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Self-Similar Force-Free Wind From an Accretion Disk | | Ramesh Narayan
; Jonathan C. McKinney
; Alison J. Farmer
; | | Date: |
27 Oct 2006 | | Abstract: | 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 $Ppropto R^
u$, 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 $
u$ 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 $
u geq 1$, the Lorentz factor of the outflow increases along a field line as $gamma approx M(z/Rfp)^{(2-
u)/2} approx R/R_{
m A}$, where $Rfp$ is the radius of the foot-point of the field line on the disk and $R_{
m A}=Rfp/M$ is the cylindrical radius at which the field line crosses the Alfven surface or the light cylinder. For $
u < 1$, the Lorentz factor follows the same scaling for $z/Rfp < M^{-1/(1-
u)}$, but at larger distances it grows more slowly: $gamma approx (z/Rfp)^{
u/2}$. For either regime of $
u$, 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 $z/Rfp approx (R/Rfp)^{2/(2-
u)}$ 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. | | Source: | arXiv, astro-ph/0610817 | | Services: | Forum | Review | PDF | Favorites | |
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