Contents List of Figures

302 6 MACRO– AND MICRO–JETS DRIVEN BY BLACK HOLES
process is the strength of the poloidal magnetic field. The standard approach (e.g.,
Moderski & Sikora 1996) to estimating BH is to set it equal to Bφ, the dominant
azimuthal magnetic field component given by the disk structure equations, yielding
and
Ljet,B = 2 × 10 45 erg s −1 m9 ˙m−2 j 2
(726)
Ljet,A = 3 × 10 49 erg s −1 m 0.8
9 ˙m−1 j 2 . (727)
for Class B (radio galaxy/ADAF) and Class A (quasar/standard disk) objects, respectively.
Note that, while the jet is not accretion-powered in this model, the
efficiency of extraction is still essentially linear in ˙m.
Basic physics of MHD acceleration and collimation: Though many models
have been proposed to generate jets, the magnetohydrodynamic (MHD) model is still
the leading one (Fig. 145). In this picture, the plasma is simplified in terms of a one–
component approximation and the conductivity is assumed to be very high so that
electric fields in the plasma are shorted out. In a first approximation, plasma is not
allowed to cross field lines, it can only flow parallel to them. In regions where the field
is weak or the plasma is dense, the rotating field will be bent backward. To accelerate
and collimate a jet with magnetic fields, all that is needed is a gravitating body to
collect the material which should be ejected, a poloidal magnetic field threading that
material, and some differential rotation, which produces a helical structure in the
field. This rotating field structure drives the confined plasma upwards and outwards
along the field lines. As this twist propagates outwards, the toroidal field pinches
the plasma towards the rotational axis. Depending on the relative importance of
the magnetic field, the plasma density and rotation, a variety of configurations are
possible from spherical winds, slowly collimated and highly collimated outflows.
Poloidal magnetic field strengths are estimated from equation disk pressure, but
(H/R) is of order unity for the low cases, and also for the high Kerr case due to
Lens-Thirring bloating of the inner disk. Otherwise (H/R) is calculated from the
electron scattering/gas pressure disk model of Shakura & Sunyaev (1973), and disk
field strengths are computed from that paper or from Narayan et al. (1998), as
appropriate. The logarithms of the resulting poloidal field strengths, and corresponding
jet powers, are represented as field line and jet arrow widths. In the Kerr
cases, the inner disk magnetic field is significantly enhanced over the Schwarzschild
cases, due in part to the smaller last stable orbit (flux conservation) and in part to
the large (H/R) of the bloated disks. The high accretion rate, Schwarzschild case has
the smallest field - and the weakest jet - because the disk is thin, the last stable orbit
is relatively large, and the Keplerian rotation rate of the field there is much smaller
than it would be in a Kerr hole ergosphere. Enhancement of the poloidal field due
to the buoyancy process suggested by Krolik (1999) is ignored here because we find