3. MAGNETIZED ACCRETION DISKS

3.1. The Disk-Jet Connection

Jets are identified with accretion disks, both observationally and theoretically. In the case of protostellar objects, there is accumulating evidence that YSO are surrounded by disks with masses ~ 0.01 - 1 M on scales ~ 10² - 10³ AU (e.g., Beckwith & Sargent 1992). The presence of a disk is inferred spectrally using infrared observations, spatially using millimeter interferometry and dynamically from molecular lines. In the case of AGN, the case is more circumstantial. Indeed, a recent conference proceedings, (Holt, Neff & Urry 1992) calls into question the general notion of an accretion disk in an AGN. The most direct evidence comes from the identification of Seyfert 2 galaxies with obscured Seyfert 1 galaxies (Lawrence & Elvis 1982) and the interpretation of X-ray spectra with reflection by a planar surface (e.g., George & Fabian 1991). Most AGN, produce weak or undetectable jets. It is only a minority, specifically radio galaxies and quasars that are associated with powerful jets. There is still no good explanation of why only some AGN produce strong jets.

AGN jets are best resolved at radio wavelengths using VLBI. One of the most impressive examples to date is the observations of NGC1275 by Venturi et al. (1992, preprint). The large scale linear outflow has been probed on scales 10¹⁷ cm and exhibits complex structure perpendicular to the jet axis. In this source, at least, there is an indication that jet collimation is not achieved close to the event horizon of the putative black hole, but over length scales some 100-1000 times larger.

Despite this, it is reasonable to suspect that the association is genuinely physical. The most significant type of connection is that jets are generically responsible for extracting both angular momentum and energy liberated by gas as it flows radially inward through the disk. Magnetic field provides a plausible link between disks and jets.

3.2. Magnetic jet collimation

We have already, indirectly, referred to some of the evidence that magnetic field plays a large role in jet collimation. In powerful AGN jets and YSO outflows, neither gas pressure nor radiation pressure appears to be adequate to the task of collimating large momentum flux. This leaves magnetic field as the prime candidate. However, the question that immediately arises is what confines the magnetic field? Ultimately, this must be gas pressure. However, if the "hoop" stress associated with the toroidal component of magnetic field extends over several decades of cylindrical radius, then the stress that need be supplied by an external, gas pressure-dominated medium can be orders of magnitude smaller than the minimum pressure inferred in the most luminous parts of the jet. This provides one mechanism for confining apparently overpressured emission sites (like the knots in M87, Biretta, these proceedings). (An alternative explanation is that they are transients, Norman, these proceedings.)

Other evidence for the importance of magnetic field in galactic nuclei comes from our Galactic center, where many long "threads" and "filaments" have been mapped (e.g., Yusef-Zadeh & Morris 1988). Morphologically these most resemble magnetic flux tubes that have been activated, somewhat similar to H and X-ray images of solar prominences. However, these features appear unusually straight and smooth which indicates that the region in which they are found is magnetically-dominated.

A quite different environment where magnetic stresses may possibly be seen at work, collimating an outflow is in the Crab Nebula. An X-ray jet has been reported along the inferred direction of the pulsar symmetry axis. In addition the formation of the optical bays may be attributable to the action of magnetic hoop stress (Begelman & Li 1992, preprint).

3.3. Magnetic Accretion Disks

The magnetic fields that are being invoked to account for jet collimation may be anchored to accreting gas orbiting the central compact object. As has been reviewed elsewhere, (e.g., Blandford 1989, Königl & Ruden 1992), poloidal magnetic flux may be dragged radially inward by the accreting gas until its dissipative escape, driven by the gradient in magnetic pressure limits its growth. Provided that the magnetic field makes an angle of less than 60° with the radius vector at the disk (assumed to be in Keplerian motion), it will be energetically favorable for gas to leave the disk in a centrifugally driven wind. A stationary, hydromagnetic flow along these field lines must pass through three critical points associated with the slow, intermediate and fast MHD waves. We can think of the slow point as controlling the rate of mass loss from the disk, the intermediate point as adjusting the torque, and the fast point, which may be removed to infinity as dictating the asymptotic behavior of the jet. Presumably, the detailed magnetic field geometry at the disk can adjust so that the flow is self-limiting. The rotation of the disk will also create a toroidal magnetic field so that the magnetic stress acting on the disk surface can exert a torque and extract angular momentum. Detailed models have been developed to exhibit this simple picture and show that it can be internally consistent and related more usefully to the observations (e.g., Königl 1989, Pelletier & Pudritz 1992). Formal analysis of axisymmetric MHD solutions leads to a modified "Grad-Shafranov" equation for a magnetic stream function (which labels magnetic surfaces, e.g., Lovelace et al. 1986). Solutions with both even and odd magnetic symmetry have been studied, the latter perhaps having some relevance to one-sided jets (Wang, Sulkanen & Lovelace 1992). It has been argued that under some quite general assumptions, collimation of the outflow to either parabolic or cylindrical surfaces is inevitable asymptotically (Heyvaerts & Norman 1989; see Chiueh, Li & Begelman 1992 for the relativistic case). Unfortunately, theses analyses are sensitive to the assumptions made about the boundary conditions at large cylindrical radius.

However, real accretion disks may be much more complex. They probably exhibit meridional circulation, in addition to differential rotation, the two ingredients of a fast dynamo (e.g., Tout & Pringle 1992, preprint). More directly, as Balbus & Hawley (1992) have shown, vertical magnetic field lying within the disk is susceptible to dynamical instability. A small radial displacement of the field line will continue to grow as long as its wave vector k satisfies k . a > 3^1/2 , where a is the vector Alfvén velocity and is the disk angular frequency. The non-linear development of this instability is still a matter of speculation; buoyant escape of magnetic flux presumably limits the growth of magnetic pressure. However, it seems difficult to escape the conclusion that magnetic torques, either internal or external, control the dynamics of accretion disks.

3.4. Magnetic Confinement of AGN Broad Emission Line Clouds

I would now like to describe briefly an extension of these ideas, developed elsewhere (Emmering, Blandford & Shlosman 1992). This develops the notion that the broad emission clouds in AGN are magnetically confined (e.g., Rees 1987) and, furthermore, that they be identified with the gas flowing away from an AGN accretion disk. Specifically, there are now good reasons to suspect that the outer parts of AGN disks are predominantly molecular in form and impregnated with dust grains that re-radiate incident ultraviolet radiation in the infrared. Cooling of molecular gas is only effective as long as the grains can avoid sublimation, at temperatures 1800 K (Sanders et al. 1989). This criterion allows molecular gas to survive well into the broad line region, which is believed to be concentrated at distances ~ 10¹⁸ cm from the central continuum source. If molecular gas leaves this disk in a centrifugal wind, then it will be accelerated to speeds typically a few times the orbital speeds of the magnetic foot points, and of order several thousand km s^-1. It is envisaged that the intensity of the ionizing UV radiation is much greater at high latitude and that dust that was partially shielded close to the disk quickly sublimes, allowing the accompanying gas to heat and ionize (cf. Calvet, Hartmann & Kenyon 1992, preprint, Safier 1992, in preparation, for the YSO analogue). Only one hemisphere is likely to be observed because the disk itself will be quite opaque. The resultant line profiles should then exhibit blue shifts and asymmetries as has been reported.

This explanation cannot account for the full width of observed permitted lines and so it is predicted that the wings are created by electron scattering in a hot intercloud medium with temperature ~ 10⁶ K and thermally stabilized by the strong magnetic field. This model implies several observable features, including smooth, polarized wings to the emission lines, and UV molecular hydrogen lines.

3.5. Flips* and Flops

MHD is harder to understand than gas dynamics and numerical investigations are even more valuable as a guide for our precarious physical intuition. It is therefore encouraging that there has been substantial progress in developing difference schemes for 2D and 3D MHD simulations (as reviewed by Norman these proceedings). It is to these numerical "experiments", to which we will ultimately turn, to assess the viability of magnetic collimation by accretion disks. However the problems that we want to solve are not very well posed for numerical simulation. In particular, as we discuss further below, it may be necessary to define a grid extending over several decades of radius in order to effect good collimation. Furthermore, although most simulations to date have been concerned with transient flows in which a magnetic field is twisted and flow starts from rest (e.g., Shibata & Uchida 1989), we really want to evolve to a quasi-stationary state, if one exists. This will take many disk orbital periods at the outer radius, and yet the computational timestep will be determined by the dynamical time at the inner radius which is very much shorter. A hybrid scheme, that accommodate such a large range of scales, may be needed.

Yet another difficulty is that in both AGN and YSO, the radiative cooling timescales may be quite short. Adiabatic gas dynamics may be a very poor approximation. Departures form perfect MHD are also to be expected, particularly in the predominantly neutral outflows from YSO. The disk itself poses another problem. Its internal dynamics, perhaps controlled by local MHD instabilities, dictates the release of plasma along each flux tube and the shape adopted by the magnetic surfaces over an Alfvén crossing time. On an even longer timescale, radial inflow (combined with effective electrical resistivity of the disk) determines the radial distribution of magnetic flux.

As has been amply demonstrated by the numerical simulations of the jets themselves (e.g., Clarke 1992), the most productive, initial use of simulations is when they are used to answer specific and individual physical questions and the results are carefully analyzed and elucidated in terms of elementary physical principles.

* Frontal lobe image processing system