Numerical Simulations of Astrophysical Jets from Keplerian Disks. I. Stationary Models

We present 2.5-dimensional time-dependent simulations of the evolution of nonrelativistic outflows from Keplerian accretion disks orbiting low-mass protostars or black holes accreting at sub-Eddington rates. The gas is injected at a very small speed (v_inj = 10^-3v_K) from the surface of the disk (a fixed boundary in our simulations) into a cold corona. The corona is in stable equilibrium and is supported by Alfvénic turbulent pressure. The initial magnetic field configuration in the corona is poloidal and is given by a potential field (J = 0). This configuration is extended smoothly into the disk where the toroidal magnetic field is taken to scale inversely with the disk radius. We present the analytical and the numerical approaches to our problem, as well as many results for a steady state simulation. We find that the gas is centrifugally accelerated through the Alfvén and the fast magnetosonic (FM) surfaces and collimated into cylinders parallel to the disk's axis. The collimation of the outflow is due to the pinch force exerted by the dominant toroidal magnetic field generated by the outflow itself. Beyond the FM surface, we found that a "Hubble" flow is present; v_z ∝ z. The velocities achieved in our simulations are of the order of 180 km s^-1 for our standard young stellar object (a 0.5 M_☉ protostar) and of the order or 10⁵ km s^-1 for our standard active galactic nuclei (a 10⁸ M_☉ black hole). Our jet solutions, dominated mainly by the poloidal kinetic energy ρv²_p, are very efficient in magnetically extracting angular momentum and energy from the disk. We find the ratio of the disk accretion rate to the wind mass flux rate to be of the order of _a/_w ≃ 6.0. We find that our stationary outflows have many similarities to steady state models of MHD disk winds.