The curvature condition for self-consistent scale-free galaxies

We modify the curvature condition for the existence of self-consistent scale-free discs, introduced by Zhao, Carollo & de Zeeuw. We survey the parameter space of the power-law discs, and show that the modified curvature condition is in harmony with the results of Schwarzschild's numerical orbit superposition method. We study the orbital structure of the power-law discs, and find a correlation between the population of centrophobic banana orbits and the non-self-consistency index. We apply the curvature condition to other families of scale-free elongated discs and find that it rules out a large range of power-law slopes and axis ratios. We generalize the condition, and apply it, to three-dimensional scale-free axisymmetric galaxy models.Comment: 14 pages, 14 figures, Accepted for publication in MNRA

Mapping the inner regions of the polar disk galaxy NGC4650A with MUSE

[abridged] The polar disk galaxy NGC4650A was observed during the commissioning of the MUSE at the ESO VLT to obtain the first 2D map of the velocity and velocity dispersion for both stars and gas. The new MUSE data allow the analysis of the structure and kinematics towards the central regions of NGC4650A, where the two components co-exist. These regions were unexplored by the previous long-slit literature data available for this galaxy. The extended view of NGC~4650A given by the MUSE data is a galaxy made of two perpendicular disks that remain distinct and drive the kinematics right into the very centre of this object. In order to match this observed structure for NGC4650A, we constructed a multicomponent mass model made by the combined projection of two disks. By comparing the observations with the 2D kinematics derived from the model, we found that the modelled mass distribution in these two disks can, on average, account for the complex kinematics revealed by the MUSE data, also in the central regions of the galaxy where the two components coexist. This result is a strong constraint on the dynamics and formation history of this galaxy; it further supports the idea that polar disk galaxies like NGC~4650A were formed through the accretion of material that has different angular momentum.Comment: 14 pages, 10 figures; accepted for publication in Astronomy & Astrophysic

Kinematics of Metal-Poor Stars in the Galaxy. III. Formation of the Stellar Halo and Thick Disk as Revealed from a Large Sample of Non-Kinematically Selected Stars

(Abbreviated) We present a detailed analysis of the space motions of 1203 solar-neighborhood stars with metal abundances [Fe/H] <= -0.6, on the basis of a recently revised and supplemented catalog of metal-poor stars selected without kinematic bias (Beers et al. 2000). This sample, having available proper motions, radial velocities, and distance estimates for stars with a wide range of metal abundances, is by far the largest such catalog to be assembled to date. Unlike essentially all previous kinematically selected catalogs, the metal-poor stars in our sample exhibit a diverse distribution of orbital eccentricities, e, with no apparent correlation between [Fe/H] and e. This demonstrates, clearly and convincingly, that the evidence offered by Eggen, Lynden-Bell, and Sandage (1962) for a rapid collapse of the Galaxy, an apparent correlation between the orbital eccentricity of halo stars with metallicity, is basically the result of their proper-motion selection bias. However, even in our non-kinematically selected sample, we have identified a small concentration of high-e stars at [Fe/H] = -1.7, which may originate, in part, from infalling gas during the early formation of the Galaxy. The implications of our results for the formation of the Galaxy are also discussed, in particular in the context of the currently favored CDM theory of hierarchical galaxy formation.Comment: 51 pages, including 17 figures, to appear in AJ (June 2000), full paper with all figures embedded available at http://pluto.mtk.nao.ac.jp/people/chiba/preprint/halo5

Reply to "Comment on 'Scalar-tensor gravity coupled to a global monopole and flat rotation curves' "

In Brans-Dicke theory of gravity we explain how the extra constant value in the formula for rotation velocities of stars in a galactic halo can be obtained due to the global monopole field. We argue on a few points of the preceding Comment and discuss improvement of our model.Comment: 4 pages, RevTeX4 fil

An Upper Limit on the Mass of a Central Black Hole in the Large Magellanic Cloud from the Stellar Rotation Field

We constrain the possible presence of a central black hole (BH) in the center of the Large Magellanic Cloud (LMC). This requires spectroscopic measurements over an area of order a square degree, due to the poorly known position of the kinematic center. Such measurements are now possible with the impressive field of view of the Multi Unit Spectroscopic Explorer (MUSE) on the ESO Very Large Telescope. We used the Calcium Triplet (~850nm) spectral lines in many short-exposure MUSE pointings to create a two-dimensional integrated-light line-of-sight velocity map from the ~$10^8$ individual spectra, taking care to identify and remove Galactic foreground populations. The data reveal a clear velocity gradient at an unprecedented spatial resolution of 1 arcmin$^{2}$. We fit kinematic models to arrive at a $3\sigma$ upper-mass-limit of $10^{7.1}$ M$_{Sun}$ for any central BH - consistent with the known scaling relations for supermassive black holes and their host systems. This adds to the growing body of knowledge on the presence of BHs in low-mass and dwarf galaxies, and their scaling relations with host-galaxy properties, which can shed light on theories of BH growth and host system interaction.Comment: 12 pages, 11 figures, 1 table, ApJ - in pres

Measuring non-axisymmetry in spiral galaxies

We present a method for measuring small deviations from axisymmetry of the potential of a filled gas disk. The method is based on a higher order harmonic expansion of the full velocity field of the disk. This expansion is made by first fitting a tilted-ring model to the velocity field of the gas disk and subsequently expanding the velocity field along each ring into its harmonic terms. We use epicycle theory to derive equations for the harmonic terms in a distorted potential. The phase of each component of the distortion can vary with radius. We show that if the potential has a distortion of harmonic number m, the velocity field as seen on the sky exhibits an m-1 and m+1 distortion. As is to be expected, the effects of a global elongation of the halo are similar to an m=2 spiral arm. The main difference is that the phase of the spiral arm can vary with radius. Our method allows a measurement of epsilon_pot sin(2 phi_2), where epsilon_pot is the elongation of the potential and phi_2 is one of the viewing angles. Using \hi data, one can probe the potential at radii beyond the stellar disk, into the regime where dark matter is thought to be the dominant dynamical component. The method is applied the spiral galaxies NGC 2403 and NGC 3198 and the harmonic terms are measured up to ninth order. We find epsilon_pot sin(2 phi_2) to be 0.064 +/- 0.003 for NGC 2403 and 0.019 +/- 0.003 for NGC 3198. More galaxies should be examined to separate viewing angle from elongation in a statistical way.Comment: 17 pages, 8 figures. To be published in Monthly Notices of the Royal Astronomical Societ

Global Dynamics in Galactic Triaxial Systems I

In this paper we present a theoretical analysis of the global dynamics in a triaxial galactic system using a 3D integrable Hamiltonian as a simple representation. We include a thorough discussion on the effect of adding a generic non--integrable perturbation to the global dynamics of the system. We adopt the triaxial Stackel Hamiltonian as the integrable model and compute its resonance structure in order to understand its global dynamics when a perturbation is introduced. Also do we take profit of this example in order to provide a theoretical discussion about diffussive processes taking place in phase space.Comment: Accepted A&

Simple Three-Integral Scale-Free Galaxy Models

The Jeans equations give the second moments or stresses required to support a stellar population against the gravity field. A general solution of the Jeans equations for arbitrary axisymmetric scale-free densities in flattened scale-free potentials is given. A two-parameter subset of the solution for the second moments for the self-consistent density of the power-law models, which have exactly spheroidal equipotentials, is examined in detail. In the spherical limit, the potential of these models reduces to that of the singular power-law spheres. We build the physical three-integral distribution functions that correspond to the flattened stellar components. Next, we attack the problem of finding distribution functions associated with the Jeans solutions in flattened scale-free potentials. The third or partial integral introduced by de Zeeuw, Evans and Schwarzschild for Binney's model is generalised to thin and near-thin orbits moving in arbitrary axisymmetric scale-free potentials. The partial integral is a modification of the total angular momentum. For the self-consistent power-law models, we show how this enables the construction of simple three-integral distribution functions. The connexion between these approximate distribution functions and the Jeans solutions is discussed in some detail.Comment: 14 pages, 7 postscript figures, to appear in Monthly Notice

Velocity profiles of Osipkov-Merritt models

A simple algorithm is presented for the calculation of the projected line-of-sight velocity profiles (VPs) of non-rotating anisotropic spherical stellar dynamical models with a phase-space distribution function of the Osipkov-Merritt type. The velocity distribution in these models is isotropic inside the anisotropy radius r_a and becomes increasingly radially biased at larger radii. VP shape parameters are presented for a family of models in which the luminous mass density has an r^{-gamma} power-law cusp at small radii and an r^{-4} power-law fall-off at large radii. Self-consistent models and models in which the luminous matter is embedded in a dark halo are discussed. The effects of changes in the cusp slope gamma and in the anisotropy radius r_a are documented, and the area in the (gamma,r_a)-plane that contains physical models is delineated. The shapes of the VPs of the models show a considerable (and observable) variation with projected galactocentric radius. These models will be useful for interpreting the data on the VP shapes of elliptical galaxies that are now becoming available.Comment: 10 pages, uuencoded compressed PostScript, includes 7 figure