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Abstract:

The nuclear stellar disc (NSD) is a flattened high-density stellar structure that dominates the gravitational field of the Milky Way at Galactocentric radius $30\, {\rm pc}\lesssim R\lesssim 300\, {\rm pc}$. We construct axisymmetric self-consistent equilibrium dynamical models of the NSD in which the distribution function is an analytic function of the action variables. We fit the models to the normalized kinematic distributions (line-of-sight velocities + VIRAC2 proper motions) of stars in the NSD survey of Fritz et al., taking the foreground contamination due to the Galactic Bar explicitly into account using an N-body model. The posterior marginalized probability distributions give a total mass of $M_{\rm NSD} = 10.5^{+1.1}_{-1.0} \times 10^8 \, \, \rm M_\odot$, roughly exponential radial and vertical scale lengths of $R_{\rm disc} = 88.6^{+9.2}_{-6.9} \, {\rm pc}$ and $H_{\rm disc}=28.4^{+5.5}_{-5.5} \, {\rm pc}$, respectively, and a velocity dispersion $\sigma \simeq 70\, {\rm km\, s^{-1}}$ that decreases with radius. We find that the assumption that the NSD is axisymmetric provides a good representation of the data. We quantify contamination from the Galactic Bar in the sample, which is substantial in most observed fields. Our models provide the full 6D (position + velocity) distribution function of the NSD, which can be used to generate predictions for future surveys. We make the models publicly available as part of the software package agama.

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.