RevMexAA (Serie de Conferencias), 13, 66–70 (2002)A NEW YSO OUTFLOW MODEL, JET SIMULATIONS, AND THEIREMISSIONT. LeryDublin Institute for Advanced Studies, IrelandEmission Lines from Jet Flows (Isla Mujeres, Q.R., México, November 13-17, 2000)Editors: W. J. Henney, W. Steffen, A. C. Raga, & L. BinetteRESUMENEn el esquema teórico común de la formación estelar, el jet es eyectado de un disco de acreción magnetizado,y el flujo molecular es impulsado por el jet o por un viento más abierto proveniente del disco. Proponemos unmodelo unificado alterno para los flujos alrededor de YSOs (siglas en inglés: Young Stellar Objects; ObjetosEstelares Jóvenes). Además de un motor de acreción-eyección que mueve al jet, el flujo molecular es impulsadopor la materia que cae y sigue un patrón de circulación alrededor del objeto central sin ser absorbido por el flujoque proviene del interior. Soluciones para jets que parten de este modelo han sido utilizadas como condicionesiniciales para simulaciones de propagación de jets pulsados. Se presentan mapas sintéticos de las simulacionesde jets.ABSTRACTIn the usual theoretical picture of star formation a jet is ejected from a magnetized accretion disk, with amolecular outflow being driven either by the jet or by a wider wind coming from the disk. We propose analternative unified model for the flows surrounding YSOs. In addition to a central accretion-ejection enginedriving the jet, the molecular outflow is powered by the infalling matter and follows a circulation pattern aroundthe central object without being entrained by an outflow. Jets solutions from this model have been used asinitial conditions for simulations of the propagation of pulsed jets. Synthetic maps from the jet simulations arepresented.Key Words: ISM: JETS AND OUTFLOWS — MAGNETOHYDRODYNAMICS — STARS: PRE-MAIN-SEQUENCE1. INTRODUCTIONStar formation occurs in molecular clouds, andobservations have shown that the accretion phase,during which the central object builds up its mass,is very often accompanied by the powerful ejectionof prominent bipolar outflows, which correspond tofast jets and molecular outflows. A consensus seemsto prevail on the magneto-centrifugal origin of jets,either launched from the accretion disk (disk wind)or from the location of the interaction of the protostar’smagnetosphere with the disk (X-wind). Onthe other hand, the precise mechanism generatingmolecular outflows is poorly understood. The latterare generally believed to be driven by the jet or by awide-angle wind, but both possibilities present somedifficulties (Cabrit, Raga, & Gueth 1997). Insteadof the usual mechanisms invoked for the origin ofthe molecular outflows, we propose a global model,where, in addition to a central accretion-ejection enginedriving the jet, the molecular outflow is poweredby the infalling matter and follows a circulationpattern around the central object. Ultimatelythe molecular outflow may still undergo entrainmentfrom the fast jet but only in polar regions.2. THE CIRCULATION MODELWe suggest that the molecular gas that circulatesaround the source can be described by theself-similar, heated, quadrupolar and axisymmetricmagnetohydrodynamic model (Henriksen & Valls-Gabaud 1994; Fiege & Henriksen 1996; Lery et al.1999a). In the infall region, the flow is slowed downby the increasing radial pressure gradients due toheating by the central source, by the increase in thecentrifugal barrier resulting from the magnetic fieldwith proximity to the central object, and due to theincreasing rotational speed. This pressure ‘barrier’deflects and accelerates, by means of its poloidalgradient, much of the infalling matter into an axialoutflow. The Poynting flux included in the modelincreases both the velocity and collimation of theoutflows by helping to transport mass and energyfrom the equatorial regions. The solutions are developedwithin the context of radial self-similarity66
A NEW YSO OUTFLOW MODEL 67wherein a power of r multiplies an unknown functionof θ; the spherical coordinates r, θ and φ beingused. The power laws of the self-similar symmetryare determined, up to a single parameter α, if we assumethat the local gravitational field is dominatedby a fixed central mass. In terms of a fiducial radialdistance, r 0 , the self-similar symmetry is soughtas a function of two scale invariants, r/r 0 and θ, ina separated power-law form. The self-similar indexα is a free parameter of the solution, but it is constrainedby boundary conditions to lie in the range1/4 ≥ α > −1/2 (Lery et al. 1999a).The calculations produce solutions (see Figure 1)where the outflow can have large opening angles, andwhere massive protostars produce faster and less collimatedoutflows. Larger opening angles are associatedwith smaller magnetic fields. Consequently, agradual evolutionary loss of magnetic flux may resultin outflows that widen as they age. Syntheticspectral lines from 13 CO (J = 1 → 0) allow directcomparison with observational results via channelmaps, maps of total emission, position-velocityand intensity-velocity diagrams. The model is nowat a stage where synthetic CO spectra reproducevery well the observational features. The resultsstrengthen the idea that the Poynting flux and theradiative heating are ultimately the energy sourcesdriving the outflow. This new picture of the accretion/outflowphase provides a possible explanationfor asymmetric outflows, molecular cavities andjet collimation. Self-similar models cannot of coursebe globally consistent in time even if they are nonstationary,since they are ignorant of initial conditions.The self-similar circulation model is intermediatein space in that regions such as the axis and theequator are strictly excluded from the domain of selfsimilarityalthough they may be approached asymptotically.The axial region is therefore modeled by ajet model that is not self-similar as described in thenext section.Emission Lines from Jet Flows (Isla Mujeres, Q.R., México, November 13-17, 2000)Editors: W. J. Henney, W. Steffen, A. C. Raga, & L. BinetteFig. 1. Streamlines and density contours of the hydrogennumber density (in logarithmic scale) for the circulationmodel with α = −0.2. The density levels shown arebetween 10 5 to 10 7 cm −3 . Length scales are in AU.3. THE JET MODELThe jet model is based on a simple model thatproposes asymptotic MHD jet equilibria that accountfor the properties of the emitting source (Leryet al. 1998; Lery et al. 1999b; Lery & Frank 2000).The model is axisymmetric and stationary. It assumesthe magnetic surfaces possess a shape whichis known a priori inside the fast critical surface. Asa first approximation, the magnetic surfaces weretaken to be cones in this region. Since the jet behaviourcan be directly related to the properties ofthe emitting source, the model can provide a betterunderstanding of jet interactions with their surroundingmedium, their propagation and instabilities,with respect to the source itself.The MHD flow properties must be determinedby solving for the equilibrium of forces parallel andperpendicular to the magnetic surfaces (the former isdescribed by using the Bernoulli equation for a polytropicequation of state and the latter is solved viathe Grad-Shafranov equation). The balance of forcesperpendicular to magnetic surfaces is accounted foron the Alfvén surface and at the base of the flow.The equilibrium parallel to the surfaces takes theform of criticality conditions at the two other (fastand slow) MHD critical points. This correspondsto the differential form of the Bernoulli equation onconstant a with respect to ρ and r vanishing at thecritical points. We further assume the density ρ tobe related to the pressure p by a polytropic equationof state, p = Q(a)ρ γ where γ is the polytropicindex. In the general case, the model yields five integralsof motion that are preserved on any axisymmetricmagnetic surface a. Two of the integrals aregiven as boundary conditions in the model. Theseare the angular velocity Ω(a) and an entropy factorQ(a). These are supplied as a model for thesource rotator. The Alfvén regularity condition togetherwith the criticality conditions then determinethe three other unknown integrals: namely the specificenergy, E(a); the specific angular momentum,L(a); the mass to magnetic flux ratio, α(a). Farfrom the source (large z) the flow becomes cylindricallycollimated. In this asymptotic regime the jet is
68 LERY(a)(b)43.53Multi−Fast0.40.30.2KeplerianConstant10.5ICrC2.5V z0.1B φρ0.01V φ00.003B zI CEmission Lines from Jet Flows (Isla Mujeres, Q.R., México, November 13-17, 2000)Editors: W. J. Henney, W. Steffen, A. C. Raga, & L. Binetteg replacements0.00500 0.5 1r0.0020.0010 0.5 1r0.20.100 0.5 1rFig. 2. (a) Example of solutions. Variations with fractional radius of components of the velocity, V , and magneticfield, B, of the density, ρ, and of the net electric current, I C. Constant (dotted lines), Keplerian (dashed), and multicomponent(solid) rotation laws are considered. (b) Schematic representation of the net electric current along the jet(heavy solid lines), and its direction (arrows), at the Alfvénic (A), and the fast (F) surfaces, and in the cylindricallycollimated regime (C).assumed to be in pressure equilibrium with an externalmedium. The pressure matching condition alongwith with the Grad-Shafranov and Bernoulli equationsare all solved in the asymptotic cylindricallycollimated regime. Three different types of rotationhave been studied, namely, rigid, Keplerian andmulti-component rotations. The multi-componentcase starts with a rigid rotation. The angular velocitythen doubles its value in order to model a jetrotating more rapidly than the central object beforereaching a Keplerian rotation.IFIArArFAn example of asymptotic solution of the jetmodel is given for the different types of rotators inFig. 2. There, the z and φ components of velocityand magnetic field are represented together with thedensity ρ and the net electric current I C , as functionsof the relative radius (normalized to the jetradius). The density is normalized to its value onthe jet axis ρ 0 , and the non-dimensional velocitiesrefer to the fast magnetosonic velocity vf2 = c 2 s + v2 Aon the axis, c s being the sound speed. The magneticfield is normalized to √ ρ 0 v f . In Figure 2, we alsopresent the net electric current on the Alfvénic andfast surfaces and in the cylindrically collimated region.The current decreases from the source to theasymptotic region. Its profile is globally independentof the distance from the source. The currentfirst increases outwards from the axis, then reaches aplateau where the magnetic pressure dominates. Finally,it decreases in the outer part of the jet. Thereexist a strong current in the core and a returningcurrent in the collar, the intermediate part of the jetbeing almost current-free. Thus rotating MHD jetsare characterized by a dense, current-carrying core,having most of the momentum, that is surroundedby a collar with an internal return current.4. THE JET SIMULATIONS AND THEIREMISSIONBy using the jet model previously developed, itis possible to obtain jet equilibria whose propertiesdirectly depend on the source. These equilibria havebeen used to model the propagation of MHD jetsinto the interstellar medium. This work differs fromprevious studies in that the cross-sectional distributionsof state variables are derived from an analyticalmodel for magneto-centrifugal launching from asource rotator. The jets in these simulations are considerablymore complex than “top-hat” profiles.
A NEW YSO OUTFLOW MODEL 69Shocked CollarSecondaryBow shockPrimaryBow shockCollarCoreEmission Lines from Jet Flows (Isla Mujeres, Q.R., México, November 13-17, 2000)Editors: W. J. Henney, W. Steffen, A. C. Raga, & L. BinetteCocoonShocked coreIntrinsic InstabilitiesNose coneFig. 3. Annotated grey-scale map of the density for an adiabatic simulation of the propagation of a Multi-componentjet given by the Given Geometry model.A multi-dimensional (2.5-D) simulation of amulti-component MHD jet have been performed usinga MHD TVD code in cylindrical symmetry. Thesimulations are initiated with the cylindrically collimatedjet equilibrium which traverses the lengthof the computational domain (256 × 1024 zones),the jet radius being 64 zones. The equilibrium isthen continuously injected at z = 0 boundary of thegrid. The pressure outside the jet was imposed bythe model through the pressure balance at the outerboundary. The jet is surrounded, in the present simulation,by a magnetized medium that has a smallpoloidal field and no toroidal component. We findthat density and magnetic field stratification (withradius) in the jet leads to new behavior including theseparation of an inner jet core from a low densitycollar. We find this jet within a jet structure, alongwith the magnetic stresses, leads to propagation behaviorsnot observed in previous simulation studies.Indeed, when the equilibrium encounters the externalmedium, the various elements of the equilibriumare shocked. This creates two bow shocks and a cocoon.The furthermost bow shock takes the formof a nose cone. Intrinsic instabilities develop in theinner part of the shocked core, as well as in the cocoon,as shown in Fig. 3. The most important aspectof the flow behavior seen in the simulation canbe traced back to the annular stratification of thejet. In particular, the radial distributions of densityvelocity, and toroidal magnetic field appear tobe the principle causes of the new behavior seen inthe simulations. The jet exhibits a core/collar structuresuch that a high density core region exits nearthe axis surrounded by one or more lower densityannuli (collars) extending out to the jet boundary.The strongest toroidal fields exist at the boundarybetween the core and collar. Since the momentumin the core is higher than that in the collar the propagationcharacteristics of the jet are dominated bythe core pulling ahead of the collar. The strong fieldsurrounding the core ensures that the two regions remainfairly distinct in terms of their dynamics. Asthe jet propagates we see the core acting as a jetwithin a jet. There exists a extremely low densityinner collar (which also has higher velocity than thesurrounding regions) and this leads to a completeseparation of core and collar. The “peel-off” of thecollar is quite dramatic.Our methodology also allows us to compare MHDjets from different types of sources whose propertiescould ultimately be derived from the behavior of thepropagating jets. By varying the properties of the
70 LERYFig. 4. Composite of the logarithm of the hydrogen number density (upper panel) and the Hα emission (lower panel)for pulsed molecular jets propagating in an inhomogeneous medium (Courtesy S. O’Sullivan).Emission Lines from Jet Flows (Isla Mujeres, Q.R., México, November 13-17, 2000)Editors: W. J. Henney, W. Steffen, A. C. Raga, & L. Binettesource, it is also possible to vary the properties ofthe jet itself. This introduces non-ad-hoc variationsof the jet and gives rise to more complex behavior ofthe propagating jet, and also of the interaction withthe ambient medium. We present such simulationsfor molecular jets in Figure 4 where the density (inthe upper panel) is represented with the Hα emission(in the lower panel) In this case, many features of thesimulation are in good agreement with observations,such as the molecular cavities, the location and shapeof the shocks, as well as the variation with distanceof the ionization fraction and density along the jet.Our results have bearing on a number of issues.The simplest conclusion that can be drawn isthat the structure imposed on a YSO jet by thelaunching and collimation process can lead to fairlycomplex propagation characteristics. Thus ourmodel builds on and extends previous work thatutilized only “top-hat” jets as initial conditions.It does however point to the fact that the jetsproduced by magnetized rotators are likely to bemore complex in their structure and, furthermore,that this complexity will be reflected in the observedjet morphologies. In recent observations ofmolecular outflows, small linear structures placedjust ahead of bow shape shocks have been observed.These structures are almost exactly pointing awayfrom the protostellar condensation position. Theseprecursors of the bow-shock show a conical shape.It could be the trace of an underlying jet in which theshock is propagating. As the central, fast, “core”jetis propagating, it entrains the surrounding molecularoutflow and forms the conical shape structure,while the outer “collar” participates in the entrainmentof the larger bow-shock. These molecular emissionsreveal a linear “precursor” to the bow-shocks,and may be a signature of the jet-driven entrainmentof the molecular outflows at the head of the jet.I am very grateful to F. Bacciotti, J. Fiege, A.Frank, T. Gardiner, R. Henriksen, S. O’Sullivan, andT. Ray for their contributions to the work discussedin this paper. The project was also supported byNSF Grant AST-0978765 and by the University ofRochester’s Laboratory for Laser Energetics.REFERENCESCabrit, S., Raga, A., & Gueth, F. 1997, in IAU Symp.182, Herbig-Haro Flows and the Birth of Low-massStars, eds. B. Reipurth & C. Bertout (Dordrecht:Kluwer), 163Fiege, J. D., & Henriksen, R. N. 1996, MNRAS, 281,1038Henriksen, R. N., & Valls-Gabaud, D. 1994, MNRAS,266, 681Lery, T., & Frank, A. 2000, ApJ, 533, 897Lery, T., Henriksen, R. N., & Fiege J. D. 1999a, A&A,350, 254Lery, T., Heyvaerts, J., Appl, S., Norman, C. A. 1998,A&A, 337, 603. 1999b, A&A, 347, 1055T. Lery: Dublin Institute for Advanced Studies, 5 Merrion Square Dublin 2, Ireland (email@example.com).