DRAFTVERSIONJANUARY24,2013 PreprinttypesetusingLATEXstyleemulateapjv.5/2/11 DOJETSPRECESS... OREVENMOVEATALL? CHRISNIXON1,2,3 &ANDREWKING2 DraftversionJanuary24,2013 ABSTRACT Observations of accreting black holes often provoke suggestions that their jets precess. The precession is usually supposed to result from a combination of the Lense–Thirring effect and accretion disc viscosity. 3 We show that this is unlikely for any type of black hole system, as the disc generally has too little angular 1 momentumcomparedwithaspinningholetocauseanysignificantmovementofthejetdirectionacrossthesky 0 onshorttimescales. Uncorrelatedaccretionevents,asinthechaoticaccretionpictureofactivegalacticnuclei, 2 changeAGNjetdirectionsonlyontimescales&107yr.InthispictureAGNjetdirectionsarestableonshorter n timescales,butuncorrelatedwithanystructureofthehost galaxy,asobserved. Wearguethatobservationsof a black–holejetsprecessingontimescalesshortcomparedtotheaccretiontimewouldbeastrongindicationthat J theaccretiondisc,andnotthestandardBlandford–Znajekmechanism,isresponsiblefordrivingthejet. This 2 wouldbeparticularlyconvincinginatidaldisruptionevent. Wesuggestthatadditionaldiscphysicsisneeded 2 to explainany jet precession on timescales shortcomparedwith the accretion time. Possibilities includethe radiationwarpinginstability,ordisctearing. ] E Subjectheadings:accretion, accretiondisks—blackholephysics— galaxies: active—galaxies: evolution —galaxies:jets H . h p 1. INTRODUCTION 2. LENSE–THIRRINGEFFECTINDISCSWITHα>H/R - Jets appear in all accreting systems, from protostars We briefly describe the evolution of a misaligned disc o (e.g. Davisetal. 1994) to AGN (e.g. Nagar&Wilson 1999; aroundaspinningblackholeintheregimewherewarpsprop- r t Kinneyetal. 2000). In all cases the terminal speed of the agate diffusively – i.e. α > H/R (Papaloizou&Pringle s jet is & the escape speed from the surface of the accret- 1983).Wediscussthewavelikecase(α H/R,andasteadywarpif thus ends up aligned (or counter–aligned) along its original α < H/R. HereαistheShakura–Sunyaevviscosityparam- totalangularmomentum(thevectorsumoftheoriginalspin eterandH/Risthediscangularsemithickness,andthetwo and disc angular momenta; Kingetal. 2005). We note that casescorrespondtodiffusiveandwavelikewarppropagation so far all calculations of the Bardeen–Petterson effect have respectively. usedShakura&Sunyaev(1973) α discs; a demonstrationof theeffectfordiscsexplicitlydrivenbythemagnetorotational chris.nixon@jila.colorado.edu instability(MRI)hasnotyetbeenattempted. 1JILA,UniversityofColorado&NIST,BoulderCO80309-0440,USA 2DepartmentofPhysicsandAstronomy,UniversityofLeicester,Uni- TheBardeen–Pettersonevolutionassumesthatthediscvis- versityRoad,LE17RHLeicester,UK cosity is strong enough to communicate the differentialpre- 3EinsteinFellow cession efficientlythroughthe disc. Recently Nixon&King 2 NIXON &KING (2012)andNixonetal.(2012a)haveshownthatforrealistic wherecisthespeedoflight. Combining(2)and(3)givesus parametersthis often does not hold. Instead the disc is torn J 1M R V intomanydistinctplaneswhichprecessalmostindependently d = d d K (4) of each other (Nixonetal. 2012a). If the disc inclination to Jh a M Rg c theblackholespinishighenoughthisgeneratessignificantly orequivalently counter-rotatingdisc orbitsand these lead to rapid accretion (cf.Nixonetal.2012b). Theseresultsmarkedlyalterthepic- J 1M R 1/2 d d d tureofhowblackholesaccrete,andmayallowforstrongpre- = , (5) J a M (cid:18)R (cid:19) cession of the innerdisc plane. We return to this possibility h g inSection4,butforthemomentconsidertheusualBardeen- whereR =GM/c2 ∼1013M cmisthegravitationalradius g 8 Pettersonevolution. (with M8 = M/108M⊙). It is clear that this ratio can take Todiscusspossiblejetprecessionswelet Jd, Jh andJt = verydifferentvaluesforvariousastrophysicalsystems,aswe Jd +Jh be the disc, hole and total angularmomentumvec- nowconsider. torsrespectively,withmagnitudesJ ,J andJ . Duringthe d h t alignmentprocessJ precessesaroundJ withaninitialam- 2.1.1. TidalDisruptionEvents h t plitudeθ definedby i Ina tidaldisruptionevent,a starona near–parabolicorbit aroundasupermassiveblackholefillsitstidallobenearperi- J ·J cosθ = h t (1) center and is torn apart. This condition implies a pericenter i JhJt separationpgivenby Thisangleis small(i.e. Jt andJh arein a similardirection) M 1/3 either when the disc is oriented in a similar direction to the p≃ R∗ (6) hole,orwhenJ ≪J (andsoJ ≃J ). (cid:18)M∗(cid:19) d h h t ItisclearthatifJd ≪ Jh alignmentcannotmovethehole where the star has mass and radius M∗,R∗. Since Rd < p spinvectorveryfar. Theinnerdiscmustquicklybecomean- andMd H/R),theLense–Thirringeffectalone thanastandardthindiscwarpedbytheLense–Thirringeffect. cannot drive repeated jet precession, unless the disc is torn Tidaldisruptioneventsmayproducegeometricallythickdiscs intomanydistinctplanes(Nixonetal.2012a). andthereforecouldpropagatewarpsaswaves(seeSection3), butthisrequiresαtobeunusuallysmall(cf.Kingetal.2007). 2.1. Dojetsmove? 2.1.2. Blackholebinaries We have argued above that sustained Lense–Thirringpre- Thiscaseappearsslightlymorepromisingthanatidaldis- cessions are inhibitedby the dynamicsof the disc–holesys- ruptionastheblackholeandthedonorstarhavecomparable tem.Wenowaskhowmuchangularmomentumcanbetrans- massesM ,M , with0.1 . M /M . 10. Howeveratany ferredfrom an accretion eventon to a black hole. In partic- 1 2 2 1 one instant only a small fraction of the donor star feeds the ular, can thischangeits directionsignificantly? We derive a blackhole andthusagainwe have M ≪ M. As favorable simple expression for J /J and use it to consider realistic d parametersforvariousasdtrophhysicalsystems. parameters we take Rg ≈ 3 ×106 cm (i.e. a 10M⊙ black hole),andalargediscradiusR .1013cm.Thelargestreal- Thediscangularmomentumis d isticdiscmassisMd .10−5M⊙(e.g.Eq.5.51ofFranketal. J ∼M (GMR )1/2 =M R V (R ) (2) 2002,withviscosityparameterα= 0.1andanaccretionrate d d d d d K d M˙ = 1019 gs−1 correspondingto the Eddingtonlimit fora where Md is the disc mass, M is the black hole mass, Rd a 10M⊙blackhole).Thisgives characteristic radius for the disc, V the Keplerian velocity andGisthegravitationalconstant. K Jd 1Md Rd 1/2 10−3 = . . (9) The spin angular momentum of a black hole with dimen- J aM (cid:18)R (cid:19) a h 1 g sionlessspinparameterais(Kumar&Pringle1985) Thusthedischasfartoolittleinstantaneousangularmomen- GM2a tumtocausetheholespinaxistomoveonadirectlyobserv- J = (3) abletimescale. We againconcludethatjetmovementwould h c Dojetsmove? 3 imply that the jet is notdriven by the black hole spin, orby Thereflectiontimescaleis∼2R /c (e.g.Nixon&Pringle out s the alignment of a standard thin disc warped by the Lense– 2010) where R is the distance the wave must travel and out Thirringeffect. Wenotethatifthediscisgeometricallythick c /2isthewavespeed(Papaloizou&Lin1995). s it could propagate warps as waves (see Section 3), but this This reasoning is not inconsistent with the simulations of requiresαtobeunusuallysmall(cf.Kingetal.2007). Fragileetal. (2007) which suggest repeated precession of a tilted disc around a black hole. Here the authors do not as- 2.1.3. ActiveGalacticNuclei sume an α viscosity, but instead simulate the MRI in an in- This case has been considered by Kingetal. (2008). The clined thick disc (H/R ∼ 0.2). As is known to happen in main constraint on J is the fact that discs which are too suchcases(e.g.Kingetal.2007),thisimpliesaneffectivevis- d largetendtofragmentintostarsunderself–gravity.Kingetal. cosityparameter(α≈0.01)ratherlowerthanimpliedbyob- (2008) show that a maximal disc of this type has J /J . servations(α ≈ 0.1−0.3). Fig. 13 of Fragileetal. (2007) d h few × 10−2a−1 and has an instantaneous mass ∼ 10−3M, showsthe value of alpha in theircomputation,rangingfrom whereM istheSMBH mass. Thusa mass∼ 0.01aM must α ≈ 0.5 near the innermost stable circular orbit (ISCO) to pass through this kind of disc, with constant orientation, to α ≈ 2 × 10−3 in the centre of their disc (R = 25Rg) to move the direction of a centrally–producedjet by ∼ 0.1 ra- α ≈ afew × 10−4 in the outer parts (R ≈ 50R ). Away g dian. This would take at least 10−2a Salpeter times, i.e. fromtheISCO thesevaluesare farfromthose inferredfrom .4×105ayrs,evenwithcontinuousaccretionattheEdding- observationsor those predicted by shearing box simulations ton rate, and typically & 107a yrsif accretionis slowerand (e.g.Simonetal.2012). Thismaywellbebecausethesimu- slightlyintermittent.Iftheorientationofsuccessiveaccretion lationruntimeisnotlongenoughtoallowtheMRItodevelop disceventschangesrandomly,asenvisagedinthechaoticac- fully;forexampletheruntimeis ∼ 10orbitsatR = 25R , g cretionpictureofAGN(King&Pringle2006,2007)thespin andonly∼3orbitsat50R . Wenotethatthediscprecession g direction would perform a random walk and so deviate less (Fig.16ofFragileetal.2007)isaveragedoverthediscregion fromitsoriginaldirection. 20R α. requiresextraphysics,asweadvocatebelow. We againfindthatrepeatedprecessionofthejetisgenerally The disc geometry needed for repeated precession in the unlikely,butthistimenotimpossible. wave–like regime is feasible for a tidal disruption event, InSection 2we assumed α > H/R, so thatwarpspropa- where the gas circularizes very close to the accreting black gate diffusively. But if α < H/R, warps instead propagate hole, and the instantaneous accretion rate can be super– efficiently as waves with near–sonic velocities, and are not Eddington. However again this is problematic: for a thick locally dampedby viscosity. It is thereforepossible that the discwithH/R∼0.1andα∼0.1theinnerdisc(R<10R ) g transmissionofsuchwavesintheinnerdiscregioncouldpro- aligns after at most a few precessions (Eq. 35 of Bateetal. duceaprecession.Howeverthisrequiresquitespecificinitial 2000). conditions–i.e. thattheaccretingmaterialbearrangedintoa radiallynarrowring, and α mustbe small. If instead the ra- 4. DISCUSSION dialextentofthediscislarge,thewaveinducedbytheLense- We have arguedthat the physicsof standard warped discs Thirringeffectpropagatesoutwards,andeitherneverreturns (diffusive or wave–like) strongly suggests that the Lense– (on timescales of interest) or significantly damps before re- Thirring effect alone is not a promising mechanism for ex- turning(thewavehastoreachtheouterdiscedgebeforere- plaining jet precessions, except possibly in rather rare cases flectingbackinwards). Lubowetal. (2002) giveanexample (seeSection3). Theessentialreasonforthisisthattheaccre- where the disc has R /R = 90 with H/R = 0.1 and tion disc generally has total angular momentum small com- out in α = 0.05. In this case the inner disc effectively settles into paredwiththatofthespinningblackhole,stronglyrestricting asteadyshapewhilethewaveslowlypropagatestotheouter the motion of any jet across the sky. Two alternative mech- disc. As Lubowetal. (2002) remark(last paragraphof their anisms,sofarlargelyunexplored,mayoffermorepromising Section4),“thesteady-stateshapeofthediscclosetothehole waysofmovingjets. is essentially established”. The disc quickly sets up a shape FirstPringle(1996)showsthatanaccretiondisccanbeun- inwhichtheinternaldisctorquesbalancetheLense–Thirring stabletowarpingdrivenbyirradiationfromacentralsource. precessiontorque.Thusforanyprecessiontooccurandmove Ifthereisinitiallyasmalltiltinthedisc,thiscangrowtopro- the jet, the inner regions must wait for the outward propa- videasubstantialglobaltiltinthediscwiththeanglebetween gating wave to reach a boundary and reflect back inwards. innerand outerparts differingby up to ∆θ ∼ π. The inner 4 NIXON &KING regions of the disc precess with a quasi–periodic change in Finally we note that interaction of the jet with super– inclination(Pringle1997). Thismechanismusestheangular Eddingtonwindscomingfromthedisccanalsogeneratepre- momentum induced by anisotropic scattering of the central cession of the jet as suggested for SS433 (Begelmanetal. accretion luminosity, so could potentially be more powerful 2006). Here the jet collides with a precessing gas mass and thantheLense–Thirringeffect. isdeflected(andslowed). Thejetprecessionhereispurelya Asecondpossibilityforlargeprecessionsofthediscplane consequenceofthedeflection. closetotheblackholeisthatforlargedisctiltsitmaybreak into distinct planes, with only tenuous viscous communica- tion between them. This happens when the Lense–Thirring WethankPhilArmitageforusefuldiscussions. Supportfor torque is strong enough to overcome the viscous torques this work was provided by NASA through the Einstein Fel- holding the disc together (Nixon&King 2012; Nixonetal. lowship Program, grant PF2-130098. Research in theoreti- 2012a). Nixonetal.(2012a)showthatrapidprecessionscan calastrophysicsatLeicesterissupportedbyanSTFCRolling occurhere.Weshallexploretheseideasinfuturepapers. Grant. 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Do jets precess... or even move at all?

Similar Do jets precess... or even move at all?