Draftversion February5,2008 PreprinttypesetusingLATEXstyleemulateapjv.6/22/04 STOPPING COOLING FLOWS WITH JETS Fabrizio Brighenti1,2, William G. Mathews1 Draft versionFebruary 5, 2008 ABSTRACT We describe 2D gasdynamical models of jets that carry mass as well as energy to the hot gas in galaxy clusters. These flows have many attractive attributes for solving the 6 galaxy cluster cooling flow problem: Why the hot gas temperature and density profiles 0 resemble cooling flowsbut show no spectral evidence of cooling to low temperatures. Using 0 an approximate model for the cluster A1795, we show that mass-carrying jets can reduce 2 the overall cooling rate to or below the low values implied by X-ray spectra. Biconical n subrelativistic jets, described by several ad hoc parameters, are assumed to be activated a when gas flows towardor cools near a central supermassive black hole. As the jets proceed J outfromthecentertheyentrainmoreandmoreambientgas. Thejetsloseinternalpressure 4 by expansion and are compressed by the ambient cluster gas, becoming rather difficult to 2 observe. For a wide variety of initial jet parameters and several feedback scenarios the global cooling can be suppressed for many Gyrs while maintaining cluster temperature 1 profiles similar to those observed. The intermittancy of the feedback generates multiple v generationsofX-raycavitiessimilartothoseobservedinthePerseusClusterandelsewhere. 5 5 Subject headings: X-rays: galaxies – galaxies: clusters: general – X-rays: galaxies: clusters 5 – galaxies: cooling flows 1 0 6 1. INTRODUCTION tropyprofilescommonlyobserved,mostofwhichare 0 Many computationally elaborate calculations of very similar. In general,the long term effectiveness / jet-heated cooling flows have been proposed to ex- of powerful jet heating in stopping the cooling has h notbeenconvincinglydemonstrated. Asafirststep p plainwhy the hotgasin galaxyclusters coolsmuch towardamoresuccessfulsolution,adoptedhere,jet- - slower than the rate expected from the cluster X- o ray luminosity, M˙ ≈(2µm /5kT )L (e.g. Cav- heatingscenariosaresoughtthatareconsistentwith r cf p vir x the globalobservationsofthe hotclustergas. Once t aliere et al. 2001; Reynolds, Heinz, & Begelman s 2001,2002; Bruggen & Kaiser 2002; McCarthy et thisproblemissolved,thenextstepistodetermine a if real black holes can indeed supply energy in the al. 2003; Hoeft et al. 2003; Basson & Alexan- : form and amount required. v der 2003; Omma et al. 2004; dalla Vecchia et al. Xi 2004; Zanni et al. 2005). In principle the energy neWaretchoensciodreershoerfecjleuts-tdeorm-ciennatteerdedfloewllsipitnicwahligchalgaaxs- created by gas accreting at rates very much less r iesisacceleratedinbipolaroutflowswhentriggered a than M˙cf onto supermassive black holes in cluster- by a supermassive black hole feedback mechanism. centered galaxies can easily balance the radiative Bothmassandenergyaretransportedoutfromthe losses L . Consequently, AGN jets have been re- x center. The feedback appears largely as an out- garded as a plausible means to distribute this en- wardflow of mass rather than energy,although the ergythroughouttheclustergas. Unfortunately,few energetics of successful flows must be understood if any jet-heated flow simulations closely resemble a postiori. We find that these more massive jets inprojectiontheX-rayemissionandradialtemper- have many desirable long term attributes. We have ature profiles observed in galaxy groups and clus- discussed elsewhere how heated, buoyant gas can ters. Surprisingly often these calculations do not rise upstream in cooling flows, transporting mass include radiative losses and therefore lack the es- and energy to distant cluster gas in a manner that sentialphysicstoprovethatcoolingcanbestopped sharply reduces the overall cooling rate and pre- bythejets. Nordothesecalculationstypicallycon- serves the thermal profiles observed (Mathews, et tinueformanyGyrs. Multi-Gyrcalculationsarees- al. 2003; Mathews, Brighenti & Boute 2004). We sentialto determine if the proposedtype of heating nowturnourattentiontothepossibilitythatmass- can keep the group/cluster gas from cooling while loaded subrelativistic jets can accomplish the same also preserving time-averaged temperature and en- desirable results. Anotherinspirationforthecalculationsdescribed 1UniversityofCaliforniaObservatories/LickObservatory, herearerecentHI(Morgantietal. 2004;2005),UV Department of Astronomy and Astrophysics, University of California,SantaCruz,CA95064 (e.g. Crenshaw et al. 1999; Kriss 2003) and X-ray 2 DipartimentodiAstronomia,Universita`diBologna,via (George et al. 1998; Risaliti et al. 2005) observa- Ranzani1,Bologna40127, Italy 2 tions of AGNs showing blue-shifted absorption or prevailing geometry in models of jet-heated cooling emission lines along the line of sight. Neither the flows cited above, but allow the jets to have larger opticaldepthnorthecoveringfactoroftheoutflow- angularsizes attheir source. Mostofthe massout- ing gas can be accurately determined from these flow in our jets arises not from the origin but by observations, but the outflowing mass flux can be entrainment of ambient gas at larger radii – such comparable to the Eddington limit, implying that a model is supported by the recent observations of relativelylittle gasis being directly accretedby the Sun,Jerius&Jones(2005)discussedbelow. Omma centralblack hole. The outflow velocity is typically etal. (2004)consideredtheinitialtransientflowre- several100kms−1 butincreasestoseveral1000km sulting from a bipolar outflow of this sort, but did s−1inafewmoreluminousobjects(Kriss2004). At not address the important question whether or not leasthalfofallAGNsexhibitoutflowssoitisplausi- such jets can shut down the cooling flow for many blethattheyexistinallobjectsandwithsubstantial Gyrs while preserving the observed thermal gradi- coveringfactors. Windsfromaccretiondisksareone ent in the hot gas. This is our objective here. possibleexplanationfortheoutflows(Narayan&Yi In the 2D gasdynamical models described here 1994;Konigl&Kartje1994;Blandford&Begelman nonrelativistic outflows are generated by assigning 1999; Proga 2000; Soker & Pizzolato 2005), partic- a fixed velocity to gas that flows into a biconical ularly those with higher velocities. source region (radius of a few kpc with half angle The highly uncertain outflowing mass flux ob- θ ∼5−20◦)attheclustercenter. Theacceleration j servedinlowluminositygalaxies(M˙ ∼1M yr−1), of gas in the source bicone is activated by a feed- ⊙ is far less than the mass flux that arrives at the backrecipetriggeredasgasflowsintotheinnermost central galaxies in group and cluster cooling flows, zones. The2Dbiconicaloutflows,whichmayforex- M˙ ∼ 10 − 300 M yr−1. However, outflowing amplerepresentadiskwind,proceedalongthe axis ⊙ gas in these more massive flows is likely to be too ofsymmetry ofthe computationalgrid. Evenwhen hot, too rarefied and too highly ionized to produce the initial outflow has rather substantial opening blueshifted UV or X-ray lines and would be diffi- angles (i.e. θj ∼20◦), the flow rapidly concentrates cultto observe. Indeed, currentlyavailableUVand within ∼ 30 kpc into a much narrower jet. This X-ray absorption observations may naturally select compressionoccursbecausetherapidpressuredrop the densest, coldest and most slowly moving gas in inthejetduetoexpansioncausesthejettobecom- each outflow. Many authors (e.g. Churazov et al. pressed and narrowed by the ambient gas pressure 2002;2005;Peterson&Fabian2005)arguethatthe whichdecreaseslessrapidlywithradiusinthe clus- mechanical outflow luminosity L from massive ter gas. As the jet proceeds, it entrains additional mech black holes can greatly exceed their bolometric lu- ambientgasanditsmassfluxincreases. Thesesolu- minosity,and this may apply to allradiativelyinef- tionshavetwoexcellentattributes: aftermanyGyrs ficient black holes (Hopkins et al. 2005). thetime-averagedgastemperatureprofileresembles As in the Blandford-Begelman accretion model, those observed, dT/dr > 0 in r <∼0.1rvir, and very we assume that the majority of gas accreted at the little gas cools below ∼ Tvir. The jet itself is diffi- outer edges of the accretion disks ultimately flows culttoobserve. Finally,becauseoftheintermittent awayfromthedisksurfaceasafastbutnonrelativis- nature of the feedback jet excitation, multiple gen- tic wind. Such disk flows are unlike the relativis- erationsoflargeX-raycavitiesarecreatedwith2or tic e± radio-emitting jets drivenfrommuchsmaller 4 visible at any time, very similar to Perseus (e.g. regions near the central hole (Blandford & Znajek Fabian et al. 2005). 1977),but the two types of outflowmay coexist. In contrast, winds driven by radiation pressure from 2. THECLUSTERA1795 thin disks, such as those described by Proga(2000) We compare our gasdynamical calculations with are confined by strong radial, polodial fields (e.g. the temperature and density profiles of the well- Blandford & Payne 1982), and may be directed observed cluster Abell 1795 (Tamura et al. 201; mostly along the equatorial plane. However, more Ettori et al. 2002) assumed to be at a distance 243 axis-orientedoutflows may be possible from thicker Mpc. Abell 1795 is a typical rich cluster with a disks or with different, more vertical field geome- central cD galaxy and a reasonably relaxed overall tries (e.g. Everett, Königl & Kartje 2001). Never- structure (Boute & Tsai 1996). Abell 1795 has the theless, fast wind-driven bipolar flows, such as we usualattributesofnormalcoolingflows: strongcen- consider, may at their originfill cones of significant tral peak in X-ray surface brightness (e.g. Tamura solid angles. For example, Proga (2003) finds that etal. 2001),a positive temperaturegradientdT/dr mostofthemassfluxindiskwindsathighvelocities in the central regions out to ∼ 500 kpc, a central v >∼ 1000 km/s, which we require in our flows, lies radiative cooling time ∼ 3×108 yrs that is much within 20 or 30 degrees from the polar axes. Such less than the cluster age (e.g. Edge et al. 1992; broad outflows are expected to entrain additional Fabian et al. 2001), optical line emission near the ambient gas as they proceed out from the central centralcD(Cowieetal. 1983),anexcessofblueand region. Therefore, for our exploratory calculations ultraviolet light possibly from massive young stars we adopt a bipolar wind geometry similar to the (Johnstone, Fabian & Nulsen 1987; Cardiel, Gor- 3 gas & Aragon-Salamanca 1998; Mittaz et a. 2001) In some calculations unphysical cooling also oc- and a central radio source 4C 26.42 (McNamara et curs (generally at small radii) along the symmetry al. 1996a,b). Chandra images near the center of axis,θ =0orπ,whereweemployreflectionbound- Abell 1795revealanX-rayemissionfeature aligned ary conditions. As gas approachesa reflecting axis, with a remarkable optical filament (Fabian et al. it is compressed and cools in a way that would not 2001). Thisfilamentandthecentraltotalmasspro- occurina full3Dcalculationwheresuchreflections file,M ∝r0.6 inside40kpc,whichissomewhatflat- do not occur. Nevertheless, this spurious, purely terthanNFW(Navarro,Frenk&White1996),may numerical cooling near the symmetry axis is nec- suggest a local deviation from hydrostatic equilib- essarilyincluded in the computations described be- rium. low. Consequently,ourestimatesofthecoolingrate We approximate the total mass profile in A1795 M˙ may be regarded as conservative upper limits. with an NFW profile with virial mass Mvir = When the flow velocity is entirely radial, as in the 1015 M⊙ and concentration c = 6.57, which also (unheated) cooling flow described in the next sec- matches the total mass found from X-ray obser- tion, this type of boundary cooling does not occur. vations, assuming hydrostatic equilibrium. The de Vaucouleurs mass profile of the central cD galaxy, 4. NORMALCOOLINGFLOWINA1795 defined by M ∼ 6×1011 and R = 8.5 kpc, has We begin with a simple evolutionarycooling flow ∗ e alsobeenincluded,butthismasshaslittle effecton forA1795inwhichthegasisallowedtoevolvefrom the overallgas dynamics. aninitialhydrostaticmodelingoodagreementwith the observed density and temperature profiles. In 3. COMPUTATIONALPROCEDURE this traditional spherical cooling flow all the gas coolsatthecenteroftheflowandthereisnodepen- The two-dimensional numerical calculations de- dence on polar angle θ. For standard cosmological scribed here are solutions of the same flow equa- parameters (Ω = 0.3; Λ = 0.7; H = 70 km s−1 tions described in our earlier paper on heated cool- Mpc−1) large clusters like Abell 1795 formed rela- ingflows(Brighenti&Mathews2002). Theseequa- tivelyrecently,so weconsiderthe internalflowevo- tions explicitly include radiative cooling. The 2D lution for only 7 Gyrs. The dotted lines in Figure computationalgridis insphericalpolarcoordinates 1 show the radial variation of the gas density and r and θ. Unless stated otherwise, the grid is com- emission-weighted temperature in the cooling flow prisedof200logarithmicallyspacedradialzonesex- after 7 Gyrs. The gas density follows the observa- tending to 3 Mpc and having a central zone of size tionsfairlywellbeyondabout50kpcbutissystem- 0.75kpc. There are 60evenly spacedangularzones atically too large closer to the center. This density intherange0<θ <π. Someofourflowshavebeen excess is typical for pure cooling flows, as discussed computed at higher resolutionwith 600 logarithmi- by Mathews & Brighenti (2003). The depression callyspacedradialzonesextendingto3Mpc,witha of the observed (azimuthally averaged) density rel- central zone of size 0.6 kpc, and 120 evenly-spaced ative to this flow within 50 kpc may be due in part angular zones. We find that all important results to unresolved X-ray cavities. (temperatureanddensityprofiles,coolingrate,etc.) areessentiallyunchangedwhentheresolutionisim- ThecoolingrateM˙ (t)forthiscoolingflow,shown proved. as a dotted line in Figure 2, increases with time, When gas in a computationalzone begins to cool approaching ∼ 400 M⊙ yr−1 after 7 Gyrs. This byradiativelossestolowtemperatures,usuallynear cooling rate is comparable to the cooling rate for the center of the flow, the density of cooling gas in A1795estimatedby Allenetal. (2000)fromdepro- the zone increasesto maintainpressure equilibrium jected ROSAT images, M˙ ∼ 500 M⊙ yr−1. How- withgasinneighboringgridzones. Thisrepresenta- ever, XMM RGS spectra show no evidence of gas tionofthecoolingprocess,discretizedandaveraged with temperatures less than ∼ 2 keV (Tamura et on the grid scale, is unphysical since gas cooling in al. 2001), indicating a much smaller cooling rate, pressureequilibriumshouldeventuallyoccupyavol- M˙ < 150 M yr−1. This upper limit is consistent ⊙ ume much smaller than that of the grid zones. In with M˙ <∼ 100 M⊙ yr−1 estimated from Chandra ordertoapproximatelyallowforthissubgridevolu- observations (Ettori et al. 2002). tion, we remove cold gas as it forms, assuming that its volume becomes vanishingly small. Cooling gas 5. JETOUTFLOWS isremovedby addingamasssinktermtothe equa- Gas flows including the effects of jet momentum tionofcontinuity,−q(T)ρ/tcool,wheretcoolisthelo- aresolvedinseveralstages. Eachcalculationbegins calradiativecooling time asdescribed by Brighenti with a static cluster atmosphere based on the ob- &Mathews(2002)andq =2exp(−T/Tq)2 becomes served temperature and density profiles in A1795. large when T <∼ Tq = 5×105 K. This mass sink During time 0 < t < 1 Gyr the configuration is term is used to remove the unphysical clutter of allowedto evolve(withoutjets)towardapurecool- zonescontainingcoldgaswithoutaffecting the flow ing flow, and later during 1 < t < 7 Gyrs the jet of hotter gas, T ≫ T , throughout the rest of the momentumisactivatedaccordingtoafeedbackcri- q cluster. terion. 4 We adopt a simple computational procedure to to a similar deviation found in the 3D models of trigger jet outflow in which all gas in a biconical Bruggenetal. (2002). Nevertheless,the creationof jet source region near the center of the flow is set multiple pairs ofbubble cavities,similar to those in into outward motion at velocity u as long as some Perseus(Fabian et al. 2003),is an encouragingfea- j feedback criterion is satisfied. The geometrical pa- ture of these jet flows. Finally, we stress that these rameters that define the jet source region are the jets carry mass as well as energy to large distances radius r and the half opening angle θ of the jet. fromthecentralAGNandinthisrespecttheydiffer j j We consider three feedback criteria to activate the from many previous calculations in which the jets jet: carried little or no mass. A: The gas velocity in the jet source re- 5.2. Additional Jet Momentum Flows gionis setto u only whenthe gascool- j ingrateM˙ isnon-zeroinside aradiusof Table 1 summarizes some of the jet-heated flows 1 kpc. we have calculated. For consistency, all results in Table1 referto flowscomputed atlowerresolution, B: The gas velocity in the jet source re- butarenotsignificantlychangedwhenthe gridres- gionissetto uj only whenthe netmass olution is refined. In addition to listing the param- flow across a sphere of radius 1 kpc is etersthatdefineeachflow,Table1givesseveralad- negative (mass inflow). ditional global results after 6 Gyrs of jet feedback: the total energy E supplied by the jet source, C: Continuous jet flow u in the jet kin j the time-averagedmechanical luminosity generated source region at all times. in the jet source region L , the total mass that mech cooledM after t=7 Gyrs and the averagecool- Duringtimeswhenthe jetoutflowisnotactive,gas cool flows through the source region in accordance with ing rate hM˙ i, and the X-ray luminosity Lx at this the usualgasdynamicalequations. Eachflowcalcu- same time. For many jet parameter combinations, lation is uniquely designated by mN(X,r ,θ ,u ) the mean cooling rate hM˙ i is less than or compara- j j j where N is a number assigned to each computed ble to the Chandra value M˙ ≈ 100 M yr−1. The ⊙ flow, X =A, B or C is the feedback criterion, rj is mechanical energy for successful flows ranges from the jet radius in kpc at the source, θj is the source ∼ 0.02Lx to ∼ Lx. We stress that the condition jet half-angle in degrees anduj is the jet source ve- Lmech >∼ Lx that is usually required to keep jet- locity in units of 103 km s−1. Flows at the higher heated flows from cooling does not necessarily ap- spatial resolution are designated with upper case ply to our flows in which mass as well as energy is MN(X,r ,θ ,u ). transported outward. Consequently, successful jet- j j j advectingflowsarepossibleevenwhenL ≪L . 5.1. A Representative Flow with Jet Momentum mech x Jet mass transfer appears to be an efficient and ro- Among the many models with satisfactory bustwaytorecirculategasandenergyoutwardwith or excellent results, we select m1(A,5,10,10) little radiative cooling while retaining the cooling as representative and discuss it in more de- flowappearanceasobservedinthedensityandtem- tail. The azimuthally averaged gas density and perature profiles. emission-weighted temperature profiles for the Regarding this latter important point, Figure 4 m1(A,5,10,10) flow are shown at three times in showsthegasdensityandtemperatureattimet=7 Figure 1. The global cooling rate M˙ (t) for this Gyrs for a sample of successful and unsuccessful flow, plotted in Figure 2, is small, indeed its time- flows listed in Table 1. The cooling rates for these averaged value hM˙ (t)i ≈ 20 M yr−1 is well be- flows (sampled each 0.5 Gyr) are shown in Figure ⊙ 5. In both Figures 1 and 4, the computed gas den- low the constraints imposed by XMM and Chan- sitywithinabout20-30kpcfromthe centerexceeds dra observations. Even more remarkable, both the that observed in A1795, but this region of A1795 density and temperature profiles shown in Figure contains a cool, transient optical filament about 60 1 retain their cooling flow appearance at time 7 kpc in diameter and may be experiencing a local Gyrs. Within about 50 kpc n(r) and T(r) for the deviation from hydrostatic equilibrium. For many m(A,5,10,10)flowliebetweenthepurecoolingflow and the observations. of the unsuccessful models with hM˙ i >∼ 100 M⊙ Figure 3 shows in more detail the 2D density yr−1, most of the cooling occurs during one or two structureatseveraltimesforthehighresolutionver- episodes. These flows would be regarded as suc- sion of this flow, M1(A,5,10,10). The four panels cessfulinmatchingtheX-raydataiftheywerecom- in Figure 3 show illustrate the growth of successive putedforonly∼2−3GyrswhenM˙ (t)isacceptably generations of buoyant X-ray cavities. Cavities are small, but star formation, which is likely to occur associated with jet intermittancy. The evolution of duringtimesofenhancedcooling,wouldbeinconsis- the buoyant cavities away from the (horizontal) jet tent with optical colors of cluster-centered galaxies axis may be an artifact of the 2D reflection bound- (e.g. McNamara 1997). Enhanced blue light from ary conditions along this axis, but it is comparable young stars typically persists for 2 - 3 Gyrs after a 5 starburst. holes and that these winds return most of the mass The mass M in column (9) of Table 1 rep- inflow received from centrally cooling gas. We cool resents all the cooled gas that has been removed implement this simple idea by insisting that the fromthegridbytheterm−q(T)ρ/t intheequa- outflow velocity remains constant and rather large cool tion of continuity. Almost all of this gas cools in throughout the biconical jet source region when- the central regions. However, M is not small ever a feedback criterion is satisfied. Although this cool and is often much larger than the mass of central model for the jet source is admittedly ad hoc, as black holes (or stars) in cluster-centered galaxies. the jets move further out they appear to develop However, there are reasons to believe that we have moreuniversalproperties. Inthis sectionwebriefly overestimated the global cooling rate in our mod- review the evolution of jets far beyond the source els. For example the sink term −q(T)ρ/t in the region. cool continuityequationnotonlyremovesthecooledgas, The physical nature of our jets is most clearly butmayalsoencouragelocalpressuregradientsthat defined when the jet activity is continuous in stimulate additional cooling. If gas in a particular time (models C) such the high resolution model grid zone begins to cool while gas is being removed M11(C,5,20,10) in which the overall flow ap- by the sink term, hot gas from adjacentzones, that proaches a quasi-steady state. The global velocity wouldnototherwisecool,maybestimulatedtoflow field and density contours for the M11(C,5,20,10) toward the cooling zone, possibly raising the local flow after 7 Gyrs are shown in Figure 6. The mag- cooling rate unrealistically. As discussed above, we nitude of the radial gas flow at time 7 Gyrs in also expect the computed cooling rate to be spuri- threeangulardirectionsareshowninFigure7. Itis ously enhanced by cooling near the symmetry axis apparent from this Figure that the cooling inflow, where reflecting boundary conditions must be em- which fills most of the cluster volume, flows toward ployed. Evidence for computational overcooling is the jet, becomes entrained and is carried outward. provided in the final two models listed in Table The continuous jet creates an extended two-sided 1, m13(B,5,10,10) and m14(B,5,10,5), in which the channel of low density gas. The difficulty of ob- sink term is set to zero, q(T) = 0. In flows with serving such a channel can be seen in the X-ray q =0,M inTable1representsthemassofcooled surface brightness images of the (high resolution) cool gas (T << T = 5× 105 K) that remains in the M1(A,5,10,10) and M11(C,5,20,10) flows shown q grid and goes into approximate free fall if it is not in Figure 8, viewed perpendicular to the jet. From at the center. Values of M for these flows are this viewing direction the jet cavitation in the con- cool very small, suggesting that nonzero q(T) does in- tinuous M11(C,5,20,10) flow produces at most a deed artificially increase the cooling rate. But real 10%reductionintheX-raysurfacebrightnessalong cooling at some level can and does occur. Signifi- the jet axis. The jet cavitation produced by inter- cant centrally-located cold gas and star formation mittent flows such as M1(A,5,10,10) is less pro- are observed in many massive clusters (e.g. Edge nouncedandmoredifficult to detect. Although our 2001). RecentCOobservationsofA1795bySalome 2D jets are constrained to flow in a axisymmetric & Combes (2004) have detected ∼1011 M of cold fashion along the θ = 0 and π axes, in a full 3D ⊙ gaswhich is entirely consistentwith our flow calcu- simulation the jets may not follow such a perfectly lations based on an approximate model for A1795. linear pathway through the cluster gas. Inmarkedcontrasttoourearliermodelsinwhich The symmetric jet cavitations visible in Figure 8 we explored a wide variety of heated cooling flows areremarkablysimilar to the Chandra observations (Brighenti & Mathews 2002; 2003), very few of the ofthedouble-jettedradiogalaxyNGC1265bySun, jet momentum flows described here have tempera- Jerius & Jones (2005). The X-ray contours in their ture anddensity profiles that strongly deviate from Figure 1a show symmetric indentations along the the observations of A1795. The relative success of radiojetaxisjustasinourFigure8,suggestingthat each jet momentum flow, expressed in column (11) ambient hot gas in NGC 1265 is being entrained of Table 1, is based largely on the magnitude of andsweptalongwith the jet. This observationalso the mean cooling rate hM˙ i. The results in Ta- supportsthebiconicaloutflowgeometrythatweas- ble 1 and Figures 2 and 5 imply limits on the jet sume here rather than disk winds in the equatorial source parameters X, r , θ , and u corresponding plane (e.g. Proga 2000). j j j to hM˙ i <∼ 100 M⊙ yr−1 as observed with Chan- It is apparent from Figure 8 that our jets are poorly resolved, often occupying only a few angu- dra. In particular, radiative cooling is effectively shut down for source regions with radii rj >∼3 kpc, lar zones even at the higher grid resolution. This halfanglesθj >∼10o andjetvelocitiesuj >∼5000km poor resolution restricts somewhat our analysis of the transversejet profiles. Nevertheless,the behav- s−1. iorofthegasoutsideofthesmalljetregions–which 5.3. Nature of the Jet Flow determines the overallX-ray properties of the cluster– does notappearto be stronglyaffected by the The simple jets we employ are based on the level of numerical resolution in the jets. plausible notion that strong non-relativistic winds To understand better the details of the jet- flowfromaccretiondisksaroundsupermassiveblack 6 atmosphereinteraction,we haveexaminedthe high masstolargeradiiatthesameratethatitarrivesat resolution jet in the M11(C,5,20,10) flow. One thecenterinthecoolinginflowoutsidethejet. This natural attribute of the biconical jet source region mass conservation is approximately true for all the isthatthe originalgaswithinthe sourceisexpelled other flows, for example M˙ (90◦)≈−12±4 M /yr ⊙ very rapidly after the jet turns on. Consequently, for the flows plotted in Figure 4. duringmostofthe active phaseofthis region,most We find that the decelerating jets penetrate to of the outgoing gas is supplied by recent advection large distances in the cluster gas, well beyond sev- near the outer boundary of the bicone. As a re- eral hundred kpc. However,the maximum distance sult, most of the mass outflowing from the jet at rj to which the jet outflow continues is observed to occurs near θj so the initial jet density profile per- increase with the refinement of the computational pendicular to the jet axis is hollow with a strong grid and this must be explored in future calcula- central minimum. This type of hollow jet structure tions. In fully 3D versions of the M11(C,5,20,10) mayinfactbephysicallyappropriateifentrainment jet we expect that the lateral motions of jet due to of ambient gas occurs near the source region. shear instabilities may cause the jet to dissipate its An important feature of these jet solutions is energy at a somewhat smaller radius. the narrowing of the jets as they moves outward. Although the half angle of biconical jets θj can 6. CONCLUSIONS be rather large, these initially conical jets become Subrelativistic jet flows that entrain ambient gas nearly cylindrical as they move outward. This jet maybetheessentialkeyforsolvingtheclustercool- focusing occurs because the pressure in the jet is ingflowproblem: Whythehotgastemperatureand rapidly loweredby expansionandtends to decrease density profiles resemble cooling flows but show no with radius faster than the pressure in the ambi- spectralevidenceforcoolingbelow∼T /3atrates ent gas. As a result the jets are compressed and vir expected from the luminosity L . Many scenarios collimated by the ambient gas pressure. x have been previously consideredin which the gas is Anumberof(poorlyresolved)internalshocksap- heatedbyavarietyofmechanismsincludingjets. In pearinthejetflowthatwedonotdescribeindetail most previous jet calculations it has been assumed here. The main effect of these shocks, even inside that the jets are primarily sources of energy that the jet source region, is to raise the temperature reheat the cluster gas with no significant outward and entropy within the central jet to rather high masstransport. Overall,thesesimulationshavenot values. Gas in the jet source and just beyond flows been successful in reducing the cooling rate while approximately at the sound speed within the jet. maintaining the observed temperature and density As the jet moves further out, the mass outflow in profiles for many Gyrs. Because of the large num- the jet increases due to entrainment. The amount ber of cooling core clusters observed, cooling must ofentrainmentis approximatelyindependent ofthe be sharply reduced or arrested for many Gyrs. spatial resolution. The top panel in Figure 9 shows Themass-carryingjetsconsideredhereareavari- the variation of the (outward) mass flux transverse ant of the circulation flows we have discussed in to the jet axis in the continuous M11(C,5,20,10) which buoyant bubbles provide an outward mass jet at various cluster radii. The quantity plotted is transport while most of the X-ray emission comes dM˙ /dθ = ρv 2πr2sin(θ) M yr−1 where v (θ) is r ⊙ r fromanormalcoolinginterbubbleinflow(Mathews, the local jet velocity. It is clear from Figure 9 the et al. 2003; Mathews, Brighenti & Boute 2004). angularwidthofthejetnarrowsfromitsinitialhalf Our computational results for mass-carrying jets angle θ = 20◦ as it moves out and remains hollow j are robust in that we find satisfactory multi-Gyr to rather large distances in the cluster. solutions for a significant range of parameters de- Of particular interest is the radial increase of scribing the initial central jet outflow. The impor- the integrated mass flow in the jet, M˙ (θ) = tant global features of our flows are also insensi- Rθ(dM˙ /dθ)dθ, plotted in the lower panel of Figure tive to computational resolution. The jet outflow 0 9. The total mass outflow in the jet and its ap- is stimulated by cooling or inflowing gas near the proximate local angular width θ (r), can be es- central supermassive black hole, but the success of max timated from the maximum M˙ =M˙ (θ ) in each ourlongtermsolutionsisnotstronglydependenton max curve. The decline in M˙ (θ) for θ > θ is due to the specifics of this feedback mechanism. The nat- max ural intermittancy of the feedback generates mul- the negative contributionto the integratedflow be- tiple generations of X-ray cavities similar to those yond θ caused by slowly inflowing gas adjacent max observedinthePerseusClusterandelsewhere. Nev- to the jet. The mass flux increases from 65 M /yr ⊙ ertheless, the physics at the source of outflow is at 5 kpc to 116 M /yr at 20 kpc and reaches 170 ⊙ poorlyunderstoodandobservationalsupportislim- M /yr at 200 kpc. This increase shows that mass ⊙ ited. Moredetailedmodelsofmass-carryingjetswill entrainment is a key feature of the success of these be necessary before they can be fully accepted. simulations. For model M11(C,5,20,10) in which One possible objectionto the jet drivenmass cir- the jet is continuously active, M˙ (θ =90◦) becomes culation described here is that SNIa-enriched gas essentially zero, indicating that the jet is returning that enters the source cone (within the central E 7 galaxy) is transported out only along the jet axis, most of the SNIa iron was produced. unlike the observed iron abundance pattern which Studies of the evolution of hot gas in elliptical is spherically symmetric around the central galaxy galaxiesatUC Santa Cruzaresupportedby NASA (de Grandi et al. 2004). Either the radio jet pre- grants NAG 5-8409 & ATP02-0122-0079 and NSF cesses(Gower,etal. 1982)asintheclusterobserved grant AST-0098351for which we are very grateful. by Gitti et al. 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The dotted line shows the quasi-steadypurecoolingflowattimet=7Gyrs. Theotherlinesshowthecomputeddensityandtemperatureprofilesforflow m1(A,5,10,10)atthreetimes: 2Gyrs(long-dashed lines),4Gyrs(short-dashed lines),and6Gyrs(solid lines). 10 Fig. 2.— ThetotalcoolingrateM˙(t)forthecoolingflowsolution(dotted line)andforflowm1(A,5,10,10)(solid line).

Stopping Cooling Flows with Jets

Similar Stopping Cooling Flows with Jets