JETS, THEORY OF ARIEH KONIGL The term "jets" was originally coined to describe the narrow, elongated features that had been discovered in optical and radio maps of active galaxies and quasistellar objects. Similar features have subsequently been found on a variety of scales in our galaxy. In particular, such narrow structures are now commonly identified in association with pre-main sequence stars embedded in dense molecular clouds. The image of a collimated gas flow that is conveyed by this term is not coincidental: It is now generally accepted that jets represent energetic outflows that emanate, often in two opposite directions, from the vicinity of compact astronomical objects. In the case of radio galaxies and quasars, the central objects are thought to be massive (10**-10**M*) black holes in the galactic nuclei, whereas in the case of newly formed stars the central masses may be less than 1 M*. However, despite the vast differences in scale (galactic jets sometimes exceed 1 Mpc in length and can move at close to the speed of light near the origin, whereas stellar jets seldom extend beyond 1 pc and move at only a few hundred kilometers per second), the striking morphological similarities and the ubiquity of collimated outflows suggest that jets on all scales are a manifestation of a universal phenomenon that can be described in terms of certain basic dynamical principles. Explaining the origin of this apparent universality and the nature of the underlying physical processes are the main challenges of a successful jet theory. PRODUCTION MECHANISMS NOZZLES AND FUNNELS Possible clues to the common occurrence of jets may be sought in the circumstances under which they are formed. Unfortunately, the formation region in any of the observed jets is not directly accessible to observations, so at this stage this question is still open. In one approach to the problem, it is postulated that the central object is the source of an isotropic gas outflow (like a stellar wind) that is channeled into two oppositely directed jets by the ambient medium. Two basic mechanisms for the formation of such channels have been proposed: the transonic nozzle, which arises from the dynamical interaction of a hot gas with a slightly flattened, confining mass distribution, and the centrifugally-supported funnel, which forms a preexisting conduit for the injected gas. The transonic flow idea is based on the well-known de Laval nozzle principle of aerodynamics (after Carl G.P. de Laval): A subsonic gas that expands into a convergent-divergent nozzle undergoes a continuous reduction in its pressure and becomes supersonic after passing through the narrowest portion of the channel. In the astrophysical application, the decreasing external pressure (rather than the nozzle geometry) is assumed to be given and it is hypothesized that the flow still undergoes a sonic transition as the channel walls adjust to maintain pressure equilibrium with the surrounding medium. The required flattening of the ambient gas could be due to rotation, in which case the jets would emerge along the rotation axis. Rotation may also lead to the formation of funnels. If the compact object is embedded in a rotating cloud and accretes gas that conserves at least part of its angular momentum as it moves inward, then a central funnel will form by the action of the centrifugal force that excludes the accreted matter from the vicinity of the rotation axis. Alternatively, in the context of thick accretion disks around black holes, a funnel could form by the action of a purely general-relativistic effect that gives rise to an evacuated, roughly paraboloidal "zone of nonstationarity in the innermost region of the disk. It has been suggested that the very process of funnel formation by centrifugal forces may cause some of the inflowing matter to be redirected along the funnel walls. Additional acceleration of this matter by radiation pressure forces might then result in the formation of energetic jets. Radiation pressure could similarly expel material above the photospheres of thick accretion disks in high-luminosity sources. Although the general applicability of these ideas has not yet been demonstrated, they are nevertheless attractive in that they naturally tie the formation of jets to mass accretion in compact objects. CENTRIFUGALLY DRIVEN OUTFLOWS Another promising mechanism that relates the existence of jets to the accretion process postulates the presence of accretion disks with embedded magnetic fields. If the field has an "open" topology and the field lines are inclined at sufficiently large angles to the disk surface, then material tied to the field will be flung out as a result of the centrifugal force, much as beads are pushed out along a rotating wire. Above the disk surface, additional acceleration is provided by magnetic pressure gradients, whereas the tension of the poloidal field component and the pinch stress of the azimuthal field component act to collimate the flow. Simple models have been constructed to illustrate the possibility that hydromagnetic outflows of this type could carry away most of the excess angular momentum and the liberated gravitational energy in the disk. The important implication of these models is that jets may not merely be an incidental by-product of accretion but that they could, instead, represent an essential ingredient in this process. In this view, the ubiquity of jets in compact astronomical objects is a manifestation of the fact that centrifugally-driven outflows from the associated accretion disks transport most of the angular momentum that needs to be removed in order for accretion to proceed. So far, the strongest support for this scenario has come from observations of pre-main sequence stars, where evidence has been accumulating for the correlated presence of circumstellar disks and energetic bipolar outflows as well as for the existence of embedded magnetic fields oriented parallel to the outflow axes. However, the same mechanism is also expected to operate in other cosmic jet sources, and, in fact, is a leading candidate for energy and angular momentum extraction from accreting black holes in active galactic nuclei. CONFINEMENT AND COLLIMATION Jets produced by any of the mechanisms just discussed may initially be rather poorly collimated. However, additional collimation could be achieved at large distances * from the origin by the action of a confining ambient pressure. For this to take place, the external pressure must decrease sufficiently slowly with increasing * so that the jet can remain in pressure equilibrium with its surroundings. In the case of a supersonic, narrow jet and an ambient pressure that scales as ***, this condition implies ***. If this condition is not satisfied, then the jet will expand freely with a constant opening angle until the pressure distribution becomes flatter, at which point it will be recollimated. This behavior has, in fact, been inferred to be present in both stellar and galactic jets. A sudden increase in the ambient pressure could, however, lead to the disruption of a supersonic jet, particularly if its Mach number M* is comparatively low. The jet might then decelerate as a result of internal shocks and turbulent entrainment of the ambient gas, which would cause it to flare out. This could account for the observed morphologies of wide-angle-tailed radio galaxies. The gradual broadening exhibited by low-power radio jets is probably also associated with the deceleration of subsonic, turbulent flows. Magnetic pinch stresses, already mentioned in connection with centrifugally driven outflows, provide an alternative collimation mechanism for jets. For any expanding supersonic jet that is highly conducting and not strongly sheared, it is possible to argue, on the basis of magnetic flux conservation, that the azimuthal field component should dominate the axial component sufficiently far away from the origin. In fact, this property could be responsible for the observed transition from longitudinal to transverse projected field orientation in many weak radio jets. The "hoop" stress of the toroidal field could collimate the central regions of jets that carry a net current along the axis. The return current might flow along the outer boundary of the jet, where an overall confining pressure must still be exerted by an external agent. Nevertheless, if only the innermost, high-pressure region of the jet is visible, then this mechanism could account for the apparent discrepancy between the estimated external pressure and the much higher inferred internal pressure in certain radio jets. PROPAGATION EFFECTS THE WORKING SURFACE The interaction of a jet with the medium through which it propagates strongly influences its structure and stability. Although some of the qualitative features of this interaction were initially deduced from general principles, only with the advent of sophisticated supercomputer simulations in the last few years has it become clear that the actual behavior could be very complex and is best studied numerically. A good example is provided by the development of our understanding of the heads of high-Mach-number jets, which were proposed as the explanation for the bright emission regions ("hot spots") observed at the outer edges of high-power radio jets. The structure of the head was originally described in terms of an effectively planar "working surface" consisting of a jet shock where the flow is decelerated and a forward bow shock where the impacted ambient gas is accelerated, with the two shocked gases being separated by a contact discontinuity. On the basis of this one-dimensional flow model, it was argued that the jet head would advance into the ambient medium with a speed ********(1+*****), where v* is the jet speed and ******* is the jet-to-ambient density ratio. Although the basic aspects of the predicted morphology were subsequently confirmed by two- and three- dimensional hydrodynamical simulations (see Fig. 1*), several important new features have emerged from the numerical work. In particular, it was found that the gas flowing near the jet boundary is not stopped in a strong perpendicular shock but is instead deflected sideways by weak oblique shocks. For "light" (*****) jets, this can lead to a substantial increase in the working surface area and to a reduction in the value of v*. In addition, it was discovered that the shapes of the jet shock and of the contact discontinuity can be highly time variable as a result of quasiperiodic vortex shedding induced by the oblique shock configuration. The predicted emission patterns are, nevertheless, consistent with the observed radio hot spots. In the case of high-M*, low=* jets, the shocked jet material flows back from the head region and forms an extensive "cocoon" around the jet. However, numerical simulations of magnetized outflows have revealed that a strong toroidal magnetic field in the jet can prevent the shocked jet gas from flowing sideways and instead force it to accumulate in a narrow "nose cone" between the terminal jet shock (or "Mach disk") and the leading bow shock (Fig. 1b). This configuration may be relevant to the jet in the quasar 3C 273. Another modification of the basic working surface structure that was discovered by numerical simulations involves "radiative" jets, in which the shocked gas in the jet head can cool before it flows out of the working surface region. In this case, the cooled gas forms a dense shell between the jet shock and the bow shock (Fig. 1c). The shell is highly dynamically unstable and tends to fragment into individual clumps that move with different velocities. Such clumps provide a natural explanation for the high-proper-motion Herbig-Haro objects that are associated with the heads of stellar jets. KNOTS AND WIGGLES The relative motion between the jet and the ambient medium is expected to induce surface instabilities of the Kelvin-Helmholtz (KM) type. Such instabilities could be responsible for the common occurrence of emission knots and transverse oscillations in astrophysical jets. Specifically, these two features may correspond, respectively, to the pinch and kink modes of the KH instability. Recent analytical results on the linear development of these modes, together with numerical results on their nonlinear evolution, have provided a better understanding of the possible effects of this instability on cylindrical, supersonic jets. In the linear regime, each of these modes can be analyzed in terms of the number * of nodes in the radial direction, and a natural distinction arises between the fundamental (n=0) mode and the higher-order (n*1) reflection modes. The reflection modes, which are due to the resonant interaction between acoustic waves that propagate from one side of the jet to the other, dominate the pinch instability in jets that satisfy M**********. They develop into weak, oblique shocks that do not disrupt the jet but that could conceivably be identified with the observed quasiperiodic emission knots. A recently reported measurement of the proper motion of the knots in the stellar jet L1551 is consistent with this interpretation in view of the fact that the predicted shock pattern could, in principle, travel at a substantial fraction of the jet speed. By contrast, dense or low-Mach-number jets that do not satisfy the preceding inequality are susceptible to the fundamental pinch mode. They are expected to develop strong, planar shocks and a progressively broadening turbulent boundary layer that could eventually lead to their disruption. The formation of a turbulent boundary layer could result in the entrainment of the surrounding gas into the jet. This process was proposed as the cause of the observed star formation activity along the jet in the radio galaxy Centaurus A. In the case of the kink instability, the fastest growing perturbation is associated with the fundamental mode that evolves into an ever-steepening pattern of zig-zagging internal shocks. Recent observations of the Centaurus A jet have revealed a side-to-side limb brightening that is consistent with this pattern. However, the frequent deviation of jets from a straight trajectory may also be due to transverse pressure gradients in the ambient medium. In the extreme case of a head-tail galaxy, the two oppositely directed jets that emanate from the galactic nucleus are swept back by the ram pressure associated with the motion of the galaxy through a dense intracluster medium. MAGNETIC FIELD EFFECTS Strong magnetic fields parallel to the direction of the flow could have a stabilizing effect on the development of the KH modes. However, the embedded magnetic field may have an important effect on the apparent structure of a galactic radio jet even if its overall dynamical influence is small. This is because the intensity of the radio emission, which is produced by the synchrotron mechanism, scales with the magnetic field component that is perpendicular to the line of sight. In fact, it was shown that the energetically preferred magnetic field configurations in jets with negligible internal pressure gradients could mimic the appearance of quasiperiodic knots and wiggles even when the flow remains perfectly straight and smooth. Another possible consequence of the dependence of the observed intensity on the transverse field component is that jets with a predominantly azimuthal magnetic field could be completely obscured by the radio emission from a surrounding cocoon. RELATIVISTIC JETS The presence of outflow speeds that approach the speed of light * has been inferred in the innermost regions of many extragalactic radio jets from apparent superluminal motions, high emission variability, and the absence of a detectable counterjet. The existence of a pair of relativistic (0.26*) jets has also been inferred in the galactic compact object SS 433. The origin of such high velocities is still not fully understood. According to a recent suggestion, the superluminal jets are initially accelerated to even higher speeds by an electromagnetic or a hydromagnetic process and are then decelerated to the inferred velocity range (*0.99*) by the Compton scattering interaction with the ambient radiation field. The relation between the highly relativistic parsec-scale outflows and the kiloparsec-scale jets within which they are embedded is also still an open question, but in one well-studied case (the strong radio source 3C 120) it appears that the inner beam merges smoothly into the large-scale jet and that superluminal motion persists to a distance of more than 2 kpc from the nucleus. On the other hand, various dynamical arguments indicate that the speeds of the large-scale jets in weak radio sources do not exceed 10** km s**. Relativistic beaming of the emitted radiation and light travel time effects can strongly influence the appearance of jets, particularly in sources where the motion is not confined to one plane (as in the case of precessing jets). The relativistic focusing of the radiation in the direction of motion is, in fact, the basis for the interpretation of the most extreme members of the active galactic nuclei class in terms of relativistic jets that are observed at a small angle to the axis, for example, in the class of active galactic nuclei known as "blazars." Additional Reading Begelman, M.C., Blandford, R.D., and Rees, M.J.(1984). Theory of extragalactic radio sources. Rev. Mod. Phys. 56 255. Blandford, R.D., Begelman, M.C., and Rees, M.J.(1982). Cosmic jets. Scientific American 246 (No. 5) 124. Henriksen, R.N., ed.(1986). Jets from stars and galaxies. Can. J. Phys. 64 353. Konigl, A.(1985). The universality of the jet phenomenon. Ann. Acad. Sci. N.Y. 470 88. Lada, C.J.(1985). Cold outflows, energetic winds, and enigmatic jets around young stellar objects. Ann. Rev. Astron. Ap. 23 267. Norman, M.L.(1991). Fluid dynamics of astrophysical jets. In Nonlinear Astrophysical Fluid Dynamics, J.R. Buchler and S.T. Gottesman, eds. N.Y. Academy of Sciences, New York.