Disk-Magnetosphere Interaction and Outflows: Conical Winds and Axial Jets

1.1 MB·English

by  M. M. Romanova

Disk-Magnetosphere Interaction and Outflows:
Conical Winds and Axial Jets
M.M.Romanova,G.V.Ustyugova,A.V.Koldoba,&R.V.E.Lovelace
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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
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9
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: 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. Brittain, S., Simon, T., Rettig, T.W.,et al. 2007, Star-Disk Interaction in Young Stars, IAU
SymposiumNo.243,ed.J.Bouvier&I.Appenzeller,p.223
4. Cai,M.J.,Shang,H.,Lin,H.-H.,&Shu,F.H.2008,ApJ,672,489
5. Cabrit,S.,Edwards,S.,Strom,S.E.,&Strom,K.M.1990,ApJ,354,687
6. Edwards,S.,Fischer,W.,Hillenbrand,L.,Kwan,J.2006,ApJ,646,319
7. Fendt,C.2008,astro-ph:arXiv:0810.4154v1
8. Ferreira,J.,Dougados,C.,&Cabrit,S.2006,A&A,453,785
9. Goodson,A.P.,Winglee,R.M.,&Bo¨hm,K.-H.1997,ApJ,489,199
10. Grankin,K.N.,Melnikov,S.Yu.,Bouvier,J.,Herbst,W.,Shevchenko,V.S.2007,A&A,461,
183
11. Herbst,W.,Herbst,D.K.,Grossman,E.J.,Weinstein,D.2004,AJ,108,1906
12. Konigl,A.,&Pudritz,R.E.2000,ProtostarsandPlanetsIV,Mannings,V.,Boss,A.P.,Russell,
S.S.(eds.),UniversityofArizonaPress,Tucson,p.759
13. Kulkarni,A.,&Romanova,M.M.2008,MNRAS,386,673
14. Kwan,J.,Edwards,S.,&Fischer,W.2007,ApJ,657,897
15. Long,M.,Romanova,M.M.,&Lovelace,R.V.E.2005,ApJ,634,1214
16. Lovelace,R.V.E.,Berk,H.L.,&Contopoulos,J.1991,ApJ,379,696
17. Lovelace,R.V.E.,Romanova,M.M.,&Newman,W.I.1994,ApJ,437,136
18. Lovelace,R.V.E.,Romanova,M.M.,&Bisnovatyi-Kogan,G.S.1999,ApJ,514,368
19. Matsakos, T.,Tsinganos, K., Vlahakis, N., Massaglia, S., Mignone, A., Trussoni, E. 2008,
A&A,477,521
20. Najita,J.R.,&Shu,F.H.1994,ApJ,429,808
21. Pyo,T.-S.,Hayashi,M.,Kobayashi,N.etal.2003,ApJ,649,836
22. Pyo,T.-S.,Kobayashi,N.,Hayashi,M.,etal.2003,ApJ,590,340
10 M.M.Romanova,G.V.Ustyugova,A.V.Koldoba,&R.V.E.Lovelace
23. Ray, T., Dougados, C.,Bacciotti, F., Eislffel, J., & Chrysostomou, A. 2007, Protostars and
PlanetsV,B.Reipurth,D.Jewitt,andK.Keil(eds.),UniversityofArizonaPress,Tucson,p.231
24. Romanova,M.M.,Kulkarni,A.K.,&Lovelace,R.V.E.2008,ApJ,673,L171
25. Romanova,M.M.,Ustyugova,G.V.,Koldoba,A.V.,&Lovelace,R.V.E.2002,ApJ,578,420
26. Romanova,M.M.,Ustyugova,G.V.,Koldoba,A.V.,&Lovelace,R.V.E.2005,ApJ,635,165L
27. Romanova,M.M.,Ustyugova,G.V.,Koldoba,A.V.,&Lovelace,R.V.E.2009,MNRAS,sub-
mitted
28. Shu,F.,Najita,J.,Ostriker,E.,Wilkin,F.,Ruden,S.,Lizano,S.1994,ApJ,429,781
29. Shu,F.H,Galli,D.,Lizano,S.,Glassgold,A.E.,&Diamond,P.H.2007,ApJ,665,535
30. Shakura,N.I.,&Sunyaev,R.A.1973,A&A,24,337
31. Takami,M.,Beck,T.L.,Pyo,T.-S.,McGregor,P.,Davis,C.2007,ApJ,670,L33
32. Ustyugova,G.V.,Koldoba,A.V.,Romanova,M.M.,&Lovelace,R.V.E.2006,ApJ,646,304