Testing protostellar disk formation models with ALMA observations

5.8 MB·English

by  Daniel Harsono

Astronomy&Astrophysicsmanuscriptno.harsono14 (cid:13)cESO2015
January8,2015
Testing protostellar disk formation models with ALMA
observations
D.Harsono1,2,E.F.vanDishoeck1,3,S.Bruderer3,Z.-Y.Li4,andJ.K.Jørgensen5,6
1 Leiden Observatory, Leiden University, Niels Bohrweg 2, 2300 RA, Leiden, the Netherlands e-mail:
[email protected]
2 SRONNetherlandsInstituteforSpaceResearch,POBox800,9700AV,Groningen,TheNetherlands
3 Max-Planck-InstitutfürextraterretrischePhysik,Giessenbachstrasse1,85748,Garching,Germany
4 AstronomyDepartment,UniversityofVirginia,Charlottesville,VA,USA
5 NielsBohrInstitute,UniversityofCopenhagen,JulianeMariesVej30,2100CopenhagenØ,Denmark
6 CentreforStarandPlanetFormation,NaturalHistoryMuseumofDenmark,UniversityofCopenhagen,ØsterVoldgade5-7,1350
5 CopenhagenK,Denmark
1
0 January8,2015
2

n ABSTRACT
a
J Context.Recentsimulationshaveexploreddifferentwaystoformaccretiondisksaroundlow-massstars.However,ithasbeendifficult
7 todifferentiatebetweentheproposedmechanismsbecauseofalackofobservablepredictionsfromthesenumericalstudies.
Aims.Weaimtopresentobservablesthatcandifferentiatearotationallysupporteddiskfromaninfallingrotatingenvelopetoward

] deeplyembeddedyoungstellarobjects(Menv>Mdisk)andinfertheirmassesandsizes.
R Methods.Two3Dmagnetohydrodynamics(MHD)formationsimulationsofLiandcollaboratorsarestudied,witharotationallysup-
S porteddisk(RSD)forminginonebutnottheother(whereapseudo-diskisformedinstead),togetherwiththe2Dsemi-analytical
. model.ThedusttemperaturestructureisdeterminedthroughcontinuumradiativetransferRADMC3Dmodelling.Asimpletempera-
h turedependentCOabundancestructureisadoptedandsyntheticspectrallyresolvedsubmmrotationalmolecularlinesuptoJ =10
u
p arecomparedwithexistingdatatoprovidepredictionsforfutureALMAobservations.
- Results.3DMHDsimulationsand2Dsemi-analyticalmodelpredictsimilarcompactcomponentsincontinuumifobservedatthe
o
spatialresolutionsof0.5–1(cid:48)(cid:48)(70–140AU)typicaloftheobservationstodate.Aspatialresolutionof∼14AUandhighdynamicrange
r
t (> 1000) are required in order to differentiate between RSD and pseudo-disk formation scenarios in the continuum. The moment
s
onemapsofthemolecularlinesshowablue-tored-shiftedvelocitygradientalongthemajoraxisoftheflattenedstructureinthe
a
[ case of RSD formation, as expected, whereas it is along the minor axis in the case of a pseudo-disk. The peak-position velocity
diagramsindicatethatthepseudo-diskshowsaflattervelocityprofilewithradiusthananRSD.Onlarger-scales,theCOisotopolog

1 line profiles within large (> 9(cid:48)(cid:48)) beams are similar and are narrower than the observed line widths of low-J (2–1 and 3–2) lines,
v indicatingsignificantturbulenceinthelarge-scaleenvelopes.HoweveraformingRSDcanprovidetheobservedlinewidthsofhigh-J
7 (6–5,9–8,and10–9)lines.Thus,eitherRSDsarecommonorahigherlevelofturbulence(b ∼ 0.8kms−1)isrequiredintheinner
1 envelopecomparedwiththeouterpart(0.4kms−1).
4 Conclusions. Multiplespatiallyandspectrallyresolvedmolecularlineobservationscandifferentiatebetweenthepseudo-diskand
1 the RSD much better than continuum data. The continuum data give a better estimate on disk masses whereas the disk sizes can
0 be estimated from the spatially resolved molecular lines observations. The general observable trends are similar between the 2D
. semi-analyticalmodelsand3DMHDRSDsimulations.
1
0 Keywords. stars:formation,radiativetransfer,accretiondisks;line:profiles;methods:numerical,magnetohydrodynamics(MHD)
5
1
:
v1. Introduction Ithasbeenknownforalongtimethatthepresenceofmag-
i neticfieldscandrasticallychangetheflowdynamicsaroundlow-
X
mass stars (e.g., Galli & Shu 1993) and potentially suppresses
rThe formation of stars and their planetary systems is linked
diskformation(e.g.,Gallietal.2006).Thelatterisduetocatas-
a
through the formation and evolution of accretion disks. In the
trophic magnetic braking where essentially all of the angular
standard star formation picture, the infalling material forms an
momentumoftheaccretingmaterialisremovedbytwistedfield
accretion disk simply from angular momentum conservation
lines.Recently,Lietal.(2011)investigatethecollapseanddisk
(e.g., Lin & Pringle 1990; Bodenheimer 1995; Belloche 2013).
formation from a uniform cloud while Joos et al. (2012) and
However, magnetic field strengths observed toward molecular
Machida & Matsumoto (2011) performed simulations starting
cores(seeCrutcher2012,forarecentreview)areexpectedthe-
with a steep densityprofile and a Bonnor-Ebert sphere, respec-
oretically to be sufficient in affecting the formation and evolu-
tively. They found that rotationally supported disks (RSDs) do
tionofdisksaroundlow-massstars(e.g.,Gallietal.2006;Joos
not form out of uniform and non-uniform cores under strong
et al. 2012; Krumholz et al. 2013; Li et al. 2013, 2014a). Re-
magnetic fields unless the field is misaligned with respect to
centadvancesinbothobservationalandtheoreticalstudiesgive
the rotation axis (Hennebelle & Ciardi 2009). Turbulence has
anopportunitytotestthestarformationprocessatsmall-scales
alsobeenshowntohelpwithdiskformation(Santos-Limaetal.
(<1000AU).
Articlenumber,page1of16
A&Aproofs:manuscriptno.harsono14
2012;Seifriedetal.2012;Myersetal.2013;Joosetal.2013;Li et al. 2013). Here we apply a similar analysis on the synthetic
etal.2014b). continuumandmolecularlinedataasperformedontheobserva-
In spite of a number of disk formation and evolution simu- tionstotestthereliabilityoftheinferredmasses.
lations,onlyafewobservableshavebeenpresentedsofar.The This paper is structured as follows. Section 2 describes the
expectedobservablesinthecontinuum(spectralenergydistribu- simulationsandtheradiativetransfermethodthatareused.The
tionorSED)from1Dand2Ddiskformationmodelshavebeen syntheticcontinuumimagesarepresentedinSection3.Section4
presented in Young & Evans (2005) and Dunham et al. (2010). presentsthesyntheticCOmomentmapsandlineprofilesforthe
Continuum observables out of 2D hydrodynamics simulations differentsimulations.TheresultsarethendiscussedinSection5
with a thin disk approximation have been shown by Dunham andsummarizedinSection6.
&Vorobyov(2012)andVorobyovetal.(2013).However,only
a handful of synthetic observables from 3D magnetohydrody-
namics(MHD)simulationshavebeenpresentedintheliterature 2. Numericalsimulationsandradiativetransfer
(e.g.,Commerçonetal.2012a,b).
2.1. Magneto-hydrodynamicalsimulations
Continuumobservationsprobethedustthermalemissionand
the dust structure around the protostar. However, high spatial We utilize the 3D MHD simulations of the collapse of a 1 M(cid:12)
andspectralresolutionmolecularlineobservationsareneededto uniform,sphericalenvelopeasdescribedinLietal.(2013).The
probethekinematicalstructureasthediskforms.Theaimofthis envelope initially has a density of ρ0 = 4.77×10−19gcm−3, a
paperistopresenthigh-spatial(downto0.1(cid:48)(cid:48)or14AUatatyp- solid-body rotation of Ω0 = 10−13 Hz, and a relatively weak,
icaldistanceof140pc)syntheticobservationsofcontinuumand uniform magnetic field of B0 = 11 µG (λ = 10 where λ is the
molecular lines from two of the 3D MHD collapse simulations dimensionlessmass-to-fluxratio).Thedetailsofthesimulations
presented in Li et al. (2013). The two simulations differ in the canbefoundinLietal.(2013).
initialmagneticfielddirectionwithrespecttotherotationaxis: Asnapshotoftwosimulationsatt = 3.9×1012 s = 1.24×
aligned and strongly misaligned where the magnetic field vec- 105yearsisused.ThiscorrespondstoneartheendoftheStage0
torisperpendiculartotherotationaxis.Thetwocasesrepresent phaseofstarformationwherealmostonehalfoftheinitialcore
the two extremes of the field orientation. The synthetic obser- masshascollapsedontothestar(Robitailleetal.2006;Dunham
vationswillbecomparedwiththosefroma2Dsemi-analytical et al. 2014). The difference between the two simulations is the
diskformationmodelpresentedinVisseretal.(2009)toinves- tilt angle between the rotation axis and the direction of initial
tigate whether the predicted observables differ. The 2D models magneticfieldvector,θ0.Onesimulationstartswithaninitialtilt
allowustosimplifythedifferentinputparametersoftheMHD angleθ0 =0◦inwhichapseudo-diskformsbutnotanRSD.The
simulations into two parameters: sound speed (cs) and rotation other simulation starts with an initial tilt angle of θ0 = 90◦ in
rate.RotationaltransitionsofCOaresimulatedtotracetheob- whichanRSDforms(seeFig.1andFigure1inLietal.2013).
servablekinematicalsignatures. The RSD simulation (left) forms a flattened structure with
AnothermotivationinsimulatingCOmolecularlinesisthe numbergasdensitiesnH2 > 106.5 cm−3 intheinner300AUra-
availabilityofhigh-qualityspectrallyandspatiallyresolvedob- dius.Intheregionr > 100AU,themagnitudeoftheradialand
servationaldatatowardembeddedyoungstellarobjects(YSOs) azimuthal velocities are within a factor of 2 of each other. The
on larger scales (> 1000 AU). Spectrally resolved lines have radial velocities nearly vanish in the inner 70 AU radius (see
been obtained for low-excitation transitions J ≤ 7 (E = 155 Fig. 3). The streamlines in the RSD simulation show a coher-
u u
K)usingground-basedfacilities(e.g.,Jørgensenetal.2002;van entflattenedrotatingcomponent(seeFig.2).Inthecaseofthe
Kempen et al. 2009a,b) and higher excited lines up to Ju = 16 pseudo-disk simulation, number densities of nH2 > 106.5 cm−3
(E = 660 K) using Herschel-HIFI (de Graauw et al. 2010) encompassr<700AUregions,whichisafactorof2largerthan
u
in beams of 9–20(cid:48)(cid:48) (Yıldız et al. 2010, 2013; Kristensen et al. the RSD simulation. An outflow cavity is present in this simu-
2013). Interestingly, San Jose-Garcia et al. (2013) found that lationwithanexpandingvelocityfieldasshowninFig.1(Left)
theC18O9–8linesarebroaderthanthe3–2linesforlow-mass ofLietal.(2013).Thecavityismoreevacuatedcomparedwith
YSOs. The observed line widths are larger than that expected that in the simulation simulation that forms a rotationally sup-
fromthethermalbroadening,whichindicatesasignificantcon- ported disk although still not a canonical definition of a cavity.
tributionofmicroscopicturbulenceorsomeotherformsofmo- Themagnitudeoftheradialvelocitiesaremuchlargerthanthe
tion,suchasrotationandinfall.Throughthecharacterizationof azimuthalvelocitiesintheinnerr<300AUalongmostφdirec-
spectrally resolved molecular lines on such physical scales, we tions.Inthissimulation,thestreamlinesshowinfallingmaterial
aimtotestthekinematicspredictedinvariousstaranddiskfor- straightfromthelarge-scaleenvelopeontotheformingstar.Us-
mationmodels. ingthesetwosimulationswithverydifferentoutcomes,wecan
Anotherkeytestofstarformationmodelsistocomparethe investigatethesimilaritiesanddifferencesinbothcontinuumand
predictedmassevolutionfromtheenvelopetothestarwithob- molecular line profiles for pseudo-disk and RSD formation in
servations(e.g.,Jørgensenetal.2009;Lietal.2014a).Inferring 3D.
these properties toward embedded YSOs is not straightforward
duetotheconfusionbetweendiskandenvelope.Themassevo-
2.2. Semi-analyticalmodel
lutionofthediskandenvelopecanbededucedfrommillimeter
surveys combining both aperture synthesis and single dish ob- For comparison, synthetic images from 2D semi-analytical ax-
servations(Keene&Masson1990;Terebeyetal.1993;Looney isymmetricmodelsofcollapsingrotatingenvelopeanddiskfor-
et al. 2003; Jørgensen et al. 2009; Enoch et al. 2011). How- mation as described in Visser et al. (2009) with modifications
ever, precise determination of stellar masses requires spatially introduced in Visser & Dullemond (2010) and Harsono et al.
andspectrallyresolvedmolecularlineobservationsoftheveloc- (2013) are also simulated. These models are based on the col-
itygradientintheinnerregionsofembeddedYSOs(Sargent& lapseanddiskformationsolutionsofTerebeyetal.(1984),and
Beckwith1987;Ohashietal.1997;Brinchetal.2007;Lommen Cassen & Moosman (1981) including a prescription of an out-
et al. 2008; Jørgensen et al. 2009; Takakuwa et al. 2012; Yen flow cavity. The disk evolution follows the α-disk formalism
Articlenumber,page2of16
D.Harsonoetal.:Testingprotostellardiskformationmodels
Table1.Stellar(M ),envelope(M ),anddisk(M )massesforthethreesimulations.R istheextentoftherotationallysupporteddiskforeach
(cid:63) env d d
simulation.
Model M M Ω λ M R
(cid:63) env d d
[M ] [M ] [s−1] [M ] [AU]
(cid:12) (cid:12) (cid:12)
3DMHDRSD 0.38 0.29 10−13 10 0.06 250–300
3DMHDNoRSD 0.24 0.35 10−13 10 0.13* ...
2DRSD 0.35 0.32 10−13 ... 0.04 65
Notes.(*)Massofpseudo-diskisthesumoftheregionswithnumberdensitiesn >107.5cm−3;noradiusistabulatedforthiscase.
H2
5 6 7 8 9 10 11 12 15 23 35 54 84 129 199 306
Logn(H2)[cm−3] Tdust [K]
RSD
150
4 0 4 0
25 25
0
150
−
No RSD
150
40 40
U] 25 25
A 0
[
z
150
−
2D Model
150
4 4
0 0
0
150
−
150 0 150 150 0 150
− −
R [AU]
Fig.1.Densityanddusttemperaturestructuresintheinner200AUradiusforallthreesimulationsatt ∼1.2×105years.Temperaturecontours
at25Kand40Kareindicatedintherightpanels.Top:Averticalslice(R−zsliceatφ = 0whereRdenotesthecylindricalradialcoordinate)
of the 3D MHD simulation of RSD formation. Middle: A vertical slice of the 3D MHD simulation of a pseudo-disk (No RSD). Bottom: 2D
semi-analyticaldiskformationmodel.TheredlineshighlighttheregionofthestableRSD.
as described in Shakura & Sunyaev (1973) and Lynden-Bell & showsthephysicalstructureofthe2Dsemi-analyticalmodelat
Pringle(1974).Thedisksurfaceisdefinedbyhydrostaticequi- thetimewhena∼65AUradiusRSDispresent.
librium as described in Visser & Dullemond (2010) and is as- Amajordifferencebetweenthe2Dsemi-analyticalaxisym-
sumedtobeinKeplerianrotation.Inordertocomparewiththe metricmodelandthe3Dsimulationsistheoutflowcavity.The
MHDsimulations,weconsiderthecollapseof1 M ,c = 0.26 photon propagation is still treated in 3D. Although outflowing
(cid:12) s
kms−1,andΩ =10−13Hzcore.Thesoundspeedinthiscaseis gasispresentinthepseudo-disksimulation(NoRSD),thecav-
0
higher than that used in Li et al. (2013), which affects the final ityremainsfilledwithhighnumberdensity(105cm−3)gaswhile
diskpropertiesattheendoftheformationprocess.Thesynthetic lower density (102−3 cm−3) gas occupies the cavity in the 2D
observablesareproducedatt=3.9×1012s.ThebottomofFig.1 model. The outflowing gas generated from angular momentum
conserving gas in the pseudo-disk model has relatively low ve-
Articlenumber,page3of16
A&Aproofs:manuscriptno.harsono14
Fig. 2. Velocity streamlines for the two MHD simulations in Li et al. (2013). The simulations are rendered with paraview (http://www.
paraview.org). Left: 3D MHD simulation of a collapsing uniform sphere with the magnetic field vector perpendicular to the rotation axis.
Right:Thesimulationwithmagneticfieldvectoralignedwiththerotationaxis.Thecolorofthearrowsindicatetheazimuthalvelocityvector,υ ,
φ
inkms−1.Thesolidblackarrowsindicatethegeneralstreamlinesinthetwosimulations.Thedarkshadedcolorsindicatethedensityisocontours
ofn =107.5cm−3upto1010.5cm−3(red).
H2
ilyinhydrostaticequilibrium.ThiscanbeclearlyseeninFig.3
8
υφ RSD for the 3D simulation where υr/υθ does not satisfy the hydro-
6 υr No RSD static disk criterion along a few azimuthal angles. Using these
2D Model criteria,anRSDupto260AUisfoundinthemis-alignedsimu-
4 lation.Theextentofthe3DRSDis300AUifvφ > 1kms−1 is
1] used.Withtheformercriterion,thediskmassescontainedwithin
−
s 2 sucharegionare0.06 M(cid:12) forthe3DRSDand0.04 M(cid:12) forthe
m 2D RSD surrounding 0.38 M and 0.35 M stars, respectively
k (cid:12) (cid:12)
[ 0 (see Table 1). As Fig. 3 shows, the radial velocity component
υ
of the pseudodisk is a significant fraction of the Keplerian ve-
2 locity.Duetosuchhighradialvelocities,thesurfacedensityof
−
thepseudodiskremainslow.However,thetotalmassofthehigh
4 density regions (n > 107.5 cm−3) is a factor of 2 higher than
− H2
theRSDmass.
10 100 1000
r [AU]
2.4. Observablesandradiativetransfer
Fig.3.Radial(solid)andazimuthalvelocities(dashed)atthemidplane
(θ=π/2,φ=0)forthethreedifferentmodels:3DRSDMHDsimula-
Thefirststepbeforeproducingobservablesisthecalculationof
tion(blue),3DNoRSD(red),and2Dmodel(green).
thedusttemperaturestructure,whichiscriticalforthemolecular
abundancessinceitcontrolsthefreeze-outfromthegasontothe
dust.Thedusttemperatureiscomputedusingthe3Dcontinuum
locitiessuchthatitdoesnotclearoutthecavity.Asaresult,the
radiative transfer code RADMC3D1 with a central temperature
dusttemperaturealongthecavitywallishigherinthe2Dmodel
of 5000 K, which is the typical central temperature in the 2D
due to the direct illumination of the central star. This is readily
semi-analyticalmodelsataroundtheendofStage0phase.The
seen in the 40 K contour in Fig. 1 where it is elongated in the
central luminosity is fixed at 3.5 L for all models. The dust
z direction in the 2D case. However, we show in Section 4 that (cid:12)
thisdifferencedoesnotaffecttheresultsofthispaper. opacitiesusedarethosecorrespondingtoamixofsilicatesand
graphitegrainscoveredbyicemantles(Crapsietal.2008).The
3DMHDsimulationfromLietal.(2013)hasaninnerradiusof
2.3. Rotationallysupporteddisksizesandmasses 1014 cm(6.7AU)whilethesemi-analyticalmodelhasaninner
radiusof0.1AU.Thesimulatedobservablespresentedhereare
TheextentoftheRSDinthe2Dsemi-analyticalmodelisdefined
notsensitivetothephysicalandchemicalstructuresintheinner
by hydrostatic equilibrium. Using these properties, the RSD is 10 AU radius. Thus, these differences do not affect the conclu-
defined by a region with densities > 107.5 cm−3 and azimuthal
sions of this paper. The same opacities and central temperature
velocities υ > 1.2 km s−1. The disk evolution in 2D follows
φ are adopted for all simulations in order to focus on the general
the alpha-disk formalism with α = 10−2, which in turns define features of the observables. The gas temperatures are assumed
theradialvelocitiesasυr/υφ ∼ α(H/R)2 ∼ 10−3 where H isthe to be equal to the dust temperatures, which is valid for the op-
disk’sscaleheight.Similarcriteriaareusedtoextracttheextent
of the RSD in the 3D simulation with the additional constraint
ofvφ > vr.Notethatweapplythecriteriafromthe2Dmodelto 1 http://www.ita.uni-heidelberg.de/~dullemond/
define the RSD in the 3D simulation, thus it is is not necessar- software/radmc-3d
Articlenumber,page4of16
D.Harsonoetal.:Testingprotostellardiskformationmodels
tically thin lines simulated here that trace the bulk mass where
RSD NoRSD
T ∼T (Dotyetal.2002;Dotyetal.2004).
gas dust 2
1
CO abundance. In this paper, we concentrate on simulating 0
CO molecular lines of J = 2–1, 3–2, 6–5, and 9–8. For sim-
plicity, the 12CO abundance is set to a constant value of 10−4
2 450
with respect to H except in regions with T < 25 K, where −
2 dust
2
it is reduced by a factor of 20 to mimic freeze-out (Jørgensen
0
et al. 2005; Yıldız et al. 2013). We adopt constant isotopic ra-
tiosof12C/13C= 70,16O/18O= 540,and18O/17O= 3.6(Wilson 0 ]
2
−
& Rood 1994) to compute the abundance structures of the iso-
topologs. DEC[”] −22 850 arcsec
y
Synthetic images. This paper presents synthetic continuum ∆ 1 J
− [
mapsat450,850,1100,and1300µm.Theimagesarerendered 0 Iν
using RADMC3D with an image size of 8000 AU at scales of
5AUpixels.Theyareplacedatadistanceof140pc.Synthetic
2 1100
imagesatinclinationsof0◦ (face-on;downthez-axis),45◦,and −
90◦ are produced. The latter option is included because one of 2
theclaimedembeddeddisksourcesisclosetoedge-on(i∼90◦, 3
−
L1527 in Tobin et al. 2012). For the synthetic molecular lines, 0
the local thermal equilibrium (LTE) population levels are com-
puted using the partition functions adopted from the HITRAN
2 1300
database (Rothman et al. 2009). LTE is a good assumption be- −
2 0 2 2 0 2
causethedensitiesinthesimulationsaregreaterthanthecritical − −
densitiesofthesimulatedtransitions.Non-LTEeffectsmayplay ∆RA [”]
aminorroleforsyntheticJ ≥6linesfromthepseudo-disksim-
u
Fig.4.Continuumintensitymapsof450,850,1100,and1300µmfor
ulationduetoitslowerdensitiesrelativetotheothertwosimu-
theMHDdiskformationsimulation(leftpanels)andpseudo-disk(No
lations. The line optical depth (τ ) is also not expected to play
L RSD,rightpanels)ati = 45◦ at5AUpixels.Notethelargedynamic
a role since the focus of this paper is on the minor isotopologs
rangeneededtoseeallofthestructures.
andonthekinematicsdominatedbythelinewingswheretheir
lineopticaldepthsarelowerthanatthelinecenter.Theproper-
tiesofthemolecules(E and A )aretakenfromtheLAMDA
up ul
database (Schöier et al. 2005). Only thermal broadening is in- 0.05mJybm−1at1100µmcanbeachievedatspatialresolutions
cludedinsimulatingthemolecularlineswithoutanyadditional ≤0.1(cid:48)(cid:48)for30minutesofintegration(1.8GHzbandwidth).Inad-
microturbulence.Theimagecubesarerenderedataspectralres- dition,ahighdynamicrangeof>1000(σ= 0.001×S )can
olution of 0.1 km s−1 covering velocities from -7.5 to 7.5 km peak
also be achieved. Figure 5 presents the images convolved with
s−1. In order to simulate observations, the synthetic images are a0.1(cid:48)(cid:48) beamforthetwo3DMHDsimulations(right-mostpan-
thenconvolvedwithGaussianbeamsbetween0.1(cid:48)(cid:48) to20(cid:48)(cid:48).The
els). The color scale indicates the full range of emission, while
convolution is performed in the Fourier space with normalized
the red solid lines show the region above 3σ where σ is either
Gaussianimages.
dynamicallylimitedto1000ortotheσvalueslistedabove.This
simplymeansthatthesolidredlinesindicatethedetectablefea-
tures.Withacombinationofhighdynamicrangeandsensitivity,
3. Continuum
the features of the collapse are observable and distinguishable
3.1. ImagesandprospectsforALMA inboth450µmand1100µmcontinuummaps.Ataspatialres-
olution of 0.1(cid:48)(cid:48), most of the emission at 1100 µm is due to the
Continuumimagesarerenderedatfourwavelengthsandviewed
rotationally supported disk with a small contribution from the
at three different inclinations. Figure 4 presents the synthetic
surroundingenvelope.
450, 850, 1100 and 1300 µm continuum images at an inclina-
tion of 45◦ for the two 3D MHD simulations. The left panels AsFigs.4and 5show,boththestrengthofthefeaturesand
presenttheimagesfrom3DRSDsimulationwhiletherightpan- theirextentchangewithwavelength,asindicatedbytheredline
elsshowimagesfromthepseudo-disksimulation(labeledasNo contours.Witharesolutionof0.1(cid:48)(cid:48),theextentofthedetectable
RSD).Thefeaturesproducedduringthecollapseareclearlyvisi- emissiondecreasesfrom1.5(cid:48)(cid:48) at450µmto<1(cid:48)(cid:48) at1100µmfor
bleinthe450µmmap;mostofthemaretwoordersofmagnitude the RSD case. At long wavelengths, the dust emission is given
fainterat1300µm.Thespiralstructureinthe450µmimageis byIν ∼Tdustν2×(1−e−τdust).Sincethedustemissionisoptically
due to magnetically channelled, supersonically collapsing ma- thinatlongwavelengths,theintensityis∝T ν2τ .Thevari-
dust dust
terial on its way to the RSD, rather than a feature of the RSD ables that depend on position are T and τ ∝ ρ κ . The
dust dust dust ν
itself. frequencydependenceoftheopacityisκ ∝ν1.5 fortheadopted
ν
One of the aims of this paper is to investigate whether opacitytable.Theextentofthedetectableemissiondependson
these features are observable with current observational lim- thesequantities.Atoneparticularposition,theratiooftheemis-
its and what is possible with future Atacama Large Millime- sionatthetwowavelengthsissimplyI /I ∝ν3.5.Thus,
450µm 1100µm
ter/submillimeter Array (ALMA) data. With the full ALMA, a thepredicteddifferenceinsizeatthetwowavelengthsisdueto
sensitivity of σ=0.5 mJy bm−1 (bm = beam) at ∼ 450 µm and thefrequencydependenceoftheemission.
Articlenumber,page5of16
A&Aproofs:manuscriptno.harsono14
S450µm [Jy/bm] S1100µm [Jy/bm]
5 4 3 2 1 5 4 3 2 1
− − − − − − − − − −
2 2
R R
0 S 0 S
D D
”] 2 ”] 2
C[− C[−
E E
D D
2 2
∆ ∆
N N
o o
0 R 0 R
S S
D D
−2 100 0.500 0.100 −2 100 0.500 0.100
2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2
− − − − − −
∆RA [”] ∆RA [”]
Fig.5.Convolvedcontinuummapsintheinner5(cid:48)(cid:48) of450(left)and1100(right)µmati = 45◦.Theimagesareconvolvedwith1(cid:48)(cid:48),0.5(cid:48)(cid:48),and
0.1(cid:48)(cid:48) beamsasindicatedineachpanel.Foreachpanel,thetoprowshowssyntheticimageofRSDsimulationandthepseudo-disksimulationis
showninthebottomrow.Thecolorscalepresentsthefullrangeoftheemissionabove10−2mJy/bm,notallofwhichmaybedetectable.Solidred
contoursaredrawnfrom3σuptomaximumat6logarithmicstepswhere1σis0.01×themaximum(dynamicalrangeof100)withaminimum
at0.5mJy/bmforthe1(cid:48)(cid:48)and0.5(cid:48)(cid:48)images.Fortheimagesconvolvedwitha0.1(cid:48)(cid:48)beam,theredcontoursaredrawnwithaminimumnoiselevelof
0.5mJy/bmfor450µmand0.05mJy/bmatlongerwavelengthswithadynamicrangeof1000,asappropriateforthefullALMA.
For ALMA early science observations (cycles 0 and I), the S850µm [Jy/bm]
capabilitiesprovidedadynamicrangeonlyupto100ataspatial 4 4 3 2
− − − −
resolution of ∼ 0.5(cid:48)(cid:48). Figure 5 presents synthetic 450 and 1100
RSD NoRSD 2Dmodel
µm images convolved with 1(cid:48)(cid:48) and 0.5(cid:48)(cid:48) beams, compared with
the 0.1(cid:48)(cid:48) beam images. The color scale again indicates the full 2
range of emission, while the red solid lines now show the re-
gionabove3σwherethenoiselevel,σ,isdynamicallylimited 0 0.5
to 100 with a minimum of 0.5 mJy/beam at both wavelengths. 00
The red lines again present the observable emission. The 450 ”]
µm images convolved with a 1(cid:48)(cid:48) beam show an elongated flat- C[−2
E
tened structure for both RSD and pseudo-disk simulations and D 2
arethereforeindistinguishable.Mostoftheemissionat1100µm ∆
and longer wavelengths is not detectable at the assumed noise 0
level of 0.5 mJy bm−1. A similar result is found after convolu- 0 00.1
tionwitha0.5(cid:48)(cid:48)beam.Althoughthesyntheticobservationsfrom
the pseudodisk indicate a ‘cometary’ structure, this may be af- 2
−
fected by the presence of outflow cavity which is absent in the
2 0 2 2 0 2 2 0 2
case of RSD. Thus, the full ALMA capabilities are needed to − − ∆RA [”] −
distinguishmodelsbasedoncontinuumdataonly.
Fig.6.Synthetic850µmcontinuumimagesconvolvedwith0.5(cid:48)(cid:48) (top)
and0.1(cid:48)(cid:48)(bottom)beamsforthethreesimulationsviewedat90◦(edge-
on):RSDformation(left),pseudo-disk(center),and2Dsemi-analytical
3.2. Inclinationeffects
model(right).Theredsolidlinesaredrawnatthesamecontoursasin
The images for a face-on system (i = 0◦) are similar to those Fig.5.
ofthemoderatelyinclinedsystem(i = 45◦)presentedinFig.5.
For low inclinations between 0 to 45◦, the continuum images differenceistheextentoftheelongatedemissionwherethe2D
onlychangeslightlyintermsofabsolutefluxdensityandshow modelpredictsaverycompact(∼1(cid:48)(cid:48) radius)structurewhilethe
asmallelongationduetoorientation. pseudo-disk component shows an extended flattened structure
Incontrast,thetwosimulationsrenderedatedge-on(i∼90◦) (≤ 2(cid:48)(cid:48)). This illustrates the difficulties in testing disk formation
geometryexhibitsimilarcompactcomponentsevenatthehigh- models for highly inclined systems based solely on continuum
estangularresolution(Fig.6).Theybothshowanelongatedflat- data.
teneddisk-likeemissionsimilartothe2Dsemi-analyticalmodel.
ThissignaturesuggestsanRSD,butitisduetothepseudo-disk
4. Molecularlines
producedinthe3DMHDsimulationwhoseinitialmagneticfield
vector is aligned with rotation axis. The peak continuum emis- Thecontinuumemissionarisesfromthermaldustemissionand
sion of the pseudo-disk is a factor of 10 lower than that of the doesnotcontainkinematicalinformation.Asshowninthepre-
other two models while it is similar between the 3D RSD and vious section, a compact flattened structure is expected in the
the2Dsemi-analyticalmodels(differenceof< 10%).Themain continuummapsintheinnerregionsofallthreemodels.Kine-
Articlenumber,page6of16
D.Harsonoetal.:Testingprotostellardiskformationmodels
maticalinformationascontainedinspectrallyresolvedmolecu- benoiselimitedatthelinewingssincetheyareweakerthanthe
larlinesisessentialtodistinguishthemodelsandtoderivestel- emission near the line center for typical observations with 1–2
lar masses. The rotational lines of CO isotopologs are used to hoursintegrationtime.
investigatethis. Figure 7 presents synthetic first moment (flux-weighted ve-
Therotationallinesof13CO,C18O,andC17Oaresimulated. locity)maps.Themomentzerocontoursat20%ofpeakintensity
CO is chosen since its abundance is less affected by chemical indicatetheelongationdirection.Theflatteneddensitystructure
evolution during disk formation. We do not investigate 12CO is oriented in the east-west direction (horizontal) for all three
linessincetheyaredominatedbytheentrainedoutflowmaterial modelsasseeninFig.1.Coherentvelocitygradientsfromblue-
and are optically thick. The isotopolog lines are more optically tored-shiftedvelocityareseeninallthreemodelsbutnotneces-
thin and are expected to probe the higher density region where sarilyinthesamedirection.ThepresenceofanembeddedRSD
the disk is forming. These predicted spatially resolved molec- isrevealedinthe3DRSDand2Dmodelbythecoherentblue-to
ular line maps can be compared with ALMA data. Moreover, red-shiftedvelocitygradientintheeast-westdirectionsimilarto
highqualityspectrallyresolvedCOisotopologlinesprobingthe theflatteneddiskstructure.Ontheotherhand,inthepseudo-disk
larger-scale envelope toward low-mass embedded YSOs have simulation, the velocity gradient is in the north-south direction
beenobtainedwithsingle-dishtelescopes(see§1).Thecharac- similar to the continuum image as shown in Fig. 5 (right-most
terizationoftheseC18OandC17Olineprofilesprovideatestfor panels).Suchvelocitygradientscanbemistakentobealongthe
the kinematical and density structures of the collapsing proto- majoraxisofthediskwithouthigherspatialresolutionandsen-
stellar envelope on larger scales (e.g., Hogerheijde et al. 1998; sitivitydata.
Jørgensenetal.2002). Anumberofeffectsconspiretogenerateavelocitygradient
alongtheminoraxisoftheflattenedstructureinthepseudo-disk
simulation. First, since the magnetic braking is efficient in this
4.1. Momentmaps:RSDsornot?
case,thedominantmotionofthematerialisintheradialdirec-
tion (see Figs. 2 and 3). Second, the flattened structure in this
particular simulation has lower-density gas than the RSD sim-
υ [km s−1] ulation (see Section 2.1). The n > 106.5 cm−3 region extends
−2.0 −1.0 0.0 1.0 2.0 upto700AUinsizeandatanaHn2glewithrespecttotherotation
RSD NoRSD 2DModel axis(seeFig.1).Thus,thenorth-southdirectioninthepseudo-
disk model shows the infalling material along the streamlines
1
Ju =2 connectingthelarge-scaleenvelopeandthecentralstar.
At moderate inclinations, the pseudo-disk simulation there-
0
foreshowsacoherentvelocitygradientinamore-or-lessstraight
north-south line. The velocity gradient changes to an east-west
”] 1
C[− directionathighinclinations.Athighinclinations,theobserver
E has a direct line of sight on the high density region shown in
D
∆ 1 Ju =6 Fig. 1 and therefore the line emissions pick up the rotational
motions of the flattened structure similar to the RSD simula-
0 tions. Furthermore, the skewness that is present in the moment
one maps of RSD simulations largely disappears at high incli-
1 nations for the same reason. Thus, it is difficult to separate the
−
envelope from the disk for high inclinations (almost edge on)
1 0 1 1 0 1 1 0 1 frommomentonemapalone.
− − ∆RA [”] −
Fig.7.MomentonemapsofC18O2–1(top)and6–5(bottom)forthe
4.2. Velocityprofiles
threesimulationsviewedi=45◦convolvedwitha0.1(cid:48)(cid:48)beam.Thesolid
(cid:82)
lineshowsthe20%intensitycontourofthemomentzero( Sυdυ)peak 4.2.1. PVcuts
maptoindicatetheflattenedstructure.Theblackdashedlinesindicate
directionatwhichthePVslicesareconstructedandthedirectionofthe Observationally,thepresenceofembeddedKepleriandisksisof-
elongationinthemomentzeromaps. tenestablishedbyconstructingpositionvelocity(PV)diagrams
alongthemajoraxisofthesystemasseeninmomentzeromaps.
Observationally,thekinematicalinformationoftheinfalling Intheory,thePVanalysisisstraight-forward.Itissymmetricin
envelopeandRSDisinferredthroughmomentmaps.Elongated both position and velocity space (4 quadrants are occupied) if
momentzero(velocityintegratedintensity)mapsgiveanindica- the system is infall dominated (e.g., Ohashi et al. 1997; Brinch
tionofthepresenceofaflattenedstructurethatisassociatedwith etal.2008).Thesymmetryisbrokenifrotationispresentandthe
a disk. Meanwhile, coherent velocity gradients in the moment emissionpeaksareshiftedtolargeroffsetscorrespondingtothe
one (velocity weighted intensity) map may point to a rotating strengthoftherotationalvelocities(2quadrantsareoccupied).
component. Analysis of synthetic moment maps of the simula- Figure8presentssyntheticPVdiagramsalongthemajoraxis
tions are presented and compared in this section. We focus on ofthediskwhereitcorrespondstothedirectionoftheblue-to
presentingthesynthetic‘interferometric’mapsofopticallythin red-shifted velocity gradient. For the images in Fig. 7, an east-
C18OandC17Olinesbyconvolvingtheimagecubeswitha0.1(cid:48)(cid:48) west slice (horizontal) is taken for the RSD simulations, while
Gaussian beam. The construction of moment maps only takes anorth-south(vertical)sliceisadoptedforthecaseofthesim-
intoaccountemission>1%ofthepeakemission.Thistranslates ulationwithoutanRSD(NoRSD).Theseslicesarenotexactly
toanoiselevelof0.3%ofthepeakemission.AlthoughALMA the major axis of the moment zero map, however these direc-
canachieveadynamicrangeof> 500,itismorelikelythatthe tions pick up most of the velocity gradient present in the inner
molecularlinesofminorisotopologsfromlow-massYSOswill 1(cid:48)(cid:48). Both C18O and C17O lines are simulated. Interestingly, the
Articlenumber,page7of16
A&Aproofs:manuscriptno.harsono14
RSD NoRSD 2DModel RSD NoRSD 2DModel
3.0 C18O i=45◦ 3.0 C17O i=45◦
Ju =2 Ju =2
1.5 1.5
0.0 0.0
1.5 1.5
− −
”] ”]
[ 3.0 [ 3.0
t− t−
e e
s 3.0 s 3.0
ff ff
O Ju =6 O Ju =6
1.5 1.5
0.0 0.0
1.5 1.5
− −
3.0 3.0
− −
4 2 0 2 4 4 2 0 2 4 4 2 0 2 4 4 2 0 2 4 4 2 0 2 4 4 2 0 2 4
− − −υ−[km s−1] − − − − −υ−[km s−1] − −
Fig.8.PVmapsofC18O(left)andC17O(right)alongthevelocitygradientsasseeninFig.7foraninclinationof45◦and0.1(cid:48)(cid:48)beam.Thetoppanels
showtheJ=2–1lineandthebottompanelsshowthe6–5transition.ThebluerectangleindicatestheradiiofRSDs.Thedashedlinesindicatethe
inclinationcorrectedKepleriancurvesassociatedtothestellarmass.Theredcolorscalesshowemissionfrom10%tothepeakintensity.
PVslicessuggestthatrotationalmotionsarepresent regardless Peakpositionsaredeterminedforeachofthevelocitychan-
ofwhetheranRSDispresentornot.Thisismostreadilyseenin nel maps for each molecular line for the red and blue-shifted
theC17OPVmaps(rightofFig.8)inwhichonly2ofthe4quad- componentsseparatelytakingintoaccountchannelswhosepeak
rants are occupied by molecular emissions for all three models flux density (S in Jy bm−1) are > 1% of S . They are sub-
ν max
at i = 45◦. This shows that C17O emission readilypicks up the sequentlyrotatedaccordingtothedirectionofthevelocitygra-
rotational motion at small-scales but also that infalling motion dient.IfanRSDispresent,thepeakpositionsofbothred-and
canbeconfusedwithrotationifthewrongdirectionforthePV blue-shifted velocities are expected to follow the Keplerian ve-
cutischosen(NoRSDmodel). locity profile (υ ∝ r−0.5). The combination of infalling rotating
TheC18OPVmapsindicatecontributionsfromtheinfalling envelope and RSD, which exhibits a skewness in the moment
envelopesincethemapsaremoresymmetricthanthoseinC17O. onemap,isexpectedtoshowasteepervelocityprofile(υ∝r−1)
The C18O PV slices of the pseudo-disk simulations indicate an (Yenetal.2013).However,athighvelocities,thepeakpositions
infall-dominated structure in which the 4 quadrants are occu- ofthered-andblue-shiftedvelocitiescanbemisalignedatscales
pied.Ontheotherhand,thereisaclearindicationofarotating of5AUduetothelimitedspatialresolution.Thediskradiusis
componentforthetwoRSDsimulationsinwhichonly2ofthe4 determined by minimizing the difference (∼ 10%) between the
quadrantsarefilledatsmallradii.Thissuggeststhatspatiallyand best-fitstellarmassinsideandatthediskradius.
spectrallyresolvedC18Olinescandistinguishbetweenapseudo- The peak position-velocity diagrams (PPVs) for C18O 6–5
diskandanRSD. and C17O 2–1 are shown in Fig. 9. These lines are chosen be-
causetheyrepresenttwoobservationalextremesintermsofex-
Figures8comparesthePVmapsofthe2–1and6–5transi-
citation and optical depth. There is a clear distinction between
tions. Most of the emission in the 6–5 transition occupies only
theRSDsimulationsandapseudo-disk.Thevelocityprofileof
2ofthe4quadrantsindicatingsignaturesofrotationalmotions,
thepseudo-diskismuchflatterthanthatexpectedfromanRSD.
whereas the 2–1 lines also show some emission in the other 2
Thus,spatiallyandspectrallyresolvedmolecularlinesobserva-
quadrants from larger scales. This is a clear indication that the
tions can clearly differentiate between an RSD and a pseudo-
6–5 line is a better probe of the rotational motions in the in-
disk.
ner 100 AU than the 2–1 line. Yet, a combination of spatially
AllthreePPVsindicateavelocityprofileclosetoυ ∝ r−0.5
and spectrally resolved molecular lines are needed to confirm
(forthepseudo-diskseeC17O2–1PPVintheinner20AU).This
thepresenceofembeddedrotationallysupporteddisk.
reflects the fact that the inner 300 AU of the models is domi-
natedbyvelocitystructurethatisproportionaltor−0.5,whichis
(cid:18) (cid:113) (cid:19)
4.2.2. Peakposition-velocitydiagrams both the radial velocity υ ∝ 2GM(cid:63) and angular velocity
infall r
While it is clear that there is indeed a rotating component for (cid:18) (cid:113) (cid:19)
υ ∝ GM(cid:63) (Brinchetal.2008).Fromsuchcharacterization,
somemodels,thequestioniswhethertheextentoftheKeplerian rot r
structure can be extracted from such an analysis. A Keplerian thestellarmassescanbecalculatedandindicatedinthetopright
rotating flattened structure exhibits a velocity profile υ ∝ r−0.5, cornerofFig.9.Ingeneral,thebest-fitstellarmassesinthecase
wherer isthedistancefromthecentralsource.Thesepositions of RSD are within 30% of the true stellar masses tabulated in
are either determined from fitting interferometric visibilities of Table 1. This is not so for the 2D model in the C18O 6–5 and
each velocity channel (Lommen et al. 2008; Jørgensen et al. alsoC17O6–5(notshown)duetothefactthattheinnerflattened
2009)ordeterminationofthepeakpositionsintheimagespace envelopeiswarm(>40K)anddense.
(Tobinetal.2012;Yenetal.2013).Weheredeterminethepeak Anotherparameterthatonewouldliketoextractisthedisk
positionsdirectlyintheimagespacetoassesswhetheravelocity radius, R , as indicated by the vertical solid line in Fig. 9. The
d
profileisvisibleinthesyntheticmolecularlines. breakatR isreadilyseeninthe2Dmodelat∼ 40AUforboth
d
Articlenumber,page8of16
D.Harsonoetal.:Testingprotostellardiskformationmodels
Fig.9. Peakposition-velocitydiagramsof
C18O 6–5 (top) and C17O 2–1 (bottom) at
i =45◦ afterconvolutionwitha0.1(cid:48)(cid:48) beam.
Theredandbluesymbolscorrespondtothe
red- and blue-shifted velocity components,
respectively.Thedifferentpanelspresentthe
C18O6-5 RSD NoRSD 2DModel PPV for the different simulations. Vertical
1]− M? =0.31M(cid:12) M? =0.10M(cid:12) M? =1.03M(cid:12) sthoelidthlirneeesmshoodwelstheanddiskdarashdeiidexlitnraecstesdhofowr
ms ∝r−0.5 the steep velocity profile (υ ∝ r−1) while
υ[k 1 ∝r−1 tchuervseosl.idThceyasntellilnaresmiansdsiecsataerethiendKiceaptleedriainn
the top right of each panel. The offset be-
10 100 10 100 10 100 tween blue- and red-shifted points are due
tothelimitedspatialandspectralresolution
Distance from center [AU]
atthehighvelocities.
C17O2-1 RSD NoRSD 2DModel
1]− M? =0.32M(cid:12) M? =0.16M(cid:12) M? =0.39M(cid:12)
ms ∝r−0.5
[k 1 ∝r−1
υ
10 100 10 100 10 100
Distance from center [AU]
C18O6–5andC17O2–1.Forthecaseofthe3DMHDsimulation infallingmaterialontothediskwhileaP-Cygniprofileisassoci-
(RSD), the best-fit radius varies between 100 and 300 AU. It atedtothepseudo-disk,whichistracingtheexpandingmaterial
also exhibits a steep velocity profile (υ ∝ r∼−1) at radii > 100 duetooutflowingmaterialpresentinthepseudo-disksimulation.
AU.Thelargerangeofdiskradiiisduetotheenvelopeemission Self-absorptioncausesthedoublepeakinthe13CO3–2linedue
overwhelmsthemolecularemissionbecauseCOisfrozenoutin to optical depth (typically, τ > 5) at line center whereas it is
L
the cold part of the disk at those large radii. The issue of disk weaklyaffectingtheC18O3–2line.
versusenvelopeemissionbecomesapparentinthecaseoflarge Itisinterestingtonotethatthereisnosignificantdifference
embeddeddisk(Rd >100AU). inthe6–5linesbetweenasimulationthatformsanRSDversusa
ThecomparisonshowsthatthereisacleardistinctPPVpro- pseudo-disk.Thistransition(E ∼110K)tracesthedensewarm
u
file associated with RSD formation from r−0.5 to r−1. A steep gas where a large fraction of the emission comes from ≥ 40 K
velocity profile (υ ∝ r−1) is absent in the pseudo-disk simula- gas (Yıldız et al. 2010). The P-Cygni line profile is still visible
tion. This seems to indicate that such a steep velocity profile in the 13CO line, however it is not significant in the C18O line.
describes on-going RSD formation based on the given simula- The lines are also not Gaussian with significant wing emission
tions. A pseudo-disk is characterized by a flat velocity profile extendingupto±2kms−1.
intheinnerregions.Furthermore,thePPVmethodcansimulta- Thelineprofilesforthesemi-analyticalmodelswithina9(cid:48)(cid:48)
neouslyderivethestellarmassandtheextentoftheRSDwhile beam are shown in the bottom of Fig. 10. They are signifi-
separatingtheinfallingrotatingenvelopefromit.Withrespectto cantly different from the 3D MHD models, which arises from
differentiatingbetweenRSDandnon-RSD,PPVisabettertool the prescribed velocity structure. In Harsono et al. (2013), an
thanPV-diagrams. additionalmicroturbulentbroadeningof0.8kms−1 wasadded,
which results in Gaussian line profiles consistent with the ob-
served single-dish CO line profiles. However, in this paper, we
4.3. Single-dishlineprofiles
havenotincludedtheadditionalbroadeningterminordertoin-
The previous sections focus on features at small-scales as ex- vestigatetheemissionarisingfromthetruekinematicalinforma-
pected from interferometric observations. The next assessment tion.Thepeaksaremoreprominentthanthoseinthe3DMHD
istocomparethesyntheticmolecularlineswithsingle-dishob- simulationsduetoajumpbetweenthevelocitystructuresofthe
servations which probe the physical structure of the large-scale RSD component and the infalling envelope. In general, the 2D
envelope on scales up to a few thousand AU. The image cubes semi-analytical models produce significantly broader lines and
are convolved with 3 different beams: 9(cid:48)(cid:48), 15(cid:48)(cid:48), and 20(cid:48)(cid:48). These significantvariationsbetweentheCOisotopologsandtransitions
differentbeamsaretypicalforsingle-dishCOobservationsusing compared with 3D simulations because of a warmer disk and
theJCMT(15(cid:48)(cid:48)),AtacamaPathfinderEXperiment(APEX,9(cid:48)(cid:48)), outflow cavity wall (see Section 2.2) which allow for stronger
and Herschel (20(cid:48)(cid:48)). Figure 10 presents the synthetic CO lines wingemissions.
(J = 3, 6, and 9) for the two MHD simulations viewed face-
u
on (i ∼ 0◦) convolved with a 9(cid:48)(cid:48) beam. The face-on orientation
4.3.1. Inclinationeffects
is considered first to compare with the line profiles in Harsono
etal.(2013)forthe2Dsimulation.Thelow-lyingtransitions(Ju The simulated lines viewed face-on may not pick up all of the
=3)probethekinematicsinthelarge-scaleenvelope. dynamics of the system. Figure 11 shows how the line profiles
Doublepeakedlineprofilesarepresentinthe13COandC18O changewithinclinationforthethreedifferentsimulationswithin
3–2regardlesswhetheranRSD ispresentornot.Forthe 13CO a15(cid:48)(cid:48) beam.Thelinesbecomebroaderwithincreasinginclina-
line,aninverseP-Cygnilineprofileisseenduetothecoherent tion as they readily pick up the different velocity components.
Articlenumber,page9of16
A&Aproofs:manuscriptno.harsono14
13CO C18O C17O i=45◦ i=90◦
1.0
Ju =3 NoRSRDSD 1.0 Ju =3 NoRSRDSD
0.5 2Dmodel
0.5
x0.0
u
Fl1.0 Ju =6 0.0
alized0.5 Flux 1.0 Ju =6
m d
Nor01..00 alize 0.5
Ju =9 m
r
o 0.0
0.5 N
1.0
0.0 Ju =9
2 0 2 2 0 2 2 0 2
− Ve−locity [km s−1] − 0.5
13CO C18O C17O
1.0 0.0
Ju =3
2 0 2 2 0 2
0.5 − Velocity [km−s−1]
x0.0 Fig.11.C18Olineprofilesforthedifferentsimulationsviewedati=45◦
Flu1.0 Ju =6 andi=90◦in15(cid:48)(cid:48)beam.
d
e Table 2. FWHM (FWZI as defined at 10% of the peak emission) in
maliz0.5 ksimmusl−a1tioofnsthveie1w3CedOaatnid=C4158◦O. lines within a 20(cid:48)(cid:48) beam for the MHD
r0.0
o
N1.0 13CO C18O
Ju =9
J RSD NoRSD RSD NoRSD
0.5
3–2 0.8(1.8) 1.1(2.2) 0.9(1.8) 0.9(1.9)
6–5 1.1(2.3) 1.0(2.2) 1.3(2.3) 0.9(2.2)
0.0 9–8 2.1(3.7) 1.2(3.9) 2.3(4.0) 1.0(3.9)
2 0 2 2 0 2 2 0 2
− Ve−locity [km s−1] −
Fig.10. Top: 13CO,C18O,andC17O3–2(top),6–5(middle),and9–8 theotherhand,inthecaseofpseudo-diskformation,bothradial
(bottom)spectraati ∼ 0◦ withina9(cid:48)(cid:48) beam.Thebluelineshowsthe andazimuthalvelocitiesareofequalimportance.Theoriginof
synthetic line from simulation with an RSD while the red line is the thelinebroadeningthereforedependsonwhetherornotanRSD
simulationwithoutanRSD.Bottom: Spectrallinesconvolvedwitha isforming.IfanRSDisindeedforming,theC18O9–8isbroad-
9(cid:48)(cid:48) beam simulated from 2D semi-analytical model viewed at face-on enedbyrotationalmotionsatmoderateandhighinclinations;at
orientation.
lowinclinations,infalldominatesthebroadening.
The J = 3 lines exhibit inverse P-Cygni line profiles that are 4.3.3. Linewidthsandcomparisonwithobservation
u
associated with infalling gas. Meanwhile, the higher J transi-
Molecularlineobservationsaretypicallycharacterizedbytheir
tionsshowmorestructuredlineprofilescomparedwiththesys-
temsviewedface-on.TheC18O6–5linesaredouble-peakedin peakfluxdensities(orintensities), FWHM,andintegratedline
flux densities. While the peak flux densities and integrated line
both cases of RSD formation while it is single-peaked for the
fluxes depend on the adopted physical and chemical structure,
pseudo-disk model. On the other hand, the 9–8 line is signifi-
their FWHM should reflect the general kinematics that are
cantlybroaderthanthelow-J linesreflectingthecomplexityof
presentinthesystem.Inthispaper,wefocusonthecomparison
thedynamicsofthewarmdensegas.
of FWHM andfull-widthatzerointensity(FWZI)determined
at 10% of the peak with observations. A 10% cut-off is chosen
4.3.2. Originofthelinebroadening since most single-dish observations do not reach higher signal-
to-noise,especiallyforthehigher-Jlines.
Toinvestigatethesourceofthelinebroadening,asetofmolec- These values are calculated for 13CO and C18O lines of the
ularlinesaresimulatedwithzeroradialvelocity(υr =0kms−1) differentmodelsfromtheconvolvedimagecubes.The FWHM
and another with zero azimuthal velocity (υφ = 0 km s−1). For and FWZI withina20(cid:48)(cid:48) beamarelistedinTable2atmoderate
theMHDsimulationwithRSD,the FWHM valueoftheC18O inclination (i = 45◦) comparing the two 3D MHD simulations.
9–8linedecreasesto<0.5kms−1atallinclinationswithoutany Within such a large beam, their values for 13CO and C18O are
azimuthal velocity component. Such a decrease is not dramatic similar.TheFWHMvaluesdonotnecessarilyincreasebetween
forface-onorientation,howeveritismorethanafactorof3for J =3 and 6, in contrast with the FWZI values (see Fig. 12).
u
intermediate(i ∼ 45◦)andhighinclination(i > 75◦)cases.On Thisisexpectedsincethewingemissionsaremuchlowerthan
Articlenumber,page10of16