Magnetic fields during the early stages of massive star formation - II. A generalised outflow criterion

5.5 MB·English

by  D. Seifried

Mon.Not.R.Astron.Soc.000,1–22(2011) Printed24January2012 (MNLATEXstylefilev2.2)
Magnetic fields during the early stages of massive star
formation – II. A generalised outflow criterion
D. Seifried,1,2,3(cid:63) R. E. Pudritz,3 R. Banerjee,1 D. Duffin,3 R.S. Klessen2
1Hamburger Sternwarte, Universita¨t Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany
2
2Institut fu¨r Theoretische Astrophysik, Universit¨at Heidelberg, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany
1
3Department of Physics & Astronomy, McMaster University Hamilton, Ontario, Canada
0
2

n
Accepted2012January20.Received2011December09;inoriginalform2011September16
a
J

3
ABSTRACT
2
Numerical simulations of outflows formed during the collapse of 100 M(cid:12) cloud cores
are presented. We derive a generalised criterion from magnetohydrodynamical wind
]
R theory to analyse the launching mechanism of these outflows. The criterion is suc-
S cessfully applied to the whole outflow structure and cases with sub-Keplerian disc
. rotation. It allows us to decide whether an outflow is driven centrifugally or by the
h
toroidal magnetic pressure. We show that quantities such as the magnetic field line
p
inclination or the ratio of the toroidal to poloidal magnetic field alone are insufficient
-
o to determine the driving mechanism of outflows. By performing 12 simulations with
r variable initial rotational and magnetic energies we are able to study the influence
t
s of the initial conditions on the properties of outflows and jets around massive proto-
a stars in detail. Our simulations reveal a strong effect of the magnetic field strength
[
on the morphology of outflows. In runs with weak fields or high rotational energies,

2 wellcollimated,fastjetsareobservedwhereasforstrongfieldspoorlycollimated,low-
v velocity outflows are found. We show that the occurrence of a fast jet is coupled to
9 the existence of a Keplerian protostellar disc. Despite the very different morphologies
7 all outflows are launched from the discs by centrifugal acceleration with the toroidal
3 magnetic field increasingly contributing to the gas acceleration further away from the
4 discs. The poor collimation of the outflows in runs with strong magnetic fields is a
.
9 consequence of the weak hoop stresses. This in turn is caused by the slow build-up of
0 a toroidal magnetic field due to strongly sub-Keplerian disc rotation. The mass and
1 momentum outflow rates are of the order of 10−4 M(cid:12) yr−1 and 10−4 M(cid:12) km s−1
1 yr−1, respectively. The mass ejection/accretion ratios scatter around a mean of 0.3
:
v in accordance with observational and analytical results. Based on our results we sug-
i gest an evolutionary scenario for the earliest stage of massive star formation in which
X
initially poorly collimated outflows develop which successively get better collimated
r during their evolution due to the generation of fast jets.
a
Keywords: hydrodynamics–magneticfields–methods:numerical–stars:formation
– stars: massive – stars: winds, outflows.
1 INTRODUCTION formationofoutflowsisthemagneticfieldinthecloudcores.
Its importance can be estimated by the mass-to-flux ratio
The formation of massive stars and the evolution of asso-
µnormalisedtothecriticalmass-to-fluxratio(Mouschovias
ciated protostellar outflows is still a highly debated ques-
& Spitzer 1976) which is essentially the ratio of gravita-
tion (e.g. Beuther & Shepherd 2005; Zinnecker & Yorke
tional to magnetic energy in the region (see equation (6)).
2007). It is believed that massive stars form in high-mass
For high-mass star forming cores the observed mass-to-flux
molecular cloud cores with masses ranging from about 100
ratios are typically slightly supercritical with µ (cid:46) 5 (Fal-
M(cid:12) up to a few 1000 M(cid:12). Such cores have characteris- garone et al. 2008; Girart et al. 2009; Beuther et al. 2010;
tic sizes of a few 0.1 pc and peak densities of up to 106
Crutcher et al. 2010) indicating a significant influence of
cm−3 (e.g.Beutheretal.2007).Acrucialingredientforthe
magneticfieldsonthestarformationprocess.Inturbulence
simulations, however, also higher values of µ up to 20, i.e.
weaker magnetic fields, have been found (e.g. Padoan et al.
(cid:63) [email protected]
(cid:13)c 2011RAS
2 D. Seifried et al.
2001; Tilley & Pudritz 2007). In combination with the ob- ticular, we are able to examine how the development of
served overall slow rotation of cores (Goodman et al. 1993; a two-component outflow (Banerjee & Pudritz 2007) or a
Pirogov et al. 2003) all necessary ingredients for the forma- sphere-like outflow (Peters et al. 2011) depends on the ini-
tionofprotostellaroutflowsarepresent.Indeed,therearea tialconfiguration.Forthispurposeweusethesamesimula-
growingnumberofobservationsofoutflowsaroundmassive tions as in Paper I. We note that the initial conditions are
protostellar objects (see Beuther et al. 2002b; Zhang et al. selectedinawaytocoveralargeparameterspaceinaccor-
2005,forrecentcompilations).Thegenerationofsuchmas- dance with observations and numerical simulations. With
sive outflows, in particular their underlying driving mecha- the generalised outflow criterion derived in this work we
nism and their properties will be the focus of our interest will show that magneto-centrifugally driven outflows con-
here. sist of two different regimes described by the MHD wind
Forlow-massstarformation(Mcore∼1M(cid:12)),thegener- theory.Inthefirstregimeclosetothediscandtherotation
ation,evolutionandpropertiesofprotostellaroutflowshave axis, acceleration is dominated by the centrifugal force, i.e.
been studied in great detail over the last years (e.g. Allen gas gets flung outwards along the poloidal magnetic field
et al. 2003; Banerjee & Pudritz 2006; Mellon & Li 2008; lines, whereas in the second regime further away from the
Machida et al. 2008; Hennebelle & Fromang 2008; Hen- discBφstartstodominatetheacceleration.Furthermorewe
nebelle&Ciardi2009;Commerc¸onetal.2010;Tomidaetal. will also show that despite large morphological differences
2010; Duffin & Pudritz 2009; Duffin et al. 2011). Despite all outflows observed in this work are launched by centrifu-
theintensiveresearchinthisfieldthereisstillnoconsensus gal acceleration and that the differences in collimation are
about what drives the outflows beside the fact that all out- mainly caused by varying hoop stresses.
flowsaremagneticallydriven.Differentresultscanbefound The paper is organised as follows. In Section 2 the nu-
in literature about whether the outflow is driven by cen- mericaltechniquesandtheinitialconditionsoftherunsper-
trifugal acceleration (Blandford & Payne 1982; Pudritz & formedaredescribedbriefly.Nextwederivethegeneralised
Norman 1986; Pelletier & Pudritz 1992) or by the pressure criterion to determine the outflow driving mechanism (Sec-
of the toroidal magnetic field (Lynden-Bell 1996, 2003). A tion3).TheresultsofoursimulationsarepresentedinSec-
possiblereasonforthismightbethedifferentmethodsused tion 4. First, two representative simulations are discussed
to analyse the outflows. In this work we seek to clarify this in detail also testing the newly developed outflow criterion.
problembyderivingafullyself-consistent,generalisedcrite- Next,weanalysethelongtermevolutionandstabilityofthe
rion from magnetohydrodynamical (MHD) wind theory to outflowsbeforetheeffectofvaryinginitialconditionsonthe
determine the underlying driving mechanism. The criterion outflowpropertiesareexamined.InSection5theresultsare
is applicable in the same way to low- and high-mass proto- discussedinabroadercontextandarecomparedtotheoret-
stellar objects. ical,numericalandobservationalstudiesbeforeweconclude
Numericalstudiesontheinfluenceofmagneticfieldsin in Section 6.
massivestarformingregionshavereceivedattentiononlyre-
cently. Banerjee & Pudritz (2007) study the formation of a
protostarandtheassociatedoutflowinitsearliestevolution 2 NUMERICAL TECHNIQUES AND INITIAL
withextremelyhighspatialresolutionobservinganoutflow CONDITIONS
consistingoftwocomponents.Theinterplayofmagnetically
In the following we briefly describe the initial conditions
drivenoutflowsandionisingradiationisanalysedbyPeters
and the numerical methods used in our simulations. For a
et al. (2011) who found a sphere-like outflow morphology.
detailed description we refer the reader to Paper I. The 3-
In this context we also mention the work of Vaidya et al.
dimensional,MHDsimulationsofcollapsingcloudcoresare
(2011) who study the effect of outflow decollimation due
performedwiththeAMRcodeFLASH(Fryxelletal.2000)
to radiation forces, but at much later times than presented
usingaMHDsolverdevelopedandtestedbyWaaganetal.
here. Examining the influence of initial turbulence, an as-
(2011). The maximum spatial resolution in the simulations
pect not considered in this work, Hennebelle et al. (2011)
is∆x=4.7AUandtheJeanslengthisresolvedeverywhere
find that strong magnetic fields reduce the number of frag-
with at least eight grid cells. We use a threshold density of
ments formed during the collapse. In an accompanying pa-
per(Seifriedetal.2011,inthefollowingPaperI)weanalyse ρ =1.78·10−12gcm−3 (1)
crit
theinfluenceoftheinitialconditioninmassivestarforming
forsinkparticlecreation(forfurtherdetailsonthecreation
regions on accretion rates and the build-up of protostellar
criteria see Federrath et al. 2010).
discs. One of the main results of this study are the remark-
able similar accretion rates despite large variations in the WithsinkmassesofuptoMmax ∼4M(cid:12),themaximal
rotationvelocitiesinthediscsandoutflowvelocitiesdirectly
initial conditions which we attribute to effects of the mag-
coupled to them (Michel 1969; Pelletier & Pudritz 1992)
netic field. A second crucial result which will be of particu-
larimportanceforthispaperisthefactthatforsimulations (cid:114)
GM
withstrongmagneticfields(µ<10)onlysub-Keplerianpro- v ∼v ∼v = max (2)
out rot,max kep,max ∆x
tostellar discs can form due to the very efficient magnetic
braking. are limited to about 10 km s−1.
In the present study, we systematically analyse the in- The thermodynamical evolution of the gas is modelled
fluence of the rotational and magnetic energy on protostel- by a cooling routine of Banerjee et al. (2006) taking into
lar outflows. We focus on the underlying launching mech- account dust cooling, molecular line cooling and the effects
anism and how the initial conditions affect global outflow of optically thick gas. After the launching of the outflows,
properties like mass, momentum and morphology. In par- weintroduceadensitythresholdof1·10−15 gcm−3 within
(cid:13)c 2011RAS,MNRAS000,1–22
Magnetic fields in massive star formation II 3
67AUaroundthesimulationcentre.Thishelpstolimitthe
Table 1.Performedsimulationswithnormalisedinitialmass-to-
Alfv´enic velocity flux-ratioµ,ratioofmagnetictogravitationalenergyγ,magnetic
B fieldstrengthinthecentreB,ratioofrotationaltogravitational
vA = √4πρ (3) energyβrot,andthecorrespondingangularfrequencyω.
thereby preventing prohibitively small timesteps. As shown Run µ γ B [µG] βrot ω [10−13s−1]
in Paper I, the dynamical influence of this artificial density
26-20 26 1.13·10−3 132 2·10−1 7.07
threshold is negligible.
26-4 26 1.13·10−3 132 4·10−2 3.16
The simulated cloud cores have a mass of 100 M(cid:12) 26-0.4 26 1.13·10−3 132 4·10−3 1.00
and a uniform temperature of 20 K. This mass corresponds
26-0.04 26 1.13·10−3 132 4·10−4 0.316
to about 56 Jeans masses making the whole configuration
highly gravitationally unstable. The core has a diameter of 10-20 10.4 7.06·10−3 330 2·10−1 7.07
0.25 pc and is embedded in an ambient medium having a 10-4 10.4 7.06·10−3 330 4·10−2 3.16
10-0.4 10.4 7.06·10−3 330 4·10−3 1.00
100 times lower density than at the edge of the core and a
100 times higher temperature of 2000 K to assure pressure 5.2-20 5.2 2.82·10−2 659 2·10−1 7.07
equilibrium. The core has a density profile1 5.2-4 5.2 2.82·10−2 659 4·10−2 3.16
5.2-0.4 5.2 2.82·10−2 659 4·10−3 1.00
ρ(r)∝r−1.5. (4)
2.6-20 2.6 1.13·10−1 1318 2·10−1 7.07
Wenotethatforthepurelyhydrodynamicalcase,thisslope 2.6-4 2.6 1.13·10−1 1318 4·10−2 3.16
defines the transition between systems with low degree of
fragmentation (for steeper density profiles) and with high
susceptibility for fragmentation (for shallower density pro- µ
files) as shown by Girichidis et al. (2011). 10 1
Whereas the mass distribution described above is kept 100
fixed, the rotational and magnetic energies are changed be- 10-12
tweentheindividualsimulations.Thecoresarethreadedby 10-1
amagneticfieldwithvariablestrengthparalleltothez-axis
and declining outwards with the cylindrical radius R as
1
Bz ∝R−0.75. (5) βrot 10-2 10-13 - / sω
B does not change along the z-axis to guarantee ∇B =0.
z 10-3
In addition, the cores are rotating rigidly with the rotation
axisparalleltotheinitialmagneticfield.Wehaveperformed
12 simulations with varying rotational and magnetic ener- 10-4
gies.Theindividualrunswiththecorrespondingparameters 0.001 0.01 0.1
are listed in Table 1. Additionally, the initial values of all γ
runsareshowninFig.1.Rotational(β )andmagneticen-
rot
ergies(γ)arenormalisedtothegravitationalenergy.Ascan Figure 1. Initial values of the 12 simulations performed. The
beseen,bothβrot andγ coverawiderangeovermorethan initial rotational (βrot) and magnetic energy (γ) are normalised
two orders of magnitude around the line of equipartition, to the gravitational energy. As can be seen, the starting points
bracketthecurvewhererotationalandmagneticenergyareequal
i.e. β = γ. For comparative purposes the corresponding
rot
(blackline).Thesecondaxesshowthecorrespondingnormalised
mass-to-flux ratio (Mouschovias & Spitzer 1976)
mass-to-fluxratioµandtherotationfrequencyω.
M (cid:16)M(cid:17) M 0.13
µ= core/ = (cid:82) core /√ . (6)
Φcore Φ crit BzdA G Pelletier & Pudritz 1992) or the magnetic pressure gradi-
and the angular frequency ω are listed. We note that the ent (Lynden-Bell 1996, 2003). A frequently chosen quan-
inclusion of turbulent motions in the setup will be delayed tity is the ratio of the toroidal to poloidal magnetic field,
to a subsequent paper. B /B (e.g. Hennebelle & Fromang 2008). If this ratio
φ pol
is significantly above 1, the outflow is often believed to be
driven by the magnetic pressure. However, the considera-
3 A GENERALISED CRITERION FOR tion of Bφ/Bpol alone can be misleading as in centrifugally
MAGNETO-CENTRIFUGALLY DRIVEN driven flows this value can be as high as 10 (see Fig. 4 in
JETS Blandford & Payne 1982, henceforth BP82). Close to the
disc surface one can check the inclination of the magnetic
Several approaches can be found in literature to deter-
field lines w.r.t. the vertical axis. The field lines have to
mine whether an outflow is driven by centrifugal acceler- be inclined by more than 30◦ for centrifugal acceleration to
ation (Blandford & Payne 1982; Pudritz & Norman 1986;
work(BP82).Althoughthiscriterionisanexactsolutionof
the ideal, stationary and axisymmetric MHD equations for
1 Toavoidunphysicallyhighdensitiesintheinteriorofthecore, anoutflowfromaKepleriandisc,itsapplicabilityislimited
wecutoffther−1.5-profileataradiusof0.0125pc.Withinthis tothesurfaceofthedisc.Acriteriontodeterminethedriv-
radius the density distribution follows a parabola ρ(r) ∝ (1− ingmechanismabovethediscwasusedbyTomisaka(2002)
(r/r0)2). comparingofthecentrifugalforceFcandthemagneticforce
(cid:13)c 2011RAS,MNRAS000,1–22
4 D. Seifried et al.
F . By projecting both forces on the poloidal magnetic when describing regions in which gas is accelerated mainly
mag
field lines it can be determined which force dominates the by flinging gas outwards along the poloidal field lines. In
acceleration. For the outflow to be driven centrifugally, F contrast, magneto-centrifugal acceleration also contains the
c
hastobelargerthanF .However,forthiscriteriontobe possibility of B dominated acceleration.
mag φ
self-consistent the gravitational force and the fact that any In the following we always assume that the thermal
toroidalmagneticfieldwouldreducetheeffectofF haveto pressurecanbeneglected,i.e.h=0.Whethergascangetac-
c
be taken into account. celerated,i.e.whetherv increases,dependsonthechange
pol
In the following we derive a generalised criterion based ofthesecondtolasttermonther.h.s.ofequation(10)(sec-
on the ideal, axisymmetric, time-independent (stationary) ond line) along the poloidal field line where (cid:15) is constant.
MHD equations (Chandrasekhar 1956; Mestel 1961) to de- The general condition for acceleration is therefore
cidewhethercentrifugalaccelerationdominatesornot.The (cid:18)1 v 1 B B 1 B2(cid:19)
criterionisapplicableeverywhereintheoutflowandnotonly ∂ v2 +Φ− φ φ pol + φ <0 (11)
pol 2 φ v 4π ρ 4π ρ
atthediscsurface.Tobeginwithwereviewthebasicresults pol
of the solution of the stationary, axisymmetric MHD equa- where ∂ denotes the derivative along the poloidal mag-
pol
tions.Asthesolutionisdiscussedbroadlyinliterature(e.g. netic field. This criterion is universal and can be applied to
Blandford & Payne 1982; Pelletier & Pudritz 1992; Spruit the whole outflow structure. It describes all regions of gas
1996)weonlystatethemainresultsnecessarytoderiveour acceleration including those dominated by the effect of B .
φ
criterion. One key aspect of the solution is that it invokes Furthermore it only contains variables which are directly
four surface functions which are constant on each magnetic accessible from the simulations.
surface, i.e. along each magnetic field line. We list them in Now, we come back to our original aim to work out a
the following. criterion for identifying the regions dominated by centrifu-
galacceleration.Todoso,wefinditusefultogotoaframe
1. Combiningtheinductionequation,thedivergence-free
rotating with the magnetic field, i.e. with the angular fre-
equationandthecontinuityequationshowsthatthepoloidal
quency ω. For this purpose the Bernoulli equation (10) is
velocity is always parallel to the poloidal magnetic field
modified as follows
ρvpol =kBpol (7) (cid:15)(cid:48) =(cid:15)−lω= 1v2 + 1(v −rω)2+Φ (12)
wherek,theso-calledmassloading,isthefirstsurfacefunc- 2 pol 2 φ cg
tion, i.e. it is constant along any given field line. where Φcg is the centrifugal-gravitational potential
2. Thesecondsurfacefunctionwhichcanbederivedfrom GM 1
thethreeaforementionedequationsistheangularvelocity of Φcg(r,z,ω)=−√r2+z2 − 2ω2r2 (13)
the magnetic surface
withM beingthemassofthecentralobjectandGthegrav-
v kB
ω= φ − φ . (8) itational constant. Compared to equation (10) all magnetic
r rρ field terms have vanished. This is due to the fact that in
Here r is the cylindrical radius and v the local rotation the rotating frame the gas flow is strictly parallel to the
φ
speed of the gas. magnetic field and therefore the Lorentz force vanishes.
3. Making use of the equation of motion yields the third Wenowmaketheadditionalassumptionthatthemag-
surface function, the angular momentum invariant neticfieldisstrongenoughtoretainapurelypoloidalstruc-
ture, i.e. B =0, and to force the gas to corotate with the
rB φ
l=rvφ− 4πkφ . (9) field. Hence, we can set vφ/r = ω (compare equation (8))
causing the second term on the r.h.s. of equation (12) to
4. Finally, considering the kinetic energy equation yields
vanish. This in turn reduces the question of whether gas
the energy invariant along a poloidal field line
canbeacceleratedtothequestionofhowΦ changesalong
cg
the field line. Φ decreasing along the field line causes v
cg pol
(cid:15) = 1v2+Φ+h− rωBφ to increase, i.e. the gas gets accelerated and vice versa. We
2 4πk emphasisethatthisworksbecausegascanonlymoveparal-
1 1 v 1 B B 1 B2 lel to the poloidal magnetic field in the stationary case (see
= v2 + v2 +Φ+h− φ φ pol + φ(10)
2 pol 2 φ v 4π ρ 4π ρ equation(9)).Wenotethatsettingωinequation(13)tothe
pol
Keplerian value at the footpoint of the magnetic field line
where h is the enthalpy and Φ gravitational potential. This
in the disc yields the well-known criterion found by BP82
equation is also called the Bernoulli equation.
stating that the field lines at the disc surface have to be
In the second line of equation (10) we have used the inclined by more than 30◦ w.r.t. the z-axis for centrifugal
variableswhichcanbeinferredfromsimulationstodescribe acceleration to work. However, the expression here is more
(cid:15).WeespeciallynotethelasttermcontainingB2 describing general and sub-Keplerian velocities may also be used.
φ
theinfluenceofthetoroidalmagneticfieldonthedynamics In a numerical simulations, for an arbitrarily chosen
of outflows. It states that in magnetic wind theory besides point somewhere above the disc it is often not possible
the poloidal magnetic field flinging material outwards, the to determine the footpoint of the magnetic field line pass-
toroidalmagneticfieldcancontributetotheaccelerationof ing through that point. Therefore, it is not possible to set
gas(seealsoSpruit1996,foradetaildiscussion).Magneto- ω = Ω where Ω is the angular frequency at footpoint in
0 0
centrifugalaccelerationthereforehastworegimes;acentrifu- thediscwherethefieldlineisanchored.Undertheassump-
gally dominated and a B (magnetic pressure) dominated tionthatgasandmagneticfieldcorotate,wecancircumvent
φ
regime. In the following we will use centrifugal acceleration this problem. We therefore replace ω by the local angular
(cid:13)c 2011RAS,MNRAS000,1–22
Magnetic fields in massive star formation II 5
frequency of the gas, i.e. ω = Ω = v /r which is known of corotation, i.e. B =0, made for the derivation of equa-
φ φ
fromthesimulationdata.Hence,atanygivenpoint(R ,Z ) tion (17).
∗ ∗
we can calculate the value of the centrifugal-gravitational
potential
GM 1
Φ =Φ (R ,Z )=− − v2 . (14)
cg,∗ cg ∗ ∗ (cid:112)R2+Z2 2 φ,∗ 4 RESULTS
∗ ∗
In this section, we present the results of our collapse simu-
By solving the equation
lationsfocussingontheevolutionandthelaunchingmecha-
Φ (r,z,ω )=−√GM − 1ω2r2 =Φ =const. (15) nismofoutflows.Theevolutionofprotostellardiscsandthe
cg ∗ r2+z2 2 ∗ cg,∗ accretionpropertiesoftheprotostarswerestudiedindetail
inPaperI.Welimitourconsiderationtothephaseafterthe
undertheassumptionthatthegaswouldrotateeverywhere
first sink particle has formed to study the time evolution
with ω =v /R , one obtains the shape of an isocontour
∗ φ,∗ ∗ of the outflow and its underlying launching mechanism in
z(r,ω ,Φ )= detail. In the following, all times refer to the time elapsed
∗ cg,∗
(cid:112) since the formation of the first sink particle.
−r6ω4−4r4ω2Φ −4r2Φ2 +4G2M2
− ∗ ∗ cg,∗ cg,∗ . (16) In general, the outflows are launched shortly after the
r2ω2+2Φ
∗ cg,∗ creationofthefirstsinkparticleassoonasaprotostellardisc
Along this line the value of Φ stays constant, i.e. Φ = builds up. In each simulation the outflow evolves over time
cg cg
Φ . Assume the magnetic field line passing through the and shows no signs of re-collapse until the end of the simu-
cg,∗
point(R ,Z )isrigidlycorotatingwiththegaswiththean- lation.However,outflowmorphologiesandglobalproperties
∗ ∗
gularvelocityω ,onecaneasilydecidewhetherthegascan likemassormomentum(seeTable2)differsignificantlybe-
∗
get accelerated or not by comparing the shape of the iso- tween the individual runs. Hence, in the following we select
contour with that of the magnetic field line. Hence, taking two representative simulations with equal initial rotational
the derivative of equation (16) w.r.t. r and comparing it to energies but different magnetic field strengths to study the
the ratio B /B at the point (R ,Z ) yields the desired cri- properties and the launching mechanism of the outflows in
z r ∗ ∗
terion.Forcentrifugalaccelerationtoworkatanarbitrarily detail.
chosen point the criterion therefore is
r 1 (cid:18)v2 (cid:19)(cid:46)(cid:16)B (cid:17)
φ(r2+z2)3/2−GM z >1. (17) 4.1 Weak field case 26-4
zGM r2 B
r
4.1.1 General properties
Forthesakeofsimplicitywehaveneglectedthe∗symbolin
the above equation. Every quantity has to be taken at the We start our consideration with run 26-4 which has a weak
point considered, i.e. at (r,z). initialmagneticfieldandamoderaterotationalenergy(see
We emphasise that the criterion given in equation (17) Table1).InFig.2weshowthedensity,thepoloidalvelocity
traces the regions where acceleration is mainly by the cen- field and the outflow velocity
trifugal force, i.e. flinging out gas along the poloidal field
z
lines. As we have set Bφ = 0, there is no resulting Lorentz vz,out =vz· |z| (18)
force along the poloidal field line (see also Section 4.1 of
Spruit 1996) and the only acceleration is indeed due to the of the outflow in a slice along the z-axis at two different
centrifugalforceexceedingthegravitationalforce.Themag- times.Itcanbeseenthatinitiallytheoutflowexpandsrather
netic field only enforces the gas to rotate with the angular slowlyintothesurroundingmediumaswithinthefirst2000
frequency ω. Regions of acceleration not traced by this cri- yr it has reached a height of only ∼ 250 AU. After 2000
terion should be fit by the criterion given in equation (11) yrthegrowthrateincreasesandreachesaroughlyconstant
asheretheaccelerationbyB istakenintoaccount.There- value of about 1 AU yr−1 (cid:39) 4.7 km s−1. We will discuss
φ
fore, by comparing the results of both criteria we are able this behaviour in detail at the end of Section 4.1.2. Fig. 2
todistinguishbetweenregionsdominatedbycentrifugalac- also shows that a bow shock at the tip of the outflow de-
celeration and those by the toroidal magnetic pressure. velops extending down to the edge of the centrifugally sup-
Weagainemphasisethattheformulationgiveninequa- ported disc. As indicated by the velocity vectors, most of
tion (11) states that in magnetic wind theory, the acceler- thegaswithinthebowshockisdirectedverticallyoutwards
ation by B in magneto-centrifugal flows is implicitly con- withvelocitiesupto15kms−1.Thiscorrespondstohighly
φ
tained.Thisseemsoftentobeoverlookedinliteraturewhen supersonic motions of Mach numbers up to ∼ 55 using a
discussing the underlying outflow mechanism. Equation 11 temperatureof20Kaspresentintheundisturbed,ambient
nicely demonstrates that a classification into centrifugally medium and Mach numbers of about 15 - 20 w.r.t. tem-
driven flows on the one hand and magnetic tower flows on peratures of a few 100 K in the outflow itself. The outflow
the other might be an oversimplification as in reality there morphologyat2000yrand5000yrrevealsaself-similarap-
canbeacoexistenceofcentrifugalaccelerationandacceler- pearance.Inparticularthecollimationfactoroftheoutflow,
ation due to the pressure gradient of B . We will refer to i.e. the ratio of the length to the width of one outflow lobe,
φ
this several times in the paper. We also point out that the settles around a value of ∼ 4. We especially note the very
equations 10 and 12 are equivalent despite their very dif- turbulentstructureseenintheoutflowafter5000yrinboth
ferent appearance. The equations 11 and 17, however, are the density field and the outflow velocity. Several internal
not equivalent any more due to the additional assumption shock fronts and instabilities have occurred in the outflow
(cid:13)c 2011RAS,MNRAS000,1–22
6 D. Seifried et al.
Table 2.Listedarethemass,momentumandextensionoftheoutflows,thetotalsinkparticlemassattheendofeachsimulation,the
timetherunshavebeingfollowedafterthefirstsinkparticlehasformed,andthetimeaveragedmassandmomentumoutflowrates.
Run Mout Pout L Msink tsim M˙out P˙out
(M(cid:12)) (M(cid:12) kms−1) (AU) (M(cid:12)) (yr) (10−4 M(cid:12) yr−1) (10−4 M(cid:12) kms−1 yr−1)
26-20 0.509 0.337 707 1.85 5000 1.02 0.673
26-4 0.853 2.37 3215 2.65 5000 1.71 4.74
26-0.4 0.526 2.23 3720 3.59 5000 1.05 4.46
26-0.04 0.080 0.202 856 4.26 5000 0.16 0.404
10-20 1.09 1.02 1240 1.28 4000 2.73 2.54
10-4 0.603 0.585 669 2.23 4000 1.51 1.46
10-0.4 0.164 0.177 445 2.98 4000 0.41 0.442
5.2-20 0.875 1.70 2110 1.78 4000 2.19 4.25
5.2-4 0.656 0.715 1128 2.28 4000 1.64 1.79
5.2-0.4 0.537 0.586 1100 2.55 4000 1.34 1.46
2.6-20 0.116 0.281 1942 1.30 3000 0.39 0.938
2.6-4 0.095 0.215 1455 1.48 3000 0.32 0.717
although no perturbations are included in the initial condi- whichreducethemaximumoutflowvelocityandpreventan
tions. This turbulent structure is a consequence of instabil- efficient overall acceleration although local gas acceleration
itiesandnotofepisodicejectionevents.Wecheckedthisby is still possible. The position where this happens gradually
visual inspecting the time evolution of the outflow, finding moves outwards whereas the bulk velocity above this point
that continuous ejection occurs over the whole time range. remains almost constant with a value of ∼ 5 km s−1.
Furthermore,ahighlytimevariableejectionratewouldalso
requiresignificantvariationsinthemassaccretionrate(e.g. InFig.4weshowradialprofilesofthedensityandout-
Pudritz & Norman 1986) which is clearly not the case (see flow velocity at different vertical positions. Both quantities
Fig. 13 in Paper I). A turbulent structure as observed here are averaged azimuthally before plotting. As can be seen,
wasrecentlyalsoreportedbyStaffetal.(2010)forjetsimu- below2000AUthehighestvelocitiesoccurclosetothesym-
lations.Theenergyintheshocksdissipatesandheatsupthe metry axis of the jet. In particular the velocity profile at z
jetpossiblyresultinginopticalforbiddenlineemission(Staff = 500 AU shows a very well confined, fast velocity compo-
etal.2010).Interestingly,despitetheturbulentstructurethe nentwithaquitesharpdrop-offataradiusof150-200AU.
outflow keeps expanding with constant speed. Another in- This two velocity components, the fast, central as well as
terestingfactisthatthegasiscontinuouslyejectedfromthe theslower,enclosingcomponentarealsoseeninthePVdi-
disc over the whole 5000 yr although the protostellar disc agram(Fig.3)inparticularintheregionbetweenz=0and
starts to fragment around t (cid:39) 2500 yr and has formed 12 −1000AUwheretwo”Hubblelaws”seemtobepresent.The
further fragments by then (see Paper I, for details). Hence, goodcollimationofthefastjetcomponentismostlikelydue
fragmentation does not necessarily terminate the driving of to the strong hoop stress exerted by the toroidal magnetic
outflows, a fact which is also observed in run 26-20. field.Suchtwovelocitycomponentoutflowswithawellcol-
limated,fastcomponentclosetotheaxisoftheoutflowand
Tostudytheoutflowstructureinmoredetail,weshow a wider spread, slower component are frequently observed
theposition-velocity(PV)diagramoftheoutflowat5000yr around low-mass protostars (see e.g. Bachiller 1996, for a
in Fig. 3. The PV diagram is frequently used by observers review) and also around massive protostars (e.g. Beuther
tostudythevelocitystructureofoutflows(e.gLada&Fich et al. 2004; Ren et al. 2011). Furthermore, they are also
1996; Beltra´n et al. 2011). For the diagram shown here we observed in jet simulations (e.g. Staff et al. 2010).
only take into account outflowing gas. As indicated by the
contours, the velocity of the bulk of outflowing material in- Wenotethatthedecreaseofv closetor=0atz=
z,out
creases with distance from the midplane. Such a “Hubble 500 AU (black line in the top panel of Fig. 4) is most likely
Law” is frequently observed for outflows around low- and a numerical issue as gas very close to the z-axis cannot get
also high-mass protostellar objects (e.g. Lada & Fich 1996; accelerated properly due to the limited resolution. Above z
Arce & Goodman 2001; Beuther et al. 2003; Wang et al. = 2000 AU the velocity profile is more or less smooth over
2011; Ren et al. 2011; Beltra´n et al. 2011). The maximum thewholeradialrange.InaccordancewiththePVdiagram
outflowvelocitysaturatesaround15kms−1showingseveral (Fig. 3) for those distances no velocities higher than ∼ 6
distinct peaks which we attribute to the internal shocks in kms−1 occur.Thedensityprofiles(bottompanelofFig.4)
theoutflow(seebottompanelofFig.2).Aboveadistanceof show a relatively flat shape at all distances with variations
about2000AU,however,themaximumvelocityexperiences of about half an order of magnitude and possibly a slight
asignificantdropfromabout15to10kms−1.Atthesame increase towards the z-axis. At the outer edge the density
time the ”Hubble law“ describing the evolution of the bulk experiencesastrongincreaseduetothebowshockconfining
velocitytruncatesandthebulkvelocitysaturatesatavalue the outflow. By carefully comparing with the top panel of
of ∼ 5 km s−1. We attribute this to a strong internal shock Fig. 4, it can be seen that the material in the bow shock
front and the very turbulent structure at these distances partly reveals infall velocities.
(cid:13)c 2011RAS,MNRAS000,1–22
Magnetic fields in massive star formation II 7
t = 2000 yr log(ρ [g cm-3]) 20

300 -13.0
15
200 -13.5 10
5
1
100 -14.0 -s
m 0
k
z / AU 0 -14.5 v / z -5
-10
-100 -15.0
-15
-200 -15.5 -20
-3000 -2000 -1000 0 1000 2000 3000
-300 -16.0
-300 -200 -100 0 100 200 300 z / AU
x / AU 10 km/s
Figure 3. Position-velocity diagram for the weak-field run 26-4
t = 5000 yr log(ρ [g cm-3]) after5000yr.Thecontourshavealogarithmicspacing.Thebulk

-13 velocity increasing with distance. The maximum velocity show
severalclearpeakswhichareattributedtointernalshockfronts.
-14
2000
12
500 AU
-15 10 1000 AU
U 2000 AU
z / A 0 8 3000 AU
-16
1 6
-s
m
-2000 -17 v / kz 24
-18 0
-2000 0 2000
x / AU 10 km/s -2
t = 5000 yr v [km s-1] -15
z,out
15
2000 10 3)
-m
c
z / AU 0 5 og( / g ρ -16
l
0
-2000
-17
0 100 200 300 400 500 600 700 800 900 1000
-5
-2000 0 2000 r / AU
x / AU
Figure 4. Radial profiles of the outflow velocity (top) and the
density(bottom)atdifferentverticalpositionsfortheweak-field
Figure2.Slicealongthez-axisintheweak-fieldrun26-4,at2000 run 26-4 after 5000 yr. The quantities are averaged azimuthally
yrand5000yraftertheformationofthefirstsinkparticle.The before plotting. For z < 2000 AU the outflow velocity increases
two top panels show the density field and the poloidal velocity towards the z-axis whereas at larger distances it has an almost
vectors (black arrows). Note the different spatial scales between flatradialprofile.Thedensityprofilesareratherflatshowingonly
the top and middle panel. The outflow velocity (vz,out, bottom small variations and a prominent jump associated with the bow
panel) and the density field after 5000 yr show a very turbulent shock.
structurecausedbyinternalshocks.
(cid:13)c 2011RAS,MNRAS000,1–22
8 D. Seifried et al.
4.1.2 Launching mechanism
t = 5000 yr log(B/B )
φ pol
2
Next,weanalysetheunderlyinglaunchingmechanismofthe
outflow in the weak field case 26-4. Once again, in order to
smooth out local perturbations which inevitably would oc-
curinanarbitrarilychosenslicealongthez-axis,thequanti- 2000 1
tiesshowninthefollowingareaveragedazimuthally.Firstly,
the relative importance of the toroidal (B ) and poloidal
φ
magnetic field (B ) for the total magnetic energy content
pol U
in the outflow is studied. This is done in the top panel of z / A 0 0
Fig.5wherethevalueofB /B inaslicealongthez-axis
φ pol
is shown. As can be seen, almost the complete outflow re-
gionisdominatedbyB .Thetoroidalcomponentiscreated
φ
-1
bytherotationoftheprotostellardiscinwhichtheinitially -2000
purelypoloidalmagneticfieldisanchored.B reachesvalues
φ
largerthanB byupto2ordersofmagnitude.Hence,B
pol φ
should have a crucial effect on the evolution of the outflow.
-2
Depending on the position, the absolute values of Bφ and -2000 0 2000
x / AU
B vary between ∼ 0.01 G and ∼ 1 G.
pol
Outflowsdrivenbythepressuregradientofthetoroidal
magnetic field are described by Lynden-Bell (1996, 2003)
andareoftentermedasmagnetictowerflows.Thefactthat
the outflow region is mainly dominated by B suggest that
φ
theoutflowissuchamagnetictowerflow.However,acloser
inspection reveals that the region close to the symmetry
axis, where the highest velocities occur (see bottom panel
of Fig. 2), is either only weakly dominated by the toroidal
magneticfieldorevendominatedbyB ,i.e.B /B (cid:54)10.
pol φ pol
Weemphasisethatevenafieldconfigurationwhichisdom-
inated by B does not contradict the centrifugal accelera-
φ
tion mechanism. BP82 find values of B /B up to ∼ 10
φ pol
(see their Fig. 4) in the acceleration region in agreement
with our findings. Therefore, we assume that the outflow is
drivenbycentrifugalaccelerationalthoughthereiscertainly
a contribution to the acceleration by B as well. Of course,
φ
this assumption has to be confirmed quantitatively in the
following.
To do so, in the bottom panel of Fig. 5 we analyse the
magnetic field structure in detail concentrating on the in-
nerregionwherethejetislaunched.Thepoloidalmagnetic Figure 5. Magnetic field lines structure of the weak-field run
field lines are overplotted on the density field. In addition, 26-4, after 5000 yr in a slice along the z-axis. All quantities are
we show the poloidal velocity field and the contours where averagedazimuthally.Top:Ratioofthetoroidaltopoloidalmag-
B /B =1,10respectively.Ascanbeseen,thefieldlines neticfield.Blackcontoursgivethetransitionfromthetoroidally
φ pol
tothepoloidallydominatedregion.Almostthewholeoutflowarea
just above/below the disc are strongly inclined against the
is dominated by B . Bottom: Density field in the inner region.
z-axis.Exceptfortheinnermostparttheinclinationangleis φ
Also shown are the poloidal field lines (white lines), the veloc-
everywhere above 30◦ which is required to launch cold gas
ityfield(blackarrows)andthecontourswhereB /B =1,10
φ pol
from the disc by centrifugal acceleration (BP82). Here we
(blackanddarkbluelines,respectively).Almosteverywherethe
emphasise that an inclination angle smaller than 30◦ does poloidal magnetic fieldhas inclinationlarger than30◦ w.r.t. the
not necessarily mean that centrifugal launching is impossi- z-axissuitableforcentrifugalacceleration.
ble. The 30◦ condition is valid only for a cold gas, i.e. if
thermal pressure can be neglected. As soon as a thermal
pressuregradientispresentaidingtoacceleratethegasup- toroidal magnetic field component. However, we note that
wards, even inclination angles below 30◦ are sufficient for thetoroidalmagneticpressurealsocontributestotheaccel-
jetlaunching.Asthereisclearlyapressureincreasetowards eration of the gas as implied in the MHD wind theory (see
the centre in the simulation, the innermost region is suit- equation(11)).Asarguedbefore,thelaunchingfromthedisc
able for centrifugal acceleration as well even though the in- itself,however,ismostlikelyduetocentrifugalacceleration.
clinationisbelow30◦.Furthermore,asmentionedbeforein To further support the conclusion of a centrifugally
the inner region where the actual acceleration takes place, driven wind, we apply the two criteria derived in Section 3
the magnetic field is not or only weakly dominated by B (see equations 11 and 17). In contrast to the Blandford &
φ
in agreement with the findings of BP82. In contrast, for a Payne criterion, we can in general determine the driving
magnetic tower flow (Lynden-Bell 2003) one would expect mechanism of the outflow away from the disc surface. The
amuchmorewoundupstructurewithaclearlydominating resultsareshowninFig.6,wheretheregionswherethecri-
(cid:13)c 2011RAS,MNRAS000,1–22
Magnetic fields in massive star formation II 9
t = 5000 yr t = 5000 yr

600 600
400 400
200 200
U U
z / A 0 z / A 0
-200 -200
-400 -400
-600 -600
-600 -400 -200 0 200 400 600 -600 -400 -200 0 200 400 600
x / AU 10 km/s x / AU 10 km/s
t = 5000 yr t = 5000 yr

2000 2000
U U
z / A 0 z / A 0
-2000 -2000
-2000 0 2000 -2000 0 2000
x / AU 10 km/s x / AU 10 km/s
Figure 6. Slice along the z-axis in the weak-field run 26-4 after 5000 yr for two different scales. Gray shaded areas show the regions
wherethecriteriaderivedinSection3(equation(17)(leftpanel)andequation(11)(rightpanel))arefulfilled.Theleftpanelsshowthat
centrifugal acceleration works mainly close to the z-axis up to a height of about 800 AU which agrees very well with the region where
thehighestvelocitiesarefound.Thegeneralcriterionismorevolumefillingandtracesalsoregionsintheouterparts.
teria are fulfilled are shaded grey. As can be seen, within TakingintoaccounttheeffectofB inthemostgeneral
φ
about 800 AU above/below the disc there is a continuous expression of magneto-centrifugal driving (equation (11))
regionclosetothez-axiswherecentrifugallydominatedac- gives a markedly different result (see right panel of Fig. 6).
celerationispossible(leftpanel).Alsoatlargerheightscen- The grey shaded areas are now much more volume filling,
trifugal acceleration partly works, in particular close to the in particular in the outer parts of the outflow with radii
symmetryaxisofthejet.Thegreyshadedregionaroundthe (cid:38)200AUwhereoutflowinggasispresentaswell.Aspurely
z-axisintheupperleftpanelofFig.6agreesverywellwith centrifugaldominatedaccelerationdoesnotworkinthisre-
theregionwherethehighestoutflowvelocitiesaredetected. gion, we expect B to be mainly responsible for the out-
φ
Hence,despitethestrongassumptionslikestationarity,axis- flow driving. The results in the upper panel of Fig. 6 nicely
symmetry and corotation used to derive the criterion given demonstratethecapabilityofourcriteriontodistinguishbe-
in equation (17), it works reasonably well. In particular, it tween the different driving mechanisms which was the rea-
isapplicabletoregionsfarfromthediscsurfaceincontrast son for its derivation. An increasing importance of B for
φ
tothe30◦ -criterionofBP82.Wethereforedrawthefollow- thedrivingcanalsobeseenintheupperpartsoftheoutflow
ingconclusions:Theassumptionofcorotationisreasonably (|z| (cid:62) 800 AU). Here the situation is less suitable for pure
wellfulfilledintheinnerpartoftheoutflow(|z|(cid:54)800AU) centrifugal acceleration (bottom left panel of Fig. 6) but in
despite the partly significant toroidal magnetic field (see general magneto-centrifugal acceleration is still possible in
Fig.5).Hence,thecentraljetcanbeconsideredascentrifu- greatparts(bottomrightpanel).Thisiswhywearguethat
gally driven, i.e. gas gets flung out- and upwards along the B mustcontributesignificantlytotheoutflowdynamicsat
φ
poloidal magnetic field lines. The result also demonstrates great heights.
that the 30◦ condition – apart from the disc surface – and
We note that even the general criterion given in equa-
the ratio of B to B are not sufficient to determine the
φ pol
tion(11)doesnotcovertheentireoutflowstructure.Thisis
driving mechanism above/below the disc.
duetothefactthatthegasindeeddoesnotgetaccelerated
(cid:13)c 2011RAS,MNRAS000,1–22
10 D. Seifried et al.
everywhere, e.g. in the shock regions, but possibly also due 4.2 Strong field case 5.2-4
to the azimuthal averaging process. However, the very dif-
4.2.1 General properties
ferent results given by the two criteria, in particular in the
upperpanelofFig.6,stronglyindicatethatthetwodistinct Next, we describe global properties of the outflow gener-
outflow regions are real. ated in run 5.2-4 which has a 5 times stronger initial mag-
Although the gas in the outflow experiences several in- netic field than run 26-4 (see Table 1). The outflow shown
ternalshocks(seeFig.2),thebulkvelocitysteadilyincreases inFig.7revealssignificantdifferencescomparedtotheout-
within about 2000 AU (Fig. 3). This can be explained by flowinrun26-4(compareFig.2).Whereasthelatteriswell
the fact that acceleration is possible over almost the whole collimatedwithacollimationfactorof∼4,theformerhasa
outflowextension(bottomrightpanelofFig.6).Afterexpe- rather sphere-like morphology expanding with roughly the
riencing a shock which decreases the outflow speed, the gas same speed in all directions, therefore also maintaining a
gets reaccelerated again by centrifugal acceleration and/or self-similar morphology for all times. The outflow velocities
the toroidal magnetic field pressure. This happens repeat- reach valuesofup to5km s−1 about afactorof 2- 3lower
edly over the whole outflow extension thereby successively than in run 26-4. The expansion speed of the outflow is al-
increasingthebulkvelocity.This situationmarkedlydiffers mostconstantovertimewithavalueof0.28AUyr−1 (cid:39)1.3
from episodic jet ejection which also would produce inter- kms−1.Thisisnoticeablysmallerthantheexpansionspeed
nal shock fronts. Therefore, we conclude that the knotty of 1 AU yr−1 observed in run 26-4. Consequently also the
structure often observed in protostellar jets is not necessar- bow shock structure in run 5.2-4 is less pronounced.
ily a consequence of several outflow ejection events but can Furthermore, a closer inspection of the outflow in run
alsoresultfromacontinuouslyfedjetwheregasrepeatedly 5.2-4 reveals that in particular close to the symmetry axis
shocks and reaccelerates (see also Staff et al. 2010). andthecentreofthebubblegasisstillfallinginwardseven
at late times. Gas with outwards motion occurs mainly in
AsalreadyseeninthebottompanelofFig.5themag-
the outer wings. The outflow direction in the inner part is
neticfieldlinesgetstraightenedveryquicklyaboveandbe-
almost radial and gets collimated at relatively large radii
low the disc. We attribute this to the hoop stress produced
of ∼ 500 AU. This is remarkably different to the situation
bythetoroidalmagneticfieldcollimatingtheoutflowinggas
in run 26-4 where almost all the gas within the outflow
andthereforealsothemagneticfieldlines.Nevertheless,the
area is moving outwards and preferentially parallel to the
gasstillgetsacceleratedcentrifugallydespitethealmostver-
z-axis. A consequence of the complicated velocity structure
tical direction of the magnetic field lines (Fig. 6). Further-
observed in Fig. 7 is the complex density structure show-
more, as shown in Fig. 5, the largest part of the outflow is
ing several shock-like features in the bubble. We find that
dominatedbythetoroidalmagneticfieldcomponent.There-
the flattened structure in the midplane is a strongly sub-
foreitisnotsurprisingthatoveritscompleteextensionthe
Keplerian disc with significant infall motions (see Paper I,
outflow as a whole stays well collimated.
for a detailed discussion). The sub-Keplerian rotation is a
As mentioned in the previous section, the expansion consequence of the strong initial magnetic field decelerat-
speed is not constant over time but experiences a relatively ingtherotationoftheinitialcoreviathemagneticbraking
sharp increase after about 2000 yr. We attribute this to a mechanism (Mouschovias & Paleologou 1980).
changeintheunderlyingdrivingmechanismoftheoutflow.
Indeed, analysing the outflow with our criterion given in
equation (17) shows that within the first 2000 yr purely 4.2.2 Launching mechanism
centrifugal acceleration is not possible indicating that the
The different morphologies of the outflows in run 5.2-4 and
outflow is mainly driven by the toroidal magnetic pressure.
run26-4raisethequestionwhethertheunderlyinglaunching
Theexpansionspeedinthisphaseisalmostthesameinthe
mechanisms differ. Firstly, we examine the relative impor-
vertical and horizontal direction (see top panel of Fig. 2)
tanceofthetoroidalandpoloidalmagneticfieldcomponents
with the outer edge of the bubble coinciding with the po-
inthetoppanelFig.8.Hereagain–asinSection4.1.2–all
sition of the accretion shock at the disc edge. It is only in
quantities like velocity, magnetic field and density are aver-
thisinitialstagewhenwecalltheoutflowamagnetictower
agedazimuthallybeforebeingplottedinordertosmoothout
flow (Lynden-Bell 1996, 2003). In contrast to the situation
localvariationswhichmightcomplicatetheanalysis.Ascan
at 5000 yr in this transient phase there is no acceleration
beseen,agreatpartoftheoutflowbubbleisnotdominated
of gas from the disc. In fact, the gas is accelerated only at
bytheB incontrasttotheoutflowinrun26-4(seeFig.5).
φ
the tip of the outflow. Therefore the situation differs signif-
Interestingly,theregionswhereB dominatesareusuallyas-
φ
icantly from the later stages. After ∼ 2000 yr a fast, well
sociatedwithrelativelyfastoutflowinggas.Incontrast,the
collimatedoutflowcomponent,thecentrifugaldrivenjetde-
regions which are dominated by B either have only slow
pol
velopsintheregionclosetothez-axis.Thelaunchingofthe outflowvelocities((cid:46)1kms−1)orevenshowinfallmotions.
jetcoincideswiththebuild-upofawelldefined,extended(∼
The fact that outflowing gas seems to be associated with
100 AU) Keplerian disc whereas prior to that disc rotation
a strong toroidal magnetic field, i.e. B /B >1, suggests
φ pol
is mostly sub-Keplerian.
that the outflow might be driven by the pressure gradient
In summary, besides the magnetic field line structure, of B .
φ
theapplicationofthecriterionderivedinthisworkstrongly In the bottom panel of Fig. 8 the magnetic field line
indicates that the outflow is mainly driven centrifugally at structure in the inner region is considered in more de-
|z|(cid:54)800AUwhilethedynamicsofB getsmoreimportant tail. The poloidal field lines have a strongly pronounced
φ
at large radii and larger heights where the flow is magneto- hourglass-shaped configuration with a strong radial com-
centrifugally driven. ponent. This is caused by the rapid gas infall in the disc
(cid:13)c 2011RAS,MNRAS000,1–22