Multi-scale view of star formation in IRAS 21078+5211: From clump fragmentation to disk wind
L. Moscadelli, H. Beuther, A. Ahmadi, C. Gieser, F. Massi, R. Cesaroni, ?. Sánchez-Monge, F. Bacciotti, M.T. Beltrán, T. Csengeri, R. Galván-Madrid, Th. Henning, P.D. Klaassen, R. Kuiper, S. Leurini, S.N. Longmore, L.T. Maud, T. Möller, A. Palau, T. Peters, R.E. Pudritz, A. Sanna, D. Semenov, J.S. Urquhart, J.M. Winters, H. Zinnecker
AAstronomy & Astrophysics manuscript no. 39837corr © ESO 2021February 10, 2021
Multi-scale view of star formation in IRAS 21078 + L. Moscadelli , H. Beuther , A. Ahmadi , C. Gieser , F. Massi , R. Cesaroni , Á Sánchez-Monge , F. Bacciotti , M. T.Beltrán , T. Csengeri , R. Galván-Madrid , Th. Henning , P. D. Klaassen , R. Kuiper , S. Leurini , S. N. Longmore ,L. T. Maud , T. Möller , A. Palau , T. Peters , R. E. Pudritz , A. Sanna , D. Semenov , , J. S. Urquhart , J. M.Winters , and H. Zinnecker (A ffi liations can be found after the references) ABSTRACT
Context.
Star formation (SF) is a multi-scale process in which the mode of fragmentation of the collapsing clump on scales of 0.1–1 pc determinesthe mass reservoir and a ff ects the accretion process of the individual protostars on scales of 10–100 au. Aims.
We want to investigate the nearby (located at 1.63 ± + ∼ ∼
10 au.
Methods.
We combine the data of two recent programs: the NOrthern Extended Millimeter Array (NOEMA) large project CORE and the Proto-stellar Outflows at the EarliesT Stages (POETS) survey. The former provides images of the 1 mm dust continuum and molecular line emissionswith a linear resolution of ≈
600 au covering a field of view up to ≈ au down to a few astronomical units. Results.
In IRAS 21078 + ∼ ∼ ≈ − per 0.1 pc) LSR velocity ( V LSR ) gradient is detected across the major axis of themolecular cloud. Assuming we are observing a mass flow from the harboring cloud to the cluster, we derive a mass infall rate of ≈ − M (cid:12) yr − .The most massive cores (labeled 1, 2, and 3) are found at the center of the cluster, and these are the only ones that present a signature of protostellaractivity in terms of emission from high-excitation molecular lines or a molecular outflow. The masses of the young stellar objects (YSOs) insidethese three cores are estimated in the range 1–6 M (cid:12) . We reveal an extended (size ∼ (cid:46) ≈
14 km s − over 500 au) V LSR gradient at the position of YSO-1, oriented approximately perpendicularto the radio jet. Assuming this is an edge-on, rotating disk and fitting a Keplerian rotation pattern, we determine the YSO-1 mass to be 5.6 ± M (cid:12) . The water masers observed in the POETS survey emerge within 100–300 au from YSO-1 and are unique tracers of the jet kinematics.Their three-dimensional (3D) velocity pattern reveals that the gas flows along, and rotates about, the jet axis. We show that the 3D maser velocitiesare fully consistent with the magneto-centrifugal disk-wind models predicting a cylindrical rotating jet. Under this hypothesis, we determine thejet radius to be ≈
16 au and the corresponding launching radius and terminal velocity to be ≈ ≈
200 km s − , respectively. Conclusions.
Complementing high-angular resolution, centimeter and millimeter interferometric observations in thermal tracers with Very LongBaseline Interferometry (VLBI) of molecular masers, is invaluable in studying high-mass SF. The combination of these two datasets allows usto connect the events that we see at large scales, as clump fragmentation and mass flows, with the physical processes identified at small scales,specifically, accretion and ejection in disk-jet systems.
Key words.
ISM: jets and outflows – ISM: molecules – Masers – Radio continuum: ISM – Techniques: interferometric
1. Introduction
High-mass ( > ∼ M (cid:12) and > ∼ L (cid:12) ) stars form within youngstellar object (YSO) clusters deeply embedded inside thickdust cocoons, whose study requires the superior angular res-olution and sensitivity achieved only recently by the new orupgraded (sub)millimeter interferometers, such as the AtacamaLarge Millimeter / submillimeter Array (ALMA), the NOrthernExtended Millimeter Array (NOEMA), and the SubMillimeterArray (SMA). The processes of the formation of these clus-ters via the collapse and fragmentation of the parental molecularclump into multiple smaller cores, and mass accretion on indi-vidual cores, are not yet clear. Observing similar scales of 0.1–1 pc with comparable angular resolution of > ∼ (cid:48)(cid:48) , recent SMAand ALMA studies of infrared-quiet massive clumps have re-vealed di ff erent fragmentation properties: in some cases, lim-ited fragmentation with a large fraction of cores with masses in the range 8–120 M (cid:12) (Wang et al. 2014; Csengeri et al.2017; Neupane et al. 2020), and, in other cases, a large popu-lation of low-mass ( ≤ M (cid:12) ) cores with a maximum core mass of11 M (cid:12) (Sanhueza et al. 2019). There is a clear need for extend-ing these kind of studies to identify the main agent(s) of molec-ular clump fragmentation. In the very early evolutionary phases,one would expect negligible support against gravitational col-lapse from thermal pressure and protostellar feedback (such asoutflows or H ii regions), and theoretical models predict that themain competitors of gravity should be the internal clump turbu-lence and magnetic pressure (e.g., Federrath 2015; Klessen &Glover 2016; Hennebelle et al. 2019).The fragmentation modality determines the mass reservoirfor the formation of individual stars and a ff ects the accretionprocess as well, as discussed by the two main competing the-ories: the “core-accretion” model (McKee & Tan 2003), whichpredicts the existence of quasi-equilibrium massive cores pro- Article number, page 1 of 25 a r X i v : . [ a s t r o - ph . GA ] F e b & A proofs: manuscript no. 39837corr viding all the material to form high-mass stars, and the “compet-itive accretion” model (Bonnell et al. 2004), in which the parentclump fragments into many low-mass cores that competitivelyaccrete the surrounding gas. Within a core cluster, tidal inter-actions among nearby ( ∼ ff er perturbations (Winter et al. 2018) or trun-cation (Goddi et al. 2011), depending on the relative mass andseparation of the interacting YSOs.Surveys at infrared and radio wavelengths have discoveredthat filaments are ubiquitous in massive molecular clouds (Moli-nari et al. 2010b; Lu et al. 2018) and have a wide range inlengths (a few to 100 pc) and line masses (a few hundreds tothousands of M (cid:12) pc − ). Young stellar object clusters and high-mass YSOs are often found at the junctions (named “hubs”)of this filamentary structures in molecular clouds (see, for in-stance, Myers 2009), and longitudinal mass flows (with typicalrates of 10 − –10 − M (cid:12) yr − ) along the filaments converging to-ward the hubs have been identified (Chen et al. 2019; Schwöreret al. 2019; Treviño-Morales et al. 2019). These recent findingsstrongly suggest that hub-filament systems can play a funda-mental role in the formation of high-mass stars and have ledto complementary or alternative theories to the core-accretionand competitive-accretion models, such as the “global hierarchi-cal collapse” (Vázquez-Semadeni et al. 2019), “conveyor belt”(Longmore et al. 2014), and “inertial-inflow” (Padoan et al.2020) models. The main di ff erence among these theories regardsthe origin of the hub-filament structures inside molecular cloudsand the main driver (turbulence, density gradient, cloud-cloudcollision, etc.) of the mass flows, but they all agree that the ma-terial to form the YSO clusters can be gathered from very largescales of 1–10 pc, channeled through the molecular cloud fila-ments.Aiming at a statistical study of clump fragmentation anddisk properties in high-mass YSOs, we are carrying out thelarge program "CORE" (P.I.: Henrik Beuther; team web-page: "http: // / core"), observing a sample of 20high-mass star-forming regions with the IRAM interferometerNOEMA in the 1.37 mm continuum and line emissions at high-angular resolution (0 (cid:48)(cid:48) . CN and CH OH rotational transitions, LSR veloc-ity ( V LSR ) gradients are often detected toward the most massivecores of the cluster (Ahmadi et al. 2018; Bosco et al. 2019; Cesa-roni et al. 2019; Gieser et al. 2019). Extending over typical linearscales of (cid:46) V LSR gradients are interpreted in termsof the edge-on rotation of either a disk around a high-mass YSOor an unresolved binary (or multiple) system, or the combinationof both motions.IRAS 21078 + ± × L (cid:12) , least luminous CORE sources (Beuther et al. 2018,see Table 1). IRAS 21078 + + + ≈ (cid:48)(cid:48) . + au to 10 au. Recent Large Binoc-ular Telescope (LBT) observations are also employed to revealthe structure of the molecular outflows at the largest scales. TheCORE and LBT observational setups, data reduction and analy-sis are described in Sect. 2, including a brief summary of the PO-ETS observations of IRAS 21078 +
2. Observations
The CORE program employs IRAM / NOEMA multi-configuration interferometric observations complementedwith short-spacing IRAM 30 m single-dish data. A full descrip-tion of the IRAM / NOEMA observational strategy and sampleselection are given in Beuther et al. (2018) and the IRAM 30 mobservations are detailed in Ahmadi et al. (2018) and Mottramet al. (2020). Hereafter, we report on the observations, datareduction, and analysis specifically for IRAS 21078 + The IRAM / NOEMA interferometer observedIRAS 21078 + − + h m s + ◦ (cid:48) (cid:48)(cid:48) .
50, and the systemic V LSR was assumed equal to V sys = − − . In the course ofthe CORE observing campaign, the number of the NOEMAantennas increased from 6 to 8. The baseline lengths in the uv -plane range from 34 m to 765 m, corresponding to spatialfrequencies from 0 (cid:48)(cid:48) .
37 to 8 (cid:48)(cid:48) .
3. The gain calibrators werethe quasars J2201 +
508 and 2037 + ≈ − ),and eight narrow-band high-spectral resolution ( ≈ − )units distributed over the broad band. The wide band is usedto extract the line-free continuum, to get a chemical census ofthe region, and to study the distribution of more di ff use gasand the outflow kinematics (through low-excitation lines of the CO, H CO and SO molecules). The eight narrow-band spectral
Article number, page 2 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Table 1.
Parameters of the molecular lines employed in the analysis
Frequency Molecule Transition E u / k B (GHz) (K)218.222 H CO 3 , –2 , N 24–23 131219.560 C O 2–1 16219.949 SO 6 –5 CO 11 , –10 , CO 2–1 16220.594 CH CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 CN 12 –11 Notes.
Column 1 report the rest frequency of the transition; Col. 2 the molec-ular species; Col. 3 the quantum numbers; Col. 4 the upper state en-ergy. The quantum numbers are given depending on the symmetry ofthe molecule: J upper − J lower for linear, J upper K − J lower K for symmetric top,and J upper K a , K c − J lower K a , K c for asymmetric top molecules. units are centered at specific spectral locations to observe typi-cal dense-gas tracers (such as high-excitation lines of CH CN,CH OH, and CH CO) for investigating the gas kinematics andphysical conditions at high-angular resolution. A detailed de-scription of the spectral line coverage can be found in Beutheret al. (2018, see Table 8) and Ahmadi et al. (2018). Table 1shows the parameters, taken from the CDMS (Cologne Databasefor Molecular Spectroscopy , Müller et al. 2001, 2005) and JPL(Jet Propulsion Laboratory Catalog of Molecular Spectroscopy ,Pickett et al. 1998) databases, of all the molecular lines analyzedin this article.The NOEMA data were calibrated with the CLIC and im-aged with the MAPPING package in gildas . The continuumdata were extracted from line-free channels of the wide-bandWideX spectra. Phase self-calibration was performed on the con-tinuum data using the SELFCAL procedure. The gain table con-taining the self-calibration solutions was then applied to thenarrow- and wide-band spectral line data using the UV_CALtask. A detailed description of the phase self-calibration of theCORE continuum and spectral line data can be found in Gieseret al. (submitted).The NOEMA continuum data were imaged with uniformweighting using the Clark algorithm (Clark 1980). The synthe-sized beam of the continuum image of IRAS 21078 + (cid:48)(cid:48) .
48 and 0 (cid:48)(cid:48) .
33, and PA = ◦ . For the extended CO and SOemissions, we used the low-resolution WideX spectral line datasmoothed to a spectral resolution of 3.0 km s − . In order to avoidmissing flux due to missing short-spacings, the data were com-bined with the IRAM 30 m observations and imaged with a ro-bust parameter of 3 using the SDI algorithm (Steer et al. 1984). http: // / cdms / https: // spec.jpl.nasa.gov / For IRAS 21078 + (cid:48)(cid:48) .
70 and 0 (cid:48)(cid:48) .
61, andPA = ◦ . For the compact emissions of CH CN, HC N, andCH CO, we used the narrow-band NOEMA-only data smoothedto a spectral resolution of 0.5 km s − and imaged with uniformweighting using the Clark algorithm. The NOEMA images ofIRAS 21078 + (cid:48)(cid:48) .
46 and 0 (cid:48)(cid:48) .
31, with beam PA = ◦ . IRAS 21078 + (cid:48) × (cid:48) . Us-ing double-sideband receivers, the IRAM 30 m data cover abroader range of frequencies than the NOEMA data, between ≈
213 and ≈
221 GHz in the lower sideband and between ≈ ≈
236 GHz in the upper sideband. At 1.37 mm, the angularand spectral resolution of the single-dish observations is ≈ (cid:48)(cid:48) and 0.195 MHz (or 0.27 km s − ), respectively. Merging theIRAM 30 m telescope data and the NOEMA visibilities yieldscoverage of the uv-plane in the inner 15 m. The IRAM 30 m datawere calibrated using the CLASS package in gildas. To matchthe NOEMA observations, the IRAM 30 m data were smoothedto a spectral resolution of 3 km s − . A more detailed descriptionof the calibration of the single-dish data is provided in Mottramet al. (2020). The POETS survey complements multi-epoch VLBI observa-tions of water masers with high-angular resolution deep imagingof radio continuum emission with the JVLA in a relatively largesample (38) of massive protostellar outflows. Moscadelli et al.(2016) give a general description of the POETS program, sampleselection, observations, and data analysis. Hereafter, we resumeonly the main observational parameters of IRAS 21078 + The water maser emission (at 22.23508 GHz) inIRAS 21078 + survey (project code: BR145E) at six epochs spanning aboutone year (from May 2010 to May 2011) with a total observingtime per epoch of approximately seven hours. A generaldescription of the BeSSeL VLBA observational setup is givenin Reid et al. (2009). In the course of the observations ofIRAS 21078 + ≈ (cid:48)(cid:48) . − . In IRAS 21078 + − , respectively. The Bar and Spiral Structure Legacy (BeSSeL) survey is a VLBAkey project, whose main goal is to derive the structure and kinemat-ics of the Milky Way by measuring accurate positions, distances (viatrigonometric parallaxes), and proper motions of methanol and watermasers in hundreds of high-mass star-forming regions distributed overthe Galactic disk (Reid et al. 2014). Article number, page 3 of 25 & A proofs: manuscript no. 39837corr
Fig. 1.
Upper panel: NOEMA 1.37 mm continuum emission (color map) of IRAS 21078 + σ ( σ = − ) to the peak intensity of 35 mJy beam − , in steps of 7 σ . The little black crosses indicate the positions of theseven strongest 1.37 mm peaks labeled as in Beuther et al. (2018, see Table 5), with label numbers ordered in intensity. The restoring beam of the1.37 mm continuum map is shown in the lower left corner. Lower panel: Wide-field Infrared Survey Explorer (WISE) 4.6 µ m image (color map,Wright et al. 2010) toward IRAS 21078 + µ m continuum (Di Francesco et al. 2008), showing10 levels increasing logarithmically from 7 σ ( σ = − ) to 11.4 Jy beam − . The magenta rectangle delimits the region plotted in theupper panel.Article number, page 4 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + IRAS 21078 + ) between October 2012and January 2013 in A configuration (project code: 12B-044), inC, Ku, and K bands (centered at 6.2, 13.1, and 21.7 GHz, respec-tively). In the following, we also refer to C- and K-band observa-tions as the JVLA 5 cm and 1.3 cm continuum, respectively. Thetotal on-source time was 15 min at C and Ku bands, and 30 minat K band. We employed the capabilities of the new WIDARcorrelator to record dual polarization across a total bandwidthper polarization of 2 GHz. For the JVLA A-Array continuumimages of IRAS 21078 + (cid:48)(cid:48) . (cid:48)(cid:48) .
5, 0 (cid:48)(cid:48) .
17 and 1 (cid:48)(cid:48) .
8, 0 (cid:48)(cid:48) .
08 and 1 (cid:48)(cid:48) . µ Jy beam − , at C, Ku, and K band,respectively. Near-infrared (NIR) observations toward IRAS 21078 + × . + K s ( λ c = . µ m, FWHM = µ m) and narrow-band H ( λ c = . µ m, FWHM = µ m) filters. We operated LUCI 2 in seeing-limited imag-ing, single telescope mode, using camera N3.75, which providesa plate scale of ≈ (cid:48)(cid:48) per pixel and a field of view of 4 (cid:48) × (cid:48) . Theimages were taken according to a dithering pattern alternating apointing in which the nominal position of IRAS 21078 + ≈ (cid:48) from the frame center, so that all theframes contain the target position and skies can be obtained byselecting subsets of the more distant pointings. The H observa-tions consist of 31 dithered images with DIT = = K s observations consist of13 dithered images with DIT = .
74 s, NDIT =
18 (total integra-tion time 641 s).Data reduction was performed using standard
IRAF rou-tines. Each frame was flat-fielded using dome flat images andcorrected for bad pixels. As they are vignetted, we cut outthe outermost pixels before further steps. Skies were then con-structed for each frame by median-filtering a subset of fourframes selected from the nearest in time that also have largepointing o ff sets. For each filter, all sky-subtracted frames wereregistered and averaged together. The final mosaicked imagesexhibit point spread functions (PSFs) ≈ (cid:48)(cid:48) wide. The continuumemission in the H filter was estimated by comparing photome-try of stars in the K s and H images. The two images were thenscaled and subtracted from each other to produce an image show-ing pure H . µ m line emission. NRAO is a facility of the National Science Foundation operated un-der cooperative agreement by Associated Universities, Inc. IRAF is distributed by the National Optical Astronomy Observato-ries, which are operated by the Association of Universities for Researchin Astronomy, Inc., under cooperative agreement with the National Sci-ence Foundation.
Fig. 2.
IRAM 30 m data. Intensity-weighted velocity (color map) ofthe C O J = CO J = CO J K a , K c = , -2 , (lower panel) lines determined over a smallvelocity range, [ − − − , around V sys = − − . Theplotted region corresponds to the area in which the velocity-integratedemission of the C O J = − km s − , ≈ σ . In each panel, the black contours represent the SCUBA 850 µ mcontinuum (Di Francesco et al. 2008), showing 10 levels increasing log-arithmically from 1 to 11.4 Jy beam − . The white rectangle delimits theregion plotted in the upper panel of Fig. 1.Article number, page 5 of 25 & A proofs: manuscript no. 39837corr
As the images showed a complex blob of line emission nearthe target (which in turn appears obscured in the NIR), we de-cided to perform further adaptive optics (AO) assisted observa-tions to try resolving possible bow-shock features making up theblob. New NIR observations were then obtained with LUCI 1and FLAO (Esposito et al. 2012) at the LBT in di ff raction-limited mode on October 1, 2017, as part of the INAF program2017_2018_36 (PI: Massi). A field including both the targetnominal position and the line emission blob was imaged throughthe H and K s filters using camera N30, which provides a platescale of ≈ (cid:48)(cid:48) per pixel and a field of view of 30 (cid:48)(cid:48) × (cid:48)(cid:48) . A starwith R ≈
12 at a distance of ≈ (cid:48) from the imaged field was se-lected as a guide star. A dithering pattern with random pointingsa few arcseconds apart was selected. The H data consist of a setof 24 dithered frames with DIT =
10 s and NDIT =
15 (total in-tegration time 1 hr) and the K s data of a set of 6 dithered frameswith DIT = =
20 (total integration time 10 min).The frames were flat-fielded and bad pixels were removed. Foreach frame, a sky was constructed by median filtering the near-est (in time) four frames. The sky-subtracted frames were finallyregistered and averaged together. Unfortunately the AO correc-tion was not very e ffi cient (owing to the lack of a suitable guidestar) and a Strehl ratio of only ≈
1% was obtained. Nevertheless,these latest images (with a PSF FWHM ≈ (cid:48)(cid:48) .
3) exhibit a bet-ter spatial resolution than the previous seeing-limited images .An image showing pure H . µ m line emission was obtainedfollowing the same procedure as above.Comparing NIR images with radio and millimeter interfer-ometric data, which usually have high positional accuracy, re-quires an astrometric calibration as precise as possible. First,we obtained an astrometric solution for the seeing-limited, largefield-of-view images by cross-matching them with 2Mass PointSource Catalog entries. We were able to use about 100 rela-tively bright stars all over the field. Then, we cross-correlated theseeing-limited images and the AO-assisted images, finding ≈ (cid:48)(cid:48) .
3. Results
The upper panel of Figure 1 shows the 1.37 mm continuumemission in IRAS 21078 + − , the seven strongest of which are indicated inFig. 1 (upper panel). The global pattern of the 1.37 mm contin-uum is elongated in the SE-NW direction: the PA of the majoraxis, determined through a linear fit to the positions of the sevenstrongest cores, is 149 ◦ ± ◦ . The three strongest cores arefound inside a higher-emission plateau at the center of the clus-ter, and the lower-intensity cores draw an arc of weaker emissionencircling the plateau clockwise from SE to NW, with no coresfound to SW.The spatial distribution of the cores in the cluster revealedby the 1.37 mm continuum emission on linear scales of 10 auhas several properties in common with the patterns of di ff erentSF indicators on larger scales. The lower panel of Figure 1 showsthat the core cluster is embedded within a molecular cloud tracedby the 850 µ m emission from cold dust, which presents a similarSE-NW elongation (PA ≈ ◦ ). In turn, this molecular cloud is edged on the northeastern side with a necklace of compact4.6 µ m sources, associated with less embedded and, likely, moreevolved YSOs in the region. This distribution resembles that ofthe cores in the cluster on ten times smaller scales.To study the kinematics of the gas in the parental molecu-lar cloud enshrouding the core cluster, we use the IRAM 30 mmaps of three low-excitation ( E u / k B ≤
21 K) molecular lines: CO J = O J = CO J K a , K c = , -2 , .Figure 2 shows that, close to V sys = − − , the veloci-ties increase regularly from NW to SE along the major axis ofthe molecular cloud, reaching the highest values in correspon-dence of the core cluster. To investigate the gas kinematics insidethe cluster, Fig. 3 shows velocity-channel maps of the mergedNOEMA–IRAM 30 m observations of the CO J = V sys , namely at V LSR of − − − , the CO J = au along a SE-NW directionclose to the similarly oriented, elongation axes of the 1.37 mmcore cluster and 850 µ m molecular cloud. Despite the limitedvelocity resolution of only 3 km s − , a V LSR gradient across thewhole cluster, and its gaseous envelope, is clearly detected, thegas to N-NW emitting at lower V LSR than the gas to SE. Thus,the merged NOEMA–IRAM 30 m observations of the CO J = CO J = J N = -5 (Fig. 4) transitions. At rel-atively high absolute line of sight (LOS) velocities, that is | V LSR − V sys | ≥ − , the channel emission in both lines ischaracterized by a SW-NE elongated feature pointing to core 1(the strongest 1.37 mm continuum emitter), and placed eitherNE or SW of core 1 at high red-shifted ( ≥− − ) or blue-shifted ( ≤−
10 km s − ) V LSR . A straightforward interpretation forthis emission feature in the CO and SO lines, as discussed indetail in Sect. 4.2.1, is in terms of a collimated outflow emittedby a YSO inside core 1. In the SO J N = -5 channel maps at V LSR ≈ −
13 km s − , the emission is dominated by a strong bowshock of this outflow located ≈ (cid:48)(cid:48) SW of core 1. Aside from theprominent signature of the outflow from core 1, the only othernotable emission feature at high absolute LOS velocities is acompact source visible (especially in the SO channel maps) atvery blue-shifted velocities ( −
28 km s − ≤ V LSR ≤ −
20 km s − )to N-NE of core 4 (the northernmost core).In IRAS 21078 + E u / k B ≥
70 K)molecular lines observed in the CORE program are only de-tected from inside the higher-emission plateau at the center ofthe 1.37 mm continuum distribution. The upper panel of Figure 5shows the velocity-integrated intensity of the CH CN J K = -11 line, which is representative of the spatial distribution of allthe observed dense-gas tracers. The CH CN emission peaks atthe position of core 1 and it becomes progressively weaker mov-ing from core 3 (near core 1) to core 2 (displaced further to S; seeFig. 1, upper panel). In the lower panel of Fig. 5, the 1.37 mmcontinuum is overlaid with the tracers of the outflows discov-ered in this region, that is the SW-NE (PA = ◦ ± ◦ ), double-component radio jet detected in the POETS survey and the red-and blue-shifted integrated emission of the CORE SO J N = -5 line. It should be noted that the NE component of the radiojet with thermal emission from ionized gas near the YSO, coin-cides with core 1, and that the radio jet and the SO outflow areapproximately parallel to each other. These two findings lead usto assume that the YSO embedded in core 1 is driving the radiojet, which, in turn, powers the larger-scale molecular outflow. In Article number, page 6 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Fig. 3.
Merged NOEMA–IRAM 30 m data. Each panel presents the emission of the CO J = ff erent velocity channel.In the upper right corner of the panel, the channel V LSR (in kilometer per second) and the range of plotted intensity (in square parentheses inmilliJansky per beam) are reported. The red boxes and ticks identify the panels corresponding to the central velocities, that is | V LSR − V sys | < − . The white crosses mark the positions of the seven strongest peaks of the 1.37 mm continuum emission. At the central velocities, theblack dashed line gives the major axis of the 1.37 mm core cluster. Fig. 4.
Merged NOEMA–IRAM 30 m data. Each panel presents the emission of the SO J N = -5 line (color map) in a di ff erent velocitychannel. In the upper right corner of the panel, the channel V LSR (in kilometer per second) and the range of plotted intensity (in square parenthesesin milliJansky per beam) are reported. The red boxes and ticks identify the panels corresponding to the central velocities, that is | V LSR − V sys | < − . The white crosses mark the positions of the seven strongest peaks of the 1.37 mm continuum emission. Article number, page 7 of 25 & A proofs: manuscript no. 39837corr
Fig. 5.
Upper panel: NOEMA data. Velocity-integrated intensity (color map) of the CH CN J K = -11 line. The 1.37 mm continuum emissionis represented with black contours, showing seven levels increasing logarithmically from 11 to 35 mJy beam − . The positions of the three strongestpeaks of the 1.37 mm continuum emission are indicated, using the same labels as in Beuther et al. (2018, see Table 5). The restoring beams of theCH CN J K = -11 line and 1.37 mm continuum maps are shown in the lower right and left corners, respectively. Lower panel: The blue andred contours reproduce the emission of the SO J N = -5 line integrated over the velocity ranges [ − −
13] and [ −
1, 5] km s − , respectively.The plotted levels are from 0.03 to 2.5 Jy beam − , in steps of 0.27 Jy beam − , and from 0.6 to 2.2 Jy beam − , in steps of 0.37 Jy beam − , forthe blue- and red-shifted SO emission, respectively. The magenta contours give the JVLA A-Array continuum at 5 cm (Moscadelli et al. 2016),showing levels at 40%, 50%, and 90% of the peak emission of 95 µ Jy beam − : the magenta dashed line connects the two strongest (nearby, butresolved) 5 cm peaks. The two black dashed lines delimit the viewing angle of the blue-shifted emission of the SO J N = -5 line from the NE5 cm peak (aligned in position with core 1, see Sect. 3.1). The black contours have the same meaning as in the upper panel. Sect. 4.2.1, we check this assumption by comparing the proper-ties of the radio jet and the SO outflow. Hereafter, we refer to theYSO inside core 1 as "YSO-1".
Toward cores 1, 2, and 3, the emission of the higher-excitationmolecular lines is strong enough to allow us to study the kine-matics and physical conditions of the gas. For this purpose, weused the XCLASS (eXtended CASA Line Analysis SoftwareSuite) tool (Möller et al. 2017). This tool models the data by
Article number, page 8 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Fig. 6.
Beam-averaged spectrum (black line) of the CH CN J K = K -11 K ( K = K = K = solving the radiative transfer equation for an isothermal homo-geneous object in local thermodynamic equilibrium (LTE) in onedimension. It can produce maps of column density, tempera-ture, velocity, and line width by extracting spectra pixel-by-pixelfrom the image cubes and fitting all the unblended lines of agiven molecular species simultaneously. The finite source size,dust attenuation, and line opacity are considered as well, whichalso permits us to properly fit the transitions of relatively lower-excitation energy and higher optical depths (as the CH CN J K = K -11 K , K = ffi ciently optically thin to reliablytrace the more embedded gas kinematics. More specifically, inthis analysis we made use of the following molecular lines:CH CN J K = K -11 K ( K = CO J K a , K c = , -10 , ,and HC N J = < (cid:46) CN J K = K -11 K ( K = CN J K = K -11 K (K = CNisotopologs). Figure 7 shows the maps of the CH CN col- umn density and velocity toward the central plateau of the1.37 mm continuum, where the three most intense cores reside.The CH CN column density reaches 10 cm − toward core 1and it is a factor of 2 lower toward core 2. Two V LSR gradients areclearly detected: the first across the adjacent cores 1 and 3, char-acterized by a change of ≈ − over ≈ ≈ − over ≈ CN J K = K -11 K ( K = E u / k B varying in the range 97–326 K) is concen-trated mainly toward core 1 (see Fig. 7, upper panel), we alsoidentified a few molecular lines of slightly lower excitation, suchas the CH CO J K a , K c = , -10 , transition ( E u / k B =
76 K),which have comparable intensity toward cores 1 and 3 and canbe employed to resolve the emission of the two cores in ve-locity. The upper panels of Fig. 8 show the maps of the peakemission of the CH CN J K = -11 line toward core 1 andthe CH CO J K a , K c = , -10 , line toward core 3, whilethe lower panel of Fig. 8 reports the spectra of the two molec-ular lines integrated over the corresponding core. Among theCH CN transitions, we selected the K = E u / k B =
247 K), which allows us to better resolve the warm
Article number, page 9 of 25 & A proofs: manuscript no. 39837corr
Fig. 7.
NOEMA data. The color map reproduces the column density(upper panel) and the velocity (lower panel) of the CH CN emissiondetermined by fitting with XCLASS the CH CN J K = K -11 K (K = CN isotopologs), simultaneously. Theplotted regions correspond to the areas in which the 1.37 mm continuumemission is higher than 13 and 16 mJy beam − for the column densityand velocity plots, respectively. The 1.37 mm continuum emission isrepresented with black contours, showing six levels increasing logarith-mically from 13 to 35 mJy beam − : the positions of the three strongest1.37 mm peaks are denoted using the same labels as in Beuther et al.(2018, see Table 5). The restoring beams of the 1.37 mm continuumand CH CN maps are shown in the lower left corner of the upperpanel and lower right corner of the lower panel, respectively. gas inside core 1. To determine the area of the two cores, weused the minimum level (18.6 mJy beam − , indicated by theblack contours in Fig. 8) of the 1.37 mm continuum in corre-spondence of which two disconnected emission islands are stillobtained. We stress that in this analysis we used the emissionsof the CH CN J K = -11 and CH CO J K a , K c = , -10 , lines only to derive the velocities of the cores 1 and 3, whose ex-istence and geometrical properties are independently establishedfrom the 1.37 mm continuum emission. The two cores are sepa-rated by ≈
770 au and their LOS velocities di ff er by ≈ − .Therefore, it appears that the relative motion of the two cores canaccount for the observed V LSR gradient. This result is used inSect. 4.1.2, where we consider the possibility that the two coresare members of a binary system.Our recent H µ m LBT observations towardIRAS 21078 + µ m emission arises from shock-excited, com-pressed, and hot molecular gas placed ≈ (cid:48)(cid:48) SW of core 1, pin-pointed by the NE component of the radio jet at the center ofthe SO molecular outflow. Examining the lower panel of Fig. 9,which provides a higher-angular resolution view of the shockstructure, we note two well-shaped bow shocks at the SW tipsof the H µ m emission. Since the major axes of these bowshocks approximately coincide with the directions to core 1, itis plausible that these shocks have been excited by an outflowemerging from core 1. Assuming that the outflow source residesin core 1, Fig. 9 (upper panel) shows that di ff erent outflow trac-ers, namely, the nearby SW lobe of synchrotron emission, theweak 5 cm spur ≈ µ m bow shock ≈ ff erent PAs. In Sect. 4.4, wediscuss several scenarios to explain the spread in the directionsof the various outflow tracers. Toward IRAS 21078 + ≈
625 au (for a FWHM beam size of ≈ (cid:48)(cid:48) . ffi cient to resolve nearby molec-ular cores, on scales (cid:38) ≤ CN J K = K -11 K ( K = J = N J = J K a , K c = , -9 , ) per-mits us to study the gas kinematics on linear scales ≤ δθ / × ( σ / I ) (see,e.g., Reid et al. 1988), where δθ is the FWHM beam size and I and σ are the peak intensity and the rms noise, respectively, ofa given channel. With an average value of the ratio ( I / σ ) = (cid:46)
10 mas. For channels with resolved emission, thecentroid positions convey more complex kinematic informationbecause in these channels it is very likely that we are observ-ing the combination of di ff erent types of motions and the shapeof the emission can strongly deviate from a Gaussian. Conse-quently, for these channels the peak position obtained with theGaussian fit is less reliable.The upper panel of Figure 10 shows the distribution of chan-nel centroids for the CH CN J K = K -11 K ( K = N J = CN andHC N lines to show that the two molecules have a very similar V LSR pattern. This allows us to combine their emissions in our
Article number, page 10 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Fig. 8.
NOEMA data. Upper panels: The color maps reproduce the emission of the CH CN J K = -11 (left) and CH CO J K a , K c = , -10 , (right) lines. In the upper right corner of the panel, the channel V LSR (in kilometer per second) and the range of plotted values (in milliJanskyper beam) are reported. The white contours reproduce the 1.37 mm continuum, with the same levels as in Fig. 7: the positions of the two nearby1.37 mm peaks are denoted using the same labels as in Beuther et al. (2018, see Table 5), namely, 1 and 3 for the primary and secondary peak,respectively. In the right panel, the blue segment connects the two peaks. In the two panels, the black contours delimit the integration areas usedto produce the spectra toward cores 1 and 3, presented in the lower panel. Lower panel: Spectra of the CH CN J K = -11 line toward core 1(blue histogram) and the CH CO J K a , K c = , -10 , line toward core 3 (red histogram). The flux scales for the CH CN and CH CO spectra arereported on the left and right, vertical axes, respectively. The blue and red dashed vertical lines indicate the approximate V LSR of the cores 1 and 3,respectively. kinematical analysis. The colored contours of Fig. 10, reproduc-ing the half-peak emission levels, clearly indicate that the struc-ture is really compact only at the most extreme red- and blue-shifted velocities. At V LSR ≈ − − , the contamination fromthe nearby core 3 is evident. In the lower panel of Fig. 10 onlythe positions of the compact-emission channels at the extremevelocities are plotted. The distribution is bipolar and elongated along a direction, at PA = ◦ ± ◦ , approximately perpendic-ular to the radio jet. The compact 1.3 cm continuum emission,which best pinpoints the position of YSO-1, is located at thecenter of the distribution. In Sect. 4.2, we propose that the de-rived velocity pattern traces the accretion disk around YSO-1. Article number, page 11 of 25 & A proofs: manuscript no. 39837corr
Fig. 9.
Comparison of CORE, POETS and LBT observations. Upper panel: The gray-scale map reproduces the H µ m emission observedwith LBT toward IRAS 21078 + µ m emission to SW, respectively.The white dashed box delimits the region plotted in the lower panel. Lower panel: Adaptive-optics assisted LBT observations of the H µ memission (gray-scale map): the cyan dashed line has the same meaning as in the upper panel.Article number, page 12 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Fig. 10.
NOEMA data. Upper panel: The gray-scale map reproduces the 1.37 mm continuum emission, plotting values in the range 10–35 mJy beam − . The colored dots give the (Gaussian-fitted) positions of the channel emission peaks for the CH CN J K = K -11 K ( K = N J = V LSR . The colored contours indicate the half-peak level for the CH CN J K = -11 emission in individual channels. The yellow contours show the JVLA A-Array continuum at 1.3 cm (Moscadelli et al. 2016), showing levels at70%, 80%, and 90% of the peak emission of 0.50 mJy beam − . Lower panel: The gray-scale map, yellow contours, and colored dots have thesame meaning as in the upper panel. Only the channel emission peaks at the extreme blue- and red-shifted velocities (reported in the lower rightcorner of the panel) are shown. The white continuous and dashed lines indicate the best-fit major axis of the distribution of the peaks and thecorresponding fit uncertainty, respectively. Article number, page 13 of 25 & A proofs: manuscript no. 39837corr
4. Discussion
The 1.37 mm continuum cluster is found at the density peak ofa SE-NW elongated molecular cloud edged on the northeasternside with a necklace of less embedded YSOs and on the south-western side with a filament of di ff use 4.6 µ m emission (seeFig. 1, lower panel). These findings suggest that the molecu-lar cloud is a density enhancement of a more extended, infrareddark filament. In Sect. 3.1 we showed that the velocities of theslow-moving ( ≤ − ) gas of the cloud and the cluster varysmoothly along the major axis of the molecular cloud over lin-ear scales of 10 –10 au (see Figs. 2 and 3). This regular changein V LSR with position makes us favor the interpretation in termsof a flow in the molecular gas (converging toward the densitypeak where the most massive cores reside) compared with cloud-cloud collision, which would rather appear as a sudden jump invelocity. In the assumption of a mass flow, the observed V LSR gradient can be easily explained if the blue-shifted NW side ofthe molecular cloud is farther away from us than the red-shiftedSE side. The spatial and velocity extents of this V LSR gradient arecomparable with those of the gradients, ∼ − per 0.1 pc, ob-served in infrared dark clouds (IRDC) at the sites of YSOs (Ra-gan et al. 2012), which are often interpreted as infall. It is alsoconsistent with simulations of large-scale accretion flows alongfilaments, gravitationally accelerated toward local density peaks(see, e.g., Tobin et al. 2012; Smith et al. 2013).Assuming we are observing a mass infall toward the corecluster, we can use both the IRAM 30 m and merged NOEMA–IRAM 30 m observations of the CO J = P inf , to the length, L inf , of the flow. In Ap-pendix B, we describe the method to calculate the momentum ofa molecular outflow, by employing the CO J = CO J = − − − for the IRAM 30 m observations (see Fig. 2), and[ − − − for the merged NOEMA–IRAM 30 m data(see Fig. 3). Second, the FWHM size of the map beam is B max = B min = (cid:48)(cid:48) .
8, for the IRAM 30 m observations. It is remarkablethat, using either the IRAM 30 m or the merged NOEMA–IRAM 30 m observations, we obtain very consistent values forthe infall momentum P inf cos( i inf ) ≈ M (cid:12) km s − , where i inf is the inclination angle of the flow with respect to the LOS.Taking L inf sin( i inf ) ≈ × au, corresponding to the averagevalue between the (sky-projected) flow lengths measured in theIRAM 30 m (8 × au, see Fig. 2) and NOEMA-IRAM 30 m(4 × au, see Fig. 3) maps, we finally derive a mass infall rate˙ M inf cot( i inf ) = P inf cos( i inf ) / L inf sin( i inf ) ≈ M (cid:12) km s − / × au ≈ − M (cid:12) yr − . Following the discussion in Ap-pendix B, owing to the uncertainties in the excitation temper-ature and abundance ratio of the CO J = Fig. 11.
NOEMA data. The color map shows the distribution of therotational temperature derived by fitting with XCLASS the emission ofthe CH CN J K = K -11 K (K = CNisotopologs). The plotted region corresponds to the area in which the1.37 mm continuum emission is higher than 16 mJy beam − . The blackcontours reproduce the 1.37 mm continuum, showing the same levelsas in Fig. 7: the positions of the three strongest 1.37 mm peaks areindicated using the same labels as in Beuther et al. (2018, see Table 5).The restoring beam of the CH CN maps is shown in the lower rightcorner of the panel.
Figure 11 shows the rotational temperature determined withXCLASS by simultaneously fitting the emission of theCH CN J K = K -11 K (K = CNisotopologs). While toward core 1 the gas temperature is al-ways ≥
115 K and may reach 200 K, toward core 3 it variesin the range 90–130 K. In correspondence of core 2 the tem-perature map is less homogeneous, probably owing to insu ffi -cient signal-to-noise ratio, and has an average temperature thatis intermediate between that of core 1 and core 3. By combin-ing the maps of the 1.37 mm dust continuum and gas temper-ature, assuming that the dust emission is optically thin, we canmake a reasonable estimate of the core masses. For consistencywith Beuther et al. (2018), we adopt a dust absorption coef-ficient of 0.9 cm g − (Ossenkopf & Henning 1994) and agas-to-dust mass ratio of 150 (Draine 2011). Over the areas ofcore 2 and the combined cores 1 and 3 (see Fig. 11), the massis found to be 0.46 and 0.92 M (cid:12) , respectively. Inside the indi-vidual cores 1 and 3, whose corresponding areas are delimitedby the black contours in the upper panels of Fig. 8, we obtain agas mass of 0.42 M (cid:12) and 0.12 M (cid:12) , respectively. These valuesrepresent the mass inside the cores within radii ≤
500 au, andthey are lower than the total core masses determined by Beutheret al. (2018, see Table 5) over radii ≥ Article number, page 14 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + In Sect. 3.2, using the CH CN J K = K -11 K (K = . ± . M (cid:12) . InSect. 3.2, we showed that the V LSR gradient across the adjacentcores 1 and 3 can be well explained in terms of the relative mo-tion of the cores. Assuming that we are observing rotation seenalmost edge-on, in gravito-centrifugal equilibrium, from the spa-tial separation between the cores, ≈
770 au, and their di ff erencein velocity, ≈ − (see Sect. 3.2), we derive a total mass of ≈ M (cid:12) . Subtracting both the mass of YSO-1 of ≈ M (cid:12) and that(0.92 M (cid:12) , see above) of the gas embedded inside cores 1 and 3,we obtain a rough estimate for the mass of the YSO inside core 3of ≈ M (cid:12) . Regarding core 2, interpreting the V LSR gradient( ≈ − across ≈ ≈ M (cid:12) . After subtracting the gas mass of0.46 M (cid:12) (see above), the derived mass for the YSO inside core 2is ≈ M (cid:12) . Despite the large uncertainty in these determinations,the presence of relatively low-mass YSOs inside cores 2 and 3agrees with the lower temperature (see Fig. 11) and mass of thesecores with respect to core 1. Among the 20 cores identified in the 1.37 mm continuum emis-sion of IRAS 21078 + ≥ M (cid:12) ), show signatures of an embedded protostar. As describedin Sect. 3.1 (see also Fig. 5, upper panel), the higher-excitationmolecular lines are only detected toward these three cores, in-dicating that they are su ffi ciently warm to require local heatingby a protostar. Fitting the CH CN J K = K -11 K lines, the gastemperature over the three cores is found everywhere (cid:38)
100 K(see Sect. 4.1.2), and, through the observed V LSR gradients (seeSect. 3.2), the masses of the embedded YSOs are evaluated in therange 1–6 M (cid:12) (see Sect. 4.1.2). The concentration of the mostmassive cores (and YSOs) toward the center of the 1.37 mm con-tinuum cluster hints at mass segregation.Judging the evolutionary state of the other, less massive coresis di ffi cult with the present observations. Comparing with themost massive cores, the non-detection toward these cores ofthe higher-excitation molecular lines indicates an upper limit of (cid:46) M (cid:12) for the mass of the embedded YSOs. The fact that nomolecular outflows are detected from the less massive cores (seeSect. 3.1) would be consistent with most of these cores still be-ing in a prestellar phase. However, with our data, a molecularoutflow is observed only from the most massive YSO, YSO-1 in core 1, and this hints at a sensitivity limit when using the CO J = J N = -5 lines as outflow tracers. Fu-ture interferometric observations in the CO J = + M (cid:12) ) stars (see,for instance, Testi et al. 1999). Ae and Be PMS stars are young enough, 0.5–5 Myr, that any population of lower-mass stars bornin the same environment did not have enough time to moveaway from the birthplace. Therefore, the spatial distribution ofthe stars reflects that of the parental molecular cores. The typicalsize of these NIR stellar clusters is ≈ pc − , are found in correspondence withthe most massive ( ≈ M (cid:12) ) Ae or Be stars. In IRAS 21078 + ≈ − pc , equivalent toa density of 2 × pc − , and the most massive YSO (YSO-1) has already attained a mass close to 6 M (cid:12) . In Sect. 4.1.1,we calculated a mass infall rate of ∼ − M (cid:12) yr − from theparental molecular cloud (total mass of 177 M (cid:12) , Beuther et al.2018, see Table 1) to the core cluster, which, over the charac-teristic formation time of a few 10 yr of the Ae and Be PMSstars (Palla & Stahler 1993), would imply an infall toward thecluster of a few 10 M (cid:12) . If a relevant fraction of this mass is ac-creted by the most massive YSOs at the center of the cluster, it isvery likely that at least one high-mass ( ≥ M (cid:12) ) star will form. Inconclusion, because of the relatively high stellar density and thelikelihood of ultimately forming massive stars, we think that theIRAS 21078 + Absolute positions and proper motions of the 22 GHz watermasers observed in IRAS 21078 + ≈ ◦ , of the maser spatial distribution, and theaverage direction of the proper motions, PA ≈ ◦ (Moscadelliet al. 2019, see Table A1), are in good agreement with the orien-tation, PA ≈ ◦ , of the double-component radio jet (see Fig. 5).The faint, thermal, and nonthermal emissions from the NE andSW radio lobes, respectively, and the water masers are all mani-festations of di ff erent types of shocks produced by the jet. In thejet core, close to YSO-1, we observe free-free emission, whichlikely originates from relatively weak (C-type), internal shocksof the jet corresponding to changes in the mass loss or ejec-tion velocity (Moscadelli et al. 2016; Anglada et al. 2018); thenonthermal emission is likely synchrotron emission from elec-trons accelerated at relativistic velocities in strong jet shocksthrough first-order Fermi acceleration (Bell 1978); finally, thefast water masers emerge from relatively strong (J-type) shocks,whereas the jet impinges on very dense (molecular hydrogennumber density, n H ∼ cm − ) ambient material at high ve-locity (Moscadelli et al. 2020).As reflected in Fig. 5 (lower panel), the radio jet and themolecular outflow traced by the SO J N = -5 line at largerscales are approximately parallel to each other and, as alreadyanticipated in Sect. 3.1, the molecular outflow could be poweredby the jet. To assess the physical association between the jet andmolecular outflow, in the following we determine and comparetheir physical properties. In Appendix B, we describe the methodto calculate the momentum of the molecular outflow, P out . Weobtain P out cos( i out ) ∼ M (cid:12) km s − , where i out is the inclina-tion angle of the outflow with respect to the LOS. Employing thewater maser positions and three-dimensional (3D) velocities, themomentum rate of the jet in IRAS 21078 + Article number, page 15 of 25 & A proofs: manuscript no. 39837corr
Fig. 12.
POETS water maser observations. Upper panel: Colored dots and arrows give absolute positions and proper motions of the 22 GHzwater masers determined with VLBI observations (Moscadelli et al. 2016); colors denote the maser V LSR . The dot area scales logarithmically withthe maser intensity. The black contours indicate the JVLA A-Array continuum at 1.3 cm (Moscadelli et al. 2016), showing levels from 10% to90% of the peak emission of 0.50 mJy beam − in steps of 10%. Lower panel: Colored dots and black contours have the same meaning as in theupper panel. Colored cones are employed to visualize the maser 3D velocities, representing the inclination with respect to the LOS through theellipticity of the cone basis and the uncertainty in the direction by means of the cone aperture.Article number, page 16 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + be ˙ P jet ∼ × − M (cid:12) km s − yr − by Moscadelli et al. (2016,see Sect. 6.2, Eq. 1, and Table 5). In this calculation, a majorsource of uncertainty was the pre-shock, ambient density, whichwas assumed to be n H ∼ cm − . Now, thanks to the COREdata, we can better constrain this parameter. Averaging the de-rived mass distribution (see Sect. 4.1.2) over a cylindric volumeequal to the beam area times the beam size, in the direction ofthe continuum peak we find the value n H ≈ × cm − , whichshould be accurate to within a factor of a few. Accordingly, ournew, more precise, estimate of the momentum rate of the jet is˙ P jet ∼ × − M (cid:12) km s − yr − .We wish to derive the momentum rate of the molecular out-flow, to be compared with that of the jet. Knowing the valueof P out cos( i out ) (see above), we need to estimate the inclinationangle and timescale of the outflow. The clear spatial separationof the blue- and red-shifted lobes (see Fig. 5, lower panel) in-dicates that the gas flows along directions significantly inclinedwith respect to both the LOS and the plane of the sky. Basedon the opening angle of ≈ ◦ of the blue-shifted outflow lobe(see Fig. 5, lower panel), we judge that the outflow axis has tobe at least 20 ◦ away from both the LOS and the plane of thesky, that is 20 ◦ ≤ i out ≤ ◦ . The dynamical timescale of theoutflow, t out , can be estimated from the ratio of the size of thelobes to the corresponding maximum V LSR range. Referring tothe SO J N = -5 emission in Fig. 5 (lower panel), we have: t out tan( i out ) ≈ (cid:48)(cid:48) /
27 km s − = × yr, at a distance of1.63 kpc. We caution that previous studies have pointed out thatthe dynamical timescale of molecular outflows can largely un-derestimate (by a factor between 5 and 10) the true outflow age(see, for instance, Parker et al. 1991). Accordingly, the upperlimit for the momentum rate of the outflow is found to be ˙ P out cos ( i out ) / sin( i out ) (cid:46) × − M (cid:12) km s − yr − . Considering thatthis value is only accurate to within an order of magnitude andthat 0 . ≤ sin( i out ) / cos ( i out ) ≤ ◦ ≤ i out ≤ ◦ , we con-clude that the momentum rate of the molecular outflow is con-sistent with that of the jet. It is then plausible that the jet powersthe molecular outflow. The velocity pattern in Fig. 10 (lower panel) is consistent withthat expected for a rotating disk around a YSO. It is elongatedapproximately perpendicular to the radio jet, the blue- and red-shifted velocities lie on the two sides of the YSO, and its size of ≈
400 au agrees with the model predictions for accretion disksaround high-mass YSOs (see, for instance, Kölligan & Kuiper2018). The V LSR does not present a regular change with the po-sition, but that likely results from the limited precision in tracingthe velocity pattern using channel emission centroids and the in-su ffi cient angular resolution.Making the assumption (to be checked a posteriori, see be-low) of Keplerian rotation, we determine the central mass, M (cid:63) ,by minimizing the following χ expression: χ = (cid:88) j [ V j − ( V (cid:63) ± .
74 ( M (cid:63) sin ( i rot )) . | S j − S (cid:63) | − . )] ( ∆ V j ) , (1)where V j and S j are the channel V LSR (in kilometer per sec-ond) and corresponding peak positions (in arcsecond), the index j runs over all the fitted channels, and the + and − symbols holdfor red- and blue-shifted velocities, respectively. V (cid:63) (in kilome-ter per second) and S (cid:63) (in arcsecond) are the V LSR and position
Fig. 13.
Plot of the χ values from the Keplerian fit (see Eq. 1) vs. thefree parameter M (cid:63) sin ( i rot ). The horizontal black dashed line indicatesthe value χ + = σ confidencelevel for the χ -distribution with one free parameter (Lampton et al.1976). The two vertical blue dashed lines indicate the 1 σ confidenceinterval for the best-fit value of the free parameter. of YSO-1, respectively. The central mass M (cid:63) is given in solarmasses. Indicating with i rot the inclination of the disk rotationaxis with respect to the LOS, the factor sin ( i rot ) takes into ac-count that the disk plane is seen at an angle 90 − i rot from theLOS and the observed V LSR corresponds to the rotation velocitymultiplied by the factor sin( i rot ). To take into account the uncer-tainty on the velocity and that on the position, the global velocityerror ∆ V j is obtained by summing in quadrature two errors: thaton the velocity (taken equal to half of the channel width) and thatobtained by converting the error on the o ff set into a velocity errorthrough the function fitted to the data.The V LSR , V (cid:63) = − . − , and position S (cid:63) = (cid:48)(cid:48) . V LSR andpositions of all the channels. Thus, the term M (cid:63) sin ( i rot ) isthe only free parameter in Eq. 1. We allowed this term to varyover the range 2–14 M (cid:12) , which is consistent with the upperlimit of ≈ M (cid:12) imposed by the bolometric luminosity of ≈ L (cid:12) (Davies et al. 2011). Figure 13 reports the plot of the χ vs. the free parameter; the blue dashed lines delimit the1 σ confidence interval following Lampton et al. (1976). Thisplot shows that we do find an absolute minimum of the χ andthe determined 1 σ range for the values of the free parameter is M (cid:63) sin ( i rot ) = . ± . M (cid:12) .The fitted value of M (cid:63) is much larger than the gas mass,0.42 M (cid:12) , inside core 1, derived from the dust emission inSect. 4.1.2. As noted in Sect. 4.1.2, this is the mass inside core 1 Article number, page 17 of 25 & A proofs: manuscript no. 39837corr within a radius ≤
500 au, which is comparable to the size of thedisk structure traced by the CH CN and HC N lines aroundYSO-1 (see Fig. 10, lower panel). The YSO-1 envelope shouldextend at significantly larger radii and be much more massive.The finding that the central mass is much greater than the massof the disk supports our assumption of Keplerian rotation. Thedisk, traced by the bipolar V LSR pattern of molecular emissions(see Fig. 10, lower panel), and the radio-maser jet are approxi-mately perpendicular to each other in the plane of the sky. Thissuggests that the jet is directed close to the rotation axis of thedisk, or i jet ≈ i rot (where i jet is the inclination of the jet withrespect to the LOS). From the angular distribution of the maserproper motions, reported in Fig. 12, the semi-opening angle ofthe jet is evaluated to be ≈ ◦ by Moscadelli et al. (2016,see Table 5). Figure 12, lower panel, also shows that the watermasers are both blue- and red-shifted, which indicates that thejet intersects the plane of the sky and the relation | i jet − ◦ | (cid:46) ◦ must hold. Following these considerations, we can writesin ( i rot ) ≈ sin ( i jet ) (cid:38) sin (72 ◦ ) = ( i rot ) in the range 0.9–1, the 1 σ intervalfor the fitted YSO-1 mass is M (cid:63) = . ± . M (cid:12) .By employing the relationship between bolometric luminos-ity, L bol , and outflow momentum rate, ˙ P , for massive YSOs byMaud et al. (2015) (Log [ ˙ P / M (cid:12) km s − yr − ] = − . + . [ L bol / L (cid:12) ]), and our best estimate of the momentum rate˙ P jet ∼ × − M (cid:12) km s − yr − (see Sect. 4.2.1), we infer a lu-minosity of 5 × L (cid:12) for YSO-1. This value is consistent withthe luminosity of 1.3 × L (cid:12) of the IRAS 21078 + ∼ (cid:48) , Neugebauer et al. 1984) only . In-deed, combining the far-infrared IRAS fluxes with the mid-infrared, Wide-Field Infrared Survey Explorer (WISE; Wrightet al. 2010) and Midcourse Space Experiment (MSX; Egan et al.2003) data at higher angular resolution ( ∼ (cid:48)(cid:48) ), Moscadelli et al.(2016, see Table 1) determine a lower luminosity of 5 × L (cid:12) ,which agrees well with that inferred for YSO-1. The radio-maser jet emerging from YSO-1 is unique in com-bining two properties that, to our knowledge, for the first timeare observed associated with the same object: a lobe with non-thermal emission and jet rotation. We noted the first point sev-eral times through this article and this refers to the SW lobe ofthe double-component radio jet (see Fig. 5, lower panel), whosespectral index over the frequency range 6–22 GHz is ≤− + V LSR gradientof the water masers transversal to the jet direction. Figure 12(lower panel) shows the monotonic change of the maser V LSR along a SE-NW direction perpendicular to the SW-NE collima-tion axis of the proper motions, with red- and blue-shifted V LSR toward SE and NW, respectively. The linear correlation betweenthe maser LOS velocities, V LOS = V LSR − V (cid:63) , and positionsprojected perpendicular to the jet direction, R per , is clearly illus- Neither Herschel infrared Galactic Plane Survey (Hi-GAL; Molinariet al. 2010a,b) nor Red MSX Source (RMS; Hoare et al. 2005; Lumsdenet al. 2013) observations are available for IRAS 21078 + Fig. 14.
Plot of the maser positions projected perpendicular to the jetaxis, R per , vs. corresponding LOS velocities, V LOS , for the masers with V LOS ≥ −
20 km s − . Colored error bars are used to indicate values andassociated errors; the colors represent the distance from YSO-1 pro-jected along the jet axis, R axi , as coded in the wedge on the right-handside of the panel. The black dashed line shows the linear fit to the plottedvalues. trated in Fig. 14. A straightforward interpretation for the maser3D velocity pattern is in terms of a composition of two motions:a flow along, and a rotation around, the jet axis.The findings of nonthermal emission from a jet lobe andjet rotation are strong indications that magnetic fields play animportant role in both launching and accelerating the jet. Theinterpretation of the nonthermal continuum in terms of syn-chrotron emission requires the presence of a magnetic field suf-ficiently ordered and strong to trap electrons in jet shocks, con-fine them even at relativistic velocities, and warrant the detec-tion of their synchrotron signal. Jet rotation is considered a crit-ical test for magneto-centrifugal (MC) DW (Blandford & Payne1982; Pudritz et al. 2007), where the magneto-centrifugallylaunched jet extracts the excess angular momentum from thedisk gas, which, then, can be accreted by the protostar. Compar-ing Figs. 10 and 12, we evince that the jet and the disk of YSO-1rotate about axes approximately parallel to each other and havethe same sense of rotation, that is, toward and away from us toNW and SE, respectively. This result supports our idea that thejet rotation stems from the disk through the magnetic leverage ofa MC DW.The measurement of the 3D velocities of the jet near the YSOthrough water maser VLBI observations permits a more quanti-tative comparison with the predictions of the MC DW theory.According to the MC DW models (Pudritz et al. 2007), the YSOwind is centrifugally launched along the magnetic field lines Article number, page 18 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Fig. 15.
Plot of the components V axi vs. V Φ (see definitions in Sect. 4.3)for the 3D maser velocities shown in Fig. 12. Colored error bars are usedto indicate values and associated errors; the colors represent the distancefrom YSO-1 projected along the jet axis, R axi , as coded in the wedge onthe right-hand side of the panel. The black dashed line shows the linearfit to the subset of points within the region delimited by the horizontaland vertical black dotted lines, corresponding to V Φ ≤
20 km s − and V axi ≥ − . threading the accretion disk, it is accelerated to the Alfvén speedsliding along the rotating field lines, and then is magneticallycollimated. A large body of di ff erent MC DW simulations haveshown that, depending on the assumed magnetic field configu-ration, the final jet structure can be either collimated toward acylinder or at wide angle (Pudritz et al. 2007). In the following,we compare our water maser observations with wind models thatrecollimate within a cylindrical flow tube (see, for instance, thesimulations in Sta ff et al. (2015) and Kölligan & Kuiper (2018)).We also note that a model of a cylindrical rotating jet has been re-cently proposed by Burns et al. (2015) to interpret the 3D motionof the water masers observed with VERA (VLBI explorationof radio astrometry; Kobayashi et al. 2003) toward the massiveYSO S235AB-MIR.Let us indicate with r the radius of the footpoint of themagnetic field line anchored to the disk and with r A the dis-tance from the rotation axis at which the wind velocity equalsthe Alfvén speed. At radii r c ≥ r A , the wind recollimates, andits velocity has two (dominant) components: the main compo-nent oriented along the jet axis, Υ axi , and the azimuthal compo-nent, Υ Φ , representing the rotation around the axis. CombiningEqs. 12 and 13 of Pudritz et al. (2007), the ratio of these twocomponents can be related to the radius r c of the cylindricalflow through the expression Υ axi / Υ Φ ≈ √ r c / r A . (2)The water masers originate in shocks that arise where thejet impinges on high-density material and propagate away alongthe jet direction at a speed, assuming momentum conservation, V = (cid:112) ρ jet /ρ amb Υ (see, for instance, Masson & Chernin 1993).In this equation, ρ jet and Υ are the jet density and speed,respectively, and ρ amb is the ambient density. Since the watermasers move parallel to the wind, their motion can be described in terms of the composition of the same velocity components,that is, that directed along the jet axis and the azimuthal com-ponent. Let us indicate with V axi and V per the maser velocitycomponents in the plane of the sky parallel and perpendicularto the sky-projected jet axis (at PA = ◦ ). Since the jet is di-rected close ( ≤ ◦ , see sect. 4.2.2) to the plane of the sky, V axi approximates the component along the jet axis with a maximumerror of cos − (18 ◦ ) ≈ V Φ , isequally well approximated with V Φ ≈ (cid:113) V + V . From theconsiderations above, it is clear that the ratio of the maser ve-locity components V axi and V Φ is an accurate measurement ofthe corresponding ratio of the wind velocity components, that is, Υ axi / Υ Φ ≈ V axi / V Φ .Figure 15 shows that the ratio V axi / V Φ is approximatelyconstant for the vast majority of the water masers (with measuredproper motions). We obtain V axi / V Φ ≈ ±
1. The only no-table exception is a small maser cluster at the most blue-shiftedvelocities ( V LOS ≤ −
20 km s − ) closer to YSO-1 (axis-projectedseparation R axi ≤
150 au), for which 1 (cid:46) V axi / V Φ (cid:46)
2. Onthe basis of Eq. 2, a simple explanation for the small spread inthe ratio of the maser velocity components is that most of themasers originate within a thin cylindrical shell, tracing shockedwind material MC-launched within a thin annulus of radius r of the rotating disk. This interpretation fits with the models pre-dicting a shock origin for the water masers, since it is plausiblethat the most external layer of the jet mainly interacts with thesurrounding ambient material and the water masers are mainlyfound on the jet wall. Thus, a reasonable estimate for the radiusof the jet, r jet , can be obtained from half the spread in R per , themaser positions projected perpendicular to the jet direction, con-sidering only the water masers with V LOS ≥ −
20 km s − (seeFig. 14). We derive r jet ≈
10 mas, or ≈
16 au.The terminal poloidal velocity of a MC DW, which for acylindrical flow corresponds to Υ axi , can be approximated as(Pudritz et al. 2007, see Eq. 12) Υ axi ≈ √ r A r υ K , , (3)where υ K , is the disk Keplerian velocity at the radius r . FromEq. 2 and knowing both the ratio of Υ axi / Υ Φ ≈ r c = r jet ≈
16 au, we get r A ≈ r A / r ≈
3. Then, using the above value of r A we infer r ≈ M (cid:63) ≈ M (cid:12) , we find υ K , ≈
50 km s − , which, through Eq. 3,yields Υ axi ≈
200 km s − and Υ Φ ≈
200 km s − / ≈
60 km s − .The derived values of jet radius and terminal velocity are inreasonable agreement with the few measurements of spatially re-solved radio jets from intermediate-mass YSOs (Anglada et al.2018, see Table 1) and the results from high-resolution, 3D nu-merical simulations of MC DWs to 100 au scale (Sta ff et al.2014, see Fig. 3). It is also plausible that our estimate for the jetrotational velocity is larger than the values of a few 10 km s − typical for jets from low-mass YSOs (Bacciotti et al. 2002; Cof-fey et al. 2004; Ray et al. 2007). The ratio of the maser tothe jet speeds depends on the density contrast between the jetand the ambient medium through V / Υ = (cid:112) ρ jet /ρ amb . High-angular resolution observations toward low-mass (Podio et al.2015; Gómez-Ruiz et al. 2015) and high-mass (Anglada et al.2018) YSOs, which are also supported by recent numerical sim-ulations of MC-DWs (Sta ff et al. 2019, see Fig. 5), indicate val-ues of n H ∼ cm − for the density of the high-velocity Article number, page 19 of 25 & A proofs: manuscript no. 39837corr gas in jets. From this value and our measurement of the av-erage ambient density in core 1 n H ≈ cm − , we derive V / Υ ∼ V axi =
23 km s − to the estimate for Υ axi ≈
200 km s − .A key prediction of the MC DW theory is that the wind massflux is about 10% of the accretion flux (Pudritz & Ray 2019).Assuming that YSO-1 gathers most of the mass flowing towardthe core cluster from the parental molecular cloud, its accretionrate can be estimated as ˙ M acc ≈ ˙ M inf ≈ tan( i inf ) 10 − M (cid:12) yr − (see Sect. 4.1.1). Combining the jet momentum rate ˙ P jet ∼ × − M (cid:12) km s − yr − (see Sect. 4.2.1) with the jet termi-nal velocity Υ axi ≈
200 km s − derived above, the mass ejectionrate of YSO-1 is found to be ˙ M eje ≈ × − M (cid:12) yr − . Thus,the ratio of the ejection and the accretion rates is ˙ M eje / ˙ M acc ≈ i inf ). For an intermediate value of (the inclination of theinfall) i inf ≈ ◦ , this ratio is consistent with the value of ≈ Since there is no hint of multiple YSOs inside core 1 in our data,the di ff erent direction of the outflows from core 1 shown in Fig. 9(upper panel) is most likely due to a change in the orientation ofthe jet ejected from YSO-1. The angle between the direction, atPA = ◦ , to the far H bow shock and the axis of the compactradio jet, is ≈ ◦ . From previous studies of jet precession (see,for instance, Fendt & Zinnecker 1998; Shepherd et al. 2000) andrecent 3D magnetohydrodynamics (MHD) simulations of proto-star formation (see, for instance, Hirano & Machida 2019), it isknown that several processes can produce a large ( ≥ a few 10 ◦ )change in the jet orientation: 1) radiation-induced warping ofthe protostellar accretion disk; 2) tidal interactions between thedisk around the primary and the secondary, within a close binarysystem; 3) anisotropic accretion; and 4) magnetic braking. In thefollowing, we discuss each of these points. We can readily ex-clude the first point, since the mass and luminosity of YSO-1 isnot su ffi cient to warp the disk. By employing Eq. 1 of Shepherdet al. (2000), we find that the size of the observed disk is ordersof magnitude smaller than the critical value beyond which thedisk can be unstable to warping.Concerning now the second point, we consider the bi-nary system of YSOs inside the adjacent cores 1 and 3 (seeSect. 4.1.2). Assuming that the disk surface density is uniform,for Keplerian rotation, the precession frequency is given by theexpression (Terquem et al. 1999, see Eq. 1) w p = − M s M p (cid:18) R d D (cid:19) cos( δ ) (cid:115) GM p R , (4)where M p and M s are the masses of the primary and sec-ondary stars, respectively, R d and D are the disk radius andbinary separation, respectively, and δ is the inclination an-gle of the binary orbit with respect to the plane of the disk.From Sects. 4.1.2 and 4.2.2, we have M p = M (cid:63) ≈ M (cid:12) , M s / M p ≈ D ≈
770 au. Referring to Fig. 10 (lower panel), R d ≈
250 au is estimated by taking half the spread in posi-tion (projected along the major axis of the distribution at PA = ◦ ) for the high-velocity molecular emissions tracing theYSO-1 disk. The line, at PA = ◦ , connecting the dust emis-sion peaks of cores 1 and 3 and the disk major axis form asmall angle of ≈ ◦ , which corresponds to the projection of δ on the plane of the sky: assuming cos( δ ) =
1, we calculatean upper limit for w p . Using the listed values for the parame-ters of Eq. 4, we infer a lower limit for the precession period T p = π/ w p (cid:38) × yr. Comparing this with the dynamicaltimescale of the outflow t out ∼ × yr (see Sect. 4.2.1), wecould argue that is very unlikely that the jet has precessed acrossan angle ≥ ◦ over a tiny fraction of the precession period. Theprecession axis should be directed close to the LOS and the bi-nary orbit should be seen almost face-on, with the consequencethat the mass of the binary system inferred from the observed V LSR gradient would be exceedingly too high with respect to themass of YSO-1. However, if the dynamical time underestimatedthe true outflow age by a factor as large as 10, the outflow life-time could still be a significant fraction (i.e., up to one-sixth) ofthe precession period. Therefore, we cannot completely excludethat the change in the YSO-1 jet direction at di ff erent lengthscales is due to precession induced by the tidal interaction be-tween the YSOs in cores 1 and 3.Recent 3D nonideal MHD simulations of the collapse of arotating, magnetized molecular clump (Tsukamoto et al. 2018;Hirano & Machida 2019; Machida et al. 2020), which aim tostudy the e ff ects of a misalignment between the rotation axisof the clump and the (initially) uniform magnetic field, indicatethat the evolution of the angular momentum of the central regionis controlled by both anisotropic accretion and magnetic brak-ing. While the former occurs during the earlier phases at lowerdensity when the prestellar clump preferentially contracts alongthe magnetic field line due to flux freezing, the latter operatesat higher density close to the protostar where an outer magneti-cally supported pseudo-disk and an inner centrifugally supporteddisk form. The above simulations show that the elongation of thedisk-like structure orbiting the protostar is approximately per-pendicular to the magnetic field at large scales (10 –10 au) andto the clump rotation axis at small scales ( ∼ au). The direc-tion of the protostellar outflow changes with time by a few 10 ◦ following the evolution of the accretion disk, and converges tothe rotation axis of the clump once the centrifugally supporteddisk has grown in size.The formation of the core cluster in IRAS 21078 + = ◦ ) and thedisk around YSO-1 in core 1 (at PA = ◦ ). According to theaforementioned simulations, the direction, at PA ≈ ◦ , of thejet from YSO-1 (the most evolved YSO in the cluster) should beclose to the rotation axis of the parental clump. The large-scalemagnetic field should be oriented approximately perpendicularto the SE-NW elongated, core cluster (see Fig. 1, upper panel),whose PA is 149 ◦ ± ◦ (see Sect. 3.1). Therefore, in this sce-nario, the direction from YSO-1 to the H bow shock, at PA = ◦ , would be about parallel to the magnetic field. The H shockstrace the direction of the jet axis at an earlier time than the radiojet because they are at a larger distance from YSO-1. The ob-served change in the jet orientation could then correspond to themodel-predicted evolution of the protostellar outflow, from be-ing collimated close to the magnetic field in the earliest phasesto ultimately align with the rotation axis of the clump. This inter-pretation, relying only on marginal evidence, is speculative, butit can be tested with future measurements of the magnetic fieldconfiguration in IRAS 21078 + Article number, page 20 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 +
5. Conclusions
This work combines the data of the CORE NOEMA millimeterinterferometer and POETS VLBA-JVLA radio surveys to studythe SF in IRAS 21078 + ∼ au to ∼
10 au.The CORE dust continuum and molecular line emissions allowus to map the cluster of molecular cores, identify the positionsof the YSOs, and determine the kinematics of the associatedaccretion-ejection structures down to a few 100 au. The POETSradio continuum and water maser data complement the COREinformation by unveiling the properties of the ionized gas andthe 3D gas kinematics near the YSOs at radii as small as a fewastronomical units. Our main results can be resumed as follows: – The SE-NW elongated, core cluster (size ∼ + ∼ V LSR gradi-ent of amplitude of ≈ − per 0.1 pc is detected acrossthe major axis of the molecular cloud and the cluster. Assum-ing we are observing a mass flow from the harboring cloudto the cluster, we derive a mass infall rate of ≈ − M (cid:12) yr − . – A signature of protostellar activity, in terms of emission fromhigh-excitation molecular lines or a molecular outflow, isfound only for the most massive cores (labeled 1, 2 and 3)at the center of the cluster. The masses of the YSOs in-side these three cores are estimated in the range 1–6 M (cid:12) .If a relevant fraction of the mass infalling onto the clusteris accreted by these more massive YSOs, it is likely that theIRAS 21078 + – We detect a SW-NE collimated, bipolar molecular outflowemerging from the most massive core 1. It is about parallelto the double-lobe (separation ≈ (cid:48)(cid:48) .
5) radio jet detected in thePOETS survey, ejected from a YSO embedded in core 1. Werefer to this YSO as YSO-1. We show that the momentumrates of the radio jet and the molecular outflow are compara-ble, which, also because of the similar orientation, leads usto think that the molecular outflow is driven by the radio jet. – A V LSR gradient of amplitude of ≈
14 km s − over 500 au,directed perpendicular to the radio jet, is revealed at the po-sition of YSO-1. We propose an interpretation in terms ofan almost edge-on, rotating disk and, by fitting a Keplerianrotation to the V LSR pattern, we obtain a mass for YSO-1 of5 . ± . M (cid:12) . – The water masers observed in IRAS 21078 + – The radio-maser jet from YSO-1 is unique in presenting alobe with nonthermal emission and a signature of jet rota-tion. The latter is the monotonic change of the maser V LSR along a (SE-NW) direction perpendicular to the (SW-NE)collimation axis of the maser proper motions. – We show that the maser 3D velocity pattern is consistent withthe MC DW models predicting the recollimation of the windwithin a rotating cylindrical flow. The masers could traceshocked gas at the wall of the cylindrical jet. We determinethe jet radius to be ≈
16 au and the corresponding launch-ing radius and terminal (poloidal) velocity ≈ ≈
200 km s − , respectively. Assuming that YSO-1 gathersmost of the mass flowing toward the core cluster from theparental molecular cloud, the ratio of the mass ejection andaccretion rates of YSO-1 can be consistent with the value( ≈ Acknowledgements.
A.P. acknowledges financial support from CONACyT and UNAM-PAPIITIN113119 grant, México.A.S.M. acknowledges support from the Collaborative Research Centre 956 (sub-project A6), funded by the Deutsche Forschungsgemeinschaft (DFG) - project184018867.D.S. acknowledges support by the Deutsche Forschungsgemeinschaft throughSPP 1833: “Building a Habitable Earth” (SE 1962 / / / / CNRS (France), MPG (Germany) and IGN (Spain).The LBT is an international collaboration among institutions in the United States,Italy and Germany. LBT Corporation partners are: The University of Arizona onbehalf of the Arizona Board of Regents; Istituto Nazionale di Astrofisica, Italy;LBT Beteiligungsgesellschaft, Germany, representing the Max-Planck Society,The Leibniz Institute for Astrophysics Potsdam, and Heidelberg University; TheOhio State University, and The Research Corporation, on behalf of The Univer-sity of Notre Dame, University of Minnesota and University of Virginia.
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Fermi 5, 50125Firenze, Italye-mail: [email protected] Max Planck Institut for Astronomy, Königstuhl 17, 69117 Heidel-berg, Germany Leiden University, Niels Bohrweg 2, 2333 CA Leiden, Netherlands I. Physikalisches Institut, Universität zu Köln, Zülpicher Str. 77, D-50937 Köln, Germany Max Planck Institut für Radioastronomie, Auf dem Hügel 69,53121, Bonn, Germany Instituto de Radioastronomía y Astrofísica, Universidad NacionalAutónoma de México, P.O. Box 3-72, 58090, Morelia, Michoacán,México UK Astronomy Technology Centre, Royal Observatory Edinburgh,Blackford Hill, Edinburgh EH9 3HJ, UK Institute of Astronomy and Astrophysics, University of Tübingen,Auf der Morgenstelle 10, D-72076 Tübingen, Germany INAF - Osservatorio Astronomico di Cagliari, Via della Scienza 5,09047 Selargius (CA), Italy Astrophysics Research Institute, Liverpool John Moores University,146 Brownlow Hill, Liverpool L3 5RF, UK European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748Garching bei München, Germany Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1,85748 Garching bei München, Germany Department of Physics and Astronomy, McMaster University, 1280Main St. W, Hamilton, ON L8S 4K1, Canada Department of Chemistry, Ludwig Maximilian University, Bute-nandtstr. 5-13, 81377 Munich, Germany Centre for Astrophysics and Planetary Science, University of Kent,Canterbury CT2 7NH, UK IRAM, 300 rue de la Piscine, Domaine Universitaire de Grenoble,38406, St.-Martin-d’Hères, France Universidad Autonoma de Chile, Avda Pedro de Valdivia 425, San-tiago de Chile, ChileArticle number, page 22 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Appendix A: Velocity distributions of CH CN andHC N close to YSO-1
Figure A.1 shows that the V LSR distributions of the CH CN andHC N emissions in proximity of YSO-1 are similar. For bothmolecules, the emission of the blue-shifted channels peak W-NW of YSO-1 (pinpointed by the compact 1.3 cm emission) andthat of the red-shifted channels E-SE of YSO-1.
Appendix B: Momentum of the molecular outflow
The momentum, P out , of the molecular outflow can be calcu-lated using the CO J = J N = -5 emis-sion lines, which at su ffi ciently high absolute LOS velocities( | V LSR − V sys | ≥ − ; see Figs. 3 and 4) mainly trace theoutflowing gas. In the limit of optically thin emission, we canuse the following expressions (see, for instance, Goldsmith &Langer 1999, Eq. 10): P out cos( i out ) = F (cid:88) k = n , k (cid:88) n = n , k J (cid:88) j = I n , j δ V | V n − V (cid:63) | d δ Ω , (B.1) F =
16 ln(2) B max B min Z mol ( T ex ) e E u / ( k B T ex ) h c g u A ul µ m H X mol , (B.2)where i out is the inclination angle of the outflow with respectto the LOS, the index k considers separately the two, blue-( k =
1) and red-shifted ( k = n extends over the velocity channels ( n , k ≤ n ≤ n , k ) of eachlobe, and j runs over all the J pixels of the maps shown inFigs. 3 and 4. In Eq. B.1, I n , j and V n are, respectively, the mapintensity and V LSR at pixel j for channel n , V (cid:63) ( ≈− − ,see Sect. 4.2.2) is the V LSR of YSO-1, δ V (0.5 km s − ) is thechannel width, d the distance (1.63 kpc) and δ Ω the solid angleof the pixel. In Eq. B.2, B max and B min are the FWHM sizes ofthe map beam along the major and minor axes, respectively, T ex the excitation temperature of the line, E u , g u and A ul the energyand the statistical weight of the upper level and the spontaneousemission coe ffi cient, respectively, of the transition, Z mol ( T ex ) themolecular partition function, X mol the molecular abundance withrespect to the H molecule, µ = m H the mass of the hydrogen atom, h the Planck constant, and c the speed of light.Table B.1 reports the parameters of the CO J = J N = -5 transitions, recovered from databases of molec-ular spectroscopy. Assuming LTE conditions, the T ex of the twolines can be approximated with the gas kinetic temperature. Alower limit is the value of ≈
66 K, averaged over the full ex-tent of the cluster, derived by Beuther et al. (2018, see Table 3)by fitting the IRAM 30 m H CO data at an angular resolutionof 11 (cid:48)(cid:48) . ≈
200 K toward core 1 from the XCLASS fit ofthe CH CN J K = K -11 K (K = T ex =
100 K, which should be accurateto within a factor of 2. We verified that the error on the out-flow momentum owing to this uncertainty on T ex is less thana factor of 2. By fitting the emission of the two lines and thedust continuum with XCLASS, and assuming the same dust ab-sorption coe ffi cient and gas-to-dust mass ratio of Sect. 4.1.2, weestimated the abundance ratios (with respect to H ) of the COand SO molecules to be 2 × − and 10 − , respectively. Em-ploying a single line for each molecular species does not allowus to correct for optical depth e ff ects, which can be significant inparticular for the more abundant CO. The H column density is derived from NOEMA-only data, so due to potential missingflux (by about a factor of 2 for IRAS 21078 + V LSR ranges [ V , k , V , k ] (where V , k and V , k arethe velocities of the channels n , k and n , k , respectively) forthe blue- ( k =
1) and red-shifted ( k = CO J = J N = -5 emissions aredetected with a high signal-to-noise ratio (see Figs. 3 and 4; thechannel at V LSR = − − of the SO J N = -5 line isexcluded because it is too noisy).Summing over the two outflow lobes, we derive a momentumfor the molecular outflow of ∼ M (cid:12) km s − and ∼ M (cid:12) km s − using the CO J = J N = -5 line, re-spectively. In the following, we adopt the intermediate value of P out cos( i out ) ∼ M (cid:12) km s − , which, based on the above con-siderations, should be accurate to within an order of magnitude. Article number, page 23 of 25 & A proofs: manuscript no. 39837corr
Fig. A.1.
NOEMA data. The gray-scale map reproduces the 1.37 mm continuum emission, plotting values in the range 10–35 mJy beam − .The colored dots give the (Gaussian-fitted) positions of the channel emission peaks for the CH CN J K = K -11 K ( K = N J = V LSR . The yellow contours show the JVLA A-Array continuum at 1.3 cm(Moscadelli et al. 2016), showing levels at 70%, 80%, and 90% of the peak emission of 0.50 mJy beam − .Article number, page 24 of 25. Moscadelli et al.: Multi-scale view of IRAS 21078 + Table B.1.
Parameters employed to calculate the momentum of the molecular outflow
Transition E u a / k B g u a A ul a T ex Z mol X mol B max B min [ V , , V , ] [ V , , V , ]K s − K arcsec arcsec km s − km s − SO J N = -5 × −
100 292 b − − − − + CO J = × −
100 38 c × − − − − + Notes. . ( a ) Molecular parameters from the Cologne Database for Molecular Spectroscopy (http: // / cdms / , Müller et al. 2001, 2005). ( b ) Derived from the partition function tabulated by Barklem & Collet (2016). ( c ) Calculated using data from the Jet Propulsion Laboratory Catalogof Molecular Spectroscopy (https: // spec.jpl.nasa.gov //