Dynamical models of NGC 3115

We present new dynamical models of the S0 galaxy N3115, making use of the available published photometry and kinematics as well as of two-dimensional TIGER spectrography. We first examined the kinematics in the central 40 arcsec in the light of two integral f(E,J) models. Jeans equations were used to constrain the mass to light ratio, and the central dark mass whose existence was suggested by previous studies. The even part of the distribution function was then retrieved via the Hunter & Qian formalism. We thus confirmed that the velocity and dispersion profiles in the central region could be well fit with a two-integral model, given the presence of a central dark mass of ~10^9 Msun. However, no two integral model could fit the h_3 profile around a radius of 25 arcsec where the outer disc dominates the surface brightness distribution. Three integral analytical models were therefore built using a Quadratic Programming technique. These models showed that three integral components do indeed provide a reasonable fit to the kinematics, including the higher Gauss-Hermite moments. Again, models without a central dark mass failed to reproduce the observed kinematics in the central arcseconds. This clearly supports the presence of a nuclear black hole of at least 6.5 10^8 Msun in the centre of NGC 3115. These models were finally used to estimate the importance of the dark matter in the outer part of NGC 3115, suggested by the flat stellar rotation curve observed by Capaccioli et al. (1993).Comment: 18 pages, 22 figures, accepted for publication in MNRA

Dynamical Models for the Milky Way

The only way to map the Galaxy's gravitational potential $\Phi({\bf x})$ and the distribution of matter that produces it is by modelling the dynamics of stars and gas. Observations of the kinematics of gas provide key information about gradients of $\Phi$ within the plane, but little information about the structure of $\Phi$ out of the plane. Traditional Galaxy models {\em assume}, for each of the Galaxy's components, arbitrary flattenings, which together with the components' relative masses yield the model's equipotentials. However, the Galaxy's isopotential surfaces should be {\em determined\/} directly from the motions of stars that move far from the plane. Moreover, from the kinematics of samples of such stars that have well defined selection criteria, one should be able not only to map $\Phi$ at all positions, but to determine the distribution function $f_i({\bf x},{\bf v})$ of each stellar population $i$ studied. These distribution functions will contain a wealth of information relevant to the formation and evolution of the Galaxy. An approach to fitting a wide class of dynamical models to the very heterogeneous body of available data is described and illustrated.Comment: 10 pages, LaTeX, style file and 4 figures included. Invited talk presented at the meeting ``Formation of the Galactic Halo ... Inside and Out'', Tucson, October 9-11. Full .ps file available at ftp://ftp.physics.ox.ac.uk/pub/local/users/dehnen/MilkyWayModels.ps.g

Combinatorial models of expanding dynamical systems

We define iterated monodromy groups of more general structures than partial self-covering. This generalization makes it possible to define a natural notion of a combinatorial model of an expanding dynamical system. We prove that a naturally defined "Julia set" of the generalized dynamical systems depends only on the associated iterated monodromy group. We show then that the Julia set of every expanding dynamical system is an inverse limit of simplicial complexes constructed by inductive cut-and-paste rules.Comment: The new version differs substantially from the first one. Many parts are moved to other (mostly future) papers, the main open question of the first version is solve

Dynamical models with a general anisotropy profile

Both numerical simulations and observational evidence indicate that the outer regions of galaxies and dark matter haloes are typically mildly to significantly radially anisotropic. The inner regions can be significantly non-isotropic, depending on the dynamical formation and evolution processes. In an attempt to break the lack of simple dynamical models that can reproduce this behaviour, we explore a technique to construct dynamical models with an arbitrary density and an arbitrary anisotropy profile. We outline a general construction method and propose a more practical approach based on a parameterized anisotropy profile. This approach consists of fitting the density of the model with a set of dynamical components, each of which have the same anisotropy profile. Using this approach we avoid the delicate fine-tuning difficulties other fitting techniques typically encounter when constructing radially anisotropic models. We present a model anisotropy profile that generalizes the Osipkov-Merritt profile, and that can represent any smooth monotonic anisotropy profile. Based on this model anisotropy profile, we construct a very general seven-parameter set of dynamical components for which the most important dynamical properties can be calculated analytically. We use the results to look for simple one-component dynamical models that generate simple potential-density pairs while still supporting a flexible anisotropy profile. We present families of Plummer and Hernquist models in which the anisotropy at small and large radii can be chosen as free parameters. We also generalize these two families to a three-parameter family that self-consistently generates the set of Veltmann potential-density pairs. (Abridged...)Comment: 18 pages, accepted for publication in A&