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RevMexAA (Serie de Conferencias), 00, 1–8 (2000) THE EFFECTS OF MAGNETIC FIELDS ON RADIATIVE COOLING JETS E.M. de Gouveia Dal Pino1 and A. H. Cerqueira1 Instituto Astronômico e Geof´ısico, IAG-USP, Saõ Paulo RESUMEN El resumen será traducido al espanõl por los editores. We here review the results of recent studies of magnetic field effects on the structure and evolution of overdense, radiative cooling, steady and pulsed jets 1 which were carried out with the help of fully three-dimensionalMHD simulations. Three initial magnetic field 0 topologies are considered: (i) a helical and (ii) a longitudinal field, both of which permeate the jet and the 0 ambient medium, and (iii) a pure toroidal field in the jet. Using a set of parameters which is particularly 2 suitable for protostellar jets, we examine the emission structure of the internal knots and the leading working n surface and compare with a nonmagnetic baseline and also with 2-D MHD calculations. a J ABSTRACT 5 1 Weherereviewtheresultsofrecentstudiesofmagneticfieldeffectsonthestructureandevolutionofoverdense, radiative cooling, steady and pulsed jets which were carriedout with the help of fully three-dimensionalMHD 1 simulations. Three initial magnetic field topologies are considered: (i) a helical and (ii) a longitudinal field, v both of which permeate the jet and the ambient medium, and (iii) a pure toroidal field in the jet. Using a 7 3 set of parameters which is particularly suitable for protostellar jets, we examine the emission structure of the 2 internal knots and the leading working surface and compare with a nonmagnetic baseline and also with 2-D 1 MHD calculations. 0 1 Key Words: MAGNETO-HYDRODYNAMICS — ISM: JETS AND OUTFLOWS — STARS: PRE- 0 MAIN-SEQUENCE / h 1. INTRODUCTION jets is the presence of magnetic fields. The most p - promising mechanism for their launching involves Low-mass young stellar objects produce colli- o magneto-centrifugalforcesassociatedeitherwiththe r mated optical outflows (the Herbig-Haro, hereafter t accretiondiskthatsurroundsthestar(e.g. Königl& s HH, jets) that may extend from a few 1000 AU to Pudritz2000),orwiththedisk-starboundary(inthe a very large parsec-length scales, and have embedded : X-winds; e.g. Shu et al. 1994). The details of these v in them bright emission-line knots which are radiat- launching models are discussed elsewhere in these i ing shockfrontspropagatingwith v∼ few 100km/s X proceedings (see, e.g., Shang & Shu 2001,these pro- into the ambient medium (e.g., Bally & Reipurth r ceedings). Ineithercase,thepoloidalfieldlinesthat a 2001, these proceedings). are launchedfromthe star-disksystemare expected It has been known for sometime that the dy- to wind up like a spring, thus developing a toroidal namics of these jets is very much affected by radia- component that is able to collimate the gas outflow tive cooling due to the recombination of the shock- towards the rotation axis. Direct observations of excited gas, since the typical cooling times behind magnetic fields are difficult, and only recently Ray theshocks,whichdonotexceedafewhundredyears, et al. (1997)have obtained the first direct evidence, are much smaller than the dynamical time scales of based on polarization measurements, of B ∼ 1 G in thesejets,t =R /v ≃104 to105 yr(whereR is dyn j j j theoutflowofTTauSatadistanceoffewtensofAU the jet radius, and v its velocity). The importance j from the source. Using magnetic flux conservation of the cooling on the jet dynamics has been con- and typical jet parameters, this latter result would firmedbyextensive hydrodynamicalnumericalwork imply a plasma β = p /(B2/8π) ≃ 10−3 for a j,gas (e.g., Blondin et al. 1990, de Gouveia Dal Pino & toroidal field configuration, and ∼ 103, for a longi- Benz1993,Stone&Norman1993;seealsoReipurth tudinal field, at distances ∼0.1 pc. Since ambipolar & Raga 1999,and Cabrit et al. 1997 for reviews). diffusion does not seem to be able to significantly Another aspect that seem to play a major role dissipate them (e.g., Frank et al. 1999), the figures both in the production and collimation of the HH 1 2 DE GOUVEIA DAL PINO & CERQUEIRA above suggest that magnetic fields may also play a relevant role on the outer scales of the flow. These peaces of evidence have lately motivated several MHD investigations of overdense 1, radiative cooling jets, in a search for possible signa- tures of magnetic fields on the large scales of the HH outflows. These studies have been carried out with the help of multidimensional numerical simulations both in two-dimensions (2-D) (Frank et al. 1998, 1999, 2000; Lerry & Frank 2000; Gardiner et al. 2000; Stone & Hardee 2000; Gardiner & Frank 2000; O’Sullivan & Ray 2000), and in three- dimensions(3-D)(deGouveiaDalPino&Cerqueira 1996; Cerqueira, de Gouveia Dal Pino & Herant 1997;Cerqueira&deGouveiaDalPino1999,2001a, b). In this lecture, we try to review and summarize the main results of these studies. 2. NUMERICAL APPROACH The several models above solve the ideal-MHD conservation equations employing different numerical techniques (the 2-D calculations have used grid- based codes, while the 3-D models an SPH code; see the references above for details). Most, simply assume a fully ionized (Hydrogen) gas with an ideal equationofstate,andaradiativecoolingrate(dueto collisional de-excitation and recombination behind the shocks) given by the coronal cooling function tabulated for the interstellar gas (e.g., Dalgarno & McCray 72). O’Sullivan & Ray (2000), in particular, have also included in their model the cooling function for the H2 molecule. Given the present uncertainties related to the real orientation and strength of the magnetic field in protostellar jets, three different initial magnetic field configurations have been adopted in most of the models with the β parameter typically varying betweenβ ≃0.1−∞. Oneoftheadoptedconfigura- tionswasaninitiallyconstantlongitudinalmagnetic field parallel to the jet axis permeating both, the Fig. 1. Gray-scale representation of the midplane den- jet and the ambient medium, B~ = (B ,0,0) (e.g., sity of thehead of ahydrodynamicaljet (top);an MHD o jet with initial longitudinal magnetic field configuration Cerqueira et al. 1997). Another adopted geometry (middle); and an MHD jet with initial helical magnetic was a force-free helical magnetic field which also ex- field configuration (bottom), at atime t/t =1.65 (t = d d tends to the ambient medium (see, e.g., Fig. 1 of Rj/ca ≃38years,whereca istheambientsoundspeed). Cerqueira & de Gouveia Dal Pino 1999). In this The initial conditions are: η = nj/na = 3, na = 200 case,the maximum strengthofthe magnetic field in cm−3, average ambient Mach number Ma =vj/ca =24, the systemcorrespondsto the magnitude ofthe lon- vj ≃ 398 km s−1, qbs ≃ 8 and qjs ≃ 0.3. The initial gitudinalcomponentofthe field atthe jetaxis. The β =8πp/B2 fortheMHDcasesisβ ≃1. Thegray scale third geometry adopted was a purely toroidal mag- (from minimum to maximum) is given by: black, grey, neticfieldpermeatingthejetonly(see,e.g.,Fig. 1of andwhite. Themaximumdensityreachedbytheshellat theheadofthejetsisnsh/na ≃210(top),nsh/na ≃153 1Observations suggest that HH jets are denser than the (middle), and nsh/na ≃ 160 (bottom) (from Cerqueira, surroundingambientmedium,withnumberdensityratios1< de Gouveia Dal Pino & Herant 1997). η∼>10. MHD EFFECTS ON COOLING JETS 3 Stone & Hardee 2000). The field in this case is zero fecttheglobalcharacteristicsoftheflow. Thisoccur on the jet axis, achieves a maximum strength at a becausethesefields,beingpredominantlyperpendic- radialpositioninthejetinterior(e.g.,R ≃0.9R ), ular to the shock fronts, are not largely compressed m j andreturnsto zeroatthe jetsurface. Thisfieldcor- in the shocks and, therefore the hydrodynamical responds to a uniform current density inside the jet forceswillalwaysdominate inthese cases. However, and a return current at the surface of the jet. In they tend to increase order and inhibit instabilities the first two magnetic field configurations,the jet is in the flow (Gardiner et al. 2000; O’Sullivan & Ray assumed to have an initially constant gas pressure 2000; Cerqueira & de Gouveia Dal Pino 1999). (p ). In the toroidal configuration, in order to en- For typical HH jet parameters, the multidimen- j sureaninitialmagnetostaticequilibrium,thejetgas sional simulations also indicate the development of pressure has a radial profile with a maximum at the MHDKelvin-Helmholtzpinchinstabilitiesalongthe jet axis (Stone & Hardee 2000). flow (see Fig. 1), but these pinches are, in general, so weak that it is unlikely that they could play an 3. NUMERICAL RESULTS FOR important role in the formation of the bright emis- STEADY-STATE JETS sion knots (e.g., Cerqueira & de Gouveia Dal Pino 1999; Stone & Hardee 2000). Pure hydromagnetic Let us first briefly review the results for steady pinches have been also detected in simulations in- jets, i.e., jets which are injected with a constant ve- volving purely toroidal fields. These can be partic- locity into the ambient medium. ularly strong in the presence of intense fields, for Figure 1 compares 3-D simulations of two MHD jets with initial β ≃ 1 (the middle jet has an initial example, close to the jet source (e.g., Frank et al. 1998). constant longitudinal magnetic field, and the bottom jet has an initial helical magnetic field) with a 4. NUMERICAL RESULTS FOR PULSED JETS purehydrodynamicaljet(toppanel). Atthehead,a double shock structure develops with a forwardbow The bright emission knots immersed in the HH shockthatacceleratestheambientmediumandare- jets are one of their most prominent features. They versejetshockthatdeceleratesthejetmaterialcom- frequentlyexhibitabowshockmorphologyandhigh ing upstream. As found in previous numerical HD spatial velocity (e.g., Bally & Reiputh 2001, these work, the cooling of the shocked gas at the head re- proceedings) which indicate that they are shocks sultsinmostoftheshockedgascollectinginadense, that arise from the steepening of velocity (and/or cold shell that eventually fragments due to a combi- density) fluctuations in the underlying, supersonic nation of non-uniform cooling and Rayleigh-Taylor outflow. Strongsupportforthisconjecturehasbeen (R-T)instabilities(seetheHDjetonthetoppanel). given by theoretical studies which have confirmed While in the MHD jet with initial longitudinal field that traveling shocks created in this way reproduce the fragmentation is still retained, in the jet with the essential properties of the observed knots (e.g., initial helical field, the amplification of the toroidal Raga et al. 1990; Kofman & Raga 1992; Stone & component of the magnetic field reduces the shock Norman 1993; de Gouveia Dal Pino & Benz 1994; compressibilityandthegrowthoftheR-Tinstability Vo¨lker et al. 1999; Raga & Canto´ 1998; de Gouveia thus inhibiting the shell-fragmentation. This result Dal Pino 2001). could be an indication that the latter configuration To simulate a pulsing jet, it is usually applied a should dominate near the jet head as the observed sinusoidal velocity variation with time at the inlet: jets have a clumpy structure there (Cerqueira et al. v (t) = v [1+A·sen(2π ·t)], where v is the mean o j P j 1997). (See, however, how this result can be modi- jetspeed,Atheamplitudeofthevelocityoscillation, fied in pulsed jets.) and P the oscillation period. Foranygeometry,thepresenceofmagneticfields 2-Daxisymmetriccalculationsofpulsedjetsshow always tend to improve jet collimation in compari- that the presence of toroidal magnetic fields may sonto purely hydrodynamiccalculations,due to the cause dramatic effects on pulsed jets depending on amplificationandreorientationof the magnetic field the initial conditions. For example, Stone & Hardee components in the shocks, particularly for a heli- (2000) have found that the radial hoop stresses due cal and a toroidal geometry (e.g., Cerqueira et al. to the toroidal field confine the shocked jet material 1997;Cerqueira& de GouveiaDalPino1999;Frank in the internal pulses resulting in higher densities in et al. 1998; Hardee & Stone 2000). Longitudi- the pulseswhicharestronglypeakedtowardsthe jet nal magnetic fields of different strengths (tested for axis in comparison to purely hydrodynamic calcula- β ≃0.1−107),ontheotherhand,donotstronglyaf- tions. O’Sullivan & Ray (2000), on the other hand, 4 DE GOUVEIA DAL PINO & CERQUEIRA Fig. 2. Midplanedensitycontours (left) and distribution ofvelocity vectors(right) for(from top tobottom): a purely hydrodynamicalpulsedjet;anMHDjetwithinitiallongitudinalmagneticfield;anMHDjetwithinitialhelicalmagnetic field; and an MHD jet with initial toroidal magnetic field, at a time t/t = 1.75. The initial conditions are: average d ambient Mach number Ma =vj/ca ≃15, v0 =vj[1+Asin(2πt/P)], with vj ≃250 km s−1, A=0.25vj and P =0.54td, η=nj/na =5,β =8πp/B2=∞fortheHDmodel, andmaximumβ ≃1fortheMHDmodels. Themaximumdensity in each model (from top to bottom) is: 119, 115, 124 and 175 (1 c.u. =200 cm−3) (from Cerqueira & de Gouveia Dal Pino 2001a) . MHD EFFECTS ON COOLING JETS 5 20 15 vx 10 5 Fig. 3. Midplane density contours for the MHD jet of Fig. 2 with initial helical magnetic field at a time 0 t/t =5(fromCerqueira&deGouveiaDalPino2001b). d 60 carrying out 2-D calculations of jets with initially nsity 40 lower densities (corresponding to a density ratio be- de tween the jet and the ambient medium η = 1), and 20 whichare highly overpressurizedwith respectto the 0 ambientmedium,findthedevelopmentofmorecom- 2 plex cocoons around the beams and the formation of crossing shocks which help to refocus the beam 1.5 andthe internalpulses. Inparticular,they find that the hoop stresses associated with toroidal fields can φB 1 cause a high degree of H ionization andH2 dissocia- tion, and the disruption of the internal knots, even .5 for β ≃1. Also, in these 2-D models, nose cones are foundtodevelopattheheadofmagnetizedjetswith toroidal components. These features are extended 6 narrowplugsthatformasmostoftheshockedcooled gas between the jet shock and the bow shock at the 4 head is prevented from escaping sideways into the Bx cocoon (and confined towards the jet axis) by the 2 toroidal field. 0 Now, 3-D MHD calculations of pulsed jets re- veal significant changes relative to the 2-D mod- 0 10 2d0 30 40 els. The morphologicalfeaturestend to be generally smoothedoutin3-D,andthedifferencesthatarisein 2-D calculations with distinct field geometries seem Fig. 4. From top to bottom: velocity, density, toroidal todiminishinthe 3-Dmodels(Cerqueira&deGou- magnetic field component, and longitudinal magnetic fieldprofilesalongthebeamaxisforthejetofFig. 2with veia Dal Pino 2001a, b). As an example, Figure 2 initial helical magnetic field. Time displayed t/t ≃ 3. displaysthemidplanedensitycontours(left)andthe d (from Cerqueira & de Gouveia Dal Pino 2001a). velocityfielddistribution(right),forfoursupermag- netosonic, radiatively cooling, pulsed jets in their early evolution, after they have propagated over a distance ≈ 22R (where R is the jet radius). The j j top jet is purely hydrodynamical (HD), the second jethasaninitialconstantlongitudinalmagneticfield configuration; the third an initial helical magnetic field, and the bottom an initial toroidal field. At the time depicted, the leading working surface at the jet head is followed by 2 other features and a thirdpulse is justentering into the system. Likethe leading working surface, each internal feature con- sists of a double-shock structure, an upstream re- verse shock that decelerates the high velocity mate- 6 DE GOUVEIA DAL PINO & CERQUEIRA rial entering the pulse, and a downstream forward shock sweeping up the low velocity material ahead 4.4 4.2 ofthe pulse. Atthis time,nonethe internalworking 4.0 3.8 surfaces (IWS) or knots, has reached the jet head 3.6 yet. Later on, however, one by one of them reach 3.4 3.2 theterminalworkingsurfaceandisdisruptedbythe 3.0 D)2.8 icmocpoaocnt.tThuhseidrrdaesbtirciasllayrechpaanrtgiianlglytdheephoesaitdedmionrtpohtohle- αH(H22..46 α/2.2 ogy and providing a complex fragmented structure, H2.0 1.8 as in Figure 3, where the jet of Figure 2 with initial 1.6 MHD L helical field is depicted at a later time of its evolu- 1.4 MHD H 1.2 MHD T tion. No nose cones have developed, nor even in the 1.0 0.8 jetwithinitialtoroidalfield. Wespeculatethattheir 4 6 8 10 12 R 14 16 18 20 22 absence in the 3-D calculations could be, in part, j Fig. 5. The ratio between the Hα intensity along the explained by the fact that, as the magnetic forces jetaxiswithintheIWSsforthedifferentmagnetizedjets are intrinsically three-dimensional, they cause part of Fig. 2 and the the Hα intensity of the purely hydro- of the material to be deflected in a third direction, dynamical jet. (from Cerqueira & de Gouveia Dal Pino therefore, smoothing out the strong focusing of the 2001a). shocked material that is otherwise detected in the 2-D calculations (Cerqueira & de Gouveia Dal Pino 2001a; Stone & Hardee 2000 have also argued that Severalphysicalquantitiesalongthebeamaxisof nose cones should be unstable in 3-dimensions). the jet of Figure 3 with initial helical magnetic field Figure 2 also indicates that the overallmorphol- are depicted in Figure 4, at a time t/t ≃ 3, when d ogy of the 3-D pulsed jet is not very much affected then two more pulses have entered the system and by the presence of the different magnetic field con- developed new IWSs, and the first IWS has already figurations when compared to the purely HD calcu- merged with the jet head. The initial sinusoidal ve- lation. Instead, the distinct B-profiles tend to alter locityprofileappliedtotheflowattheinletsteepens only the detailed structure behind the shocks at the into the sawtooth pattern (top panel) familiar from head and internal knots, particularly in the helical earlier studies of oscillating jets (e.g., Raga & Kof- and purely toroidal cases. Like in steady calcula- man 1992) as the faster material catches up with tions, the pure HD jet exhibits a cold dense shell the slower, upstream gas in each pulse. The sharp at the head, formed by the cooling of the shockdensity spikes within each IWS (second panel) are heated material, that has become also R-T unstable correlated with the toroidal component of the mag- and separated into clumps. Again, these can also netic field. The third panel shows that this compo- be identified in the shell of the MHD jet with ini- nentB (thirdpanel)sharpenswithintheknotsand φ tial longitudinal field, but not in the helical or the rarefiesbetweenthem,whilethelongitudinalcompo- toroidalcases. The3-Dsimulationsalsoevidence,as nent,B (forthpanel)isstrongerbetweentheknots // in previous work (e.g., de Gouveia Dal Pino & Benz (Cerqueira & de Gouveia Dal Pino 2001a). This re- 1993), that the density of the shell (and IWSs) un- sult is in agreementwith 2-Dcalculations(Gardiner dergoes oscillations with time (with a period of the &Frank2000;O’Sullivan&Ray2000)andcould,in order of the cooling time behind the shocks) which principle, be checkedobservationallyas a diagnostic are caused by global thermal instabilities of the ra- of helical geometries. Helical fields are specially at- diativeshocks. Theprofileandmaximumamplitude tractiveforprotostellarjetsastheyarethepredicted of these oscillations are particularly affected by the geometryfrommagneto-centrifugallylaunchedmod- presence of toroidal field components (Cerqueira & els (Gardiner & Frank 2000;Lerry & Frank 2000). de Gouveia Dal Pino 2001b). Although the distinct B-geometries do not seem Some wiggling can be detected in the jet axis tosignificantlyaffecttheglobalcharacteristicsofthe in the 3-D MHD simulation with initial helical field 3-Dflows,theycanmodifythedetailsoftheemission of Figure 3. This is caused by the kink mode of structure, particularly for the helical and toroidal the K-H instability and was also detected (but in cases. In particular, Figure 5 shows the H inten- α smaller intense) in the pure hydrodynamical coun- sity alongthe jet axisevaluatedwithin the IWSs for terpart. This could provide a potential explanation the different magnetized jets of Figure 2 which are for the wiggling features often detected in HH jets. compared to the H intensity of the baseline hydro- α MHD EFFECTS ON COOLING JETS 7 dynamical jet. The H intensity is observed to be REFERENCES α strong behind the knots of the protostellar jets and Blondin, J.M., Fryxell, B.A., & Königl, A. 1990, ApJ, is predicted to have a strong dependence with the 360, 370 shock speed vs, IHα ∝ ρdvs3.8 where ρd is the down- Cabrit, S., Raga, A.C., & Gueth, F. 1997, in Herbig- streampre-shockdensity(e.g.,Raga&Canto´1998). HaroFlowsandtheBirthofLowMassStars,Eds.B. Wehaveusedthisrelationandtheresultsofthesim- Reipurth&C.Bertout,KluwerAcademicPublishers, ulatedjetsofFigure2toevaluatetheintensityratios 1997, 163 Cerqueira, A.H., de Gouveia Dal Pino, E.M., & Herant, of Figure 4. 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