Theoretical astrophysics and plasma physics at RPC

Abstract:

We present a method for extracting actions, angles and frequencies from an orbit's time series. The method recovers the generating function that maps an analytic phase-space torus to the torus to which the orbit is confined by simultaneously solving the constraints provided by each time step. We test the method by recovering the actions and frequencies of a triaxial Stäckel potential, and use it to investigate the structure of orbits in a triaxial potential that has been fitted to our Galaxy's Sagittarius stream. The method promises to be useful for analysing N-body simulations. It also takes a step towards constructing distribution functions for the triaxial components of our Galaxy, such as the bar and dark halo.

Abstract:

In the standard thin-disc formalism, the dimensionless α parameter is usually assumed to be constant. However, there are good theoretical reasons for believing, as well as evidence from simulations, that α is dependent on intrinsic disc properties. In this paper, we analyse the conditions for the stability of a thin accretion disc in which α is a function of the magnetic Prandtl number, the ratio of collisional viscosity to resistivity. In the inner disc, where the free electron opacity and radiation viscosity dominate, the disc is unstable if α is proportional to the magnetic Prandtl number with an exponent >0.5. This is within the range of values for the power-law index found in magnetohydrodynamic simulations with simple energetics. We calculate the evolution of the unstable disc within the α-formalism and show that the physically accessible solutions form a limit cycle, analogous to the behaviour seen in recurrent dwarf novae. It is noteworthy that the time-dependent global behaviour of the instability results in cyclic heating of the inner section of the disc, when parameters appropriate for an X-ray binary system are used. We calculate a model spectrum of the disc in the flaring and quiescent states and show that the behaviour is compatible with X-ray observations of the thermal accretion disc in flaring X-ray binary systems. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

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.