DOI: 10.1126/science.291.5501.84 , 84 (2001); 291Science

et al.David L. Meier,JetsMagnetohydrodynamic Production of Relativistic

www.sciencemag.org (this information is current as of November 17, 2006 ):The following resources related to this article are available online at

http://www.sciencemag.org/cgi/content/full/291/5501/84version of this article at:

including high-resolution figures, can be found in the onlineUpdated information and services,

found at: can berelated to this articleA list of selected additional articles on the Science Web sites

http://www.sciencemag.org/cgi/content/full/291/5501/84#related-content

72 article(s) on the ISI Web of Science. cited byThis article has been

http://www.sciencemag.org/cgi/content/full/291/5501/84#otherarticles 2 articles hosted by HighWire Press; see: cited byThis article has been

http://www.sciencemag.org/cgi/collection/astronomyAstronomy

: subject collectionsThis article appears in the following

http://www.sciencemag.org/help/about/permissions.dtl in whole or in part can be found at: this article

permission to reproduce of this article or about obtaining reprintsInformation about obtaining

registered trademark of AAAS. c 2005 by the American Association for the Advancement of Science; all rights reserved. The title SCIENCE is a

CopyrightAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005. Science (print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by the

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

40. J. Norris, G. Marani, J. Bonnell, Astrophys. J. 534, 248(2000).

41. E. Fenimore, E. Ramirez-Ruiz, in preparation (availableat http://xxx.lanl.gov/abs/astro-ph/0004176).

42. D. Reichart et al., in preparation (available at http://xxx.lanl.gov/abs/astro-ph/0004302).

43. S. Woosley, Astrophys. J. 405, 273 (1993).44. B. Paczynski, Astrophys. J. 494, L45 (1998).45. C. Fryer, S. Woosley, D. Hartmann, Astrophys. J. 526,

152 (1999).46. Hypernovae (44) are massive rotating stars whose core

collapse is expected to lead to a BH accreting from adebris torus resulting in a GRB, as well as the ejection ofa supernova remnant shell of energy above that of usualsupernovae. Collapsars (45) are massive stars, which inthe course of merging with a compact companion un-dergo core collapse leading to a BH, some of which resultin a GRB, leaving a supernova-like remnant. Magnetarsare ultrahigh magnetic field (B * 1015 G), fast-rotating(initially *millisecond period) neutron stars, essentiallysuper-pulsars (50, 51) resulting in a GRB; they would becreated by the collapse of a massive rotating star leavinga supernova remnant. A supranova (62) is a massive starwhose initial core collapse would lead to a neutron starand an ejected supernova remnant; this precedes by daysto weeks a second collapse of the neutron star into a BH,which leads to a GRB. NS-NS and NS-BH mergers (12)also lead to a BH accreting from a debris torus, whichwold be expected to lead to a GRB of comparable energyto those from massive stars (49); supernova remnantsfrom the formation of the initial NS or BH would haveoccurred and dissipated *107 to 108 years before theGRB. In all of these cases, strong magnetic fields and e 6,g from neutrino-antineutrino annihilation are expectedto drive a jet-like relativistic outflow that leads to thestandard fireball shock production of GRB and afterglows(44, 45, 48). In the massive progenitor cases, this wouldoccur after the jet funnels through the stellar envelope,probably leading to a highly collimated jet, whereas inthe NS-NS and NS-BH mergers the lack of an envelopemight lead to substantially less collimation.

47. D. Eichler, M. Livio, T. Piran, D. N. Schramm, Nature340, 126 (1989).

48. P. Meszaros, M. J. Rees, Astrophys. J. 482, L29 (1997).49. iiii , R. Wijers, New Astron. 4, 313 (1999).50. V. V. Usov, Mon. Not. R. Astron. Soc. 267, 1035 (1994).51. C. Thompson, Mon. Not. R. Astron. Soc. 270, 480

(1994).52. H. C. Spruit, Astron. Astrophys. 341, L1 (1999).53. R. D. Blandford, J. P. Ostriker, P. Meszaros, in

preparation.54. High Energy Transient Explorer (http://space.mit.edu/

HETE).55. Swift (http://swift.gsfc.nasa.gov).56. T. Galama, R. Wijers, in preparation (available at

http://xxx.lanl.gov/abs/astro-ph/0009367).57. P. Meszaros, M. J. Rees, Mon. Not. R. Astron. Soc. 299,

L10 (1998).58. C. Weth, P. Meszaros, T. Kallman, M. J. Rees, Astro-

phys. J. 534, 581 (2000).59. M. Bottcher, C. L. Fryer, in preparation (available at

http://xxx.lanl.gov/abs/astro-ph/0006076).60. L. Piro et al., Science 290, 955 (2000).61. L. Amati et al., Science 290, 953 (2000).62. M. Vietri, G. Perola, L. Piro, L. Stella, Mon. Not. R.

Astron. Soc. 308, L29 (2000).63. In the supranova scenario (60), the interaction of the

GRB afterglow with the supernova shell ejected weeksearlier and located about a light day from the burst isenvisaged to give rise to Fe recombination lines; thisrequires in excess of 0.1 to 1 solar masses of Fe in theshell. In a decaying magnetar model (67), a long-lived(*1 day) magnetar or accreting BH with a continuingbut decaying jet interacts with the expanding stellarenvelope to produce Fe recombination lines, requiringonly a normal Fe abundance.

64. T. Galama et al., Nature 395, 670 (1998).65. J. van Paradijs, Science 286, 693 (1999).66. J. C. Wheeler, in Supernovae and Gamma Ray Bursts,

M. Livio, K. Sahu, N. Panagia, Eds. (Cambridge Univ.Press, Cambridge, in press) (available at http://xxx.lanl.gov/abs/9909096).

67. M. J. Rees, P. Meszaros, Astrophys. J., in press (avail-able at http://xxx.lanl.gov/abs/astro-ph/0010258).

68. R. Wijers, J. Bloom, J. Bagla, P. Natarajan, Mon. Not.R. Astron. Soc. 294, L13 (1998).

69. T. Totani, Astrophys. J. 511, 41 (1999).70. A. Blain, P. Natarajan, Mon. Not. R. Astron. Soc. 312,

L35 (2000).71. S. Mao, H. J. Mo, Astron. Astrophys. 339, L1 (1998).72. D. Q. Lamb, D. Reichart, Astrophys. J. 536, L1 (2000).73. R. Perna, A. Loeb, Astrophys. J. 508, L135 (1998).74. A. Loeb, R. Barkana, Annu. Rev. Astron. Astrophys., in

press (available at http://xxx.lanl.gov/abs/astro-ph/0010467).

75. N. Hayashida et al., Astrophys. J. 522, 225 (1999).76. E. Waxman, Phys. Rev. Lett. 75, 386 (1995).77. C. Dermer, in preparation (available at http://xxx.lanl.

gov/abs/astro-ph/0005440).78. E. Waxman, J. N. Bahcall, Phys. Rev. Lett. 78, 2292

(1997).79. J. Rachen, P. Meszaros, Phys. Rev. D 58, 123005

(1998).80. E. Waxman, J. N. Bahcall, Phys. Rev. D 59, 023002

(1999).81. F. Halzen, 17th International Conference on Weak

Interactions and Neutrinos (available at http://xxx.lanl.gov/abs/astro-ph/9904216).

82. E. V. Derishev, V. V. Kocharovsky, Vl. V. Kocharovsky,Astrophys. J. 521, 640 (1999).

83. J. N. Bahcall, P. Meszaros, Phys. Rev. Lett. 85, 1362(2000).

84. P. Meszaros, M. J. Rees, Astrophys. J., inpress (available at http://xxx.lanl.gov/abs/astro-ph/0007102).

85. R. Atkins et al., Astrophys. J. 533, L119 (2000).86. N. Gehrels, P. Michelson, Astropart. Phys. 11, 277

(1999).87. L. S. Finn, S. Mohanty, J. Romano, Phys. Rev. D 60,

121101 (1999).88. Supported by NASA grants NAG5-9192 and NAG5-

9153 and by NSF grant PHY94-07194.

R E V I E W

Magnetohydrodynamic Production ofRelativistic Jets

David L. Meier,1* Shinji Koide,2 Yutaka Uchida3

A number of astronomical systems have been discovered that generatecollimated flows of plasma with velocities close to the speed of light. In allcases, the central object is probably a neutron star or black hole and iseither accreting material from other stars or is in the initial violent stagesof formation. Supercomputer simulations of the production of relativisticjets have been based on a magnetohydrodynamic model, in which differ-ential rotation in the system creates a magnetic coil that simultaneouslyexpels and pinches some of the infalling material. The model may explainthe basic features of observed jets, including their speed and amount ofcollimation, and some of the details in the behavior and statistics ofdifferent jet-producing sources.

A jet is a tightly collimated stream of fluid, gas,or plasma. It typically carries kinetic and inter-nal energy and linear momentum, and if it is setspinning about its direction of motion by some

means, it can carry angular momentum as well.A relativistic jet is one whose speed approachesthe universally constant speed of light c 5299,792.5 km s21. At such velocities, Ein-stein’s theory of relativity becomes important.The kinetic energy of motion (and possibly theinternal thermal and magnetic energy as well)adds mass to the jet, equal to Ekinetic/c

2, makingit more difficult to accelerate. Also, as seen byviewers at rest, time slows down in the movingjet material, and any light or radio emissionfrom the jet tends to be radiated in the direction

of flow, not isotropically, as would be the caseif the flow velocity were subrelativistic. Be-cause c is a maximum speed limit and becauseconditions become more extreme as it is ap-proached, the Lorentz factor

G 5 S1 2v2

c2D21/ 2

(1)

is often used to characterize the speed, ratherthan the velocity v. For example, G 5 10describes a flow at 99.5% of c, with eachparticle in the jet having a mass 10 times asmuch as it has when it is at rest.

For analyzing observations of relativisticjets, the Doppler factor

D 5 FGS1 2v

ccos uDG21

(2)

is an equally important parameter; u is the anglebetween the jet flow direction and the observ-er’s line of sight. For low-speed jets with v ,,c, this reduces to the familiar nonrelativisticDoppler factor D ' 1 1 (v/c) cos u that isresponsible, for example, for the slight frequen-

1Jet Propulsion Laboratory, California Institute ofTechnology, Pasadena, CA 91109, USA. 2Faculty ofEngineering, Toyama University, Gofuku 3190,Toyama 930-8555, Japan. 3Physics Department, Sci-ence University of Tokyo, Shinjuku-ku, Tokyo 162,Japan.

*To whom correspondence should be addressed. E-mail: David.L.Meier@jpl.nasa.gov

5 JANUARY 2001 VOL 291 SCIENCE www.sciencemag.org84

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

cy shift of spectral lines in binary stars as theyapproach or recede. The relativistic Dopplerfactor describes both the time dilation effect,which is present even when the jet motion isperpendicular to the line of sight (u 5 p/2), andthe effects of Doppler boosting and focusing. Ajet emitting at a single spectral color, for exam-ple, would appear to be emitting at a frequencyD times higher and into a solid angle D2 timessmaller—a combined factor of D3 times bright-er if moving toward us. If moving away (u .p/2), the jet would be fainter, because D wouldbe ,1.

Relativistic Astrophysical JetsRelativistic jets are common in the astrophys-ical environment. Objects known or suspect-ed to produce them include the following.

Radio galaxies and quasars. The extraga-lactic radio sources produce by far the largestand most energetic jets in the universe, al-though they do not produce the fastest onesnor those with the highest instantaneous pow-ers. The measured speeds of extragalacticradio jets range from 0.1c to G ' 20 andperhaps higher (1). The less luminous onesappear as giant elliptical radio galaxies (Fig.1), and the most luminous appear as radioquasars, generating up to 1046 erg s21 ormore of power. Often, the twin jets are point-ed at a large angle to our line of sight, allow-ing the full extent of the radio source pow-ered by the jet—up to a few megaparsecs insize—to be seen. In a few sources, however,one of the jets points nearly directly towardEarth and the other points nearly directlyaway. The approaching jet therefore appearsto be substantially Doppler brightened, andthe receding one may be so Doppler dimmedthat it is difficult or impossible to detect.

The plasma in these jets contains high-energy electrons, trapped in a magnetic field,that emit primarily radio synchrotron radia-tion, but are detectable in optical synchrotronif the source is close enough. Discovered acentury ago, the jet in the galaxy Messier 87(M87) (Fig. 1), for example, has shown mo-tion with a Lorentz factor of up to ;6 and ispointed at u , 19° to our line of sight (2). Atthe center of M87 lies a supermassive blackhole, ;3 3 109 MJ (solar masses) in size (3),that is thought to be the heart of the engineresponsible for generating the jet. Black holesof 106 to 1010 MJ are, in fact, thought topower nearly all types of active galactic nu-clei (AGN), including radio galaxies, radioquasars, radio quiet quasars, and Seyfert gal-axies. Why some of these objects appear tohave produced jets nearly continuously fortens of millions of years or longer, whereasothers have been jet-quiet for an equally longtime, is one of the major scientific questionsin this field.

Microquasars. Although the supermas-sive quasars lie at the centers of galaxies and

are fed by ambient stars and gas that collectthere and accrete into the black hole, therealso are much lower mass versions of these,scattered about the Milky Way Galaxy andfed by the stripping of atmospheric layersfrom a single companion star. A few of thesebinary x-ray sources, called microquasars,produce jets (4 ). There are two basic types ofmicroquasar: one whose central engine ispowered by a black hole of ;10 MJ and onethat is powered by an even lower mass object,a neutron star of only ;1.4 MJ. In the lattercase, the jets can be moderately relativistic,0.26c for the twin-jet star SS 433, for exam-ple (5). In the black hole cases, the jet speedsreach G ; 2.5 (0.92c). So far, a microquasarwith a Lorentz factor of 10 to 20 has not beenseen. This just may be due to small-numberstatistics: the number of high-G microquasarsin our Galaxy may be small already, and it isunlikely that Earth lies within the small-emis-sion solid angle of any one of these. Becausethe time scale for events to happen nearaccreting black holes is directly proportionalto the mass of the hole, microquasars offerthe possibility of watching a quasar-like ob-ject evolve through many stages of its life ina few years or decades rather than waiting themillions of years necessary for the extraga-lactic objects to change.

Supernovae. There is now evidence thatsupernovae, especially those that are not sur-rounded by a large red giant envelope, ex-plode in a decidedly aspherical manner (6 ).Theoretical and observational studies point to

the possibility that the asymmetry could becaused by the ejection of twin jets from thecentral core of the supernova as it collapses toform a hot neutron star (7 ). The speed of sucha jet would be about the escape speed fromthe proto–neutron star (0.25c to 0.6c). Evenif only a small fraction of the core wereejected in the jet (e.g., ;1%), it would haveenough kinetic energy to substantially alterthe structure of the expanding supernovashell, if not in fact to provide much of theobserved explosive power of 1051 to 1052

ergs in a few seconds of time.Gamma-ray bursts. Gamma-ray bursts

(GRBs) provide perhaps the most extremeexample of relativistic flow that may be a jet,exhibiting speeds of G ; 100 or more. Al-though GRBs may be associated with super-novae in some cases, they are a million timesrarer than classical supernova events (8). Ifonly those events are observed that are withinan angle u ; G21 of our line of sight, thenthere could be 104 more events Dopplerboosted in directions other than ours, bring-ing the GRB rate to within a factor of 100 orso of the supernova rate and their derivedexplosive energies down to ;1052 to 1053

ergs, about the same as that of powerfulsupernovae. The high Lorentz factors andenergies are consistent with the catastrophicformation of a stellar mass black hole of ;10MJ, with ;1% going into a jet outflow. Thiscould be the extreme example of the jet-producing supernova discussed above, inwhich instead of halting at the neutron star

Fig. 1. The jet in the galaxy M87 displays most of the important features of relativistic jets. Theapproaching northwest jet is Doppler boosted, whereas the southeast one is virtually undetectablebecause it radiates away from Earth. The lobes, consisting of decelerated jet material, radiateisotropically, and therefore both are visible. The full extent of the source projected on the sky inthis image is ;80 arc sec or 6 kpc. Because the source is at an angle of ,19° to our line of sight,its deprojected length must be at least 20 kpc. Deep in the core (inset), the jet shows an initial wideopening angle (60°) that decreases with distance from the core. This indicates that the accelerationand collimation region may be resolved. The length of the jet emission in the inset is ;0.001 arcsec or 16,000 astronomical units, which is only ;250 times the Schwarzschild radius of the central3 3 109 MJ black hole. [Images were made with the National Radio Astronomy Observatory’s VeryLarge Array and Very Long Baseline Array and are courtesy of J. Biretta and W. Junor; reprinted bypermission from Nature (37) copyright (1999) Macmillan Magazines Ltd.]

www.sciencemag.org SCIENCE VOL 291 5 JANUARY 2001 85

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

stage, the collapse continues to the black holestage, producing an even faster jet in theprocess. Other scenarios, such as the mergerof two neutron stars, could trigger a similarevent.

In all observed cases of relativistic jets,the central object is compact, either a neutronstar or black hole, and is accreting matter andangular momentum. In addition, in most sys-tems there is direct or indirect evidence thatmagnetic fields are present (detected in thesynchrotron radiation in galactic and extraga-lactic radio sources or inferred in collapsingsupernovae cores from the association ofremnants with radio pulsars). This combina-tion of magnetic fields and rotation may beresponsible for the observed relativistic jets.

Basic Physics ofMagnetohydrodynamic Accelerationand CollimationAlthough several different methods of pro-ducing and collimating jets have been pro-posed, the leading model is the magnetohy-drodynamic (MHD) model. It potentially canaccount for jet collimation and acceleration torelativistic velocities while operating withinthe gravitational collapse and/or accretionparadigms for jet-producing sources. In addi-tion, the model suggests a trigger mechanismfor some GRBs, a way of producing the mostpowerful quasar jets observed as well as thedifference between radio loud and radio quietquasars, and an explanation for the detailedchanges that occur in microquasar jets astheir accretion disks change their structure.

The flow of a magnetized plasma is mostgenerally described by kinetic theory, generalrelativity, and Maxwell’s equations for the

electromagnetic field. However, many of itsfeatures are captured by making two simpli-fying assumptions: The plasma particles actlike a fluid and the conductivity is so high inthe plasma that electric fields generated byfree charges are shorted out. Both of theseassumptions (which describe the astrophysi-cal plasmas of interest) give rise to the fieldof study of ideal magnetohydrodynamics. Al-though the equations are still complex innature, the differences between regular fluidflow and ideal MHD flow can be understoodfrom the following discussion and from Fig.2, which shows a three-dimensional MHD jetpropagation simulation (9). Under these as-sumptions, the magnetic field lines thread theplasma and are tied to it (frozen in). Thesefield lines have three important properties.First, to a good approximation, plasma cannotcross the field lines; it can only flow parallelto them. If the field is strong (i.e., if thehydrodynamic pressure of the plasma rv2 isless than the magnetic pressure B2/8p, wherer is the plasma mass density, v is its velocity,and B is the magnetic field strength) and if itis anchored in a rotating star or disk, then anyplasma trapped in the field will be flungcentrifugally outward along the field lines.On the other hand, if the field is weak or theplasma is dense, then the rotating field will bebent backward in a sweeping spiral. Second,parallel magnetic field lines tend to repeleach other. This produces a partial pressureon the plasma perpendicular to the field lines,but not parallel to them, due solely to thefield. A weak field can be strengthened bybringing together many weak parallel lines offorce to produce the equivalent of a fewstrong ones. Thus, compression perpendicu-

lar to the field lines or toroidal coiling aroundan axis for many turns can enhance the field,increasing its pressure and energy density.Third, magnetic field lines do not maintain acurved shape unless they are acted on byforces from the plasma or other field lines.Left alone, they tend to straighten likespringy wires. If coiled in a hoop or spiral,the field will try to shrink around its axis toeliminate all but the straight axial componentof the field. This hoop stress is responsiblefor the well-known pinch effect of plasmaphysics and for the collimation of relativisticjets.

To accelerate and collimate a jet withmagnetic fields, all that is needed is a gravi-tating body to collect the material to be eject-ed, a poloidal magnetic field threading thatmaterial, and some differential rotation (Fig.3). The differential rotation produces a mag-netic field helix about the rotation axis. Thisrotating field coil then drives the plasmatrapped in it initially upward and outwardalong the field lines as they try to uncoil. Asthis twist propagates outward, the toroidalfield pinches the plasma toward the rotationaxis. Depending on the relative importance ofthe magnetic field, plasma density, and rota-tion, a variety of results are possible, such asa broad uncollimated wind, a slowly colli-mating bipolar outflow, and a highly colli-mated jet.

The physics of jet production can be an-

Fig. 2. A three-dimen-sional simulation ofthe propagation of amagnetized jet, whichdepicts most of theproperties of the MHDmodel. The diagramshows flow velocity(arrows), the plasmadensity field (color,with white and blueindicating high andlow pressure, respec-tively), and the mag-netic lines of force(metallic tubes). Theinitially axisymmetric,rotating jet has devel-oped a helical-kink in-stability that distortsits shape. The plasmaflow still follows thefield lines. Such an instability may explain the wiggles observed in some parsec-scale radio jets. Thesuper–Alfvenic jet terminates in a strong shock wave at right, as it propagates into a region withdecreasing Alfven velocity. High-energy particles accelerated in the rotating magnetic twists, andespecially in the compressed field behind the bow shock, will emit synchrotron radiation. This shocktherefore may correspond to the hot spot often seen at the end of jets in many radio sources.[Courtesy of M. Nakamura]

Fig. 3. Schematic diagram depicting the MHDacceleration and collimation model. Magne-tized and rotating inflow toward a compactobject (solid arrows) winds the magnetic fieldlines into a rotating helical coil called a torsion-al Alfven wave train (TAWT). Magnetocentrifu-gal forces expel some of the material along thefield lines and magnetic pressure and pinchingforces (short open arrows) further lift and col-limate it into a jet outflow (long open arrows).

5 JANUARY 2001 VOL 291 SCIENCE www.sciencemag.org86

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

alyzed by comparing time scales on whichdifferent processes occur. In this case, themost important time scale is the dynamicaltime td, which is the characteristic time forinformation to propagate through the system.In a magnetized plasma, td 5 R0/cms, wherethe magnetosonic sound speed cms includesboth plasma and magnetic field pressure andR0 is the characteristic size of the jet-produc-tion region. Because the system is initially inequilibrium and confined by gravity, the dy-namical time is comparable to the free-fall orescape time tesc0 5 (R0

3/ 2GM )1/ 2 (which isa constant factor 1/23/2p 5 0.11 shorter thanthe orbital period at R0), where M is the massof the central object and G is the gravitationalconstant.

The response of a jet-producing system tothe twisting of the magnetic field depends onthe time it takes for the magnetic energy to,say, double. If this takes longer than a dy-namical time, then the system’s internalstructure can adjust in a quasi-static fashionto accommodate the new conditions. Howev-er, if the increase occurs in less than a dy-namical time, then the new conditions sur-prise the system, forming shock waves thatdistribute the new information in less thana sound-crossing time. Often, such rapidchanges in the system result in a catastrophe,such as an explosion or a collapse. Determin-ing which type of jet outflow results andfinding what its effects are on the jet-produc-ing system are some of the chief goals of thestudy of MHD jet production.

Astrophysical Applications of theMHD MechanismOne of the earliest applications of the MHDmodel was pulsar wind theory, developed toexplain observations of the Crab Nebula (10,11). The observations showed that a largeamount of particle energy was being injectedcontinually into a supernova remnant, proba-bly from the pulsar at the center of the nebula.Because the magnetic fields near a pulsar arevery strong (B2/8p .. rv2 ) and the particledensity is low, radial outflow was expected,not a collimated jet. Therefore, work on pul-sar winds tended to focus on accelerating theparticles and feeding the nebula. Much later,however, the twin-jet star SS 433 was discov-ered, which may be a pulsar buried in a denseaccreting envelope (5, 12). This object isprobably an example of the opposite extreme:as the dense material falls toward the neutronstar, it bends the pulsar magnetic field back-ward, producing a tight helical coil that re-sults in a narrow jet (Fig. 4A). In addition,new images from the Chandra X-ray Obser-vatory now show that even isolated pulsarscan produce jetlike structures (13).

Also in the late 1960s, and quite indepen-dently, investigators studying the late stagesof stellar evolution performed computer sim-

ulations of the effects of a magnetic field onthe collapse of a rotating stellar core as itforms a proto–neutron star (14, 15). The sim-ulations found that, even if the initial mag-netic field were weak, during the core col-lapse it was enhanced by differential rotationto such large values, in less than a dynamicaltime, that a magnetic explosion occurred,driving away the stellar layers by magneticpressure alone, sometimes in a jet along therotation axis (Fig. 4B). Further studies of thismechanism (16 ) concluded that explosiveMHD jets would not occur in most collapsingsupernova cores. Instead, over several dy-namical time scales, a magnetic bubblewould be produced in each of the northernand southern hemispheres and then buoyantlyrise up the rotation axis, bursting into thesurrounding stellar envelope. Only in a fewrare energetic cases would a narrow fast jetform.

Modern MHD jet theory, and its relationto accreting stars and black holes, began inthe mid-1970s when it was shown that thesame MHD processes occurring in pulsarsand collapsing magnetized supernova coresalso could occur in magnetized disks inKeplerian rotation about accreting stars andblack holes (17, 18), as well as near thehorizon of the spinning black hole (19). In the

latter case, the magnetic field extracts energyand angular momentum not from the accret-ing matter but rather from the black hole’srotation. These two related jet mechanismsare pictured in Fig. 4, C and D.

One way to study these MHD accelerationproblems is to set up and solve the full set ofeight partial differential MHD equations on acomputer, making as few assumptions as pos-sible. Such simulations often run for severalhours or days on large supercomputers, cal-culating the evolution of a rotating disk orstellar core of magnetized plasma and show-ing the effects of the field on the flow, and theflow on the field. Multidimensional and su-personic processes, such as jets, rotation, andshock waves, can be followed in detail.

With the exception of the early work onMHD supernovae, until the mid-1980s mostMHD acceleration models were semi-analyt-ic; that is, by making several simplifyingassumptions, the eight MHD partial differen-tial equations were reduced to one ordinarydifferential equation that could be solvedquickly on a modest computer. One of themost widely used assumptions was that of asteady state, in which the plasma flow andmagnetic field structure do not change withtime. This assumption causes the solution tofocus on the long-term structure that forms

Fig. 4. Schematic dia-grams of four astro-physical scenarios inwhich differential rota-tion of a magnetic fieldmight generate relativ-istic jet outflow. Coloris used to aid in identi-fication of the fieldlines. (A) The dipolefield of a heavily ac-creting, rapidly rotatingpulsar can be sweptback by the accretingmatter as close as afew tens of kilometersfrom the stellar surface.Some of this materialwill be ejected in a jetat the local escapespeed. (B) A slowly ro-tating pre-supernovawhite dwarf or densestellar core will collapseto a rapidly rotatingproto–neutron star.Even an initially uni-form axial field will bedrawn inward andwound into a tight coil,ejecting some of the dense core material. The jet may have sufficient power to alter the shape of thesupernova ejecta or even drive the explosion on its own. (C) The poloidal magnetic field protruding froman accretion disk orbiting a compact object will fling disk coronal material outward in a wind.Conservation of angular momentum will slow the wind’s rotation and, if the outflow is dense enough,sweep back and coil the field lines. (D) Near a rotating black hole, the space itself rotates differentially.This dragging of inertial frames is particularly strong inside a radius about twice that of the hole—theergosphere—where material must rotate with the hole. Here only the twisting of vertical field lines isshown, but as the plasma accretes toward the black hole, these lines will be drawn inward, creating astructure similar to that in (B) or (C).

www.sciencemag.org SCIENCE VOL 291 5 JANUARY 2001 87

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

after transient effects due to the initial condi-tions have died away. Other assumptionswere made to simplify the geometry of theproblem, such as that of self-similarity. Thisassumes that the structure scales with dis-tance from the compact object, so that it lookssimilar at every radius. Under these simplify-ing assumptions, most semi-analytic studiesshowed that, although MHD winds shouldform, the acceleration should be slow, and theoutflow should occur in a rather broad bipolarstructure, not a tightly collimated jet (20, 21).The broad structure found from steady-statestudies was inconsistent with the narrow jetfound in dynamical supercomputer simula-tions of collapsing supernova cores (14 ).

Semi-analytic studies and numerical sim-ulations provide complementary ways inwhich jet formation can be investigated. An-alytic or semi-analytic studies often ignorethe effects of an inner accretion disk bound-ary, for example, or of a central black holehorizon, and they usually do not treat thetime-dependent nature of the flow. On theother hand, because their results are ex-pressed in terms of simple parameters (cen-tral object mass, magnetic field strength,etc.), they often are applicable to many dif-ferent situations. Both approaches are criti-cally dependent on the initial conditions andboundary conditions that are applied. In thecase of numerical simulations, these condi-tions even can cause spurious effects, partic-ularly along boundaries where the plasmashould flow out of the computational domainunimpeded. Sometimes the boundary instead

reflects waves back into the grid, modifyingthe flow in an unphysical manner. Such errorsare minimized by locating outflow bound-aries as far away as possible by progressivelyincreasing the spacing between mesh pointsbeyond the region of interest. When per-formed and interpreted carefully, numericalsimulations have an ability to characterize thetwo- or three-dimensional structure of theplasma flow and magnetic field that is un-equaled by any other technique. The goal is tocreate a third field of study, complementingobservation and theory, in which the compu-tations themselves are sophisticated enoughthat numerical experiments on them, withcomputer visualization techniques, can yieldinsight into the inner workings of astrophys-ical processes that could not be obtained inany other way.

Dynamical MHD SupercomputerSimulations: Narrow Jets at theEscape VelocityNumerical simulations of magnetized accre-tion disks around stars (22, 23) and super-massive objects (24–26 ) have shown that acollimated jet, similar to that discovered forcollapsing stellar cores, is a general feature ofrapidly rotating, gravitationally confinedplasmas that are threaded with a magneticfield. A typical simulation of this type, usinghigh-fidelity modern supercomputer and vi-sualization techniques, is shown in Fig. 5.

The simulation begins with a rather thickaccretion disk or torus surrounding a pointmass at the center. This initial disk is in

rotational equilibrium about the central ob-ject, producing differential rotation in theradial direction. The torus also is threadedwith an axial (vertical) magnetic field of suf-ficient strength to exert a braking force on therotating plasma. As the simulation proceeds,the braking force removes angular momen-tum from the torus, transferring it up alongthe magnetic field lines and to the coronalplasma (which also is frozen to the fieldlines), in a large-amplitude torsional Alfvenwave train (TAWT). As these rotating mag-netic twists propagate out in bipolar direc-tions along the rotation axis, they push outand pinch the coronal plasma into a slenderspinning jet. The loss of angular momentumto the jet allows the disk material to falltoward the central object, with half of thegravitational energy released in this accretiongoing into additional kinetic energy of rota-tion that continues to power the TAWT andthe accretion. This process is most effectivenear the surface of the torus, resulting in anavalanche type of accretion in the surfacelayers.

This sweeping pinch mechanism appearsto be nearly universal. It can occur in acollapsing star, above an accretion disk, ornear a rotating black hole. In a few dynamicaltimes, a differentially rotating magnetic fieldcan produce twin tightly collimated jets alongthe rotation axis from what would otherwisehave been only a flattened system. The twojets carry away angular momentum and rota-tional energy and, if not exactly balanced inlinear momentum, also may impart a thrust tothe accreting object.

Apart from the collimation itself, perhapsthe most interesting parameter determined bythese simulations is the speed of the ejectedjet. In most simulations performed, the jetspeed is close to the escape speed as mea-sured at the base of the jet (27 ). For all starsfor which the rotation is nonrelativistic, in-cluding nonrotating black holes, the escapespeed is given by vesc0 5 (2GM/R0)1/ 2. Inthe more general case of rotating black holes,the escape Lorentz factor (given by the in-verse of the gravitational lapse function) is

Gesc0 5 5F1 1 S1 1 2Rg

R0DSj

Rg

R0D2G

F1 2 2Rg

R01 Sj

Rg

R0D2G 6

1/2

(3)

where Rg 5 GM/c2 is the gravitational radiusof the black hole (one-half the Schwarzschildradius) and j 5 J/Jmax is the black holeangular momentum normalized to the maxi-mum possible value, Jmax 5 GM 2/c. Whenj 5 0, Eqs. 1 and 3 reduce to the familiarexpression for vesc0.

Fully general relativistic simulations of jetproduction have been performed for accretion

Fig. 5. An MHD simulation of a thick magnetized torus surrounding a supermassive (108 MJ)central object (26). (A) Initial state showing the torus in rotational equilibrium with an axialmagnetic field. (B) As the simulation begins, the differentially rotating torus drags the field lines inthe azimuthal direction, creating a braking force that allows the material to accrete inward and gainadditional rotational energy. The effect of this process is to produce a torque on the externalmagnetic field, generating a torsional Alfven wave and a spinning plasma jet that carries awaymatter, angular momentum, and energy from the system. Far above the disk, the torsional waveswill be unstable to the helical-kink instability, generating the wiggled structure seen in Fig. 2.

5 JANUARY 2001 VOL 291 SCIENCE www.sciencemag.org88

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

disks around both nonrotating (Schwarzs-child) black holes with j 5 0 and rotating(Kerr) holes with j 5 0.95 (28–31). In theSchwarzschild case (Fig. 6A), the radius ofthe inner edge of the accretion disk is aboutequal to that of the last stable orbit (6Rg),making the jet-production region aroundR0 5 7Rg to 8Rg in size. In the Kerr case(Fig. 6B), stable orbits exist nearly down tothe horizon at 1.31Rg, so R0 must be of orderof the radius of the ergosphere (Re 5 2Rg).The ergosphere is the region surrounding arotating black hole, inside of which accretingmaterial must rotate in the same direction asthe black hole rotates. From Eq. 3, we expectjet speeds of about Gesc0 5 1.18 and 2.54(vesc0 5 0.53c and 0.92c, respectively). Thisis confirmed by the simulations in Fig. 6.

In the Schwarzschild case, the jet is drivenby the orbital motion of the accretion diskaround the black hole. In the Kerr case, how-ever, although we gave the disk no initialrotation, a powerful G . 2 jet still formed.The reason is that, as the accreting matterplunged into the ergosphere, it becamecaught up in the rotating space around theblack hole (Fig. 4D). This rotation with re-spect to the outside material created a sweep-ing pinch in a manner similar to that in theorbiting disk case. The jet was driven not byany intrinsic rotation in the disk but by therotation of the black hole itself.

In all the above simulations, the processof accreting the inner disk, winding the field,and ejecting the jet is a dynamical one, oc-curring in one or two rotation times. Howev-er, it is not necessarily a transient one. Ifaccreting material and the magnetic field arecontinually supplied from the outer region ofthe disk at a rate comparable to that fallinginto the hole plus that ejected by the jet, then

the system will reach a steady state in whicha jet is continuously produced. On the otherhand, if the disk is depleted by the rapidaccretion and jet at a rate faster than it isreplenished from the outside, then the jet willcease and begin again only after the diskrefills.

Steady-State Simulations: Broad Jetsat the Escape VelocityThe above model works as long as the as-sumption of a magnetic field frozen into theplasma remains valid. This certainly will bethe case when the infall rate is close to thefree-fall rate, as it is in the above simulations.However, if the rate at which the magneticfield is being dragged inward by the accretioninflow is slower than the rate at which itdiffuses outward against that flow, then thefield in and above the disk at a given radiuswill be determined mainly by local turbulentdynamo processes generating that field. In-flow of magnetic field will be negligible.This probably will be the case when the diskis in Keplerian rotation and the inflow veloc-ity is a factor of 10 or more smaller than thefree-fall rate. Because one wants to avoid thecomplications of the internal dynamo pro-cesses in the disk, to simulate this oppositeextreme case, it is frequently assumed that thedisk is infinitely thin along the equatorialboundary and continuously boiling off mate-rial into poloidal magnetic field lines that areembedded in it (32–34 ). Although these sim-ulations begin with an initial disk coronaconfiguration, they are typically run for verylong times (1000 dynamical times or more)until that initial configuration has been ex-pelled by the MHD wind from the disk. Atthis point, the magnetic field structure andplasma flow cease to change with time and

the system reaches a steady state, just asassumed in the early semi-analytic studies ofMHD acceleration. The resulting structurewill be a function of the boundary conditionsonly and not the initial conditions.

The process of jet formation in this case issimilar to that in Figs. 5 and 6, but the meansof inducing differential rotation is different.The matter injected from the disk boundary isinitially flung outward along the field lines;conservation of angular momentum in thatmaterial then bends back the field into aspiraling coil that eventually lifts and colli-mates the flow along the rotation axis. Thisprocess is depicted schematically in Fig. 4C,and a numerical simulation of it is shown inFig. 7. As suggested by the earlier semi-analytic studies (20), the acceleration issmoother and the collimation is slower thanin the dynamical sweeping pinch. The speedsteadily increases along the outflow until itexceeds the local escape velocity, the localpoloidal Alfven speed (vAp 5 Bp/(4pr)1/2,where Bp 5 (BR

2 1 BZ2)1/2 is the combined

poloidal field strength in the cylindrical radial(R) and axial (Z) directions and r is theplasma mass density), and finally the localtotal Alfven speed vAt, which includes thetoroidal component Bf (Fig. 7). vAt is thespeed with which magnetic waves travelalong the twisted field. The jet eventuallycollimates and reaches a speed of order vesc0,but this does not occur until well above thedisk. There is a large region (perhaps 100 Rg

or so in size in the black hole case) where theflow is rather broad.

The numerical simulations suggest that,when a jet-producing system enters an activedynamical phase, it should generate tightly col-limated jets that may be time dependent. On theother hand, more quiescent sources should pro-

Fig. 6. Two fully general rel-ativistic simulations of jetproduction by accretiondisks around black holes.Each begins with an axialfield. Plots are meridionalcuts, with length units inSchwarzschild radii (2Rg),and show the plasma densityin blue-white color, poloidalvelocity vectors with whitearrows, and a poloidal mag-netic field as solid whitelines. (A) A nonrotating,Schwarzschild hole with amoderately strongly magne-tized Keplerian disk whoserotation drives an MHD jetat the escape speed (;0.4c)[from (28)]. (In this simula-tion, a gas-pressure-drivenoutflow also is ejected froma radius interior to the laststable orbit at a somewhat higher speed.) (B) A rotating Kerr hole ( j 5 0.95) (in the lower left corner) with a nonrotating disk [from (30)]. Preliminaryanalysis indicates that the dragging of inertial frames drives the jet from a region just outside the ergosphere at R ; 1rS to 2rS (2Rg to 4Rg) at theescape speed of ;0.93c (G ' 2.7).

www.sciencemag.org SCIENCE VOL 291 5 JANUARY 2001 89

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

duce steady-state flows that collimate moreslowly. Observations of some microquasars andradio galaxies lend support to this model. Themicroquasar GRS 19151105 often undergoesbright unsteady outbursts, in which the x-rayluminosity reaches close to the limit establishedby Eddington for radiation pressure on freeelectrons. During these outbursts, the inner diskexhibits cyclic behavior, firing off a jet every 12to 60 min, as the disk is emptied by the jet andthen refilled by accretion (35). However, after amajor outburst subsides, GRS 19151105 entersa quiescent phase that lasts for several days.About 18 hours after the beginning of thisphase, a steady weak jet appears and remainsuntil the next outburst (36). So the source pro-duces transient jets when it is bright and dy-

namic and a steady jet when it is in quiescence.In addition, high-resolution images of the

core of the radio galaxy M87 at 43 GHz (37 )may have resolved the jet-collimation regionin the source and show a possible broad flowthat collimates slowly (Fig. 1). The radiopower of this galaxy is rather weak (1041 ergs21) for the mass of its black hole (3 3 109

MJ). Both its possible broad collimation re-gion and its weak jet power, therefore, areconsistent with it being in a steady state likethat depicted in Fig. 7.

Finally, the steady-state calculations maydescribe the behavior of a newly formed pul-sar just after collapse of the supernova core.A recent reanalysis of the collapsing super-nova core problem (38) shows that, after thecollapse halts, the proto–neutron star enters adeleptonization phase in which its radiusshrinks from 50 to 10 km as it emits neutri-nos. This phase should last 5 to 10 s, which is.104 dynamical times. This is enough timefor the many buoyant bubbles produced tomerge into a steady, slowly collimating bipo-lar flow along the rotation axis (Fig. 7). Theenergy and momentum in the flow shouldcause an already-occurring supernova explo-sion to be aspherical. Furthermore, althoughstill controversial, this MHD outflow in factcould be the deciding factor in assisting asupernova explosion that otherwise wouldhave failed (7 ).

The Steady-State Strong-Magnetic-FieldCase: Fast and Narrow JetsEjection of jets at the local escape speed maybe able to explain the jet speeds observed inmicroquasars and those in radio galaxies andquasars with G & 3. This model even offerssuggestions on how jets might arise in col-lapsing supernova cores to effect asymmetryin the ejecta and perhaps even assist in driv-ing the ejection itself. However, jets pro-pelled at the escape velocity, even from thevicinity of black holes, have a difficult timeexplaining the Lorentz factors of 10 to 20seen in the most powerful quasars, and theycannot explain the G . 100 outflow seen inGRBs. Even for a maximal Kerr hole ( j 50.998), G ; 10 to 20 requires that most ofthe jet be ejected from a region only 1.12Rg

to 1.21Rg in radius, and G . 100 requires thatit occur within a mere ;0.2% of the horizonat 1.063Rg. The need for such contrived sce-narios, which so far are not borne out by thenumerical simulations of black hole accre-tion, motivates us to look for another mech-anism to achieve high Lorentz factors.

One method of increasing the jet speed inthe MHD model is to increase the strength ofthe magnetic field accelerating the jet and/orreduce the density of the material loading thefield lines. This will result in a higher Alfvenspeed, which ultimately will produce a higherterminal jet speed. The range of parameter

space where high jet speeds are expected isdetermined as follows. The MHD power isgiven by (19)

LMHD 5 Bp02 R0

4V02/32c (4)

It depends only on the poloidal magnetic fieldBp protruding from the jet-production regionat radius R0 and on the angular velocity ofthat field V0. If r0 is the plasma density there,then we define the critical power to be thatgiven by the energy needed for the plasma toreach escape speed divided by the dynamical(free-fall) time

Lcrit 5 4pr0R02 SGM

R0D3/ 2

(5)

For example, if the central object rotates atthe Keplerian rate, then the criterion LMHD *Lcrit is equivalent to having an Alfven veloc-ity greater than the escape speed (vA0 * vesc0

or B2/8p * rvKepler2 ).

There are two extremes in this high-mag-netic-power case: efficient and inefficient ac-celeration. Compared to the steady-state,weak-field case, these cases correspond to,respectively, rapid acceleration that reachesterminal speed much nearer the black holeand slow acceleration in which the terminalspeed is achieved much farther from the hole.If the efficiency of conversion of MHD pow-er to kinetic power is high near the centralobject (;50%), then the acceleration of thejet material to its terminal speed will occur ina time shorter than tesc0 and within a radiusR0 of the central object. The final kineticpower Lk 5 GMjetc

2 will equal 0.5LMHD,where Mjet is the rate of mass outflow in thejet, with the other 50% being mostly inPoynting flux—the energy carried by the tor-sional Alfven waves generated by the rotat-ing twisted magnetic field. Solving for theLorentz factor gives an equipartition Lorentzfactor of Geq 5 (vA0

2 R02V0

2)/(32c3v0). If thespeed v0 at which the plasma is boiling offthe disk is small compared to the Alfven andorbital speeds, which are nearly c if the cen-tral object is a black hole, then, potentially,Geq can be much larger than unity. A numer-ical simulation of efficient acceleration in anaccretion disk corona for the high-magnetic-power case is shown in Fig. 8. Although thisis a nonrelativistic simulation, extrapolationof this result indicates that Lorentz factors of10 to 20 may be possible (39). The jet reachesthe equipartition speed, and the high magnet-ic field strength produces tight collimation ofthe jet near the accretion disk.

On the other hand, if the acceleration ef-ficiency is well below 50%, then almost all ofthe power will be in Poynting flux in theTAWT (40–42). In that case, the jet terminalspeed should be on the order of the Alfvenspeed, which will be much higher than vesc0

for sufficiently low plasma density and highfield strength, and it will be potentially highly

Fig. 7. An accretion disk wind in a steady state[from (34) and similar to results in (33)]. Thecentral object is at (0, 0), and the infinitely thindisk is along Z 5 0. Arrows indicate velocityvectors. Lines anchored in the disk and archingupward are contours of magnetic flux; thedashed curve indicates the surface above whichthe strength of the azimuthal (Bf) componentof the twisting magnetic field exceeds thepoloidal field strength [Bp 5 (BR

2 1 BZ2)1/2]; and

the three labeled curves show surfaces wherethe poloidal velocity achieves the escape veloc-ity, the poloidal Alfven velocity (determined bythe poloidal field alone), and the total Alfvenvelocity. Any transient properties of the flowhave disappeared, leaving a slowly acceleratingbipolar wind that collimates from opening an-gles of ;40° to 50° to only a few degrees overmany tens of inner disk radii. Such a picture isqualitatively and, perhaps, quantitatively simi-lar to the wide opening angles observed in M87in the inner core (Fig. 1). [Figure courtesy of R.Krasnopolsky]

5 JANUARY 2001 VOL 291 SCIENCE www.sciencemag.org90

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

relativistic (21). So far, however, numericalsimulations of this case have produced jetswith speeds well below the Alfven speed.This is probably because the Alfven point liesso far from the central object that it has notbeen included yet in the computational do-main (the area of space being simulated).Relativistic simulations that include theAlfven point should be able to achieve theexpected factor of G . 10. An importantresult from the present numerical simulationsof Poynting flux–dominated jets, which wasnot predicted by the semi-analytic steady-state studies, is that these jets are highlycollimated, like the strong-field cases aboveand unlike the steady weak-magnetic-fieldcase. Therefore, because of the strong pinchthat develops, a narrow jet that delivers itsthrust in a narrow solid angle may be ageneral feature of strong rotating magneticfields (LMHD * Lcrit), not only for accretiondisks but also perhaps for many jet-producingobjects.

A Magnetic Trigger for Some GRBs?A particularly interesting, though still some-what preliminary, application of these narrowjets is in the case of collapsing stellar cores.The condition LMHD * Lcrit also may resultin a narrow jet in this situation, similar to theresults of LeBlanc and Wilson (14 ). In theirsimulation, the magnetic field grew to a dy-namically important value in less than a dy-namical time, which is the condition forforming explosive MHD jets in collapsingsupernova cores (16 ). However, this is thesame condition for a strong magnetic field.So, although most rotating magnetized pro-to–neutron stars with low MHD power(LMHD , Lcrit) should produce broad slowlycollimating jets in a steady or quasi–steadystate, a few high power ones should producenarrow fast jets, with the outflow possiblylasting many dynamical times. Although car-rying more power, this highly collimated jetwill be much less efficient in imparting en-ergy and momentum to the outer stellar layersthan a broad bipolar flow (7 ).

This suggests that, because of their broad-er outflow, cores with low-power MHD out-flows should be more efficient at producingasymmetry in their supernova ejecta, whereasthe high-power ones should be less efficientin doing so. Furthermore, if MHD outflowsfrom the core are a necessary component insupernova explosions, then those few coreswith LMHD .. Lcrit may not explode. Theymay act similarly to the failed supernovamodel for GRBs, continuing to accrete muchof the surrounding stellar layers and collapseto a black hole. This continued collapse hasthe potential for producing an even faster andnarrower jet, just outside the forming andexpanding black hole horizon, which couldovertake the precursor jet formed in the initial

collapse and bounce (43). Therefore, in addi-tion to providing a possible means for achiev-ing high Lorentz factors, strong magneticfields may also provide a possible mechanismfor triggering some GRBs.

Achieving the Observed High JetPowers in Radio Galaxies and Quasars:The Need for Black Hole Rotation andThick DisksIn addition to the relativistic jet speeds, an-other parameter that can be compared to theobservations is the total jet power. The pre-dicted jet powers from standard accretiondisks around black holes are much too low(44 ). One solution to this problem producesthe highest jet powers observed, and it alsosuggests a fundamental explanation for whyAGN separate into various classes (such asradio loud or radio quiet) and why jet pro-duction in microquasar jets is correlated withthe state of the accretion disk (45).

Standard accretion disk models indicatethat accretion disks should have a substan-tial toroidal magnetic field strength (Bf) toexplain the inward spiraling of materialonto the black hole. However, it is thepoloidal field protruding from the disk thatdrives the jet, not the toroidal field, and Bp

is expected to be only a fraction (H/R)n ofthe toroidal field strength, where H is thehalf-thickness of the disk and n ; 1 (44 ).Equation 4 then becomes

LMHD 5 Bf02 H 0

2R02 V0

2/32c (6)

If the disk is thin (H0 ,, R0), as is the casefor the standard models (46 ), then LMHD willbe small. For a 109 MJ black hole accreting at10% of the maximum rate allowed by radia-tion pressure (the Eddington accretion rate of;1018 g s21 M/MJ), the largest powers gen-erated from a radius R0 ; 7 Rg are 1042 to1043 erg s21, several orders of magnitudeweaker than the power of ;3 3 1045 erg s21

seen in the most powerful radio sources thatare thought to harbor a hole of this mass (47 ).

For some accreting sources, however,particularly those that produce hard x-rays,standard disks are not good models. Instead,a geometrically thick (H0 ; R0) and hot(.109 K) disk or torus gives a better fitto the data. Several types of geometricallythick disk models have been proposed, in-cluding advection-dominated accretion flows(ADAFs), which carry most of the disk’sthermal energy into the black hole (48); con-vection-dominated accretion flows, which in-clude convection as well (49); and advection-dominated inflow/outflow solutions, whichcarry some of the disk’s internal energy out-ward in a thermal wind (50). Because thepoloidal magnetic field strength [Bp ; (H0/R0) Bf] increases with disk thickness, thevertical magnetic field should be much stron-ger in thick disks than in thin ones, leading to

much stronger jets. However, when theADAF solutions, for example, are used toevaluate Eq. 6, the results yield a jet powernot much above 1044 erg s21 (still a factor of30 below the most luminous observed jets).The jet power is low because, although thickdisks have strong fields, they are partiallypressure supported and so do not rotate at theKeplerian rate.

One way to generate the highest observedradio jet powers is to place the thick accretiondisk around a rapidly rotating Kerr blackhole. The frame dragging near the hole’sergosphere produces a differential rotationthat is nearly as rapid as Keplerian rotation,making both H0 and V0 large in Eq. 6. WithR0 ; 2 Rg as the characteristic radius of thejet-production region near a Kerr hole and amass accretion rate of 10% of the Eddingtonlimit, the predicted jet power for a rapidlyrotating 109 MJ black hole is a few times1045 erg s21, similar to the maximum ob-served. The idea that rapidly rotating blackholes produce strong radio jets and slowlyrotating holes produce weak sources is calledthe spin paradigm. It provides a possible ex-planation for why radio loud and radio quietquasars look so similar in the optical but onlysome, those with rapidly rotating black holes,have radio jets (51).

Fig. 8. Illustration of an efficient high MHDpower jet, with LMHD 5 1.5Lcrit [from (54)]. Thediagram shows the strength of the magneticpressure (B2/8p) at a model time of ;10 innerdisk rotation times, with red indicating thestrongest pressure and blue indicating theweakest. Acceleration occurs much faster thanthe dynamical rate. The flow reaches a quasi–steady state quickly, with a tightly collimatedjet above the escape speed. Although morepowerful, the jet delivers its thrust in a narrowsolid angle, affecting the surrounding ambientmaterial much less than the slower, broad out-flow in Fig. 7.

www.sciencemag.org SCIENCE VOL 291 5 JANUARY 2001 91

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from

The Association of Jet Production withAccretion Disk State: Toward GrandUnification of All Accreting BlackHoles

The above analysis also predicts that micro-quasars with black hole engines will containrotating Kerr black holes, not Schwarzschildblack holes, and that jets will be producedonly when the accretion disk is geometricallythick and hot. There is strong observationalevidence for the second prediction (52). InGX 339-4, for example, a jet is producedwhen the x-ray source is in the low/hard state.In this state, the disk electron temperature isT ; 109 K, indicating a thick disk. On theother hand, when the source enters the high/soft state (with a thin T ; 107 K disk), the jetradio emission disappears to a level at least35 times weaker than that in the low/hardstate. Equation 6 predicts a suppression factorof ;100 between geometrically thin andthick disks around a Kerr black hole, consis-tent with the observed value (45).

Little is known about the relation betweenjet production in the more massive accretingblack holes (such as Seyfert galaxies, radiogalaxies, and quasars) and the state of theirconstituent accretion disks. However, a sim-ilar association of hot thick accretion flowwith the strongest jets is expected. Accretionstates similar to those in binary black holesalso should exist in supermassive black holes.Different types of hard and soft Seyfert gal-axies may be an example of this (53). In thosesources that display jets, the jet should beproduced only when the disk is in a hardaccretion state (either a steady low/hard stateor an unstable very high state that cyclesthrough both soft and hard periods) and notwhen the disk emission is soft. Testing thisprediction in quasars will require statistical

studies, because the typical limit cycle time isexpected to be hundreds to thousands ofyears. Confirmation of this effect will pro-vide additional evidence for a grand unifica-tion of all accreting black hole sources, stellarand supermassive alike, and for the MHDproduction model of relativistic jets.

References and Notes1. R. C. Vermeulen, IAU Symp. 175, 57 (1996).2. J. A. Biretta, W. B. Sparks, F. Macchetto, Astrophys. J.

520, 621 (1999).3. F. Macchetto et al., Astrophys. J. 489, 579 (1997).4. I. F. Mirabel, L. F. Rodriguez, Annu. Rev. Astron. As-

trophys. 37, 409 (1999).5. B. Margon, Annu. Rev. Astron. Astrophys. 22, 507

(1984).6. L. Wang et al., Astrophys. J. 467, 435 (1996).7. A. M. Khokhlov et al., Astrophys. J. 524, L107 (1999).8. R. A. M. J. Wijers et al., Mon. Not. R. Astron. Soc. 294,

L13 (1998).9. M. Nakamura et al., New Astron., in press.

10. C. F. Michel, Astrophys. J. 158, 727 (1969).11. P. Goldreich, W. H. Julian, Astrophys. J. 160, 971

(1970).12. S. D’Odorico et al., Nature 353, 329 (1991).13. Images are available at http://chandra.harvard.edu/

photo/0052/ and http://chandra.harvard.edu/photo/cycle1/vela/.

14. J. M. LeBlanc, J. R. Wilson, Astrophys. J. 161, 541(1970).

15. G. S. Bisnovatyi-Kogan, Sov. Astron. A.J. 14, 652(1971).

16. D. L. Meier et al., Astrophys. J. 204, 869 (1976).17. R. Lovelace, Nature 262, 649 (1976).18. R. D. Blandford, Mon. Not. R. Astron. Soc. 176, 465

(1976).19. iiii , R. Znajek, Mon. Not. R. Astron. Soc. 179,

433 (1977).20. R. D. Blandford, D. Payne, Mon. Not. R. Astron. Soc.

199, 883 (1982).21. Z.-Y. Li, T. Chiueh, M. C. Begelman, Astrophys. J. 394,

459 (1992).22. Y. Uchida, K. Shibata, Publ. Astron. Soc. Jpn. 37, 515

(1985).23. K. Shibata, Y. Uchida, Publ. Astron. Soc. Jpn. 38, 631

(1986).24. R. Matsumoto et al., Astrophys. J. 461, 115 (1997).25. Y. Uchida et al., Astrophys. Space Sci. 264, 195

(1999).

26. Y. Uchida et al., IAU Symp. 195, 213 (2000).27. T. Kudoh, R. Matsumoto, K. Shibata, Astrophys. J. 508,

186 (1998).28. S. Koide, K. Shibata, T. Kudoh, Astrophys. J. 495, L63

(1998).29. iiii , Astrophys. J. 522, 727 (1999).30. S. Koide et al., in Proceedings of the 19th Texas

Symposium on Relativistic Astrophysics, E. Aubourg, T.Montmerle, J. Paul, Eds. ( World Scientific, Paris,1999), 01/15, pp. 1–10.

31. S. Koide et al., Astrophys. J. 536, 663 (2000).32. G. V. Ustyugova et al., Astrophys. J. 439, L39 (1995).33. R. Ouyed, R. E. Pudritz, Astrophys. J. 482, 712 (1997).34. R. Krasnopolsky, Z.-Y. Li, R. D. Blandford, Astrophys. J.

526, 631 (1999).35. I. F. Mirabel et al., Astron. Astrophys. 330, L9 (1998).36. V. Dhawan, I. F. Mirabel, L. F. Rodriguez, Astrophys. J.

543, 373 (2000).37. W. Junor, J. A. Biretta, M. Livio, Nature 401, 891

(1999).38. J. C. Wheeler, D. L. Meier, J. R. Wilson, in preparation.39. D. L. Meier et al., Nature 388, 350 (1997).40. M. Nakamura et al., in Numerical Astrophysics, S. M.

Miyama et al., Eds. (Kluwer, Dordrecht, Netherlands,1999), pp. 239–240

41. S. A. Colgate, H. Li, IAU Symp. 195, 255 (2000).42. G. V. Ustyugova et al., Astrophys. J. 541, L21 (2000).43. A. I. MacFadyen, S. E. Woosley, Astrophys. J. 524, 262

(1999).44. M. Livio, G. I. Ogilvie, J. E. Pringle, Astrophys. J. 512,

100 (1999).45. D. L. Meier, Astrophys. J., in press.46. N. I. Shakura, R. A. Sunyaev, Astron. Astrophys. 24,

337 (1973).47. M. J. Ledlow, F. N. Owen, Astron. J. 112, 9 (1996).48. R. Narayan, I. Yi, Astrophys. J. 444, 231 (1995).49. R. Narayan, I. V. Igumenshchev, M. A. Abramowicz,

Astrophys. J. 539, 793 (2000).50. M. C. Begelman, R. D. Blandford, Mon. Not. R. Astron.

Soc. 303, L1 (1999).51. A. S. Wilson, E. J. M. Colbert, Astrophys. J. 438, 62

(1995).52. R. Fender et al., Astrophys. J. 519, L165 (1999).53. W. N. Brandt, IAU Symp. 195, 207 (2000).54. D. L. Meier, S. Koide, in Astrophysical Phenomena

Revealed by Space VLBI, Proceedings of the First VSOPSymposium, H. Hirobayashi et al., Eds. (ISAS, Sagami-hara, Japan, 2000), pp. 31–38.

55. Part of this research was carried out at the JetPropulsion Laboratory, California Institute of Tech-nology, under contract to NASA.

5 JANUARY 2001 VOL 291 SCIENCE www.sciencemag.org92

H I G H E N E R G Y A S T R O P H Y S I C S

on

Nov

embe

r 17

, 200

6 w

ww

.sci

ence

mag

.org

Dow

nloa

ded

from