John Magorrian

Abstract:

We use the problem of dynamical friction within the periodic cube to illustrate the application of perturbation theory in stellar dynamics, testing its predictions against measurements from N-body simulations. Our development is based on the explicitly time-dependent Volterra integral equation for the cube’s linear response, which avoids the subtleties encountered in analyses based on complex frequency. We obtain an expression for the self-consistent response of the cube to steady stirring by an external perturber. From this, we show how to obtain the familiar Chandrasekhar dynamical friction formula and construct an elementary derivation of the Lenard–Balescu equation for the secular quasi-linear evolution of an isolated cube composed of N equal-mass stars. We present an alternative expression for the (real-frequency) van Kampen modes of the cube and show explicitly how to decompose any linear perturbation of the cube into a superposition of such modes.

Abstract:

<jats:title>Abstract</jats:title> <jats:p>The nuclear stellar disc (NSD) is a flattened stellar structure that dominates the gravitational potential of the Milky Way at Galactocentric radii 30 ≲ R ≲ 300 pc. In this paper, we construct axisymmetric Jeans dynamical models of the NSD based on previous photometric studies and we fit them to line-of-sight kinematic data of APOGEE and SiO maser stars. We find that (i) the NSD mass is lower but consistent with the mass independently determined from photometry by Launhardt et al. (2002). Our fiducial model has a mass contained within spherical radius r = 100 pc of $M(r&amp;lt;100\, {\rm pc}) = 3.9 \pm 1 \times 10^8 \, \rm M_\odot$ and a total mass of $M_{\rm NSD} = 6.9 \pm 2 \times 10^8 \, \rm M_\odot$. (ii) The NSD might be the first example of a vertically biased disc, i.e. with ratio between the vertical and radial velocity dispersion σz/σR &amp;gt; 1. Observations and theoretical models of the star-forming molecular gas in the central molecular zone suggest that large vertical oscillations may be already imprinted at stellar birth. However, the finding σz/σR &amp;gt; 1 depends on a drop in the velocity dispersion in the innermost few tens of parsecs, on our assumption that the NSD is axisymmetric, and that the available (extinction corrected) stellar samples broadly trace the underlying light and mass distributions, all of which need to be established by future observations and/or modelling. (iii) We provide the most accurate rotation curve to date for the innermost 500 pc of our Galaxy.</jats:p>

Abstract:

We present a method for fitting orbit-superposition models to the kinematics of discrete stellar systems when the available stellar sample has been filtered by a known selection function. The fitting method can be applied to any model in which the distribution function is represented as a linear superposition of basis elements with unknown weights. As an example, we apply it to Fritz et al.'s kinematics of the innermost regions of the Milky Way's nuclear stellar cluster. Assuming spherical symmetry, our models fit a black hole of mass $M_\bullet=(3.76\pm0.22)\times10^6\,M_\odot$, surrounded by an extended mass $M_\star=(6.57\pm0.54)\times10^6\,M_\odot$ within $4\,\pc$. Within $1\,\pc$ the best-fitting mass models have an approximate power-law density cusp $\rho\propto r^{-\gamma}$ with $\gamma=1.3\pm0.3$. We carry out an extensive investigation of how our modelling assumptions might bias these estimates: $M_\bullet$ is the most robust parameter and $\gamma$ the least. Internally the best-fitting models have broadly isotropic orbit distributions, apart from a bias towards circular orbits between 0.1 and 0.3 parsec.