A Description of Narrow Jets Using a QuasiOnedimensional Model. I. Jets with Constant Opening Angle
Abstract
Using a quasionedimensional MHD model for narrow jets (which we develop by projecting the system of the ideal MHD equations onto the jet axis), we examine the relative importance of the combined effects of rotation and magnetic fields upon the acceleration of matter in jets. We also examine the relative importance of the gas pressure and the gravitational field of the source on the flow and the position of the three critical points (Alfven, slow, and fast magnetosonic). When the model is used for jets with constant opening angle, the results are very similar to the ones obtained in solar wind models. The model allows both a "pressure confinement" and/or a "magnetically assisted confinement," implying that the gas pressure (given by a polytropic equation of state) and the centrifugal pressure (which is the result of the rotation of the flow) are balanced by an external medium and/or the tension of the "frozenin" magnetic field lines. For a jet with constant opening angle we find the form of the pressure of the external medium necessary to provide pressure balance. We study the analytic structure of the equations using parameters appropriate to jets emanating from black holes, neutron stars, and protostars. We confirm the results and conclusions of our previous paper in which we had set the gas pressure, gravitational field of the source, and the rcomponent of the velocity and magnetic field equal to zero. For all cases the flow is initially subsonic, and it accelerates only if the gravitational field is large enough to simulate the throat of a nozzle (as in the solar wind case). For the black hole and neutron star cases, the combination of magnetic fields and rotation is a very important acceleration mechanism, producing relativistic velocities far away from the source. For a typical black hole case, acceleration to v_max_ ~ 0.4c occurs over a distance of a few 100 AU from the source. The minimum resolution needed to observe such effects in this region (corresponding to Cen A, the closest extragalactic source with clear morphological jets) is a few 0.01 mas. For the solution to go through the slow magnetosonic and sonic points the value of the injection velocity and gas temperature at the origin cannot be arbitrary; instead, one determines the other (as in the solar wind case). Using "characteristic" values for the parameters of interest at the jet origin, we find that an outflow exists only if the polytropic index is 1 <= γ <~ 1.239. Unless γ = 1, the initial temperature required is so high (e.g., 3 x 10^9^ K <~ T_0_ <~ 10^12^ K for γ = 1.001) that it seems probable that the outflow originates from a hightemperature region surrounding the black hole, in much the same way as the solar wind originates from the corona surrounding the Sun. The asymptotic value of the jet Mach number is 1 <~ M_p_ <~ 5. Assuming equipartition between the magnetic and kinetic energy densities for a jet emanating from an active galactic nucleus, we find that if the flow is to be physical the plasma beta factor at the origin must satisfy β_0_ >~ (γ  1)/γ. As a typical neutron star case we use SS 433, for which the jet reaches relativistic velocities (ν <~ c) at a distance of ~ 10^10^ cm, requiring a resolution of ~ 2 x 10^3^ mas. The large magnetic field strength at the jet origin imposes an upper limit to the jet opening angle. The general behavior of the solution is the same as for the black hole case and requires 1 <= γ <~ 1.473. The initial temperature required is also high, and the presence of a high temperature region surrounding the neutron star is probable. For protostar cases we find that the velocity reaches its asymptotic value of ~ 300 km s^1^ (for γ = 1.2, and strongly dependent on γ and ν_0_) at a distance of ~ 10^4^ pc; in these cases the gas pressure is the primary acceleration mechanism. For the solution to go through the sonic and fast magnetosonic points and using "characteristic" values for the parameters of interest, we find that 1 <= γ <~ 1.498 and T_0_ < 1.5 x 10^6^ K. The asymptotic value of the jet Mach number is 5 <~ M_p_ <~ 40, consistent with observations. From the behavior of the density and magnetic field strength at large distances we estimate that at the origin ρ_0_ ~ 10^10^10^8^ g cm^3^ and B_0_ ~ 1 G. For all cases considered the model leads naturally to a hollow jet (i.e., ρ is proportional to r^P^, where p > 0), consistent with recent observations.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 1990
 DOI:
 10.1086/169321
 Bibcode:
 1990ApJ...363...79K
 Keywords:

 Astronomical Models;
 Interstellar Magnetic Fields;
 Plasma Jets;
 Black Holes (Astronomy);
 Gravitational Fields;
 Magnetohydrodynamics;
 Neutron Stars;
 Astrophysics;
 BLACK HOLES;
 GALAXIES: JETS;
 HYDROMAGNETICS;
 PARTICLE ACCELERATION;
 STARS: PREMAINSEQUENCE