Theoretical astrophysics and plasma physics at RPC

Abstract:

I present a new framework for estimating a galaxy's gravitational potential, Phi, from its stellar kinematics. It adopts a fully non-parametric model for the galaxy's unknown phase-space distribution function, f, that takes full advantage of Jeans' theorem. Given an expression for the joint likelihood of Phi and f, the likelihood of Phi is calculated by using a Dirichlet process mixture to represent the prior on f and marginalising. I demonstrate that modelling machinery constructed using this framework is successful at recovering the potentials of some simple systems given perfect kinematical data, a situation handled effortlessly by traditional moment-based methods, such as the virial theorem, but in which the more modern extended-Schwarzschild method fails. Unlike moment-based methods, however, the models constructed using this framework can easily be generalised to take account of realistic observational errors and selection functions.

Abstract:

Conventional radially-local neoclassical calculations become inadequate if the radial gradient scale lengths of the H-mode pedestal become as small as the poloidal ion gyroradius. Here, we describe a radially global $\delta f$ continuum code that generalizes neoclassical calculations to allow stronger gradients. As with conventional neoclassical calculations, the formulation is time-independent and requires only the solution of a single sparse linear system. We demonstrate precise agreement with an asymptotic analytic solution of the radially global kinetic equation in the appropriate limits of aspect ratio and collisionality. This agreement depends crucially on accurate treatment of finite orbit width effects.