Self-Similar Force-Free Wind From an Accretion Disk
  We consider a self-similar force-free wind flowing out of an infinitely thin disk located in the equatorial plane. On the disk plane, we assume that the magnetic stream function $P$ scales as $P\propto R^\nu$, where $R$ is the cylindrical radius. We also assume that the azimuthal velocity in the disk is constant: $v_\phi = Mc$, where $M<1$ is a constant. For each choice of the parameters $\nu$ and $M$, we find an infinite number of solutions that are physically well-behaved and have fluid velocity $\leq c$ throughout the domain of interest. Among these solutions, we show via physical arguments and time-dependent numerical simulations that the minimum-torque solution, i.e., the solution with the smallest amount of toroidal field, is the one picked by a real system. For $\nu \geq 1$, the Lorentz factor of the outflow increases along a field line as $\gamma \approx M(z/\Rfp)^{(2-\nu)/2} \approx R/R_{\rm A}$, where $\Rfp$ is the radius of the foot-point of the field line on the disk and $R_{\rm A}=\Rfp/M$ is the cylindrical radius at which the field line crosses the Alfven surface or the light cylinder. For $\nu < 1$, the Lorentz factor follows the same scaling for $z/\Rfp < M^{-1/(1-\nu)}$, but at larger distances it grows more slowly: $\gamma \approx (z/\Rfp)^{\nu/2}$. For either regime of $\nu$, the dependence of $\gamma$ on $M$ shows that the rotation of the disk plays a strong role in jet acceleration. On the other hand, the poloidal shape of a field line is given by $z/\Rfp \approx (R/\Rfp)^{2/(2-\nu)}$ and is independent of $M$. Thus rotation has neither a collimating nor a decollimating effect on field lines, suggesting that relativistic astrophysical jets are not collimated by the rotational winding up of the magnetic field. 
Ramesh Narayan (1,2), Jonathan C. McKinney (2), Alison J. Farmer (1,2)   ((1) Harvard University, (2) Institute for Theory a...