Mass Flux and Terminal Velocities of Magnetically Driven Jets from Accretion Disks

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Abstract
In order to investigate astrophysical jets from accretion disks, we solve 1.5-dimensional steady MHD equations for a wide range of parameters, assuming the shape of poloidal magnetic field lines. We include a thermal effect to obtain the relation between the mass flux of the jet and the magnetic energy at the disk, although the jet is mainly accelerated by the magnetic force. It is found that the mass flux of the jets () is dependent on the magnetic energy at the disk surface, i.e., ~ (ρAa|Bp/B|)slow ~ (ρAa|Bp/B|)slow ∝ Emgα [where ρ is the density, a is the sound velocity, A is the cross section of the magnetic flux, B = (Bp2 + B2)1/2, Bp and B are the poloidal and toroidal magnetic field strength, respectively, Emg is the magnetic energy in unit of the gravitational energy at the disk surface, and the suffix "slow" denotes the value at a slow point], when the magnetic energy is not too large. The parameter α increases from 0 to 0.5 with decreasing magnetic energy. Since the scaling law of Michel's minimum energy solution nearly holds in the magnetically driven flows, the dependence of the terminal velocity on the magnetic energy becomes weaker than had been expected, i.e., v∞ ∝ Emg(1 − α)/3. It is shown that the terminal velocity of the jet is an order of Keplerian velocity at the footpoint of the jets for a wide range of values of Emg expected for accretion disks in star-forming regions and active galactic nuclei. We argue that the mass-loss rates observed in the star-forming regions would constrain the magnetic energies at the disk surfaces.

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