Time-dependent quasi-spherical accretion

Differentially rotating, "advection-dominated" accretion flows are considered in which the heat generated by viscous dissipation is retained in the fluid. The equations of time-dependent quasi-spherical accretion are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. A self-similar solution is presented that has finite size, mass, angular momentum and energy. This may be expected to be an attractor for the initial-value problem in which a cool and narrow ring of fluid orbiting around a central mass heats up, spreads radially and is accreted. The solution provides some insight into the dynamics of quasi-spherical accretion and avoids many of the strictures of the steady self-similar solution of Narayan & Yi. Special attention is given to the astrophysically important case in which the adiabatic exponent gamma=5/3; even in this case, the flow is found to be differentially rotating and bound to the central object, and accretion can occur without the need for powerful outflows.Comment: 6 pages, 3 figures, to be published in MNRA

Nonlinear bending waves in Keplerian accretion discs

The nonlinear dynamics of a warped accretion disc is investigated in the important case of a thin Keplerian disc with negligible viscosity and self-gravity. A one-dimensional evolutionary equation is formally derived that describes the primary nonlinear and dispersive effects on propagating bending waves other than parametric instabilities. It has the form of a derivative nonlinear Schroedinger equation with coefficients that are obtained explicitly for a particular model of a disc. The properties of this equation are analysed in some detail and illustrative numerical solutions are presented. The nonlinear and dispersive effects both depend on the compressibility of the gas through its adiabatic index Gamma. In the physically realistic case Gamma<3, nonlinearity does not lead to the steepening of bending waves but instead enhances their linear dispersion. In the opposite case Gamma>3, nonlinearity leads to wave steepening and solitary waves are supported. The effects of a small effective viscosity, which may suppress parametric instabilities, are also considered. This analysis may provide a useful point of comparison between theory and numerical simulations of warped accretion discs.Comment: 15 pages, 2 figures, to be published in MNRA

The non-linear fluid dynamics of a warped accretion disc

The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave propagation found in inviscid Keplerian discs does not occur. The equations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc. They are reduced using asymptotic methods for thin discs, and solved to extract the equation governing the warp. In general, this is a wave equation of parabolic type with non-linear dispersion and diffusion, which describes fully non-linear bending waves. This method generalizes the linear theory of Papaloizou & Pringle (1983) to allow for an arbitrary rotation law, and extends it into the non-linear domain, where it connects with a generalized version of the theory of Pringle (1992). The astrophysical implications of this analysis are discussed briefly.Comment: 23 pages, 5 figures, to be published in MNRA

Jet launching from accretion discs in the local approximation

The acceleration of an outflow along inclined magnetic field lines emanating from an accretion disc can be studied in the local approximation, as employed in the computational model known as the shearing box. By including the slow magnetosonic point within the computational domain, the rate of mass loss in the outflow can be calculated. The accretion rates of mass and magnetic flux can also be determined, although some effects of cylindrical geometry are omitted. We formulate a simple model for the study of this problem and present the results of one-dimensional numerical simulations and supporting calculations. Quasi-steady solutions are obtained for relatively strong poloidal magnetic fields for which the magnetorotational instability is suppressed. In this regime the rate of mass loss decreases extremely rapidly with increasing field strength, or with decreasing surface density or temperature. If the poloidal magnetic field in an accretion disc can locally achieve an appropriate strength and inclination then a rapid burst of ejection may occur. For weaker fields it may be possible to study the launching process in parallel with the magnetorotational instability, but this will require three-dimensional simulations.Comment: 8 pages, 4 figures, to be published in MNRA

Global evolution of the magnetic field in a thin disc and its consequences for protoplanetary systems

The strength and structure of the large-scale magnetic field in protoplanetary discs are still unknown, although they could have important consequences for the dynamics and evolution of the disc. Using a mean-field approach in which we model the effects of turbulence through enhanced diffusion coefficients, we study the time-evolution of the large-scale poloidal magnetic field in a global model of a thin accretion disc, with particular attention to protoplanetary discs. With the transport coefficients usually assumed, the magnetic field strength does not significantly increase radially inwards, leading to a relatively weak magnetic field in the inner part of the disc. We show that with more realistic transport coefficients that take into account the vertical structure of the disc and the back-reaction of the magnetic field on the flow as obtained by Guilet & Ogilvie (2012), the magnetic field can significantly increase radially inwards. The magnetic-field profile adjusts to reach an equilibrium value of the plasma $\beta$ parameter (the ratio of midplane thermal pressure to magnetic pressure) in the inner part of the disc. This value of $\beta$ depends strongly on the aspect ratio of the disc and on the turbulent magnetic Prandtl number, and lies in the range $10^4-10^7$ for protoplanetary discs. Such a magnetic field is expected to affect significantly the dynamics of protoplanetary discs by increasing the strength of MHD turbulence and launching an outflow. We discuss the implications of our results for the evolution of protoplanetary discs and for the formation of powerful jets as observed in T-Tauri star systems.Comment: 19 pages, 12 figures, accepted for publication in MNRA