ALMA observations and modeling of the rotating outflow in Orion Source I
J. A. López-Vázquez, Luis A. Zapata, Susana Lizano, Jorge Cantó
DDraft version October 2, 2020
Preprint typeset using L A TEX style AASTeX6 v. 1.0
ALMA OBSERVATIONS AND MODELING OF THE ROTATING OUTFLOW IN ORION SOURCE I
J.A. L´opez-V´azquez , Luis A. Zapata , Susana Lizano , and Jorge Cant´o Instituto de Radioastronom´ıa y Astrof´ısica, Universidad Nacional Aut´onoma de M´exico,Apartado Postal 3-72, 58089 Morelia, Michoac´an, M´exico Instituto de Astronom´ıa, Universidad Nacional Aut´onoma de M´exico,Apartado Postal 70-264, 04510, CDMX, M´exico
ABSTRACTWe present SiO(J=8–7) ν =0, SiS (J=19–18) ν =0, and SiO (J=8–7) ν =1 molecular line archiveobservations made with the Atacama Large Millimeter/Submillimeter Array (ALMA) of the molecularoutflow associated with Orion Source I. The observations show velocity asymmetries about the flowaxis which are interpreted as outflow rotation. We find that the rotation velocity ( ∼ − )decreases with the vertical distance to the disk. In contrast, the cylindrical radius ( ∼ ∼ − ), and the axial velocity v z ( ∼ -1–10 km s − ) increase with thevertical distance. The mass estimated of the molecular outflow M outflow ∼ (cid:12) . Given akinematic time ∼
130 yr, this implies a mass loss rate ˙M outflow ∼ . − × − M (cid:12) yr − . Thismassive outflow sets important contraints on disk wind models. We compare the observations witha model of a shell produced by the interaction between an anisotropic stellar wind and an Ulrichaccretion flow that corresponds to a rotating molecular envelope in collapse. We find that the modelcylindrical radii are consistent with the SiO(J=8–7) ν =0 data. The expansion velocities and theaxial velocities of the model are similar the observed values, except close to the disk ( z ∼ ±
150 au)for the expansion velocity. Nevertheless, the rotation velocities of the model are a factor ∼ Keywords: accretion – ISM: jets and outflows – stars: individual (Orion Source I, Kleinmann-LowNebula) – pre-main sequence INTRODUCTIONThe molecular outflows and the protostellar jets arepresent in the star formation process and appear to bemore powerful and collimated during the earliest phasesof young stellar sources (e.g., Bontemps et al. 1996),however, their origin is under debate. Two scenariosare proposed to explain the formation of the molecularoutflows. In the first case, several authors (e.g., Pudritz& Norman 1986, Launhardt et al. 2009, and Pech et al.2012), propose that the molecular outflows are ejecteddirectly from the accretion disk. Other authors suggest(e.g., Shu et al. 1991, Cant´o & Raga 1991, and Raga &Cabrit 1993), that the molecular outflows are a mixturebetween the entrained material with from the molecularcloud and a fast stellar wind.The magnetocentrifugal mechanism (Blandford &Payne 1982) is the principal candidate for producingjets and stellar winds (see reviews by K¨onigl & Pudritz2000 and Shu et al. 2000), in this mechanism, the ro-tating magnetic field anchored to the star–disk systemdrives and collimates these winds (Pudritz et al. 2007; Shang et al. 2007). Nevertheless, it is not clear wherethe magnetic fields are anchored to the disk. The mag-netocentrifugal mechanism has two different origins: X-wind (Shu et al. 1994) and disk winds (Pudritz & Nor-man 1983). In the first model, these winds are launchedclose to the star, from the radius where the stellar mag-netosphere truncates the disk. In the second model,these winds come from a wider range of the radii. An-derson et al. (2003) found a general relation betweenthe poloidal and toroidal velocity components of themagneto-centrifugal winds at large distances and the ro-tation velocity at the ejection point. Therefore, the ob-served rotation velocity of the jet could give informationabout its origin on the disk.In recent years, evidence of the rotation in protostellarjets and the molecular outflows has been found. Forexample, the jets HH 211 (Lee et al. 2009) and HH 212(Lee et al. 2017) present signature of the rotation of afew km s − . Molecular outflows with signature of therotation are: CB 26 (Launhardt et al. 2009), Ori-S6(Zapata et al. 2010), HH 797 (Pech et al. 2012), DG a r X i v : . [ a s t r o - ph . S R ] S e p Tau B (Zapata et al. 2015), Orion Source I (Hirota etal. 2017), HH 212 (Tabone et al. 2017), HH 30 (Louvet etal. 2018), and NGC 1333 IRAS 4C (Zhang et al. 2018).Zapata et al. (2015), argued that slow winds ejectedfrom large disk radii do not have enough mass, thus,these winds cannot account for the observed linear andangular momentum rates of the molecular outflow ofDG Tau B. Their argument assumed that the massloss rate of the wind is a small fraction f ∼ . M w ∼ f ˙ M d , a ). Never-theless, recent non-ideal magnetohydrodynamic simula-tions of magnetized disk winds show that this fractioncan be very large, f ∼ − M d ∼ . M (cid:12) (Guilloteau etal. 2011). Given the observed outflow mass loss rate1 . − . × − M (cid:12) yr − (de Valon et al. 2020), the disklifetime is τ = M d / ˙ M d , a = f M d / ˙ M w ∼ f (2 − × yr.Depending on the value of f , the disk lifetime could besmaller than the age of DG Tau B, which has been cat-aloged as a Class I/II source (Hartmann et al. 2005;Luhman et al. 2010).The large masses of the molecular outflows can beexplained if the outflow is formed mainly by entrainedmaterial from the parent cloud. L´opez-V´azquez et al.(2019), hereafter LV19, modeled the molecular outflowas a thin shocked shell, formed by the collision betweenan anisotropic stellar wind and a rotating molecularcloud in collapse, described by Ulrich (1976). Theyfound that the mass of the molecular outflow, proba-bly, comes from the parent cloud, but the angular mo-mentum could come from both the stellar wind and theparent cloud.Located at the center of the Kleinmann-Low Nebulain Orion, at a distance ∼ ± ∗ > (cid:12) ) star (Hirota et al. 2014; Plambeck &Wright 2016; Hirota et al. 2017; Ginsburg et al. 2018).The central object of the Orion Src I has a high lu-minosity ∼ L (cid:12) (Menten & Reid 1995; Reid et al.2007; Testi et al. 2010). The bipolar outflow presentslow radial velocities ( ∼
18 km s − ) along the northeast-southwest direction, with a size ∼ µ α cos δ = +2 . ± . − and µ δ = − . ± . − , where the angle δ ∼ − ◦ (Rodr´ıguez et al.2017). In fact, the Orion Kleinmann-Low Nebula ex-hibits evidence of a violent explosive phenomenon (e.g.,Bally & Zinnecker 2005; G´omez et al. 2008; Zapata etal. 2009; Bally et al. 2017; Zapata et al. 2017). Theproper motions of the sources I, BN, and n reveal thatthis explosion appears to have taken place 500 year ago Table 1 . Molecular lines.
Molecular RestSpecie Frequency [GHz] SiO(J=8–7) ν = 0 342.9808SiS (J=19–18) ν = 0 344.7794 SiO(J=8–7) ν = 1 344.9162 (e.g., Luhman et al. 2017; Rodr´ıguez et al. 2017).We present archive SiO (J=8–7) ν =0, SiS (J=19–18) ν =0, and SiO (J=8–7) ν =1 line observation, madewith the Atacama Large Millimeter/Submillimeter Ar-ray (ALMA) of the molecular outflow associated withthe young star Orion Src I. We also compare the obser-vational results with the thin shell model of LV19. Thepaper is organized as follows: The Section 2 details theobservations. In Section 3 we present our observationalresults and compare with the outflow model. Finally,the conclusions are presented in Section 4. OBSERVATIONSThe archive observations of Orion Src I were carriedout with the Atacama Large Millimeter/SubmillimeterArray (ALMA) in band 7 in 2016 October 31st and2014 July 26th as part of the programs 2016.1.00165.S(P.I. John Bally) and 2012.1.00123.S (P.I. Richard Plam-beck), respectively. At that time, the array counted with31 (2014) and 42 (2016) antennas with a diameter of 12myielding baselines with projected lengths from 33 to 820m (41 – 1025 k λ ) and 18 to 1100 m (22 – 1375 k λ ), re-spectively. The primary beam at this frequency has afull width at half-maximum (FWHM) of about 20 (cid:48)(cid:48) , sothat in both observations the molecular emission fromthe outflow of Orion Src I falls well inside of this area.The integration time on-source was about 25 min., and32 min. was used for calibration for the 2014 observa-tions, while for the 2016 observations was about 13 min.on-source, and 37 min. for calibration. The ALMA digi-tal correlator was configured with four spectral windowscentered at 353.612 GHz (spw0), 355.482 GHz (spw1),341.493 GHz (spw2), and 343.363 GHz (spw3) with 3840channels and a space channel of 488.281 kHz or about0.4 km s − for the 2014 observations and at 344.990GHz (spw0), 346.990 GHz (spw1), 334.882 GHz (spw2),and 332.990 GHz (spw3) with 1920 channels and a spacechannel of 976.562 kHz or about 0.8 km s − for the 2016observations. The spectral lines reported on this studywere found in the spw2 ( SiO) of the 2014 observationsand the spw0 (SiO and SiS) of the 2016 observations(see Table 1).For both observations, the weather conditions werereasonably good and stable for these high frequen-cies. The observations used the quasars: J0510+1800,
Right Ascension (arcsec) -2-1.5-1-0.500.511.52 D e c li n a t i o n ( a r c s e c ) (a) V e l o c i t y ( k m s ) Right Ascension (arcsec) -2-1.5-1-0.500.511.52 D e c li n a t i o n ( a r c s e c ) (b) V e l o c i t y ( k m s ) Right Ascension (arcsec) -2-1.5-1-0.500.511.52 D e c li n a t i o n ( a r c s e c ) (c) V e l o c i t y ( k m s ) Figure 1 . ALMA first moment or the intensity weighted velocity of the emission from the different molecule lines from the outflow. (a) Emissionof SiO (J=8–7) ν =0. (b) Emission from SiS (J=19–18) ν =0. (c) Emission from SiO (J=8–7) ν =1. The diagonal dashed lines indicate thepositions where the position-velocity diagrams were made. The color scale bar on the right side shows the V LSR in km s − . The synthesized beamof the image is shown in the lower left corner. In these plots the white contours show the continuum emission from the disk and are the 20 σ , 40 σ ,60 σ , and 80 σ . The magenta arrows indicate the proper motion of this source. The size these arrows indicates the proper motions for a period of100 years. The solid arrows indicate the proper motion and the dashed arrows indicate the proper motion considering the error in right ascension. J0522 − − − −
013 and J0541 − − (SiO and SiS)at a angular resolution of 0.19 (cid:48)(cid:48) × (cid:48)(cid:48) with a PA of − ◦ and about 20 mJy Beam − ( SiO) at an angularresolution of 0.30 (cid:48)(cid:48) × (cid:48)(cid:48) with a PA of +58 ◦ . Self-calibration was attempted on the continuum, however,we did not obtain a relatively good improvement in theline maps. RESULTS AND DISCUSSIONHirota et al. (2017) present observational results withALMA at 50 au resolution from the emission of theSi O and H O molecular lines of the molecular outflowof Orion Src I. These lines trace the inner part of themolecular outflow. In contrast, the archive observationsused in this work trace the outer part of the molecu-lar outflow, the latter, because this improves an easilycomparison with the thin shell model of LV19.3.1.
Results from the observations
Figure 1 presents the first moment or the intensityweighted velocity of the emission from the three molec-ular lines, SiO (J=8–7) ν =0 (panel a), SiS (J=19–18) ν =0 (panel b), and SiO (J=8–7) ν =1 (panel c).These panels show that the east side of the molecularoutflow presents blueshifted velocities, while the westside presents redshifted velocities. This difference of thevelocity is interpreted as rotation around the outflowaxis (Hirota et al. 2017). Moreover, Figure 1 indicatesthat the molecular outflow is not on the plane of the sky, i.e., the outflow has an inclination angle i (cid:54) = 0 ◦ :In the lower edge of the outflow (left and middle pan-els), the molecular outflow has velocities of the order to12 km s − , this high velocity respect to the local stan-dard of the rest velocity V LSR = 5 km s − (Plambeck& Wright 2016), can be explained as the axial velocity.Here, we assume an inclination for the outflow of i =10 ◦ ,which is similar to the value reported by Plambeck &Wright (2016), Hirota et al. (2017), and B´aez-Rubio etal. (2018). In addition, in the panels (a) and (b), onecan observe that the size of the molecular outflow is ∼ SiO (J=8–7) ν =1 traces the inner mostpart of the molecular outflow of Orion Src I. Figure 1also shows the 1.3 mm continuum emission (in whitecontours) from Orion Src I. This continuum emission istracing the disk surrounding this source, see Hirota etal. (2017); Plambeck & Wright (2016).The position-velocity diagrams of the emission fromthe molecular line of SiO (J=8–7) ν =0 are shown inFigure 2. This Figure presents parallel cuts at differ-ent distances from the disk mid-plane, these cuts weremade from z =480 au to z = −
480 au with intervals of80 au (see the dashed lines in panel (a) of Figure 1).One can observe that in regions near to the disk, thismolecule fills the molecular outflow, while, for regionsfar from the disk, this molecule presents a thin–shellstructure in expansion. In addition, one can observethat all position-velocity diagrams present signatures ofthe rotation (see panel a of Figure 5).In Figure 3 we have done a similar analysis to Figure2 for the emission from the molecular line of SiS (J=19–18) ν =0. The position-velocity diagrams show a thinshell structure where the emission from this molecule isvery prominent. The width of the shell is ∆ r ∼
120 auwhich is ∼
400 300 200 100 0 - - - - -20-1001020 V l s r ( k m s − ) z=0AU z=80AU z=160AU z=240AU z=320AU z=400AU z=480AU
400 300 200 100 0 - - - - Angularoffset(AU) -20-1001020 V l s r ( k m s − ) z= −80AU −400−300−200−1000 100200300400z= −160AU −400−300−200−1000 100200300400z= −240AU −400−300−200−1000 100200300400z= −320AU −400−300−200−1000 100200300400z= −400AU −400−300−200−1000 100200300400z= −480AU 0.000.250.500.751.001.251.501.752.00 J y / b e a m Figure 2 . Position-velocity diagrams parallel to the disk mid-plane from the emission of the SiO (J=8–7) ν =0 transition at different heightsfrom z = 480 au to z = −
480 au with an interval of 80 au. The vertical axes are the line of sight velocity with respect to the LSR velocity andthe horizontal axes are the perpendicular distances with respect to the outflow axis. The color scale bar on the right side shows the intensity inJy/beam.
400 300 200 100 0 - - - - -20-100102030 V l s r ( k m s − ) z=0AU z=80AU z=160AU z=240AU z=320AU z=400AU z=480AU
400 300 200 100 0 - - - - Angularoffset(AU) -20-100102030 V l s r ( k m s − ) z= −80AU −400−300−200−1000 100200300400z= −160AU −400−300−200−1000 100200300400z= −240AU −400−300−200−1000 100200300400z= −320AU −400−300−200−1000 100200300400z= −400AU −400−300−200−1000 100200300400z= −480AU 0.00.20.40.60.81.0 J y / b e a m Figure 3 . Position-velocity diagrams parallel to the disk mid-plane from the emission of the SiS (J=19–18) ν =0 transition for the same heightsand the same description as Figure 2.
400 300 200 100 0 - - - - -20-100102030 V l s r ( k m s − ) z=0AU z=80AU z=160AU z=240AU z=320AU z=400AU z=480AU
400 300 200 100 0 - - - - Angularoffset(AU) -20-100102030 V l s r ( k m s − ) z= −80AU −400−300−200−1000 100200300400z= −160AU −400−300−200−1000 100200300400z= −240AU −400−300−200−1000 100200300400z= −320AU −400−300−200−1000 100200300400z= −400AU −400−300−200−1000 100200300400z= −480AU 0.00.20.40.60.81.0 J y / b e a m Figure 4 . Position-velocity diagrams parallel to the disk mid-plane from the emission of the SiO (J=8-7) ν =1 transition for the same heightsand the same description as Figure 2. (a) (b) (c) Figure 5 . Position-velocity diagrams parallel to the disk midplane at a height z = −
80 au. (a) Emission from the molecular line of SiO (J=8–7) ν = 0. (b) Emission from the molecular line SiS (J=19–18) ν = 0. (c) Emission from the molecular line of SiO (J=8–7) ν = 1. The horizontaldashed line shows the value of the LSR velocity of the source. The vertical dashed lines represent the cylindrical radius (cid:36) obs defined in Figure 6.The solid line in each panel indicates the rotation signature. Fuente I de Orion Momento angular en flujos bipolares
Figura 5.5: Diagramas posici´on-velocidad paralelos al plano medio del disco a una altura z =
80 AU.Panel izquierdo: emisi´on de la l´ınea molecular de SiO (J=8-7) ⌫ = 0. Panel medio: emisi´on de la l´ıneamolecular de SiS (J=19-18) ⌫ = 0. Panel derecho: emisi´on de la l´ınea molecular de SiO (J=8-7) ⌫ = 1.La l´ınea punteada horizontal muestra el valor de la velocidad local de reposo V LSR de la fuente. Lasl´ıneas punteadas verticales muestran el radio externo R out . La l´ınea ´solida inclinada muestra el perfil derotaci´on de la fuente. Figura 5.6. El panel (a) de esta figura, muestra el radio externo obtenido de las tres l´ıneasmoleculares observadas y del modelo. El radio observado fue medido a la velocidad local dereposo V lsr , que para Orion Src I es de 5.5 km s (Hirota et al. 2016), de los diagramas posici´on-velocidad. Este radio fue medido con la diferencia entre las l´ıneas verticales punteadas de la figura5.5. El radio te´orico, es el radio cil´ındrico de la c´ascara R out = R s sin ✓ , dicho radio se muestraen la Figura WWWW. Se puede observar, que el radio incrementa con la distancia al planomedio del disco, y que el modelo tiene el mismo comportamiento que los datos observacionales.Adem´as, tanto los valores te´oricos como observacionales, son consistentes.El panel (b) de la figura 5.6 muestra la velocidad de expansi´on. Los valores observacionales deesta velocidad son medidos en el centro del flujo, mientras que los valores te´oricos es la proyecci´onde la velocidad radial sobre la l´ınea de visi´on. Se puede notar que la velocidad incrementa conla distancia al plano medio, y tanto los valores observacionales y te´oricos son consistentes.La velocidad de rotaci´on se presenta en el panel (c) de la figura 5.6. Los valores obtenidosde las observaciones son medidos en el radio externo (panel [a] de esta figura), mientras quelos valores te´oricos es la proyecci´on de la velocidad total sobre la l´ınea de visi´on (considerandolas componentes radial y azimutal de la velocidad). Esta velocidad decrece con la distancia aldisco. Se puede notar, que los valores observacionales son mayores a los valores te´oricos en unfactor de 3 - 10. Tambi´en, el comportamiento de los datos te´oricos es diferente a los valoresobservacionales. La velocidad de rotaci´on del modelo decrece r´apidamente conforme la distanciaal disco aumenta; por otra parte, la velocidad de rotaci´on observada decrece suavemente con ladistancia al plano medio del disco.Finalmente, el ´angulo de apertura se define como ✓ opening = tan ✓ R out R cen z ◆ , (5.1)este ´angulo decrece con la altura y se muestra en el panel (d) de la figura 5.6. Se puede notarque los valores te´oricos son consistentes con los observacionales. 51 Fuente I de Orion Momento angular en flujos bipolares
Figura 5.5: Diagramas posici´on-velocidad paralelos al plano medio del disco a una altura z =
80 AU.Panel izquierdo: emisi´on de la l´ınea molecular de SiO (J=8-7) ⌫ = 0. Panel medio: emisi´on de la l´ıneamolecular de SiS (J=19-18) ⌫ = 0. Panel derecho: emisi´on de la l´ınea molecular de SiO (J=8-7) ⌫ = 1.La l´ınea punteada horizontal muestra el valor de la velocidad local de reposo V LSR de la fuente. Lasl´ıneas punteadas verticales muestran el radio externo R out . La l´ınea ´solida inclinada muestra el perfil derotaci´on de la fuente. Figura 5.6. El panel (a) de esta figura, muestra el radio externo obtenido de las tres l´ıneasmoleculares observadas y del modelo. El radio observado fue medido a la velocidad local dereposo V lsr , que para Orion Src I es de 5.5 km s (Hirota et al. 2016), de los diagramas posici´on-velocidad. Este radio fue medido con la diferencia entre las l´ıneas verticales punteadas de la figura5.5. El radio te´orico, es el radio cil´ındrico de la c´ascara R out = R s sin ✓ , dicho radio se muestraen la Figura WWWW. Se puede observar, que el radio incrementa con la distancia al planomedio del disco, y que el modelo tiene el mismo comportamiento que los datos observacionales.Adem´as, tanto los valores te´oricos como observacionales, son consistentes.El panel (b) de la figura 5.6 muestra la velocidad de expansi´on. Los valores observacionales deesta velocidad son medidos en el centro del flujo, mientras que los valores te´oricos es la proyecci´onde la velocidad radial sobre la l´ınea de visi´on. Se puede notar que la velocidad incrementa conla distancia al plano medio, y tanto los valores observacionales y te´oricos son consistentes.La velocidad de rotaci´on se presenta en el panel (c) de la figura 5.6. Los valores obtenidosde las observaciones son medidos en el radio externo (panel [a] de esta figura), mientras quelos valores te´oricos es la proyecci´on de la velocidad total sobre la l´ınea de visi´on (considerandolas componentes radial y azimutal de la velocidad). Esta velocidad decrece con la distancia aldisco. Se puede notar, que los valores observacionales son mayores a los valores te´oricos en unfactor de 3 - 10. Tambi´en, el comportamiento de los datos te´oricos es diferente a los valoresobservacionales. La velocidad de rotaci´on del modelo decrece r´apidamente conforme la distanciaal disco aumenta; por otra parte, la velocidad de rotaci´on observada decrece suavemente con ladistancia al plano medio del disco.Finalmente, el ´angulo de apertura se define como ✓ opening = tan ✓ R out R cen z ◆ , (5.1)este ´angulo decrece con la altura y se muestra en el panel (d) de la figura 5.6. Se puede notarque los valores te´oricos son consistentes con los observacionales. 51 Fuente I de Orion Momento angular en flujos bipolares
Figura 5.5: Diagramas posici´on-velocidad paralelos al plano medio del disco a una altura z =
80 AU.Panel izquierdo: emisi´on de la l´ınea molecular de SiO (J=8-7) ⌫ = 0. Panel medio: emisi´on de la l´ıneamolecular de SiS (J=19-18) ⌫ = 0. Panel derecho: emisi´on de la l´ınea molecular de SiO (J=8-7) ⌫ = 1.La l´ınea punteada horizontal muestra el valor de la velocidad local de reposo V LSR de la fuente. Lasl´ıneas punteadas verticales muestran el radio externo R out . La l´ınea ´solida inclinada muestra el perfil derotaci´on de la fuente. Figura 5.6. El panel (a) de esta figura, muestra el radio externo obtenido de las tres l´ıneasmoleculares observadas y del modelo. El radio observado fue medido a la velocidad local dereposo V lsr , que para Orion Src I es de 5.5 km s (Hirota et al. 2016), de los diagramas posici´on-velocidad. Este radio fue medido con la diferencia entre las l´ıneas verticales punteadas de la figura5.5. El radio te´orico, es el radio cil´ındrico de la c´ascara R out = R s sin ✓ , dicho radio se muestraen la Figura WWWW. Se puede observar, que el radio incrementa con la distancia al planomedio del disco, y que el modelo tiene el mismo comportamiento que los datos observacionales.Adem´as, tanto los valores te´oricos como observacionales, son consistentes.El panel (b) de la figura 5.6 muestra la velocidad de expansi´on. Los valores observacionales deesta velocidad son medidos en el centro del flujo, mientras que los valores te´oricos es la proyecci´onde la velocidad radial sobre la l´ınea de visi´on. Se puede notar que la velocidad incrementa conla distancia al plano medio, y tanto los valores observacionales y te´oricos son consistentes.La velocidad de rotaci´on se presenta en el panel (c) de la figura 5.6. Los valores obtenidosde las observaciones son medidos en el radio externo (panel [a] de esta figura), mientras quelos valores te´oricos es la proyecci´on de la velocidad total sobre la l´ınea de visi´on (considerandolas componentes radial y azimutal de la velocidad). Esta velocidad decrece con la distancia aldisco. Se puede notar, que los valores observacionales son mayores a los valores te´oricos en unfactor de 3 - 10. Tambi´en, el comportamiento de los datos te´oricos es diferente a los valoresobservacionales. La velocidad de rotaci´on del modelo decrece r´apidamente conforme la distanciaal disco aumenta; por otra parte, la velocidad de rotaci´on observada decrece suavemente con ladistancia al plano medio del disco.Finalmente, el ´angulo de apertura se define como ✓ opening = tan ✓ R out R cen z ◆ , (5.1)este ´angulo decrece con la altura y se muestra en el panel (d) de la figura 5.6. Se puede notarque los valores te´oricos son consistentes con los observacionales. 51 Tabla 3.2: Valores de crit para distintos valores del par´ametro ↵ y para el radio m´ınimo r s , min dado enla tabla 3.1. ↵ crit Figura 3.3: Forma de la c´ascara para el par´ametro ↵ = 0 . . Las ecs. (3.30) - (3.34) describen las propiedades f´ısicas de la c´ascara. Las ecuaciones adimen-sionales para los flujos de momento en la direcci´on radial y polar, y para el radio se resuelvennum´ericamente y se complementan con las soluciones algebr´aicas para el flujo de masa y el flujode momento en la direcci´on azimutal.La integraci´on num´erica se hace para un valor del cociente de la tasa de p´erdida de masadel viento estelar y la tasa de acreci´on ↵ = 0 .
1, un valor t´ıpico para flujos moleculares (e.g.,ver figura 14 de Ellerbroek et al. 2013). Adicionalmente, se hace la integraci´on para distintosvalores del cociente de las tasas de momento del viento estelar y el flujo de acreci´on , los cualesest´an dentro del rango min < < (ver tabla 3.1). Una vez establecidos los valores de lospar´ametros ↵ y , se c´alculan las condiciones de frontera en el polo descritas en la secciones3.2.2 y 3.2.3. Finalmente, la integraci´on num´erica inicia en un angulo de 10 radianes.Con la finalidad de recuperar unidades f´ısicas, se consideran los par´ametros de la estrellacentral del flujo molecular CB 26 (Launhardt et al. 2009), los cuales son una masa estelar deM ⇤ = 0 . y un radio centr´ıfugo de 200 AU (Launhardt & Sargent 2001). Con estos datos seobtiene una velocidad de ca´ıda libre (ver eq. [2.24]) de 1.5 km s .La figura 3.3 muestra la forma de la c´ascara para valores de = 1 .
5, 1.6, 1.7 y 1.8. Se puedenotar que para vientos estelares d´ebiles, valores de peque˜nos, se tienen c´ascaras esf´ericas,mientras que para vientos estelares fuertes, valores de grandes, se obtienen c´ascaras elongadas T a b l a3 . : V a l o r e s d e c r i t p a r a d i s t i n t o s v a l o r e s d e l p a r ´a m e t r o ↵ y p a r a e l r a d i o m ´ ı n i m o r s , m i n d a d o e n l a t a b l a3 . . ↵ c r i t . . . . . . . . F i g u r a3 . : F o r m a d e l a c ´a s c a r a p a r a e l p a r ´a m e t r o ↵ = . y d i f e r e n t e s v a l o r e s d e l p a r ´a m e t r o . . . R e s u l t a d o s L a s ec s . ( . ) - ( . ) d e s c r i b e n l a s p r o p i e d a d e s f ´ ı s i c a s d e l a c ´a s c a r a . L a s ec u a c i o n e s a d i m e n - s i o n a l e s p a r a l o s flu j o s d e m o m e n t o e n l a d i r ecc i ´o n r a d i a l y p o l a r , y p a r a e l r a d i o s e r e s u e l v e nnu m ´ e r i c a m e n t e y s ec o m p l e m e n t a n c o n l a ss o l u c i o n e s a l g e b r ´a i c a s p a r a e l flu j o d e m a s a y e l flu j o d e m o m e n t o e n l a d i r ecc i ´o n a z i m u t a l. L a i n t e g r a c i ´o nnu m ´ e r i c a s e h a ce p a r a un v a l o r d e l c o c i e n t e d e l a t a s a d e p ´ e r d i d a d e m a s a d e l v i e n t o e s t e l a r y l a t a s a d e a c r ec i ´o n ↵ = . , un v a l o r t ´ ı p i c o p a r a flu j o s m o l ec u l a r e s ( e . g ., v e r fi g u r a14 d e E ll e r b r o e k e t a l. ) . A d i c i o n a l m e n t e , s e h a ce l a i n t e g r a c i ´o np a r a d i s t i n t o s v a l o r e s d e l c o c i e n t e d e l a s t a s a s d e m o m e n t o d e l v i e n t o e s t e l a r y e l flu j o d e a c r ec i ´o n ,l o s c u a l e s e s t ´a nd e n t r o d e l r a n go m i n < < ( v e r t a b l a3 . ) . U n a v eze s t a b l ec i d o s l o s v a l o r e s d e l o s p a r ´a m e t r o s ↵ y , s ec ´a l c u l a n l a s c o nd i c i o n e s d e f r o n t e r a e n e l p o l o d e s c r i t a s e n l a s ecc i o n e s . . y . . . F i n a l m e n t e ,l a i n t e g r a c i ´o nnu m ´ e r i c a i n i c i a e nun a n g u l o d e r a d i a n e s . C o n l a fin a li d a dd e r ec up e r a r un i d a d e s f ´ ı s i c a s , s ec o n s i d e r a n l o s p a r ´a m e t r o s d e l a e s t r e ll a ce n t r a l d e l flu j o m o l ec u l a r C B ( L a unh a r d t e t a l. ) ,l o s c u a l e ss o nun a m a s a e s t e l a r d e M ⇤ = . M y un r a d i o ce n t r ´ ı f u go d e AU ( L a unh a r d t & S a r g e n t ) . C o n e s t o s d a t o ss e o b t i e n e un a v e l o c i d a dd ec a´ ı d a li b r e ( v e r e q .[ . ] ) d e . k m s . L a fi g u r a3 . m u e s t r a l a f o r m a d e l a c ´a s c a r a p a r a v a l o r e s d e = . , . , . y . . S e pu e d e n o t a r q u e p a r a v i e n t o s e s t e l a r e s d ´ e b il e s , v a l o r e s d e p e q u e ˜ n o s , s e t i e n e n c ´a s c a r a s e s f ´ e r i c a s , m i e n t r a s q u e p a r a v i e n t o s e s t e l a r e s f u e r t e s , v a l o r e s d e g r a nd e s , s e o b t i e n e n c ´a s c a r a s e l o n ga d a s Comparison with the outflow model
The position-velocity diagrams, presented in Figures2-4, show the detailed structure of the outflow velocityas a function of the distance from the disk mid–plane.With these diagrams, we can also obtain informationabout the kinematic and physical properties of the out-flow and compare with the outflow model of LV19.Goddi et al. (2011) suggested that this source is abinary system with a stellar mass of ⇠
20 M , and aseparation of the stars <
10 au. Since this separation isvery small compared to the size of the outflow, even ifeach star has its own stellar wind, a single stellar windemanating from the center is a good approximation.The proper motion of the Orion SrcI with respect tothe center of the explosive event that occured 500 yrago (Rodr´ıguez et al. 2017) will change the environmentof the central star. Its envelope will not be a gravita-tional collapsing envelope of the Ulrich type since thefree fall time of a gas parcel starting at an outflow dis-tance ⇠ ⇤ = 15 M (Ginsburg et al. 2018) and a cen-trifugal radius of R cen = 40 au, within the range of 21au - 47 au reported by Hirota et al. 2017.report a centrifugal radii between 21 - 47 au).This model depends of two parameters associated withthe properties of the stellar wind and the accretion flow.The first parameter is the ratio between the wind massloss rate ˙M w , and the mass accretion rate ˙M a ↵ = ˙M w ˙M a , (2)for this case, we assume a value of ↵ = 0 .
1, a typi-cal value the molecular outflows (Ellerbroek et al. 2013;Nisini et al. 2018). The second parameter is the ratiobetween the stellar wind and the accretion flow momen-tum rates = ˙M w v w ˙M a v = ↵ v w v , (3) where v w is the velocity of the stellar wind, and v isthe free fall velocity at the centrifugal radius, given by v = ✓ GM ⇤ R cen ◆ / . (4)For inferred values M ⇤ = 15 M and R cen = 40 au, thefree fall velocity is v = 19 km s . Assuming a stellarwind velocity ⇠
800 km s , of the order of the escapespeed for a star with R ⇤ ⇠ R , implies that ' ⇢ w = ˙M w ⇡r v w f ( ✓ ) , (5)where f ( ✓ ) is the anisotropy function given by f ( ✓ ) = A + B cos n ✓A + B/ (2 n + 1) . (6)The physical properties of the shell model that willbe compared with the observations are: the cylindri-cal radius $ , the expansion velocity v exp , the rotationvelocity v rot , and the opening angle ✓ opening . Figure 6presents a schematic diagram of the molecular outflowthat shows the cylindrical radius, the height over thedisk mid-plane, and the opening angle.We considered two models: a shell formed by anisotropic stellar wind with B = 0; and a shell formedby a very anisotropic stellar wind, with A = 1, B = 35,and n = 5. The parameters of the anisotropic modelare chosen to reproduce the shape of the most extendedoutflow emission as traced by the SiO (J=8–7) ⌫ = 0transition. We choose the parameters that minimize ,defined as = 1 N X ( $ out $ model ) $ , (7)where $ out is the observed cylindrical radius, $ model is the model cylindrical radius, and N is the number ofobserved values along the z axis. This analysis is shownin Figure 7. We integrate in time the shell model froma small initial shell radius r s (0) ' R ⇤ /R cen ⇠ ,close to the stellar surface, until the lobe reaches theobserved cylindrical radii at t = 65 yr, as shown inFigure 8. Because the shell decelerates with time, thedynamical time (65 yr) is half of the kinematic time (130yr) calculated in section 3.2.Figure 8 shows shell produced by the isotropic (dashedline) and the anisotropic (solid line) model superimposedon the ALMA first moment of the line emission SiO(J=8–7) ⌫ =0 (panel a), SiS (J=19–18) ⌫ =0 (panel b),and SiO (J=8–7) ⌫ =1 (panel c).The comparison between both outflow models withthe observational data is shown in Figure 9. Since theisotropic model (dotted lines) does not reproduce the Figure 6 . Schematic diagram of a molecular outflow. This diagram shows the opening angle of the molecular outflow θ opening ,the cylindrical radius (cid:36) , the centrifugal radius R cen , and the height z . molecule shows that the outflow is in expansion becausethe size of the thin shells increases with the distancefrom the disk. In these diagrams the rotation of themolecular outflow is confirmed. The biggest rotationvelocity corresponds to a height of z = ±
80 au (seepanel b of Figure 5).Figure 4 shows the position-velocity diagrams of theemission from the molecular line SiO (J=8–7) ν =1 forthe same distances from the disk mid-plane of the Fig-ures 2 and 3. In contrast to the other two molecules,in this molecular line the thin shell structure does notappear. This Figure confirms the presence of the ro-tation in the molecular outflow (see panel c of Figure5). Finally, the absence of the emission for distances of z ≥ ±
320 au means that this molecule is only tracingthe inner part of the molecular outflow. This is maybe due to excitation conditions.Hirota et al. (2017) measured the rotation velocitiesfor heights between z = −
200 au and z = 200 au, andthey found that these velocities decrease with the heightand have values between ∼ − . In this work, wereported rotation velocities for the same heights of theorder of 4–8 km s − , these values are similar to thosereported by these authors.Finally, Figure 5 clearly shows the evidence of the ro-tation and the expansion in Orion Src I. . In this figure,we have made a zoom to the position-velocity diagrams If the gas is expanding and rotating, the position velocitydiagrams show an elliptical structure with the semi major axisinclined with respect to the position axis (see, e.g, panel d of theSupplementary Figure 1 of Hirota et al. 2017). n B − − χ Figure 7 . χ analysis for different anisotropy parameters B and n , with A = 1, α = 0 . β = 4, and an integration time of t = 65 yr. Right Ascension (arcsec) -2-1.5-1-0.500.511.52 D e c li n a t i o n ( a r c s e c ) (a) V e l o c i t y ( k m s ) Right Ascension (arcsec) -2-1.5-1-0.500.511.52 D e c li n a t i o n ( a r c s e c ) (b) V e l o c i t y ( k m s ) Right Ascension (arcsec) -2-1.5-1-0.500.511.52 D e c li n a t i o n ( a r c s e c ) (c) V e l o c i t y ( k m s ) Figure 8 . Comparison between the ALMA first moment or the intensity weighted velocity of the emission from the differentmolecule lines with the best outflow model (see text). (a) Emission of SiO (J=8–7) ν =0. (b) Emission from SiS (J=19–18) ν =0. (c) Emission from SiO (J=8–7) ν =1. The dashed line represents the isotropic model for parameters α = 0 . β = 4, and B = 0. The solid black line represents the outflow model for the parameters α =0.1, β =4, r s (0) = 10 − , A =1, B =35, and n =5. of the Figures 2, 3, and 4 at a distance of z = −
80 aufrom the disk for the molecular lines of SiO (J=8–7) ν =0 (panel a), SiS (J=19–18) ν =0 (panel b), and SiO(J=8–7) ν =1 (panel c), respectively.3.2. Mass of the outflow
Assuming that the SiO (J=8-7) ν = 1 emission isoptically thick, the excitation temperature is (e.g., Es-talella & Anglada 1994) T ex ( SiO) = hν/k ln (cid:16) hν/kT a ( SiO)+ J ν ( T bg ) (cid:17) , (1)where h is the Plank constant, k is the Boltzmannconstant, ν is the rest frequency in GHz (see Table 1), T a ( SiO) = 19 K is the observed antenna tem-perature of SiO, and J ν ( T bg ) is intensity in units oftemperature at the background temperature T bg = 2 . ν given in Table 1, we obtain T ex ( SiO) = 26 K. Assuming that the SiO and SiOmolecules coexist and share the same excitation temper-ature, T ex ( SiO) = T ex ( SiO) = T ex , we can estimatethe optical depth of the SiO molecule as (e.g., Estalella& Anglada 1994) τ ( SiO) = − ln (cid:20) − T a ( SiO) J ν ( T ex ) − J ν ( T bg ) (cid:21) , (2)where T a ( SiO) = 14 K is the observed antenna tem-perature of SiO and J ν ( T ex ) is the intensity in units of − − − − − −
80 0 80 160 240 320 400 480 z (AU) $ ( AU ) (a) IsotropicAnisotropic SiO(J = 8 − ν = 0SiS(J = 19 − ν = 0SiO(J = 8 − ν = 1 − − − − − −
80 0 80 160 240 320 400 480 z (AU) θ o p e n i n g (b) Figure 9 . Panel (a) shows the cylindrical radii of the outflow (cid:36) ; panel (b) shows the opening angle of the outflow θ opening .These observed values are derived from the position-velocity diagrams in Figures 2, 3, and 4. The error bars are derived from thegaussian fit (see Appendix A for the measurement procedure). The dotted line shows an isotropic model with the parameters α = 0 . β = 4, r s (0) = 10 − , and B = 0. The black line shows the best anisotropic stellar wind model with the parameters α = 0 . β = 4, r s (0) = 10 − , A = 1, B = 35, and n = 5. Both models were integrated up to a dynamical time of 65 yr. − − − − − −
80 0 80 160 240 320 400 480 z (AU) . . . . . . . . . v e x p ( k m s − ) (a) IsotropicAnisotropic SiO(8 − ν = 0SiO ν = 1 − − − − − −
80 0 80 160 240 320 400 480 z (AU) − v z ( k m s − ) (b) − − − − − −
80 0 80 160 240 320 400 480 z (AU) v r o t ( k m s − ) (c) Figure 10 . Panel (a) shows the expansion velocity perpendicular to the outflow axis v exp measured at the cylindrical radius;panel (b) shows the axial velocity v z ; panel (c) shows the rotation velocity v rot measured at the cylindrical radii. These observedvalues are derived from the position-velocity diagrams in Figures 2, 3, and 4. The error bars are derived from the gaussian fit(see Appendix A for the measurement procedure). The dotted line shows the isotropic model with the parameters of Figure 9.The black line shows the best anisotropic stellar wind model with the parameters of Figure 9. The dashed dotted line of thepanel (c) corresponds to the best fitting of the function v rot = az γ + b (see text). temperature at the excitation temperature. With thesevalues, we obtain τ ( SiO) = 1 .
3, which is not opticallythin. Thus, assuming local thermodynamic equilibrium,we calculate the mass of the outflow as a function of the SiO optical depth asM outflow M (cid:12) = 5 × − (cid:0) d ∆Ω (cid:1) m (H ) X (cid:16) SiOH (cid:17) × exp (cid:104) . T ex (cid:105) − exp (cid:104) − . T ex (cid:105) T ex τ ( SiO)∆ v, (3)where m (H ) is the mass of the molecular hydrogen,X (cid:16) SiOH (cid:17) = 6 − × − is the fractional abundance of SiO with respect to H . To obtained this value, we as-sumed a relative abundance of SiO with respect to H of 1 . − . × − , obtained by Ziurys & Friberg (1987)in OMC1 (IRc2), and a relative abundance of SiO withrespect to SiO of 5 × − , obtained by Soria-Ruiz et al.(2005) toward evolved stars. The distance d is (418 ± v is the velocity width of the line ( ∼
30 km s − ),and ∆Ω is the solid angle of the source ( ∼ . × − sr). With these values, the estimated mass of the out-flow of Orion Src I is M outflow (cid:38) . − . (cid:12) . Thismass is a lower limit because the SiO abundance couldbe lower by up to two orders of magnitude due to theuncertainty in the molecular hydrogen column densities(Ziurys & Friberg 1987).In addition, for an expansion velocity v ∼
18 km s − (Greenhill et al. 2013) and a size z = 480 au, the kine-matic time is t kin ∼
130 yr. Then, the mass loss rateof the molecular outflow as ˙M outflow = M outflow / t kin (cid:38) . − × − M (cid:12) yr − .Hirota et al. (2017) proposed that molecular outflowof Orion Src I is produced by a slow magnetocentrifugaldisk wind. The observed values of the rotational ve-locities of the outflow can be reproduced by this modelwhich predicts that the wind is eject from footpoints inthe disk at radii r ∼ −
25 au.A disk wind requires a very large mass loss rate toaccount for the mass observed in the outflow. As men-tioned in the Introduction, recent MHD simulationsshow that disk winds around T Tauri stars can have˙ M w = f ˙ M d , a , where the fraction can be f ∼ − M outflow = ˙ M w . Inthe case of Orion SrcI, this implies a very large disk ac-cretion rate, f ˙ M d , a (cid:38) (5 . − × − M (cid:12) yr − . Then,massive disk winds face two problems. The first problemhas to do with the fact that the mass flux in the disk willeventually fall into the star. Assuming that the disk ro-tates with Keplerian speed v K , the material accreted tothe star has to dissipate its energy, 1 / M d , a v K . Thus,the accretion luminosity at the stellar surface is givenby L a = η GM ∗ ˙ M d,a R ∗ , where G is the gravitational con-stant, M ∗ is the stellar mass, R ∗ is the stellar radius, The factors 58.6 and 16.7 in this equation, are the result of4 . × − × B e J ( J + 1) and 4 . × − × B e ( J + 1), respectively,where B e = 21 . SiO, J = 7 is the lower level, the factor of 4 . × − is the ratioof h/k in GHz − . and η ∼ .
5. Assuming M ∗ = 15 M (cid:12) (Ginsburg et al.2018) and R ∗ = 7 . R (cid:12) (Testi et al. 2010), the accre-tion luminosity is L a (cid:38) (1 /f )1 . × L (cid:12) . This value ishigher than the observed source luminosity L ∗ ∼ L (cid:12) (e.g., Menten & Reid 1995; Reid et al. 2007), unless f ∼
15. Note that a factor f ∼
15 implies that (locally)94% of the mass the mass escapes into the wind andonly 6% accretes towards the star. Disk wind modelswould have to produce these high f values in the case ofwinds around massive stars. The second problem, thatwas already mentioned in the case of DG Tau B (Sec-tion 1), is the short disk lifetime. For a maximum diskmass M d (cid:46) M ∗ / M (cid:12) , necessary for gravitationalstability (Shu et al. 1991), and an accretion rate suchthat f ˙ M d , a (cid:38) . − × − M (cid:12) yr − , the disk lifetimeis very small, τ = M d / ˙ M d , a (cid:46) f ×
980 yr (see also theshort disk lifetimes in Fig. 33 of B´ethune et al. 2017for disks around low mass stars). This estimate of thedisk lifetime assumes that the disk mass is not replen-ished. Nevertheless, Orion Src I has a massive accretingenvelope that could replenish the disk. The disk windmodels would have to explore if the disk mass could bereplenished in short timescales ( (cid:46) yr) by the in-falling envelope. Both, the accretion luminosity and thedisk lifetime, are important constraints on the disk windmodels.Moreover, if there is an accreting envelope around theOrion Src I, a stellar or disk wind will necessarily collideagainst it, driving a shell of entrained material. Forthis reason, in this work we explore a model where themolecular outflow is a shell produced by the interactionof a stellar wind and an accretion flow as the scenariofirst proposed by Snell et al. (1980). The shell is fed byboth the stellar wind and the accretion flow. The lattercan have very large mass accretion rates as observed inthe case of young massive stars (e.g., Zapata et al. 2008;Wu et al. 2009). We will verify under which conditionsthis shell model can acquire the observed mass.3.3. Comparison with the outflow model
The position-velocity diagrams, presented in Figures2-4, show the detailed structure of the outflow velocityas a function of the distance from the disk mid–plane.With these diagrams, we can also obtain informationabout the kinematic and physical properties of the out-flow and compare with the outflow model of LV19.Goddi et al. (2011) suggested that this source is abinary system with a stellar mass of ∼
20 M (cid:12) , and aseparation of the stars <
10 au. Since this separation isvery small compared to the size of the outflow, even ifeach star has its own stellar wind, a single stellar windemanating from the center is a good approximation.The proper motion of the Orion Src I with respect tothe center of the explosive event that occured 500 yrago (Rodr´ıguez et al. 2017) will change the environmentof the central star. Its envelope will not be a gravita-tional collapsing envelope of the Ulrich type since thefree fall time of a gas parcel starting at an outflow dis-tance ∼ r ∼ / ∗ = 15 M (cid:12) (Ginsburg et al.2018) and a centrifugal radius of R cen = 40 au, withinthe range of 21 au - 47 au reported by Hirota et al. 2017.This model depends of two parameters associated withthe properties of the stellar wind and the accretion flow.The first parameter is the ratio between the wind massloss rate ˙M w , and the mass accretion rate of the envelope˙M a α = ˙M w ˙M a , (4)for this case, we assume a value of α = 0 .
1, a typi-cal value the molecular outflows (Ellerbroek et al. 2013;Nisini et al. 2018). The second parameter is the ratiobetween the stellar wind and the accretion flow momen-tum rates β = ˙M w v w ˙M a v = α v w v , (5)where v w is the velocity of the stellar wind, and v isthe free fall velocity at the centrifugal radius, given by v = (cid:18) GM ∗ R cen (cid:19) / . (6)For inferred values M ∗ = 15 M (cid:12) and R cen = 40 au, thefree fall velocity is v = 19 km s − . Assuming a stellarwind velocity ∼
800 km s − , of the order of the escapespeed for a star with R ∗ ∼ . R (cid:12) (Testi et al. 2010),implies that β (cid:39) ρ w = ˙M w πr v w f ( θ ) , (7)where f ( θ ) is the anisotropy function given by f ( θ ) = A + B cos n θA + B/ (2 n + 1) . (8) The physical properties of the shell model that willbe compared with the observations are: the cylindri-cal radius (cid:36) , the opening angle θ opening , the expansionvelocity v exp , the axial velocity v z , and the rotation ve-locity v rot . Figure 6 presents a schematic diagram ofthe molecular outflow that shows the cylindrical radius,the height over the disk mid-plane, and the opening an-gle. The procedure used to measured these quantities isdescribed in Appendix A.We considered two models: a shell formed by anisotropic stellar wind with B = 0; and a shell formedby a very anisotropic stellar wind, with A = 1, B = 35,and n = 5. The parameters of the anisotropic stellarwind model are chosen to reproduce the shape of themost extended outflow emission as traced by the SiO(J=8–7) ν = 0 transition. We choose the parametersthat minimize χ , defined as χ = 1 N (cid:88) ( (cid:36) obs − (cid:36) model ) (cid:36) , (9)where (cid:36) obs is the observed cylindrical radius, (cid:36) model isthe model cylindrical radius, and N is the number ofobserved values along the z axis. This analysis is shownin Figure 7. We integrate in time the shell model froma small initial shell radius r s (0) (cid:39) R ∗ /R cen ∼ − ,close to the stellar surface, until the cylindrical radii ofthe model (cid:36) model reaches the observed cylindrical radii (cid:36) obs at different heights as shown in panel (a) of theFigure 9, which happens at t = 65 yr. The shell model R s ( θ ) is shown in Figure 8. Because the shell deceler-ates with time, the dynamical time (65 yr) is half of thekinematic time (130 yr) calculated in Section 3.2. Fig-ure 8 shows shell produced by the isotropic wind (dashedline) and the anisotropic stellar wind (solid line) modelsuperimposed on the ALMA first moment of the lineemission SiO (J=8–7) ν =0 (panel a), SiS (J=19–18) ν =0 (panel b), and SiO (J=8–7) ν =1 (panel c).The comparison between both outflow models withthe observational data is shown in Figures 9 and 10.Since the isotropic wind model (dotted lines) does notreproduce the observations, hereafter, we will only dis-cuss the properties of the anisotropic stellar wind model.The panel (a) of the Figure 9 shows the cylindricalradius obtained from the three line observations andfrom the anisotropic stellar wind model. These radii areshown as vertical dashed lines in Figure 5. The cylin-drical radius (cid:36) increases with the height above the diskmid-plane, and one can see that the model (black solidlines) agree well with observational data.For fixed centrifugal radius R cen , the opening anglecan be defined as θ opening = tan − (cid:18) (cid:36) − R cen z (cid:19) . (10)0This angle is shown in panel (b) of the Figure 9. The ob-served values and the model (black solid lines) are con-sistent. The fact that the opening angle decreases withthe height above the disk, indicates that the molecularoutflow could close up at higher heights. Nevertheless,one needs observations of a molecule that emits at higherdisk heights to establish the outflow shape.The panel (a) of the Figure 10 shows the expansionvelocity for the three molecules indicated in the panel.This velocity increases with the height above the diskmid-plane. The model expansion velocities (black solidlines) are similar to the observed values except close tothe disk ( z < ±
150 au).Panel (b) of the Figure 10 shows the measured ax-ial velocity v z . This velocity increases with the heightabove the disk mid–plane. The axial velocity of theanisotropic stellar wind model corrected by the incli-nation angle i = 10 ◦ and a system velocity V LSR =5 km s − (e.g., Plambeck & Wright 2016) fits the datawell.The rotation velocity is shown in panel (c) of the Fig-ure 10. For the molecular line of SiO (J=8–7) ν = 0(blue points), the rotation velocity is in the range 5–8km s − : at z = ±
80 au above the disk the rotation veloc-ity is ∼ − and it decreases with height. The SiS(J=19–18) ν = 0 line (yellow points) has a similar be-havior. The SiO (J=8–7) ν = 1 emission (red points)behaves in the same way but has slightly lower velocities,in the range 4–6 km s − . The observed rotation velocityis a factor of 3 −
10 larger than those of the anisotropicstellar wind model. Furthermore, the rotation velocityof the model decreases steeply with the height; the ob-served rotation velocity slowly decreases. For reference,a polynomial function ( v rot / kms − ) = a (z / au) γ +b with a = − . × − , γ = 1 .
2, and b = 8 . M outflow = ˙ M a R cen v (cid:90) π/ p m dθ, (11)where p m is the non dimensional mass flux (eq. [47]of LV19). For the anisotropic stellar wind model, (cid:82) π/ p m dθ = 6 .
0, in non dimensional units. Therefore,for the values of the centrifugal radius and free fall ve-locity above, one requires a mass accretion rate of theenvelope ˙M a = 1 . − . × − M (cid:12) yr − to obtain theobserved mass of the shell, M outflow = 0 . − . M (cid:12) .Such large mass envelope accretion rates have been in-ferred in regions of high mass star formation (e.g., Za-pata et al. 2008; Wu et al. 2009.) This accretion ratecorresponds a mass loss rate of the molecular outflowcorrected by the dynamical time ˙ M (cid:48) outflow = (0 . − . (cid:12) ) /
65 yr = 1 - 2 × − M (cid:12) yr − which is very similarto ˙ M a . Thus, the small fraction of mass that slides alongthe shell towards the equator does not increase the diskmass significantly.In summary, the comparison between the anisotropicstellar wind model and the observations of the outflowfrom Orion Src I fits very well the outflow cylindricalradius. The opening angle is a function of the cylindri-cal radius, therefore, it also fits the observations well.The expansion velocity and the axial velocity v z have abehavior similar to the observations, although the slopeis somewhat different. Nevertheless, the model rotationvelocity is much lower (3 −
10 times) than the observedvelocity.The smaller rotation velocity profile of the model indi-cates that the envelope of Ulrich (1976) can not explainthe rotation in molecular outflows. This problem couldbe alleviated if one includes a stellar wind or disk windwith angular momentum, or increases the angular mo-mentum of the envelope.For a representative height of z ∼
240 au, the ob-served rotation velocity is a factor ∼ ∼
17% ofthe observed specific angular momentum. The missingangular momentum could come from an accreting enve-lope with more angular momentum, or from an extendeddisk wind. CONCLUSIONSIn this study, we present new and sensitive ALMAarchive observations of the rotating outflow from OrionSrc I. In the following, we describe our main results. • The Orion Src I outflow has a mass loss rate˙ M outflow = 5 . − × − M (cid:12) yr − . This massiveoutflow poses stringent constraints on disk windmodels concerning the accretion luminosity andthe disk lifetime. • We find that the opening angle (in a range of ∼ ◦ ) and the rotation velocity (in a range of ∼ − ) decrease with the height to the disk.In contrast, the cylindrical radius (in a range of ∼ ∼ − ), and the axial velocity v z (in arange of ∼ -1–10 km s − ) increase with respect tothe height above the disk. • We compare with the outflow model of LV19,where the molecular outflow corresponds to a shellproduced by the interaction of a stellar wind andan accretion flow. An X wind comes from radii very close to the central star, soit has little angular momentum.
800 400 0 − − − . . . . . . . . F l u x ( J y / b e a m ) (a)
800 400 0 − − . . . . . F l u x ( J y / b e a m ) (b)
800 400 0 − − . . . . . . . F l u x ( J y / b e a m ) (c) Figure A1 . Intensity profiles at V LSR = 5 km s − of the position-velocity diagrams at a height z = −
80 au, as indicated byhorizontal dashed lines in panels (a)–(c) in Figure 5. The red line shows the best Gaussian fit to the intensity profile of (a) SiO (J=8–7) ν = 0, (b) SiS (J=19–18) ν = 0, and (c) SiO (J=8–7) ν = 1. − −
12 0 12 24V lsr (kms − ) − . . . . . . . F l u x ( J y / b e a m ) (a) − −
12 0 12 24V lsr (kms − )0 . . . . . F l u x ( J y / b e a m ) (b) − −
12 0 12 24V lsr (kms − )0 . . . . . . . F l u x ( J y / b e a m ) (c) Figure A2 . Intensity profiles at the outflow axis of the position-velocity diagrams at a height z = −
80 au in Figure 5. The redline shows the best Gaussian fit to the intensity profile of (a) SiO (J=8–7) ν = 0, (b) SiS (J=19–18) ν = 0, and (c) SiO(J=8–7) ν = 1. For reference, the dashed lines indicate the V LSR velocity. • We find that the observed values of the cylindricalradius, the opening angle, the expansion velocity,and the axial velocity v z show a similar behaviorto LV19 anisotropic stellar wind model. However,the rotation velocity of the model is lower (by afactor of 3–10) than the observed rotation velocityof the Orion Src I outflow. • We conclude that the Ulrich flow alone cannot ex-plain the rotation of the molecular outflow orig-inated from Orion Src I and other possibilitiesshould be explored.We thank the referee for very useful commentsthat improved the presentation of the paper. J.A.L´opez-V´azquez and Susana Lizano acknowledge sup-port from PAPIIT–UNAM IN101418 and CONACyT 23863. Luis A. Zapata acknowledges financial supportfrom DGAPA, UNAM, and CONACyT, M´exico. JorgeCant´o acknowledges support from PAPIIT–UNAM–IG 100218. This paper makes use of the followingALMA data: ADS/JAO.ALMA − −
12 0 12 24V lsr (kms − )0 . . . . . . . F l u x ( J y / b e a m ) $ obs − −
12 0 12 24V lsr (kms − ) − $ obs − −
12 0 12 24V lsr (kms − )0 . . . . . . F l u x ( J y / b e a m ) $ obs − −
12 0 12 24V lsr (kms − ) − $ obs − −
12 0 12 24V lsr (kms − )0 . . . . . . . F l u x ( J y / b e a m ) $ obs − −
12 0 12 24V lsr (kms − ) − $ obs Figure A3 . Intensity profiles at the position of the cylindrical radii (cid:36) obs (left panels) and − (cid:36) obs (right panels) in Figure 5 ata height z = −
80 au. The red line shows the best Gaussian fits to the intensity profiles of SiO (J=8–7) ν = 0 (upper panels),SiS (J=19–18) ν = 0 (middle panels), and SiO (J=8–7) ν = 1 (lower panels). APPENDIX A. MEASUREMENT PROCEDUREThe position-velocity diagrams in Figures 2–4 were analyzed to derive the physical parameters: the cylindrical radius (cid:36) obs , the expansion velocity v exp , and the rotation velocity v rot , as a function of the height z . These properties werecompared with the physical properties of the thin shell model of LV19.Figure A1 shows the intensity profiles at V LSR = 5 km s − as a function of the distance to the outflow axis ata height z = −
80 au for the molecular lines SiO (J=8–7) ν = 0 (panel a), SiS (J=19–18) ν = 0 (panel b), and SiO (J=8–7) ν = 1 (panel c). These panels also show a Gaussian fit to the intensity profiles (red solid lines). Thecylindrical radius (cid:36) obs is the width of the Gaussian profile and the error if given by the Gaussian fit. In panel (b),the three peaks correspond to the emission from three shells. For our measurements, we only consider the two mostprominent peaks. The cylindrical radius of the shell model is the projection of the spherical radius R s at a given3height, (cid:36) model = R s sin θ , where θ = cos − ( z/R s ).Figure A2 shows the intensity profiles at a height z = −
80 au at the outflow axis (angular offset =0 au in Figure 5)as a function of velocity for the three molecular lines, SiO (J=8–7) ν = 0 (panel a), SiS (J=19–18) ν = 0 (panel b),and SiO (J=8–7) ν = 1 (panel c). The expansion velocity is calculated at the outflow axis as v exp = ( v + − v − ) / v ± are the radial velocities corresponding to the width of the Gaussian profile. The axial velocity v z is calculatedas v z = ( v + + v − ) /
2. The errors are given by the Gaussian fit. In the case of the anisotropic stellar wind model, for agiven inclination angle i , one calculates v ± as the projection along the line of sight of the velocity of the two sides ofthe shell. The axial velocity is also corrected by the system velocity V LSR .Figure A3 shows the intensity profiles as a function of the velocity at the cylindrical radii, (cid:36) obs (left panels) and − (cid:36) obs (right panels), shown as vertical dotted lines in Figure 5, for the three molecular lines, SiO (J=8–7) ν = 0(upper panels), SiS (J=19–18) ν = 0 (middle panels), and SiO (J=8–7) ν = 1 (lower panels). The red solid linesshow the Gaussian fits, some of which require 2 Gaussians.The rotation velocity is given as the difference between the outer edges of widths of the intensity profiles at ± (cid:36) obs ,indicated by the dashed line in each panel (see also the inclined solid lines in Figure 5). The error bars are given bythe Gaussian fit. For the model, we use the rotation velocity v φ .Figures A1–A3 show, as an example, the analysis to obtain the observed quantities (cid:36) obs , v exp , v z , and v rot at z = − z in Figures 9 and 10.REFERENCESin Figures 9 and 10.REFERENCES