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Disk-Magnetosphere Interaction and Outflows: Conical Winds and Axial Jets M.M.Romanova,G.V.Ustyugova,A.V.Koldoba,&R.V.E.Lovelace 9 0 0 2 n a J 4 2 AbstractWeinvestigateoutflowsfromthedisk-magnetosphereboundaryofrotat- ingmagnetizedstarsincaseswherethemagneticfieldofastarisbunchedintoan ] R X-typeconfigurationusingaxisymmetricandfull3DMHDsimulations.Suchcon- S figurationappearsifviscosityinthediskislargerthandiffusivity,oriftheaccretion . rateinthediskisenhanced.Conicaloutflowsflowfromtheinneredgeofthedisk h to a narrow shell with an opening angle 30-45 degrees. Outflows carry 0.1-0.3 of p - thediskmassandpartofthedisk’sangularmomentumoutward.Conicaloutflows o appeararoundstarsofdifferentperiods,howeverincaseofstarsinthe“propeller” r t regime,anadditional-muchfastercomponentappears:anaxialjet,wherematteris s accelerateduptoveryhighvelocitiesatsmalldistancesfromthestarbymagnetic a [ pressureforceabovethesurfaceofthestar. Exploratory3Dsimulationsshowthat conical outflows are symmetric about rotational axis of the disk even if magnetic 1 v dipole is significantly misaligned. Conical outflows and axial jets may appear in 8 differenttypesofyoungstarsincludingClassIyoungstars,classicalTTauristars, 5 andEXors. 8 3 . 1 0 9 0 : M.M.Romanova v Dept. of Astronomy, Cornell University, Ithaca, NY 14853 e-mail: i X [email protected] r G.V.Ustyugova a Keldysh Inst. of the Applied Math. RAS, Moscow, 125047, Russia e-mail: [email protected] A.V.Koldoba Institute for Mathematical Modeling RAS, Moscow, 125047, Russia e-mail: [email protected] R.V.E.Lovelace Dept.ofAstronomy,CornellUniversity,Ithaca,NY14853e-mail:[email protected] 1 2 M.M.Romanova,G.V.Ustyugova,A.V.Koldoba,&R.V.E.Lovelace 1 Introduction Jets and winds are observed in young stars at different stages of their evolution from very young stars up to classical T Tauri stars (CTTSs) where smaller-scale jetsandwindsareobserved(seereviewbyRayetal.2007).A significantnumber ofCTTSshowsignsofoutflowsinspectrallines,inparticularinHeI(Edwardset al.2006;Kwan,Edwards,&Fischer2007).High-resolutionobservationsshowthat outflows often have an “onion-skin” structure, with high-velocity outflows in the axialregion,andlower-velocityoutflowatlargerdistancefromtheaxis(Bacciotti etal.2000).Highangularresolutionspectraof[FeII]l 1.644m memissionlinetaken alongthe jets fromDG Tau, HL Tau and RW Aurigarevealedtwo components:a high-velocitywell-collimatedextendedcomponentwithv∼200−400km/sanda low-velocity∼100km/suncollimatedcomponentwhichisclosetoastar(Pyoetal. 2003,2006).High-resolutionobservationsofmolecularhydrogenin HL Tau have shownthatatsmalldistancesfromthestartheflowshowsaconicalstructurewith outflowvelocity50−80km/s(Takamietal.2007). Differentmodels have been proposedto explain outflowsfrom CTTSs (see re- view by Ferreira, Dougados,& Cabrit2006),includingmodelswhere the outflow originatesfromtheinnerregionsoftheaccretiondisk(e.g.,Lovelace,Berk&Con- topoulos1991;Ko¨nigl& Pudritz2000;Ferreiraetal. 2006),andthe X-windtype models(Shuetal.1994;2007;Najita&Shu1994;Caietal.2008)wheremostof thematterflowsfromthedisk-magnetosphereboundary.Inthisworkwe consider onlythesecondtypeofmodels.WedevelopedconditionsfavorableforX-typeout- flowsandperformedaxisymmetricandexploratory3DMHD simulationsforboth slowlyandrapidlyrotatingstarsincludingstarsinthepropellerregime. Fig. 1 Snapshots from axisymmetric simulations of conical winds. The background shows the matterfluxwithlightcolorcorrespondingtohigherflux.Thelinesaremagneticfieldlines. Disk-MagnetosphereInteractionandOutflows 3 Fig.2 Typicalflowinconicalwinds(att=380days).Thebackgroundshowsmatterflux,lines areselectedfieldlines,arrowsareproportionaltovelocity.Thenumbersshowpoloidalv andtotal p v velocitiesandnumberdensityatsampleplacesofthesimulationregion. tot Fig.3 Twocomponentsofwindsfromslowlyrotatingstararelabeled. Fig.4 Leftpanel:matterfluxtothestarM˙ andtoconicalwindM˙ (calculatedattheradius star wind R=0.1AU)asfunctionoftime.Rightpanel:samebutforashortertime-interval. 4 M.M.Romanova,G.V.Ustyugova,A.V.Koldoba,&R.V.E.Lovelace Fig.5 Conicalwindsobtainedin3DMHDsimulationsforQ =30◦.Leftpanel:densitydistribu- tionandsamplefieldlinesinthemW -plane.Rightpanel:samebutintheperpendicularplane. 2 Conical Winds Axisymmetric(2.5D)simulations.Toinvestigateoutflowsfromthedisk-magnetosphere boundaryitwasimportantthatthe magneticfieldlinesbebunchedintoanX-type configuration.Such bunching will occur if magnetic field lines threading the disk moveinwardtothestarfasterthantheydiffuseoutward.Thishappensforexample whentheviscosityin thediskis largerthanthe diffusivity.Inaxisymmetricsimu- lationswehavebothviscosityanddiffusivityincorporatedinthecode,bothina - prescription (Shakura& Sunyaev1973). The coefficientsa and a controlthese v d processes (Romanova, et al. 2005; Ustyugova et al. 2006). We investigate a wide rangeofparameters:0.01<a <1and0.01<a <1andchoosea =0.03and v d v a =0.1asamaincase.Weassumethatafterperiodoflowaccretionratethedisk d mattercomestotheregionfromtheboundary.Matterefficientlybunchesfieldlines and in ourcase a >a this configurationexists for a long time. The disk matter v d comesclosetothestar,isstoppedbythemagnetosphere,andpartofitmovesinto persistentconicaloutflows(seeFig.1). Our simulationsare dimensionless.As an examplewe chose parametersof the typicalCTTSwithmassM∗=0.8M⊙,R∗=2R⊙,magneticfieldB∗=1kG,period P∗=5.4days.IntheFigs.1-3theinnerboundarycorrespondstotworadiiofthestar. Weacceptedthischoiceofunitssoastocompareresultswiththepropellercase(see §4)wheretheinnerboundaryisafactoroftwosmaller.Analysisofconicalwinds done by Romanova et al. (2009) have shown that they are driven mainly by the magneticpressureforce(e.g.,Lovelaceetal.1991)whichislargestrightabovethe diskandactsuptodistancesofabout12stellarradii.Fig.2showstypicalparameters inaconicalwind.Fig.2showsthatmatterstarttoflowtoaconicalwindwithvery highazimuthalvelocity,equaltoKeplerianvelocityatthebaseoftheoutflow(vf ≈ 130km/sinourmaincase).Thepoloidalvelocityincreasesalongtheflowfromfew km/s right above the disk up to v =40−60 km/s at larger distances. Azimuthal p velocity remains larger than poloidal velocity inside the simulation region. In the conicalwindmatterflowsintoarelativelynarrowshellandtheconehasanopening angle,q =30◦−40◦.Thismaybeexplainedbythefactthatthemagneticpressure forceactsalmostvertically.Thismayalsoexplainfrequenteventsofreconnection of the inflating magneticfield lines in the outflow. We note that in additionto the mainconicalwindthereis matteraccelerationalongmagneticfield linescloserto Disk-MagnetosphereInteractionandOutflows 5 theaxis.Thelow-densitymatterisaccelerateduptohundredsofkm/srightnearthe starandmaybeimportantinexplanationofsomehighlyblue-shiftedspectrallines whichformnearCTTSs.Matterwhichisacceleratedinthisregionmaycomefrom thestar,ormaybepartiallycapturedfromthemainaccretionflow.Fig.3showstwo componentsoftheflowaroundaslowlyrotatingstar. Thefluxesofmatterandangularmomentumflowingtooroutfromthestarand fluxesflowingwithconicalwindsthroughthesurfacewithradiusR=0.1AUwere calculated. Fig. 4 shows that matter flux to the wind is only severaltimes smaller thanthattothestar,M˙ ≈0.2−0.3M˙ .Thematterfluxgoingtothewindvaries, wind star whichisconnectedwithfrequenteventsofreconnectionofthemagneticflux.Itis oftenthecasethatmatterisoutburstedtotheconicalwindsinanoscillatoryregime, in particular if a and a are not very small, a ∼0.1−0.3. If the diffusivity v d v,d is small, a =0.01−0.03,then outburststo winds are sporadic and occur with a d longer time-scale. Analysis of the angular momentumshows that in the case of a slowlyrotatingstarthestarspins-upbyaccretingmatter(throughmagnetictorque atthesurfaceofthestar,e.g.Romanovaetal.2002).Conicalwindscarryawaypart oftheangularmomentumofthedisk(0.5inthisexample),howeverastarmayspin- up or spin-downdependingon P∗. It spins-upin our exampleof a slowly rotating star. We also checked the case of very slow rotation, P∗ =11 days, and observed thatpersistentconicalwindsforminthiscaseaswell. 3Dsimulations.Weperformedexploratory3DMHDsimulationsofconicalwinds inthecasewherethedipolemagneticfieldismisalignedrelativetorotationalaxis byan angleQ =30◦. Comparedwith the axisymmetricsimulations,the accretion disk is situated at r>10R∗ and the simulation regionis much larger. Viscosity is incorporated in the code and we chose a =0.3 while the diffusivity is not in- vis corporatedandis onlynumerical(small,atthe levela =0.01−0.02atthedisk- d magnetosphereboundary).Weobservedthatthediskmovedinward,bunchedfield linesandformedconicalwinds.Fig.5showsthatconicalwindsareapproximately symmetric about rotation axis. There is however enhancement in the density dis- tributioninsideconicalwindswhichisassociatedwitha spiralwavegeneratedby themisaligneddipole.Recent3Dmodelinghaveshownthatatawiderangeofpa- rametersmatterpenetratesthroughthemagnetosphereduetointerchangeinstability (Romanova,Kulkarni&Lovelace2008;Kulkarni&Romanova2008).3Dsimula- tionsofconicalwindshowthatformationofconicalwindsoccursatlargerdistances fromthestarandarenotinfluencedbyinstabilities. 3 Enhanced Accretion andOutflows CTTSs are strongly variable on different time-scales including a multi-year scale (Herbstetal.2004;Grankinetal.2007).Thisisconnectedwithvariationoftheac- cretionratethroughthediskwhichmayleadtotheenhancementofoutflows(e.g., Cabritetal.1990).Simulationshaveshownthatthebunchingoffieldlinesbythe newmatterafterperiodofthelow-densityaccretionmayleadtoquitelongoutburst 6 M.M.Romanova,G.V.Ustyugova,A.V.Koldoba,&R.V.E.Lovelace Fig.6 SchematicmodelofanExorV1647Ori.Duringtheoutbursttheaccretionrateisenhanced sothatthemagnetospheric radius R decreases andthemagneticfieldlineswerebunched (A). m Thisresults inafast, hot outflow. As theaccretion rate decreases, thedisk moves outward and thisresultsinaslower, coolerCOoutflow(B). Furtherdecrease intheaccretion rateleadstoa quiescencestatewheretheproductionofwarmoutflowsstops(C).FromBrittainetal.(2007). Fig.7 Outflowsinthepropellerregime.Thebackgroundshowsmatterflux,linesareselectedfield lines,arrowsareproportionaltovelocity.Labelsshowtotalvelocityanddensityatsamplepoints. ofmattertotheconicalwindsandmaybethereasonforformationofmicro-jetsin theCTTSs.IfCTTSisinabinarysystem,thenanaccretionratemaybeepisodically enhancedduetointeractionwiththesecondarystar.Eventsoffast,implosiveaccre- tionarepossibleduetothermalinstabilityorglobalmagneticinstability,wherethe accretionrateisenhancedduetotheformationofdiskwinds(Lovelace,Romanova, & Newman1994).Enhancedaccretionmay lead to outburstsin EXors,wherethe accretionrateincreasesupto10−5M⊙/yrandstrongoutflowsareobserved.Brittain etal.(2007)reportedontheoutflowofwarmgasfromtheinnerdiskaroundEXor V1647observedintheblueabsorptionoftheCOlineduringthedeclineoftheEXor activity.Heconcludedthatthisoutflowisacontinuationofactivityassociatedwith early enhancedaccretion and bunching of the field lines (see Fig. 6). In our main exampleofaCTTSthediskstopsatRm=2.4R∗.InEXors,wetaketheradiusofa starattheFigs.1-3equaltotheinnerboundary,sothatthediskstopsmuchcloser Disk-MagnetosphereInteractionandOutflows 7 to the star, Rm =1.2R∗. Then all velocities are a factor 1.4 higher and densities a factorof32higher(comparedtoFigs.2,7),andmatterfluxesinFigs.4and9area factorof11higherthaninthemainexamplerelevanttoCTTSs. 4 Outflows inthe “Propeller” Regime In the propeller regime the magnetosphere rotates faster than inner region of the disk.Thisoccursiftheco-rotationradiusR =(GM/W 2)1/3 issmallerthanmag- cr ∗ netosphericradiusR (e.g.,Lovelaceetal.1999).Youngstarsareexpectedtobein m the propellerregimein two situations:(1)At the early stages of evolution(say, at T <106years),whenthestarformedbutdidnothavetimetospin-down,and(2)at laterstagesofevolution,suchasatCTTSstage,whenthestarisexpectedtobeon averageintherotationalequilibriumstate(e.g.,Longetal.2005)butvariationofthe accretionrateleadstovariationofR aroundR ,whereR <R ispossible.We m cr cr m performedaxisymmetricsimulationsofaccretiontoa star inthepropellerregime, takingastarwiththesameparametersasincaseofconicalwinds,butwithperiod P∗=1day(Romanovaetal.2005;Ustyugovaetal.2006).Wechosea v=0.3and a =0.1andthusbunchedthefieldlinestotheX-typeconfigurationWeobserved d thatinadditiontoconicalwindthereisafastaxialjet(seeFig.7)sothattheoutflow Fig.8 Twocomponentsofoutflowsinthepropellerregime. Fig. 9 Left panel: matter fluxes to the star M˙ and to the conical wind M˙ (calculated at star wind R=0.1AU)asfunctionoftime.Rightpanel:samebutforashortertime-interval. 8 M.M.Romanova,G.V.Ustyugova,A.V.Koldoba,&R.V.E.Lovelace hastwocomponents(Fig.8).Theconicalwindinthiscaseismuchmorepowerful - it carries most of the disk matter away. The axial jet carries less mass, but it is acceleratedtohighvelocities.Accelerationoccursduetothemagneticpressureof the“magnetictower”whichformsabovethestarasaresultofwindingofmagnetic field lines of the star. Outbursts to conical winds occur sporadically with a long time-scaleinterval(seeFig.9)whichisconnectedwiththelongtime-scaleinterval ofaccumulationanddiffusionofthediskmatterthroughthemagnetosphereofthe star(seealsoGoodsonetal.1997;Fendt2008).Thesepropelleroutflowswereob- tainedinconditionsfavorableforsuchaprocess:whenthestarrotatedfastandan X-typeconfigurationdeveloped.Futuresimulationsshouldbedoneforthecaseof propeller-drivenoutflowsfromslowerrotatingCTTS.Collimationofconicalwinds mayoccuratlargerdistancesfromthestarforexample,bydiskwinds(e.g.,Ko¨nigl &Pudritz2000;Ferreiraetal.2006;Matsakosetal.2008). 5 Conclusions We discovered a new type of outflows - conical winds - in numericalsimulations where magnetic field lines are bunched into an X-type configuration.In many re- spectsthesewindsaresimilartoX-windsproposedbyShuandcollaborators(e.g., Shu et al. 1994):(1) They both require bunchingof the field lines; (2) They both have high rotation of the order of Keplerian rotation at the base of outflow, and gradual poloidal acceleration; (3) They both are driven by magnetic force. How- ever,thereareanumberofimportantdifferences:(1)Conicalwindsflowinathin shell, while X-winds flow at different angles below the “dead zone”; (2) Conical windsformaroundstarsofanyrotationrateincludingslowrotation,anddonotre- quirethefinetuningofangularvelocityoftheinnerdisktothatofmagnetosphere; (3)Conicalwindsarenon-stationary:themagneticfieldconstantlyinflatesandre- connects;(4)Conicalwindscarryawaypartoftheangularmomentumoftheinner diskandarenotresponsibleforspinning-downthestar,whileX-windsarepredicted totakeawayangularmomentumfromthestarandthustosolvetheangularmomen- tumproblem;(5)Inconicalwindsthereisafastcomponentoftheflowalongfield linesthreadingthestar.Someofthesedifferences,suchasnon-stationarityofconi- calwindsisconnectedwithnaturalrestrictionsofthestationarymodelofX-winds. Conicalwinds can explainconicalshape of outflowsnearyoungstars of different type(CTTSs,EXors,TypeIobjects)whichhavebeenrecentlyresolved.Inanother example,Alencaret al. (2005)analyzedblue-shiftedabsorptionof Hb line in RW Aurigae and concluded that conical shape wind with opening angle 30−40◦ and narrowannulusgivesbestmatchtotheobservationsofthisline(seeFig.10). Inthepropellerregimetheflowhastwocomponents:(1)arapidlyrotating,rela- tivelyslow,denseconicalwind,and(2)afast,lowerdensityaxialjetwherematter is accelerated by magnetic pressure up to hundredsof km/s very close to the star. Young stars of classes 0 and I may be in the propeller regime and can lose most of their angular momentum by this mechanism (Romanova et al. 2005). Or any Disk-MagnetosphereInteractionandOutflows 9 Fig.10 ModelingoftheHb lineinRWAurigaeledto theconclusionthataconical shaped windwithopening angle30−40◦ andanarrow annulusgivesthebestmatch totheobservationsofthisline (fromAlencaretal.2005). slowerrotatingmagnetizedstarsmayenterthepropellerregimeiftheaccretionrate becomes sufficiently low and the magnetospheric radius becomes larger than the corotationradius.Thelastpossibilityrequiresadditionalnumericalsimulationsand analysis. Acknowledgements TheauthorsweresupportedinpartbyNASAgrantNNX08AH25Gandby NSF grants AST-0607135 and AST-0807129. MMR thanks NASA for use of the NASA High PerformanceFacilities.AVKandGVUweresupportedinpartbygrantRFBR06-02016608,Pro- gram4ofRAS.MMRandRVELthanktheorganizersforaveryinterestingmeetingandMMRis gratefultotheorganizersforthegeneroussupport. References 1. Alencar,S.H.P.,Basri,G.,Hartmann,L.,Calvet,N.2005A&A,440,595 2. Bacciotti,F.,Mundt,R.,Ray,T.P.,Eislffel,J.,Solf,J.,Camezind,M,ApJ,537,L49 3. 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