The collimation of magnetic jets by disc winds

The collimation of a Poynting-flux dominated jet by a wind emanating from the surface of an accretion flow is computed using a semi-analytic model. The injection of the disc wind is treated as a boundary condition in the equatorial plane, and its evolution is followed by invoking a prescribed geometry of streamlines. Solutions are obtained for a wide range of disc wind parameters. It is found that jet collimation generally occurs when the total wind power exceeds about 10 percents of the jet power. For moderate wind powers, we find gradual collimation. For strong winds, we find rapid collimation followed by focusing of the jet, after which it remains narrow over many Alfvén crossing times before becoming conical. We estimate that in the later case, the jet's magnetic field may be dissipated by the current-driven kink instability over a distance of a few hundreds gravitational radii. We apply the model to M87 and show that the observed parabolic shape of the radio jet within the Bondi radius can be reproduced provided that the wind injection zone extends to several hundreds gravitational radii, and that its total power is about one-third of the jet power. The radio spectrum can be produced by synchrotron radiation of relativistically hot, thermal electrons in the sheath flow surrounding the inner jet.