The evolution of Kerr discs and late-time tidal disruption event light curves
Monthly Notices of the Royal Astronomical Society Oxford University Press 481:3 (2018) 3348-3356
Abstract:
An encounter between a passing star and a massive black hole at the centre of a galaxy, a so-called tidal disruption event or TDE, may leave a debris disc that subsequently accretes onto the hole. We solve for the time evolution of such a TDE disc, making use of an evolutionary equation valid for both the Newtonian and Kerr regimes. The late time luminosity emergent from such a disc is of interest as a model diagnostic, as it tends to follow a power law decline. The original simple ballistic fallback model, with equal mass in equal energy intervals, produces a −5/3 power law, while standard viscous disc descriptions yield a somewhat more shallow decline, with an index closer to −1.2. Of four recent, well-observed tidal disruption event candidates however, all had fall-off power law indices smaller than 1 in magnitude. In this work, we revisit the problem of thin disc evolution, solving this reduced problem in full general relativity. Our solutions produce power law indices that are in much better accord with observations. The late time observational data from many TDEs are generally supportive, not only of disc accretion models, but of finite stress persisting down to the innermost stable circular orbit.Demonstration of a magnetic Prandtl number disc instability from first principles
Monthly Notices of the Royal Astronomical Society Oxford University Press 472:3 (2017) 3021-3028
Abstract:
Understanding what determines the strength of MHD turbulence in accretion discs is a question of fundamental theoretical and observational importance. In this work we investigate whether the dependence of the turbulent accretion disc stress (α) on the magnetic Prandtl number (Pm) is sufficiently sensitive to induce thermal-viscous instability using 3D MHD simulations. We first investigate whether the α-Pm dependence, found by many previous authors, has a physical or numerical origin by conducting a suite of local shearing-box simulations. We find that a definite α-Pm dependence persists when simultaneously increasing numerical resolution and decreasing the absolute values of both the viscous and resistive dissipation coefficients. This points to a physical origin of the α-Pm dependence. Using a further set of simulations which include realistic turbulent heating and radiative cooling, and by giving Pm a realistic physical dependence on the plasma temperature and density, we demonstrate that the α-Pm dependence is sufficiently strong to lead to a local instability. We confirm that the instability manifests itself as an unstable limit cycle by mapping the local thermal-equilibrium curve of the disc. This is the first self-consistent MHD simulation demonstrating the Pm instability from first principles. This result is important because a physical Pm instability could lead to the global propagation of heating and cooling fronts and a transition between disc states on timescales compatible with the observed hard/soft state transitions in black hole binaries.When is high Reynolds number shear flow not turbulent?
Journal of Fluid Mechanics Cambridge University Press (CUP) 824 (2017) 1-4
The general relativistic thin disc evolution equation
Monthly Notices of the Royal Astronomical Society Oxford University Press 471:4 (2017) 4832-4838
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.Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.
Proceedings of the National Academy of Sciences National Academy of Sciences (2016)