Theoretical astrophysics and plasma physics at RPC

Abstract:

In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of WKB, local techniques, and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenolgical studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.

Abstract:

Observations of the Orion A integral shaped filament (ISF) have shown indications of an oscillatory motion of the gas filament. This evidence is based on both thewave-likemorphology of the filament and the kinematics of the gas and stars, where the characteristic velocities of the stars require a dynamical heating mechanism. As proposed by Stutz & Gould, such a heating mechanism (the 'Slingshot') may be the result of an oscillating gas filament in a gas-dominated (as opposed to stellar-mass dominated) system. Here we test this hypothesis with the first stellar-dynamical simulations in which the stars are subjected to the influence of an oscillating cylindrical potential. The accelerating, cylindrical background potential is populated with a narrow distribution of stars. By coupling the potential to N-body dynamics, we are able to measure the influence of the potential on the stellar distribution. The simulations provide evidence that the slingshot mechanism can successfully reproduce several stringent observational constraints. These include the stellar spread (both in projected position and in velocity) around the filament, the symmetry in these distributions, and a bulkmotion of the stars with respect to the filament. Using simple considerations, we show that star-star interactions are incapable of reproducing these spreads on their own when properly accounting for the gas potential. Thus, properly accounting for the gas potential is essential for understanding the dynamical evolution of star-forming filamentary systems in the era of Gaia (GaiaCollaboration 2016).

Abstract:

The present-day response of a Galactic disc stellar population to a non-axisymmetric perturbation of the potential has previously been computed through perturbation theory within the phase-space coordinates of the unperturbed axisymmetric system. Such an Eulerian linearized treatment, however, leads to singularities at resonances, which prevent quantitative comparisons with data. Here, we manage to capture the behaviour of the distribution function (DF) at a resonance in a Lagrangian approach, by averaging the Hamiltonian over fast angle variables and re-expressing the DF in terms of a new set of canonical actions and angles variables valid in the resonant region. We then follow the prescription of Binney, assigning to the resonant DF the time average along the orbits of the axisymmetric DF expressed in the new set of actions and angles. This boils down to phase-mixing the DF in terms of the new angles, such that the DF for trapped orbits depends only on the new set of actions. This opens the way to quantitatively fitting the effects of the bar and spirals to Gaia data in terms of DFs in action space.