Radio Jet Interactions with Massive Clouds

THE ASTROPHYSICAL JOURNAL, 534 :201È212, 2000 May 12000. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

RADIO JET INTERACTIONS WITH MASSIVE CLOUDS

Z. WANG,1 PAUL J. WIITA, AND JAGBIR S. HOODA2Department of Physics and Astronomy, Georgia State University, Atlanta, GA 30303 ; wiita=chara.gsu.edu

Received 1999 August 18 ; accepted 2000 January 3

ABSTRACTThree-dimensional simulations of hydrodynamic jets are computed at rather high resolution using the

ZEUS-3D code. The parameters we employ are suitable for moderate-to-highÈpower radio jets emergingthrough a galactic atmosphere or halo and eventually crossing a tilted pressure-matched interface with ahotter intracluster medium. Before they cross this interface, these simulations aim the jets so that they hitmassive clouds within the galactic halo, with densities 10 or more times higher than the ambient atmo-spheric density and hundreds to thousands times the jet density. Such clouds are set up with radiiseveral times that of the jet and could correspond to giant molecular cloud complexes or small canni-balized galaxies. We Ðnd that while powerful jets eventually disperse the clouds, for o†-center collisions,nonaxisymmetric instabilities are induced in those jets. Those instabilities grow faster for lower Machnumber jets and can disrupt the jets substantially sooner than occurs for similar simulations of jets nothitting clouds. Such interactions could be related to some compact steep-spectrum source morphologies.Weak jets can be e†ectively halted or destroyed by reasonably massive clouds, and this type of inter-action may have relevance for the paucity of extended radio jets in spiral galaxies. Slow, dense jets maybe bent yet remain stable for fairly extended times, and such interactions can be responsible for some ofthe wide-angle tail and most of the ““ dogleg ÏÏ radio source morphologies.Subject headings : galaxies : active È galaxies : jets È hydrodynamics È radio continuum: general

1. INTRODUCTION

An extragalactic jet can interact powerfully with theenvironment along its path. One common morphologicalclass of radio sources, the wide-angle tail (WAT) sources,may show both gradual and rather abrupt bends, with thedeÑection corresponding to a region of enhanced emissivity(e.g., OÏDea 1985 ; OÏDonoghue, Eilek, & Owen 1993). Onepossible way to explain some of these structures would befor the jets to strike large dense clouds in the interstellarmedium (ISM) or intracluster medium (ICM) so that thejet/cloud interactions produce deÑections. However,numerical simulations have shown that strong gas motionsin the ICM, induced by galactic mergers, can produce manyaspects of WAT structures (e.g., Loken et al. 1995). Still, thevery abrupt bends seen in some powerful double sources,sometimes called ““ dogleg ÏÏ quasars (e.g., 3C 270.1, 3C 275.1,and 4C 25.01 : Stocke, Burns, & Christiansen 1985) may beattributed to collisions between jets and massive clouds orsmaller galaxies. Similar distorted structures were found tobe moderately frequent in a survey by Hintzen, Ulvestad, &Owen (1983).

Recent support for the concept of strong interactions hascome from an investigation of the radio-optical alignmente†ect (e.g., McCarthy et al. 1987 ; Chambers, Miley, & vanBreugel 1987) by Best, Longair, & (1997) andRo� ttgeringBest et al. (1998). Using images taken by the Hubble SpaceTelescope and high-resolution radio observations, Best et al.(1997, 1998) found radio jets strongly correlated with thebright optical knots for 3C 34, 3C 324, and 3C 368. Theobject 3C 441 (Lacy et al. 1998) shows a similar structure.X-ray emission has been detected by Harris, Leighly, &Leahy (1998) around a hot spot of the radio jet in 3C 390.3.

1 Current address : Department of Physics, Massachusetts Institute ofTechnology, Cambridge, MA 02139 ; wangzx=space.mit.edu.

2 Current address : Institute of Paper Science and Technology, Atlanta,GA 30309 ; Jagbir.Hooda=ipst.edu.

These observations indicate that a jet may impact a densecloud or galaxy and produce noticeable excess emission andmorphological changes. A detailed discussion of other evi-dence for jets striking clouds appears in Higgins, OÏBrian, &Dunlop (1999).

Canto & Raga (1996) studied two-dimensional jets bothanalytically and numerically ; their work was restricted tothe special case where the jetÏs diameter was very smallcompared to the cloudÏs size. They found that in this situ-ation the jet is deÑected by the cloud without substantiallydisturbing the bulk of the cloud ; in most circumstances, thejet basically drills a hole through the cloud. Other recenttwo-dimensional simulations were performed by Ste†en etal. (1997) in the context of jets hitting gas clouds in thenarrow-line regions of Seyfert galaxies.

Previous three-dimensional simulations of the inter-actions of a jet with a cloud were presented by De Young(1991), who found that jet/cloud interactions could deÑectjets only transiently. Furthermore, his models indicated thatstrong jets would quickly disrupt clouds, while weak jetswould be so dramatically slowed that they should disrupt.This earlier work made the signiÐcantly limiting supposi-tion that the jet densities equaled ambient medium den-sities, while the clouds were 100È10,000 times denser thaneither. Since the grid was relatively coarse, at 40] 40 ] 100zones, the narrow jets he modeled were not transverselyresolved in De YoungÏs work ; furthermore, the ““ beamscheme ÏÏ code (Sanders & Prendergast 1974 ; De Young1991) is highly dissipative and did not employ techniquesthat could optimally resolve shocks and contact discontin-uities. Another early three-dimensional computation byBalsara & Norman using a Riemann solving code wasdescribed by Norman (1993). Their higher resolutionapproach found that a pair of oblique shocks could form inthe region where the jet impacts the cloud, e†ectively yield-ing a de Laval nozzle which reaccelerates the Ñow and pro-duces a fairly stable bent jet. This code was not extensively

201

202 WANG, WIITA, & HOODA Vol. 534

tested or calibrated, and the results di†ered from those ofDe Young. Thus, the question of the outcome of jet/cloudinteractions certainly could beneÐt from reinvestigationusing well-tested codes and more powerful computers.

Very recently, and after this work was well underway,Higgins et al. (1999) presented several three-dimensionaladiabatic simulations aimed at studying the e†ects of di†er-ent hydrodynamical and geometrical parameters inattempts to reproduce the observed structure of radiosources, particularly WATs. Their code is based on theGodunov method of Falle (1991) and assumes reÑectionsymmetry about a plane bisecting the cloud and the jet.Higgins et al. (1999) also estimated the intensity of synchro-tron emission for the jet in order to make approximatematches to the observed radio maps with bends or hotspots. De Gouveia Dal Pino (1999), using a three-dimensional code using the smoothed particle hydrody-namics technique, has just completed a similar series ofinteraction simulations focused on conditions expected forthe jets emerging from protostellar nebulae which areassociated with Herbig-Haro objects. She found thedeÑected beams looked similar to some observed Herbig-Haro systems. In this case, however, unlike the radio jetsituation, the density of the jet is larger than that of theambient medium, and cooling is important. We would thusexpect the bent protostellar jets to be relatively more stablethan lighter extragalactic jets, and a comparison with herresults should be less illuminating than a comparison withthose of Higgins et al. (1999).

In this paper, we expand upon our previous three-dimensional simulations involving interactions of jets withasymmetric environments (Hooda & Wiita 1996, 1998,hereafter HW96, HW98) to investigate the situation where ajet impacts a massive cloud in the ISM. The most importantparameters for our simulations are the density ratiobetween the jet and the ISM, the density ratio between theISM and the cloud, and the jet Mach number. We describeour numerical approach and input parameters in ° 2. In ° 3,the results of simulations are given. In ° 4, our results arediscussed and compared with those of other groups. Ourconclusions are presented in ° 5.

2. NUMERICAL SETUP AND INPUT PARAMETERS

2.1. CodeThese simulations employed the well-tested general

purpose three-dimensional code ZEUS-3D, version 3.4(Clarke & Norman 1994 ; Clarke 1996a), an extension of thetwo-dimensional code ZEUS-2D which is described indepth in Stone & Norman (1992a, 1992b) and Stone,Mihalas, & Norman (1992). This incarnation of ZEUS-3Dis an explicit Eulerian Ðnite-di†erence code employing thepiecewise parabolic advection method of Collela & Wood-ward (1983). Shock waves are treated using the vonNeumannÈRichtmyer prescription for artiÐcial viscosity.The algorithms used in these codes have been tested exten-sively against a variety of Ñow problems where the solutioneither is known analytically or has been determined experi-mentally (Stone & Norman 1992a ; Clarke 1996a). The codeworks very well in most situations, but gives small errors forshocks inclined at angles to the grids. Additional details aregiven in HW96.

Our simulations were carried out on the San DiegoSupercomputer Center Cray T90, and postprocessing was

performed using Spyglass/Fortner TRANSFORM andNCAR interactive graphical software packages.

2.2. ISM and ICMFor the ambient media through which the jet propagates,

we use the same density and pressure structures that wereemployed in our earlier e†orts (HW96; HW98). The ISM istaken to be isothermal with a nominal temperature, TISM\107 K, and density varying as

o(x, y, z) \ o0M1.0] [(z/zscale)zH/(zH [ x tan h)]2Nb , (1)

where represents the longitudinal (z) locationzH [ x tan hof the tilted interface between the ISM and the ICM and zHis given in multiple of the initial jet radius, which deÐnesR0,the length unit for our calculations ; is the scale lengthzscalefor the density of an ISM with power-law decline (of half-index b) along the z-direction. To provide physical units, wechoose the initial number density, cm~3 at z\ 0,n0\ 0.01and take a mass density with k \ 0.6. We seto \ km

pn,

and b \ 0.6 for all our simulationszH \ 30, zscale \ 26.7,(see HW96 for a discussion of parameter choices). The inter-face tilt angle from the (x, y)-plane is set as h \ 30¡. Oncrossing the ISM/ICM interface, the density drops to

while the temperature rises by a factor of 5 to0.2o(zH),provide a pressure-matched boundary ; the density andpressure for the ICM, i.e., for the region, z[ zH [ x tan h,are kept constant.

These simulations were all run on grids of 250 activeuniformly spaced points along the jet propagation directionfor 0¹ z¹ 45. Eighty active zones are used in both thetransverse (x and y) directions, with 36 uniform zones ofbetween [ 1.2¹ (x, y) ¹ ]1.2 and 44 ratioed zones from1.2¹ o (x, y) o¹ 12, with the smallest being 0.0667 initial jetradii in size. (See HW96 and HW98 for more details.) Withthis type of gridding, the ZEUS code can resolve manyinteresting features, including reverse shock structureswithin the ambient material and cocoon, at least for themore important regions close to the jet axis ; such multipleshock structures are most clearly seen in one-dimensionalcuts of the density and velocity.

2.3. JetsIn that the morphologies of powerful radio sources

strongly support the idea that the jetsÏ densities are substan-tially less than those of the ambient medium (e.g., Normanet al. 1982) as well as supersonic, we employ jet densitiesusually set to 10~1.5 of the initial ambient galactic gasdensity The initial radius of the[g 4 o

j/oISM(0)\ 0.0316].

jet, our basic size unit, is set to a canonical value of 1R0,kpc when we evaluate quantities in physical units, but ofcourse everything can be scaled for di†erent assumptionsabout the jet size. For all of our simulations, we assume thatthe jetÏs initial pressure matches that of the ISM at z\ 0 ;therefore, for example, the initial nominal temperature ofthe jet is K for g \ 10~1.5, supposing thatT

j\ 3.16] 108

mean molecular weights are the same for the jets and theambient media. The other important parameter we vary inthis work is the jet Mach number where u is theM

j4 u/a

j,

initial jet velocity and is the sound speed in the jet. Forajthe nominal ambient temperature of 107 K and scale length

of 1 kpc, the time unit used in our simulations isB2.0] 106 yr. Table 1 identiÐes our Ðve complete simula-

No. 1, 2000 RADIO JET INTERACTIONS WITH MASSIVE CLOUDS 203

TABLE 1

SIMULATION PARAMETERS AND INTERACTION TIMES

Run Mj

g gcl rscale Cloud Type m e tint(1) (2) (3) (4) (5) (6) (7) (8) (9)

A . . . . . . 6.0 0.0316 10 2.0 Isothermal 0.045 30.2 2.04B . . . . . . 3.0 0.0316 10 2.0 Isothermal 0.023 4.33 4.64C . . . . . . 1.5 0.0316 50 4.0 Isobaric 0.0098 4.55 StalledD . . . . . . 2.0 0.0316 25 4.0 Isobaric 0.016 7.06 11.12E . . . . . . 1.5 0.316 50 4.0 Isobaric 0.039 1.43 20a

a Estimated ; see text for details.

tions in column (1) and gives the Mach numbers andjet/ISM density ratios used in them in columns (2) and (3).

2.4. CloudsIn these simulations a cloud is always set up as a sym-

metric sphere which is denser than the ambient mediumsurrounding it. The density of the cloud is obviously veryimportant, and in our simulations we took the ratio ofgcl,the central density of the cloud to the density of ambientmedium, as an input parameter given in column (4) of Table1. In all cases we set the radius of the cloud Rcl\ 4.0R0.This value is a reasonable size for a giant cloud complex inthe ISM or for a small galaxy (perhaps in the process ofmerging with the active galaxy). Still, this choice of cloudsize (radius 4 times that of the jet) was primarily motivatedby its improving the opportunity to develop more inter-esting interaction e†ects, particularly in comparison to themore easily analyzed cases where the cloud is much largerthan (or smaller than) the jetÏs diameter.

The cloudÏs density is taken to vary as a quasiÈpower-lawdecline with distance from the center of the cloud as(rcl)

ocl(rcl)\gclo(X, Y , Z)

[1.0] (rcl/rscale)2]bcl(2)

for and 0 elsewhere. In equation (2) (X, Y , Z) is thercl¹ Rcllocation of the cloudÏs center and is a scale length forrscalethe density decline which basically determines the sharpnessof the interface between the cloud and the ISM; is thebclpower-law index within the cloud. The value is chosenrscaleas an input parameter for the clouds (col. [5] of Table 1),while is then computed by our cloud subroutine so as tobclmake the density at the edge of cloud smoothly match theaverage density of ambient medium around the cloud atrcl\ Rcl.We considered clouds that are either isothermal or iso-baric with respect to the surrounding ISM (col. [6] of Table1). Since the density of a cloud declines from the center tothe edge, an internal pressure gradient exists in a cloud setup to have a higher density than but the same temperatureas the surrounding ISM (isothermal case) ; such a cloud isunstable to expansion on a long enough timescale.However, for fast jets (fairly large Mach numbers) and notterribly overdense clouds, we found the cloud was e†ec-tively stable long enough for the interaction with a jet to becompleted. Our runs A and B satisfy this criterion, and wehave utilized isothermal clouds for our most extensive simu-lations of this type. For runs with slower jets and denserclouds, the time during which the jet and cloud interact islonger, and we set the clouds to the isobaric type ; otherwisethey would spread out on their own before the jet has Ðn-

ished interacting with them. Such isobaric clouds have tem-peratures which rise from their cores to their edges.

The cloud is o†set in the x-direction, which allows the jetto hit it approximately at a 45¡ angle, thereby maximizingthe chance of seeing the jet bending (e.g., Stocke et al. 1985).Explicitly, we have always chosen ([2.0, 0.0, 6.0) to be thecoordinates of the cloud center, with the center of the jetÏsbase set at (0, 0, 0). With this choice of cloud location, the jethits the cloud rather early in the simulation, thereby allow-ing the postinteraction development in which we are pre-dominantly interested to consume the bulk of thecomputational e†ort.

The geometrical structure of our simulations can be seenin Figure 1. A jet goes in from the center of the grid on theleft while the center of a cloud is o†set by 2 length unitsfrom the axis of the jet. There is a tilted interface betweenthe ISM and ICM visible on the right-hand side of Figure 1.The transverse zones are small and constant in size close tothe jet axis so that 30 zones span the jet diameter, therebyallowing internal structures to be well resolved. The outertransverse zones are ratioed so as to adequately cover theless important interactions far from the jet axis. The coordi-nate grid extends to ^12 in the transverse (x and y) direc-tions and from 0 to 45 in the longitudinal (or axial, z)direction, with lengths given in units of the initial jetR0,radius.

2.5. Predictive Dimensionless RatiosTwo global dimensionless ratios of use in predicting the

fate of a jet striking a cloud can be deÐned in terms of themass and energy of the portion of the jet that is ““ currently ÏÏinteracting with the cloud. First consider the ratio betweenthe mass of that part of the jet and the mass of the entire

FIG. 1.ÈContour graph of log o for stage 1 of run A, with Mj\

and This Ðgure, a slice through the entire (z, x)-6.0, gj\ 0.0316, gcl\ 10.

plane (0¹ z¹ 45,[ 12 ¹ x ¹ ]12), also shows the general geometry weused in the simulations.


cloud :

m4m5 q

cmcl

, (3)

where the jet mass Ñux with andm5 \ojuA, A\nR02,the cloud sound crossing time in terms of theq

c\ 2Rcl/aclcloud sound speed, We integrate equation (2) to Ðndacl.the cloud mass, For isothermal clouds, Wemcl. acl\ aISM.

use the mean cloud density to determineocl \ 3mcl/4nRcl3the appropriate value of for isobaric clouds since weaclhave a pressure balance between the cloud and the localISM, and therefore The values ofaISM2 o(X, Y , Z)\ acl2 ocl .m are given in column (7) of Table 1.

Now consider the ratio between the energy of the portionof the jet striking the cloud and the cloudÏs internal energy,

e4m5 [(1/2)u2] e

j]q

cEcl

, (4)

where the speciÐc internal energy of the jet andej\ 3P

j/2o

jthe total internal energy of the cloud Ecl\For the isothermal clouds while/ 6nrcl2 Pcl(rcl)drcl. PclP ocl,for the isobaric clouds it is constant. For highly supersonicjets the internal energy term can be neglected in comparisonwith the kinetic energy term, but the former makes a con-siderable contribution for The values of e are givenM

j¹ 3.

in column (8) of Table 1.One expects that for large enough values of both m and e

the jet will just tear through the cloud and be little a†ectedby it. On the contrary, if both m and e are small, the jetshould stall and be destroyed by the cloud. In the casewhere m is low but e is high, the jet can penetrate into thecloud but should entrain quite a lot of mass from it ; there-fore, it should slow rather dramatically, and the highdensity ratio should encourage hydrodynamical instabilitiesto grow quickly, yielding disruption of the jet rather shortlyafter it exits the cloud. For rather high m but low e, massentrainment will not be important, but the cloudÏs densitygradient can control the dynamics of the interaction andcan deÑect the beam.

Of course these global indications will be modiÐed by themessy details of the interactions. In particular, the implicitassumption made above that the entire length of the jetcrossing through the cloud is a†ected uniformly is clearlygreatly oversimpliÐed. Local dimensionless ratios, particu-larly will vary throughout the actual(P

j] 0.5o

jvj2)/Pcl,interaction, as the cloudÏs density and pressure gradients are

signiÐcantly modiÐed by the impact of the jet. The vorticesshed from the Mach disk at the head of the jet also haveimportant e†ects upon the further propagation of the jets(cf. HW96; HW98) but are highly variable in time. Suchlocalized perturbations play important moderating rolesand prevent clear-cut predictions as to what values of m ande yield which type of result.

3. SIMULATION RESULTS

3.1. Powerful JetsIn runs A and B, we explore the interactions between

fairly fast jets of 6 and 3, respectively) and relatively(Mjlow-mass clouds Run A has the highest values of(gcl\ 10).

both m and e, and B also has rather high values of both, sowe would anticipate that these jets could bore through theseclouds. The density of these clouds is set to change rather

rapidly from their centers for clouds with a(rscale\ 2.0) ;Ðxed radius and the same central density, a smaller rscaleimplies a smaller total cloud mass.

We describe the entire jet/cloud interactions for runs Aand B in terms of four stages. The Ðrst stage is when the jetjust starts to contact the cloud, as shown in Figure 1. The jethits the cloud o†-center ; this Ðgure also clearly shows theMach disk terminating the jet and the bow shock propagat-ing into the ambient ISM in front of the jet. The timesrequired to get to stage 1 for our powerful simulations arevery short, with t B 0.1 for run A and t B 0.2 for the half-as-fast run B.

The second stage is deÐned as beginning when the bowshock arrives at the distance z\ 6.0, where the center of thecloud is located along the direction of jet propagation.Figure 2 shows this stage in its upper panels. As can beclearly seen, the bow shock is not symmetric with respect tothe jet because of the strong interaction with the cloud ; it isshifted upward into the less dense part of the ISM. There-fore, a tilted interacting surface is formed along the regionof intersection of the bow shock with the cloud. This regionand the surrounding area within the cloud are denserbecause the cloud is being pushed and compressed by thejet. The times when this stage is reached are t \ 0.84 andt \ 2.08, respectively, for run A and run B, thereby illustrat-ing a relatively greater deceleration for the case.M

j\ 3.0

The basic shock structures around the jet are almost thesame for runs A and B; however, the run B jet produces abroader cocoon than does the faster run A jet. In the (y, z)-plane, where the cloud is centered and the ISM is not tilted(as is seen in the density image of the central x \ 0 plane forrun A in Fig. 3, upper left), the bow shock along the z-direction in front of the jet is symmetric and a symmetriccocoon is also seen. Figure 3 (upper right) also shows thepressure in the (z, x) central plane for t \ 0.84 of run A. Theimage illustrates the modest tilt in the isodensity and iso-pressure surfaces in the ISM, a slightly tilted intense inter-action area, with the highest pressure between the jet andthe cloud in the region where the jet strikes the cloud, aswell as a longer sharply deÐned high-pressure area whichcorresponds to the compressed and pushed portion of thecloud. We can see this whole ““ working area ÏÏ exhibits highpressure and presumably signiÐcant synchrotron emissivity(see ° 3.4). Furthermore, the pressure of the cloud is alsohigher than that of the ambient medium around it, since weset the cloud up so as to be isothermal with the ISM.

As the jet continues to propagate, the cloud is pushedaway and eroded. Figure 2 also shows this intermediatestage 3 for both of our more powerful jet simulations(middle panels), when the clouds were totally displaced fromtheir original positions by the impact of the jets. The timefor run A to reach this stage is t \ 2.16 and for run B ist \ 4.88 ; therefore, the total interaction times (which wedeÐne as the interval between the beginning of stage 1 tothis intermediate stage 3), are and 4.64 for runs Atint \ 2.04and B, respectively. Interaction times deÐned in this way arerecorded in column (9) of Table 1 for all the simulations. Itis obvious that the cocoon is very asymmetric by this point.Most of the interaction remnants Ñow upward away fromthe cloud into the low-density ISM, while there is a muchsmaller cocoon along the lower part of the jet. This side ofthe cocoon is very thin, especially for run A, since the cloudhas compressed the backÑow in the cocoon on the lowerpart of the jet. Most of the backÑow is diverted upward


FIG. 2.ÈThe left panels give gray-scale logarithmic density plots for run A, and the right panels give the same plots for run B (identical, except thatThese images are in (z, x)-plane slices for y \ 0 and cover the entire grid. The images for run A, from top to bottom, correspond to t \ 0.84, 2.16,M

j\ 3.0).

and 6.4. The images for run B similarly correspond to t \ 2.08, 4.88, and 17.52, respectively.

thanks to the interaction with the cloud, thereby making abroader upper portion of cocoon ; for run A, this ““ upper ÏÏcocoon is as wide or even wider than the correspondingpart of the cocoon in run B. The internal structures of thejets, exhibiting reconÐnement shocks, are clearly shown inFigures 2 and 3.

We also show the pressure for the run A case (Fig. 3,lower left) at the same time as the middle density graph(t \ 2.16) in Figure 2. The pressure plot indicates a similarstructure to the earlier stages in the sense that the tworegions with the highest pressure are one small spotlikeinteracting area just in front of the jet and one larger areawhich is a part of the pushed cloud. Some of the workingarea as deÐned in the density image is found to have arelatively low pressure, while the distorted cloud retains itshigh pressure.

The last stage we present for these strong jet cases is atthe point when the jet crosses the interface between theISM/ICM after undergoing interaction with the cloud. Thetwo images at the bottom of Figure 2 are the Ðnal stages forthe runs, with respective times of t \ 6.4 for run A andt \ 17.52 for run B. We stopped run A when the Mach diskof its jet Ðnally arrives at z\ 32 ; the jet in run B wasallowed to propagate a little further and reaches the sameplace at t \ 15.4. Thus, the times required to reach the

interface are in the ratio 2.4 :1.0 for run B:run A. Since theinitial Mach numbers and velocities were in a direct 1 :2ratio, this quantiÐes how the jet in run B is more severelya†ected and slowed through its interaction with the cloud.Furthermore, the time for the bow shock preceding the jetto reach the interface is t \ 6.04, which is 1.0 time unitslonger than the M6 run presented in HW98 (which wascloudless, but otherwise identical to run A). We thus seethat the dalliance with the cloud slowed the progress of theMach 6 jet by just about 20%.

As is clear from Figure 2, the slower run B jet develops abroader cocoon, as expected from earlier simulations (e.g.,Norman et al. 1982 in two dimensions ; HW96, HW98 inthree dimensions) and evinces a substantially unstable andwiggly structure by the end of the simulation. Figure 4 givesseveral cross-sectional slices of both density and z-directionvelocity through the run B jet at t \ 17.52, further illustrat-ing this point. The jet cross section changes from circular tomore complex, eventually becoming ribbon-like at largedistances from the origin. This illustrates the growth ofunstable nonaxisymmetric modes, dominated by an ellip-tical shape change and a helical rotation (e.g., Hardee,Clarke, & Howell 1995). Regions exhibiting signiÐcantbackÑow form rather close to the jet and illustrate that theMach 3 jet is coming close to breaking up at a signiÐcantly


FIG. 3.ÈThe upper portion gives images of run A at t \ 0.84. The left panel is the slice of ln o in the (z, y)-plane for x \ 0, and the right panel is the sliceof ln p in the (z, x)-plane for y \ 0. The bottom images give ln p structures of run A at t \ 2.16 and t \ 6.4 in the (z, x)-plane for y \ 0.

earlier stage than did the similar simulation (M4) describedin HW98.

The faster run A, on the other hand, takes a much shortertime to reach the interface, and remnants of the high-densitycloud can still be seen embedded in portions of the bowshock toward the end of the simulation. The run A jet alsoshows relatively stable inner structure, although weakernonaxisymmetric modes have clearly been signiÐcantlyexcited by then ; the last panel in Figure 3 indicates thepressure structure for the Ðnal stage of run A. The highestpressure region, corresponding to the radio ““ hot spot,ÏÏ iscertainly still in front of the main jet ; the main interactionregion is in one compact area and is a weakened Mach disk.A longer curved region shows higher pressure than the restof the compressed ambient medium. The main interactionarea, which evinced a spotlike structure at the earlier times,now shows a wiggly morphology, indicating the nonlineargrowth of nonaxisymmetric modes.

In both cases, the rates at which instabilities develop arelarger than for identical or very similar simulations per-formed with no clouds in the way of the jets ; those earliercomputations were subjected only to very weak non-axisymmetric perturbations due to the tilt of the ISMisobars with respect to the jet normal (HW96; HW98).While that tilt did induce minor deviations from axisym-

metry, we note (without surprise) that hitting a much densercloud is far more e†ective in engendering instabilities.Nonetheless, for these rather fast, light jets, we see that theclouds are quickly destroyed. This is true even for isobariccloud simulations for otherwise identical parameters thatwe carried out to check if these results were sensitive to thecloud structure. Although these isobaric simulations werecomputed only for substantially shorter times, during thoseinteraction periods (roughly up to stage 3) no signiÐcantdi†erences were seen in the morphologies of the isobaricand isothermal situations. In particular, the cloud wasessentially as stable for the isothermal case as for the iso-baric one, which is unsurprising given the relatively briefinteraction times.

3.2. Weak JetsRun C is a case with a low-velocity jet striking(M

j\ 1.5)

a dense cloud The other parameters are given in(gcl\ 50).Table 1. This simulation has the lowest value of m and amoderate value of e, so we might anticipate it could notpenetrate through the cloud. The cloud density scale ischanged to 4.0 to make the ISM/cloud interface moreabrupt and simultaneously to make the cloud even moremassive. To prevent any expansion during the lengthy inter-action phase, this and all subsequent clouds are set to be of


FIG. 4.ÈSlices of ln o (left) and (right) for run B takenvz

(Mj\ 3.0),

perpendicular to the jet at t \ 17.52. These slices are located at z\ 1.8,18.0, and 36.9, from top to bottom, and illustrate the growth of non-axisymmetric modes.

the isobaric type instead of the isothermal situation con-sidered for the complete versions of runs A and B discussedin ° 3.1.

We show the interaction process in the left portion ofFigure 5, which illustrates results only out to an axial extentof z¹ 24 so as to give a more detailed image of the inter-esting portion of the computational grid. The times for thetwo panels for run C in Figure 5 are t \ 4.0 and t \ 9.44,respectively. After the jet impacts the cloud, it makes slowheadway and Ðnally is e†ectively stalled by the cloud. Toquantify this point, the distance the jet progresses is onlyD1.5 spatial units between t \ 4.0 and t \ 9.44, despitehaving traveled out to t \ 4.0, and the advance ofD4.2R0the jet continues to decelerate throughout this period. Themean head velocity corresponds to about 3% of the jetÏsinput velocity during this interaction.

The interaction between the jet and cloud graduallyyields a cocoon with a nearly circular longitudinal crosssection on the side away from the cloud (Fig. 5, upper left).Some signiÐcant backÑow along the jet is seen to form onthe side striking the denser parts of the cloud (Fig. 5, lowerleft). As can be seen in the later stage of evolution in Figure5, the main body of the jet is actually bent a little bit down-ward into the cloud instead of being ““ refracted ÏÏ away fromit. This counterintuitive result can be explained in terms ofthe interaction between the faster forming cocoon on the

upper side and the jet itself ; the vortical Ñow in the cocoonexerts pressure on the jet on the side away from the cloud ;this tends to push the jet deeper into the dense cloud core.While a narrow, very slow stream of matter is seen to Ñowupward along the jet/cloud interface, we note it really justfeeds into the ““ circular ÏÏ cocoon. Of course, the cloud isbeing a†ected by the jetÏs impact upon it and is signiÐcantlydistorted by the bow shock. By t \ 9.44 the cloud has lostits spherical shape but could clearly resist the onslaught ofthis feeble jet for a much longer time. Thus, we argue thatthis very weak jet is e†ectively destroyed by this very densecloud.

In order to investigate a more intermediate case of jetpower against cloud resistance, we increased the Machnumber of the jet to 2 and decreased the central density ofthe cloud to 25 in run D; all other parameters are the sameas for run C. Thus, this case has m-values intermediatebetween those of runs B and C but a somewhat largere-value than either. The results for t \ 4.0 and 10.08 are alsoshown in Figure 5 (right). Compared with run C at t \ 4.0,the jet of course has moved more deeply into the cloud andmakes a broader cocoon. A tilted interaction area forms inthe front of the jet. Nonetheless, the vortical backÑow exertspressure on the jet from the top side, thus causing the pen-etrating part of the jet to bend slightly downward.

As time goes along, the jet keeps advancing less and lessrapidly, but it does manage to push the cloud slowlyoutward. By t \ 10.08, shortly before we terminated thissimulation at t \ 11.76 (Fig. 5), the jet has almost gonethrough the entire cloud and has eroded most of the tophalf of the cloud, reaching a maximum distance of z\ 9.1. Avery extensive cocoon forms on the top side of the jet. Theinteraction between the cocoon and the jet induces the jet toevince a substantially wiggly structure. Again, there is acurved interaction area where the jet hits the cloud, whichsqueezes a weak stream of plasma upward. This streamgains a vortical motion near the uppermost portion of thecloud as it merges into the circular cocoon. Figure 5 alsoillustrates how a weakened bow shock has propagated farahead of the stalled jet ; it extends a little bit further on theupper side. Given the extremely slow rate of progress,despite substantial computational cycles being required, wedid not follow this simulation further. Considering theresults from run B, we are certain that the jet would soonbecome quite unstable, having entrained a good bit of cloudand ambient material and having slowed dramatically. Wenote that this type of weak transonic Ñow provides a goodmodel for many Fanaro†-Riley type I sources (e.g., DeYoung 1991 ; Bicknell 1995 ; Gopal-Krishna & Wiita 2000).

3.3. A Bent JetThe Ðnal simulation we present, run E, is of a relatively

slow but rather heavy jet. In this simulation, we raise thedensity of the jet so that 10 times the value of theg

j\ 0.316,

jetÏs density in runs AÈD; all other parameters are set to thesame values as in run C. However, since the pressure of thejet is always chosen to be equal to the pressure of ambientmedium at the inlet, this increase in density implies a dropin jet temperature, so the absolute velocity of the jet isindeed decreased by a factor of (1/10)1@2, even though we set

the same as for run C. In terms of the globalMj\ 1.5,

dimensionless parameters, this simulation has a relativelyhigh value of m but a very low value of e, so the possibilitythat the jet will be bent is quite good.


FIG. 5.ÈThe two left panels give images of ln o for run C and the right two panels are ln o images for run D for(Mj\ 1.5, gcl\ 50), (M

j\ 2.0, gcl \ 25)

slices in the y \ 0 plane. The times of the Ðgures for run C are t \ 4.0 and 9.44. The times of the Ðgures for run D are t \ 4.0 and 10.08. The z extension islimited to 0¹ z¹ 24.

The results of the run E simulation are shown in Figure 6,which again shows results only out to an axial extent ofz¹ 24. At Ðrst, when the jet just starts to interact with thecloud, the morphology is very similar to those of runs C orD (° 3.2), with a broader cocoon extending beyond the jetbeing formed by the upward stream while a thin cocoonforms below the jet (Fig. 6, upper left, corresponding tot \ 8.0). However, after a short time of interaction, a quitedi†erent structure forms. As can been seen from the upperright panel of Figure 6 (t \ 11.2), a small taillike shapeforms below the jet while a cocoon with a quasi-circularcross section forms on the top of the jet. However, in thiscase the material feeding the cocoon is in the form of adeÐnite beam emanating from the locale where the jetimpinges upon the cloud ; this beam extends upward alongthe cloud.

Run E basically retains this structure for a very extendedtime as the maximum extent of the main jet slowly advanceswith nearly constant velocity ; therefore we could reason-ably estimate the total interaction time quoted in Table 1 as

even though we did not follow the simulation outtint \ 20,

quite that long. At the same time, the lower ““ tail ÏÏ continuesto extend downward and backward, while the upward beaminteracts with the upper portion of the cloud and theambient ISM. A very broad cocoon forms above the inci-dent jet and behind the bent beam. This bent beam extendsfor a distance substantially longer than the diameter of thejet, and by the time we end this simulation, it has extendednearly as far as the original jet traveled before it struck thecloud (cf. Fig. 6, lower left, for t \ 17.6). This panel alsoshows that the small tail eventually breaks up near itsmiddle. The whole tail and the bent beam are nearlycolinear, forming an extended structure which extendsbeyond the position of the original cloud at a nearly 45¡angle to the jet direction.

The pressure image at t \ 17.6 is shown in the lower rightpanel of Figure 6. The standard reconÐnement shock isclearly seen in the main jet before it strikes the cloud. In thehigh-pressure region of the interaction area between jet andcloud, we can see a weak double-shock structure thatmanages to divert much of the matter in the original jetupward. This structure is very similar to one obtained by


FIG. 6.ÈThe upper left, upper right, and lower left panels are ln o images for run E at t \ 8.0, 11.2, and 17.6, respectively.(Mj\ 1.5, g

j\ 0.316, gcl \ 50)

The lower right panel is a ln p image at t \ 17.6. The slices and dimensions are as in Fig. 5.

Balsara & Norman (Norman 1993). We note another high-pressure region along the area where the bent beam strikesthe ambient medium and upper part of the cloud. Althoughthese calculations contain no magnetic Ðelds, the increase inboth density and pressure would imply this corresponds toa weak hot spot ; however, the highest pressure remains atthe location where the original jet collides with the cloud, sothe most intense synchrotron emission is still expected toarise there, as discussed further in ° 3.4. The pressure mapalso clearly shows how a weakened bow shock has nowpropagated far beyond the cloud.

3.4. Pseudoemissivity MapsThese simulations do not include magnetic Ðelds, even as

nondynamically important tracers, and thus it is not pos-sible to produce even approximate synchrotron maps as hasbeen done by several other groups (e.g., Clarke 1996a ;Higgins et al. 1999 ; Rosen et al. 1999). While most studiesinvolving MHD simulations (e.g., Rosen et al. 1999) haveindicated that reasonable strength magnetic Ðelds do nothave dominant dynamical e†ects, they certainly can playsigniÐcant roles and are of great importance in estimating

the emissivity. Thus, the dynamics traced by our simulatedÑows are probably good approximations to realistic jet/cloud interactions in extragalactic radio sources, and thedensity, pressure, and velocity plots displayed in Figures1È6 are of substantial utility in understanding the physics ofjet propagation. But of course the observable in the case ofextragalactic jets is the synchrotron emission, and ourmodels cannot produce very accurate estimates of whatwould actually be seen when observing a source.

Still, in a very crude approximation, one can estimate thesynchrotron emissivity as (e.g., Miley 1980),Fsynch PP7@4and we have done so for runs A and E. Single snapshots ofemissivity estimates (on logarithmic scales) for late stages ofboth a powerful and a bent jet are displayed in the upperpanels of Figure 7. For run A, the standard expectation forpowerful jet maps is clearly seen, with the peak emissivityfrom the hot spot at the end of the jet and substantial knotsof emissivity corresponding to internal shocks within thejet. However, this type of approximate emissivity map over-estimates the emission from the bow shock, where bothlower magnetic Ðelds and lower densities of relativistic par-ticles actually would be present.


FIG. 7.ÈThe upper and lower left panels are, respectively, logarithmic plots of synchrotron and bremsstrahlung ““ emissivities ÏÏ computed on slices in they \ 0 plane for run A at t \ 6.4. The upper and lower right panels are, respectively, logarithmic plots of synchrotron and bremsstrahlung ““ emissivities ÏÏcomputed on slices in the y \ 0 plane for run E at t \ 17.6. The entire computational grid is shown for all panels.

For run E, the most intense emissivity arises from theregion of the interaction between the jet and the cloud.However, the region of high emissivity is somewhat elon-gated along the direction of the diverted Ñow, and a weakerhot spot can be seen at the terminus of the bent jet (to theupper right of the collision region). Again, this simple pre-scription for the synchrotron emissivity produces a regionwhere it provides a gross overestimate ; in this case, thecentral portions of the cloud, which have high pressures butessentially no magnetic Ðelds or relativistic particles, appearas a bright spot, which they really would not be. Becausethe ZEUS code does not track the origin of particles, thereis no precise way to remove the ““ emission ÏÏ from regions(such as the cloud core) which have high pressures but areunlikely to contain signiÐcant B-Ðelds. Future simulationsshould include magnetic Ðeld evolution so as to enablemore realistic (if still only approximate, because of lack ofknowledge of relativistic particle distributions) predictionsof synchrotron emissivity. One should then integratethrough various lines of sight to the emission to obtainimproved pseudomaps of synchrotron emission.

It is also possible to produce approximate maps ofbremsstrahlung emissivity by computing a quantity,

In the lower panels of Figure 7 we haveFbremP o2T 0.5.displayed such images of the logarithm of the bremsstrah-lung emissivity at the same times and for the same slices as

the above synchrotron emissivity estimates. In that we haveleft out dissipative processes and other cooling mechanisms,these maps are again very crude. The scale bars have arbi-trary units so the larger numbers on the lower panelsshould not be taken to imply that this emission mechanismwould dominate the synchrotron output. What is clear isthat the bulk of this emission does not come from the low-density jets and lower density cocoons, but rather from thebow shock and postshock ambient material (run A) and thecompressed cloud (run E).

4. DISCUSSION

Using the well-tested ZEUS hydrocode, we have per-formed and analyzed a series of Ðve simulations for jet/cloud interactions which we believe adequately span theinteresting range. Our parameters also come close to cover-ing the range considered some time ago by De Young(1991), who used a very dissipative code and lowerresolution as well as computations made at more similarresolutions by Balsara & Norman (Norman 1993) andHiggins et al. (1999) ; while these last two groups used sig-niÐcantly di†erent types of codes (cf. ° 1), they should begenerally comparable to ZEUS in accuracy.

Still, there are several signiÐcant di†erences between theapproach we have taken and those of earlier e†orts toaddress the e†ects of jets striking clouds. We set the density


of the cloud declining with truncated power laws from thecenter to the edge of the cloud, which we believe is some-what more realistic than the hard-edged clouds assumed bythe other authors ; this is more particularly true if the““ cloud ÏÏ is really the gas associated with a smaller galaxy inthe process of merging with the larger active galaxy. Also,some important parameter choices are signiÐcantly di†er-ent. For example, in De YoungÏs simulations, the density ofthe jet is set to be equal to the density of ambient medium(which was assumed to be of constant density, aside fromany clouds), and the velocities of all cases were the same ; asnoted in many earlier simulations (e.g., Norman et al. 1982),most jet morphologies are only well explained if g > 1, soour values of g are more reasonable than those of De Young(1991). Higgins et al. (1999) chose density ratios of jet toambient medium and cloud to ambient medium similar toours, but, because the Ðducial temperature they assumed fortheir jet was higher than ours, the absolute velocities of theirjets were larger than those we considered, even for similarMach numbers. For this reason, runs with the same Machnumbers in their work would require denser clouds toproduce similar e†ects. Nonetheless, we and the otherauthors have certainly investigated similar jet/cloud cases : alight, fast jet striking a moderately massive cloud ; a light jethitting a more massive cloud ; a heavier, slow jet impactinga massive cloud. Thus, it is clearly worthwhile to compareour results with theirs.

For the case of fast jets and less massive cloudsÈour runsA and B, case I-1 of De Young (1991), and simulations 3 and4 of Higgins et al. (1999)Èall show that the less massivecloud can be pushed away and Ðnally destroyed. However,the parameters we chose did not give rise to the temporarybent jet argued for by the other authors. In the short inter-action time relevant for these fast jets, our code yielded onlynonsymmetric cocoons around the jet. In other words,striking the cloud o†-center forced most of the backÑowtoward the side away from the cloud. Recall that for DeYoungÏs simulations, the density of jet is set to be equal tothe density the ISM, which will clearly cause di†erences inresults even when the ratios of the cloud density to jetdensity are similar. In particular, his jet thereby has ane†ectively higher thrust and therefore more coherence,possibly explaining the bulk of the di†erences ; in addition,his jet is not well resolved transversely, so the e†ects ofinternal shocks could not be incorporated in his e†orts. Wewere somewhat surprised to see that there are bends seenearly in the simulations of Higgins et al., particularly sincewe note the absolute velocities of their jets are very large fortheir fastest jets (D0.36c), which is over 6 times larger thanvelocities (D0.057c) of our fastest jets. This di†erence comesabout because their canonical values are g \ 0.01 and

K, compared to the g \ 0.0316 andTISM\ 5 ] 107 TISM\ 1] 107 K for most of our simulations. As the bends theyfound are rather short-lived, this di†erence in results isprobably not too important and might be related to theirassumption of reÑection symmetry, which we do notemploy.

Our run C, the case with a slow and weak jet but a densecloud, is somewhat similar to the case I-2 in De YoungÏssimulations (except that he always chose g \ 1 and largervalues of and more similar to simulations 1 and 2 ingcl)Higgins et al.Ïs work. De Young states that the weak jet isÐrst bent nearly 90¡ but that the jet will eventually erode thecloud. We do Ðnd a similar small bent stream which appar-

ently corresponds to the trajectory of marker particles in DeYoungÏs work ; however, we would not classify this Ñow as acontinuing jet given its small radius and associated weakthrust. No strong deÑection shown in simulations 1 and 2 ofHiggins et al. has been found in our run C; instead, theweak upward stream is blocked by the cloud and ambientmedium, thus Ðnally forming a cocoon with a circular crosssection on the top side of the jet. Furthermore, ourintermediate-power run D shows that a jet can go throughthe cloud slowly while making a similar, but wider structureas compared to run C.

Higgins et al. (1999) performed simulations 5 and 6 forslow, heavy jets, which are similar to our run E simulation.Our simulation E is also in the general parameter range forthe successfully bent jet considered by Balsara & Norman

We Ðnd a bent ““ arm ÏÏ structure during(Mj\ 4, g \ 0.2).

the process of the interaction with an upward Ñow and adownward Ñowing stream, as did Higgins et al. However,our downside tail is much sharper while the top-side cocoonshows a nearly circular cross section. Moreover, our pres-sure image clearly shows that the bent stream interacts withthe cloud and ambient medium at an area above the jet, andwe believe the area could be thought of as another hot spot,which Higgins et al. (1999) have not clearly found in eitherof their slow, heavy jet simulations. Our modestly betterresolution near the jet axis or the reÑection symmetryassumed by Higgins et al. could explain this di†erence,although it could also be caused by the modest di†erencesin the parameters we employed.

5. CONCLUSIONS

These simulations have conÐrmed that certain radiosource morphologies can indeed be understood in terms ofcollisions of jets with massive clouds. Some WAT sourcescould certainly be produced in this manner, even if most ofthem can be explained in terms of ““ stormy weather ÏÏinduced in the ICM by galactic mergers (e.g., Loken et al.1995). The small group of ““ dogleg ÏÏ quasars (e.g., 3C 270.1,3C 275.1, and 4C 25.01 : Stocke et al. 1985) are indeed prob-ably best understood in terms of fairly long-lived stages ofjet/cloud or jet/small galaxy interactions.

The results of this paper, along with those of De Young(1991), Norman (1993), and Higgins et al. (1999), stronglysuggest that only a small range of parameter space iscapable of producing fairly long-lived bent jets. These jetsshould be relatively dense with respect to the ISM and alsorelatively slow, as indicated by the lack of such structures insimulations of a fast but heavy jet (Higgins et al.Ïs cases 7and 8). In other words, high values of m along with modestor low values of e are indeed most likely to yield stably bentjets. Alternatively, if the jets started o† relativistically, theyshould have entrained enough matter so as to have becomefairly dense and only transonic (e.g., Bicknell 1995) by thetime they hit the cloud. Given that only a small fraction ofradio sources show morphologies that clearly indicateabruptly bent stable jets or show associated optical orX-ray emission that allow us to conÐdently infer an inter-action with a massive cloud, the fact that numerical simula-tions rarely yield such morphologies is not surprising.

Compact steep-spectrum radio galaxies are almost cer-tainly quite young (e.g., Fanti et al. 1990). Nonetheless, thereis strong theoretical (e.g., Gopal-Krishna & Wiita 1991 ;Jeyakumar et al. 2000) and statistical (Saikia et al. 1995,2000) evidence that they interact with denser and more

212 WANG, WIITA, & HOODA

asymmetric media in the inner portions of their host gal-axies than do typical powerful radio galaxies. Carvalho(1998) has performed analytical estimates of how muchextra conÐnement can be accomplished if the medium con-tains many dense clouds, and he argues that a good under-standing of GHz peaked-spectrum and compactsteep-spectrum sources can be achieved if jet/cloud colli-sions are more common in these sources.

More powerful jets will be only slightly and temporarilydiverted by interactions with clouds, which they will eitherdrill through (if the cloud is much bigger than the jetÏsdiameter) or demolish (if the cloud is comparable in size tothe jet). While we have seen that such jets are rendered moreunstable by a collision with a cloud, they would not typi-cally produce morphologies that show clear evidence of thejet/cloud interaction, particularly if the source is viewed at alate stage in its life, by which time the jet has gone wildlyunstable.

Finally, very weak jets can be halted (or at least nearlycompletely conÐned for very extended periods) when theyhit a massive cloud with more than a glancing blow. Thistype of situation appears to be not uncommon in activespiral galaxies. While Seyfert galaxies rarely show large-scale jets, careful studies of nearby objects sometimes revealevidence of subgalactic-scale radio jets interacting with gas

clouds (e.g., NGC 1068 and NGC 4151 : Wilson & Ulvestad1982). These numerical simulations support the idea thatweaker jets can indeed be smothered by the more commondense clouds found in spiral galaxy ISMs.

More sophisticated three-dimensional computations thatincorporate dynamically important magnetic Ðelds in a self-consistent fashion (e.g., Clarke 1996b) and also utilize morerealistic models for particle acceleration and synchrotronradiation (e.g., Jones, Tregillis, & Ryu 2000) will be neededto make models sufficiently detailed so that one couldprovide convincing explanations of individual sources.While difficult, such simulations are now becoming compu-tationally possible, and they are well worth attempting.

We thank James Joyce and Lynne McKee for producinganimations which were very helpful in our analyses of thesesimulations. The suggestions of the anonymous referee ledto several signiÐcant improvements in the text, includingthe material presented in °° 2.5 and 3.4. This work wassupported in part by NASA ATP grant NAG 5-3098 and byResearch Program Enhancement funds at Georgia StateUniversity. The computations were performed at theNPACI Cray T90 at the San Diego Supercomputer Centerunder award GSU200.

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Radio Jet Interactions with Massive Clouds

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