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

0.09 MB·English

by  Chris Nixon

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)inSection3.
a
[ ing object. Studies of protostellar jets usually assume that The diffusive case is considered at length in the lit-
the ultimate power source is the accretion energyof the gas erature (e.g. Bardeen&Petterson 1975; Pringle 1992;

1 disc forming the star, mediated by strong magnetic fields Scheuer&Feiler 1996; Lodato&Pringle 2006 and
v (e.g. Priceetal. 2012, and references therein). To tap the Nixon&King 2012). The Lense–Thirring effect of
1 maximumaccretion energy, a jet producedin this way must a spinning black hole makes tilted disc orbits precess
2
come from the innermost part of the disc near the stellar around its angular momentum vector at a frequency
3 surface, and so naturally gives a terminal velocity of or- Ω = a(R/R )−3Ω (R ) (where a is the Kerr spin
5 LT g K g
der the escape speed. For black holes there is debate as parameter, R = GM/c2 is the black hole’s gravitational
. g
1 to whether the jet driver is again the disc accretion energy radius, and Ω (R ) is the Kepler frequency at disc radius
K g
0 (e.g. Blandford&Payne 1982; Livioetal. 1999) or instead R ) which decreases strongly with radius (Thirring 1918;
g
3 theblackholespin(Blandford&Znajek1977). Lense&Thirring 1918). This differential precession is
1 Observations of jets from AGN often encourage sugges- communicated through the disc by its viscosity, which acts
v: tionsthatthejetsprecess(e.g.Falceta-Gonc¸alvesetal.2010; to co– or counter–align the disc with the plane of the hole.
i Kharbetal.2010;Gongetal.2011;Mart´ı-Vidaletal.2011). The inner parts of the disc quickly settle in the equatorial
X Forthetwosuggestedtypesofblackholejet–driving,thisre- planeoftheblackholeandtheouterpartsremainmisaligned,
r quiresprecessioneitherofthedisc planeclose tothecentral with the two parts joined by a warped region. This is the
a accretor(wherethejetislaunched),orinstead,oftheblack– Bardeen–Petterson effect (Bardeen&Petterson 1975) (but
hole spin axis. In this Letter we consider these processes, notethattheequationsofthatpaperdonotconserveangular
and show that precessing jets are not easy to obtain via any momentum; see Papaloizou&Pringle 1983). If an external
ofthemechanismsusuallyinvoked. Thereasonsaresimply: torque(e.g. fromamisalignedbinarycompanion)maintains
(1) the angular momentum of any single realistic accretion thetiltattheouteredgeofthediscthewarpcanremainsta-
event is always smaller than the angular momentum of the tionary,butotherwisethewarppropagatesoutwardsuntilthe
hole;and(2)theinnerdiscsettlesrapidlyintoasteadyshape. entirediscliesintheequatorialplane. Thehole–discsystem
Thisisalignedtothespinifα > 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
[email protected]
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 <M∗ wefind
choredtothespinplaneofthehole(e.g.Kingetal.2005),so
alignment cannot move the inner disc very far either. So if Jd 1 M∗ 5/6 R∗ 1/2
Jd ≪Jh theLense–Thirringeffectcannotdriveaprecessing Jh < a(cid:18)M (cid:19) (cid:18)Rg(cid:19) . (7)
jet.
Thus if we have the usual Bardeen–Petterson evolution, Eveninthemostfavorablecaseofagiantstar(R∼1013cm),
precessions are confined at best to cases where J & J . (7)impliesatinyratio
d h
Howeverthis still does not generate repeated jet precession.
The initial amplitude of the precession can be large, since Jd .3×10−7M−1/2. (8)
J ≫ J . But the alignment and precession timescales for Jh 8
t h
the disc are similar (Scheuer&Feiler 1996): after only one This makes it obviousthat any observationalevidence for
precessiontimetheholeissignificantlyalignedwiththedisc. themovement(letaloneprecession)ofajetinatidaldisrup-
ThisisshownexplicitlyinLodato&Pringle(2006),whoget tion event is incompatible with jet driving by the hole spin,
atmosta single precessionofthe jet (see theirFigs 6& 11) asis centralto the standardaxisymmetricBlandford–Znajek
withsignificantamplitude. mechanism.Ifinsteaditisassumedthatthejetisdrivenbythe
We concludethat in a tilted disc propagatingwarps in the inneraccretiondisc,thismustinvolvephysicsmorecomplex
diffusiveregime(α>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 <R<50R . Wealsonotethatthetimescaleonwhich
g g
Weagainconcludethatdetectablejetprecessionisunlikely thediscisexpectedtoreachasteady(notprecessing)shapeis
inAGN.Inthechaoticaccretionpicturejetsgenerallymove ∼1/(αΩ)(seeEq.4ofLubowetal.2002). Thistimescaleis
very little for timescales . afew ×106 yr. However a se- muchlongerthantheruntimeofthesimulationsshowingpre-
quence of significant but random accretion events can move cession.Longerrunsareneededtocheckwhetherforrealistic
AGN jets across the sky on longer timescales (& 107 yrs). viscositiesanddiscsizestherepeatedprecessionobservedin
These conclusions agree with the facts that jets with rela- Fragileetal.(2007)remains,ratherthandampingawayafter
tively stable or closely correlated directions are seen (e.g. onlyafeworbitsofthedisc.
Kharbetal. 2006), but jet directions do not correlate at all Athick(H/R&α)small(R≪c t )disccaninprin-
s damp
withanyfeaturesofthehostgalaxy(Kinneyetal.2000). ciple precess. If one can arrange a disc like this to make a
sharp transition (on a scale length less than the warp wave-
3. LENSE-THIRRINGEFFECTINDISCSWITHα<H/R
length)to a thin disc outside it, the wave could see this as a
We have argued above that Lense–Thirring precession in hard boundaryand efficiently reflect back inwards. The dy-
standardthindiscscannotberesponsibleforrepeatedpreces- namics of such a setup is largely unexplored, but since the
sionsofjets. Howeveritisunlikelythattheinnermostregions thick region is fed by the thin region, a minimum condition
of blackhole accretiondiscs remainthin. In thissection we is that the tilt in the thin region must be maintained. This
discussthepossibilityofprecessionindiscswithH/R > 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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