, they obey the Kuzmin property also in MOND. The ordinary differential equation relating their potential and density along the z-axis is an Abel equation of the second kind that, in the oblate case, can be explicitly reduced to canonical form.Comment: 17 pages, 4 figures (low resolution), accepted by MNRA

Mapping young stellar populations towards Orion with Gaia DR1

We use the first data release of the Gaia mission to explore the three dimensional arrangement and the age ordering of the many stellar groups towards the Orion OB association, aiming at a new classification and characterization of the stellar population. We make use of the parallaxes and proper motions provided in the Tycho Gaia Astrometric Solution (TGAS) sub-set of the Gaia catalogue, and of the combination of Gaia and 2MASS photometry. In TGAS we find evidence for the presence of a young population, at a parallax $\varpi \sim 2.65 \, \mathrm{mas}$, loosely distributed around some known clusters: 25 Ori, $\epsilon$ Ori and $\sigma$ Ori, and NGC 1980 ($\iota$ Ori). The low mass counterpart of this population is visible in the color-magnitude diagrams constructed by combining Gaia and 2MASS photometry. We study the density distribution of the young sources in the sky. We find the same groups as in TGAS, and also some other density enhancements that might be related to the recently discovered Orion X group, the Orion dust ring, and to the $\lambda$ Ori complex. We estimate the ages of this population and we infer the presence of an age gradient going from 25 Ori (13-15 Myr) to the ONC (1-2 Myr). We confirm this age ordering by repeating the Bayesian fit using the Pan-STARRS1 data. The estimated ages towards the NGC 1980 cluster span a broad range of values. This can either be due to the presence of two populations coming from two different episodes of star formation or to a large spread along the line of sight of the same population. Our results form the first step towards using the Gaia data to unravel the complex star formation history of the Orion region in terms of the different star formation episodes, their duration, and their effects on the surrounding interstellar medium.Comment: 17 pages, 17 figure