A 10- M ⊙ YSO with a Keplerian disk and a nonthermal radio jet
Luca Moscadelli, Alberto Sanna, Riccardo Cesaroni, Victor M. Rivilla, Ciriaco Goddi, Kazi L.J. Rygl
AAstronomy & Astrophysics manuscript no. 34366corr c (cid:13)
ESO 2019January 10, 2019
A 10- M (cid:12) YSO with a Keplerian disk and a nonthermal radio jet
L. Moscadelli , A. Sanna , R. Cesaroni , V. M. Rivilla , C. Goddi , , and K. L. J. Rygl INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italye-mail: [email protected] Max Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121, Bonn, Germany Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands Department of Astrophysics / IMAPP, Radboud University, PO Box 9010, 6500 GL, Nijmegen, The Netherlands INAF - Istituto di Radioastronomia & Italian ALMA Regional Centre, Via P. Gobetti 101, 40129, Bologna, ItalyJanuary 10, 2019
ABSTRACT
Context.
To constrain present star formation models, we need to simultaneously establish the dynamical and physical properties ofdisks and jets around young stars.
Aims.
We previously observed the star-forming region G16.59 − Methods.
We performed high-angular-resolution (beam FWHM ≈ (cid:48)(cid:48) .
15) 1.2-mm continuum and line observations towardsG16.59 − Results.
The main dust clump, with size ≈ au, is resolved into four distinct, relatively compact (diameter ∼ OCH and CH OH, we derived gas temperatures inside the mm sources inthe range 42–131 K, and calculated masses of 1–5 M (cid:12) . A well-defined Local Standard of Rest (LSR) velocity ( V LSR ) gradient isdetected in most of the high-density molecular tracers at the position of the high-mass YSO, pinpointed by compact 22-GHz free-freeemission. This gradient is oriented along a direction forming a large ( ≈ ◦ ) angle with the radio jet, traced by elongated 13-GHzcontinuum emission. The butterfly-like shapes of the P-V plots and the linear pattern of the emission peaks of the molecular lines athigh velocity confirm that this V LSR gradient is due to rotation of the gas in the disk surrounding the high-mass YSO. The disk radiusis ≈
500 au, and the V LSR distribution along the major axis of the disk is well reproduced by a Keplerian profile around a central massof 10 ± M (cid:12) . The position of the YSO is o ff set by (cid:38) (cid:48)(cid:48) . Key words.
ISM: jets and outflows – ISM: molecules – Masers – Radio continuum: ISM – Techniques: interferometric
1. Introduction
The formation of stars in the mass interval 1-20 M (cid:12) involves ac-cretion disks and fast collimated outflows or jets. Atacama LargeMillimeter Array (ALMA) observations at very high angular res-olution ( ≤ (cid:48)(cid:48) .
1) have recently provided clear examples of disk-jetsystems around young stellar objects (YSO) with luminositiesfrom low-mass to late O-type zero-age-main-sequence (ZAMS)stars (Lee et al. 2017; Ginsburg et al. 2018; Sanna et al. 2018a).From a theoretical point of view, the role played by turbulence,magnetic field, gravitational instability and radiation feedbackin defining the properties of the system (disk size and velocityprofile; jet orientation and collimation) is still highly debated(Matsumoto et al. 2017; Tan et al. 2014; Kuiper & Hosokawa2018). Detailed studies of disk-jet systems are therefore essen-tial to constrain current star-formation models.Since all star-formation models state that accretion and ejec-tion are intimately related, studying the properties of the out-flows from YSOs, which are much more extended and easier toobserve than the small accretion disks, can be an e ff ective way ofprobing the disk-jet systems. Observations reveal di ff erent char-acteristics for solar-type and B-type YSOs: 1) the molecular outflows tend to be less collimated with increasing YSO mass(Beuther & Shepherd 2005), and 2) only a few radio jets areknown in B-type YSOs, whereas they are commonly observedtowards low-mass protostars (Moscadelli et al. 2016; Sanna et al.2018b). If the larger distances and the more rapid evolution of B-type YSOs could in part explain these di ff erences, we know thatadditional processes are at work in the formation of the mostmassive stars. In comparison with low-mass protostars, the for-mation of B-type YSOs involves more energetic stellar radiation,which can ionize the surrounding gas and exert radiation pres-sure on it. The combined action of the magnetic field, the thermalpressure of the ionized gas, and the radiation pressure has beenmodeled by several authors (see, e.g., Peters et al. 2011; Vaidyaet al. 2011), and results in a lower collimation of the outflow. An-other notable di ff erence is that more massive B-type stars form inricher clusters (Carpenter et al. 1997; Hillenbrand & Hartmann1998), and dynamical and radiative interactions among clustermembers can significantly a ff ect the properties of the disk-jetsystems, causing disk fragmentation, jet precession, or even dis-ruption of the system (see, e.g., Farias & Tan 2018). Article number, page 1 of 16 a r X i v : . [ a s t r o - ph . S R ] J a n & A proofs: manuscript no. 34366corr
In this paper we report on recent ALMA observations of thestar-forming region (SFR) G16.59 − − ∼ L (cid:12) (Moscadelli et al. 2013) at a distance of 3.6 ± ≈ ≈ M (cid:12) (Beuther et al. 2002), the VLA C-Array obser-vations at 3.6, 1.3, and 0.7 cm by Zapata et al. (2006) identifiedtwo compact cm sources, named “a” and “b”, separated by ≈ (cid:48)(cid:48) along the SE–NW direction. From previous mm interferomet-ric observations we know that, while source “a” coincides withthe peak of the dust emission, indicating that this source is themost embedded, source “b” is found in good positional corre-spondence with intense, high-density molecular tracers, markinga hot molecular core (HMC).European VLBI Network (EVN) observations of the 6.7-GHz methanol masers demonstrate that this maser emission isassociated with the HMC and traces an elongated structure of ≈ ≈ M (cid:12) (Moscadelli et al. 2013). The sensi-tive Jansky Very Large Array (JVLA) A-Array observations at5, 2.3, and 1.3 cm by Moscadelli et al. (2013, see their Fig. 1) re-solve the compact cm source “b” into a radio jet, elongated ≈ (cid:48)(cid:48) along the E–W direction. The spectral index of the jet is nega-tive, indicating nonthermal emission over most of the jet, exceptthe peak close to the maser disk, where thermal free-free emis-sion is observed (Moscadelli et al. 2013, see their Fig. 2). Watermasers, monitored with the Very Long Baseline Array (VLBA)by Sanna et al. (2010), are distributed close to the HMC, and ap-pear to trace a wide, fast bow-shock at the head of the westernlobe of the radio jet.The combination of a rotating disk, as suggested by the 6.7-GHz maser proper motions, and a nonthermal radio jet, oneof the few observed in high-mass SFRs (see, e.g., Rodríguez-Kamenetzky et al. 2017), makes G16.59 − −
2. ALMA observations
ALMA observed G16.59 − − − ≈ ◦ . To check the astrometric accuracy, ALMA also observedthe quasar J1830-1606, separated from the target by ≈ ◦ . Wehave verified that the peak emission of the phase-calibrated im- age of J1830-1606 di ff ers from the nominal position by lessthan 10 mas, which provides an estimate of the astrometric un-certainty of our ALMA images.The correlator frequency setup consisted of six spectral win-dows (SPWs), one broad 2-GHz spectral unit to obtain a sen-sitive continuum measurement at ≈
242 GHz, and five nar-rower SPWs to cover a large number of lines, in particular theCH CN (J = OH, and SiO rotational transitions. Foreach SPW, Table 1 reports the frequency coverage, spectral res-olution, and sensitivity, and also indicates the most prominentmolecular species.Data calibration was performed using the pipeline forALMA data analysis in the Common Astronomy Software Ap-plications (CASA, McMullin et al. 2007) package, version 4.7.For each SPW, looking at the plots of (baseline-averaged) uv -amplitude versus channels, we selected the most intense emis-sion line (always > ∼
10 times stronger than the continuum levelof the uv -amplitude spectra), self-calibrated its channel-averagedemission, and, before imaging, applied the self-calibration phasesolutions to all the channels of the SPW. Self-calibration im-proves the signal to noise ratio (S / N) of the final images of theSPWs by a factor of 1.1–1.5, with the larger gain factors ob-tained in correspondence with the stronger self-calibrated lines.The dynamical range of the line images varies in the range 20–50, depending on the considered SPW. The images for the con-tinuum and line emissions were produced manually using theCLEAN task, with the robust parameter of Briggs (1995) set to0.5, as a compromise between resolution and sensitivity to ex-tended emission. The clean beam FWHM of the resulting im-ages varies in the range 0 (cid:48)(cid:48) . (cid:48)(cid:48) .
17. The mm continuum imageof G16.59 − σ rms noise level of 0.08 mJy beam − ,limited by the dynamic range. The 1 σ rms noise in a single spec-tral channel varies in the interval 1–3 mJy beam − , dependingon the considered SPW / channel.We have employed a specific procedure to determine the con-tinuum level of the spectra and subtract it from the line emission.Since all the observed SPWs present a “line forest”, identifyingthe channels where no line emission is present is a very di ffi -cult task. For each SPW, we use STATCONT (Sanchez-Mongeet al. 2017), a statistical method to estimate the continuum levelat each position of the map from the spectral distribution of theintensity at that position.
3. Results
This section presents the main results of our ALMA observa-tions, first reporting on the physical properties of the parentalcore and then focusing on the kinematics of the embedded high-mass YSO, the main target of our study. − The ALMA 1.2-mm continuum map presented in Fig. 1 revealsfour main sources, distributed from SE to NW over a region of ∼ au. The source B corresponds to the HMC identified inprevious interferometric observations at 3 and 1 mm (Furuyaet al. 2008; Beuther et al. 2006), named source “b” in Moscadelliet al. (2013). The compact “mm core” from previous, lower-angular-resolution, interferometric observations, named source“a” in Moscadelli et al. (2013), is now resolved into three distinctsources, labeled A1, A2, and A3, separated by 2000–3000 au. Article number, page 2 of 16. Moscadelli et al.: A Keplerian disk around a 10 M (cid:12) YSO
Table 1.
Spectral windows covered by the correlator set-up, with corresponding spectral resolutions and noise per channel.
SPW Frequency range Resolution 1- σ noise a Molecule b (GHz) (km s − ) mJy beam − CN3 241.629–241.863 0.30 2.9 CH OH4 240.899–241.133 0.30 2.5 C S5 241.499–241.733 0.60 2.6 SO Notes. ( a ) For the SPW 0, the reported noise is for the frequency-averaged image, while for the other SPWs it has been estimated in the channel corre-sponding to the strongest emission in the bandwidth. This value is only indicative, as it can change significantly from channel to channel. ( b ) Most prominent species in the SPW.
Considering emission down to 10% of the peak, the sources B,A2, and A3 are relatively compact with size < ∼ (cid:48)(cid:48) .
5, while A1 hasa significantly flatter spatial distribution extending up to ≈ (cid:48)(cid:48) . CN and CH OH linesprominent in our ALMA frequency setup, extracted at the posi-tion of the 1.2-mm peak for each of the four continuum sources.In agreement with previous findings, the molecular emission issignificantly stronger towards B (by a factor of 2.5–5). While insources A1 and A2 the intensity of the CH CN and CH OHlines is comparable, in A3 only weak CH OH emission is de-tected. Table 2 lists all the molecular lines analyzed in this paper.The intense lines of CH CN and CH OH are mostly employedto trace the gas kinematics inside B. While the optical depth ofthese lines close to the peak approaches 1 in some cases, theline wings are always optically thin and allow us to map the gaskinematics around the high-mass YSO in B with good S / N. Us-ing the SLIM (Spectral Line Identification and Modeling) tool ofMADCUBA , we surveyed the spectra of the four mm sourcesto search for molecular species with a relatively large num-ber of unblended and optically thin lines suitable for derivingthe gas physical conditions. We selected the transitions of theCH OCH and CH OH molecules reported in boldface char-acters in Table 2, which have optical depths of less (or much less)than 0.5, and cover a su ffi ciently wide range in excitation en-ergy to guarantee a good estimate of the excitation temperature.To derive the physical parameters we used the tool AUTOFITof MADCUBA, which compares the observed spectra with theLTE synthetic spectra, taking into account all transitions andthe line opacities. Leaving four parameters free to vary, that is,column density ( N col ), excitation temperature ( T ex ), Local Stan-dard of Rest (LSR) velocity ( V LSR ), and line width (FWHM),AUTOFIT provides the best nonlinear least-squared fit using theLevenberg-Marquardt algorithm. Figure 3 shows that the emis-sion profiles of the unblended CH OCH and CH OH tran-sitions are reasonably well fitted with MADCUBA, determin-ing the values of column density, temperature, velocity and linewidth listed in Table 3. The masses in molecular gas of the mmsources are derived from the mm fluxes (integrating inside thecontours at 10% of the peak marked in Fig. 1) and the fitted gastemperatures, assuming a dust opacity of 1 cm g − at 1.4 mm Madrid Data Cube Analysis on Image (MADCUBA) is a soft-ware developed in the Center of Astrobiology (Madrid, INTA-CSIC)to visualize and analyze astronomical (single) spectra and data cubes(Martín et al, in prep.; Rivilla et al. 2016); website: http: // cab.inta-csic.es / madcuba / Portada.html. CH OH transitions are used to derive the physical conditions in A3only, since in this source the emission of CH OCH is not detected. (Ossenkopf & Henning 1994) and a gas-to-dust mass ratio of100. We used the mm continuum peak flux and the fitted gastemperature to estimate the optical depth of the dust emissioninside the mm sources, ranging from 0.25 for source B to 0.45for source A3. For each mm source, the mass value reported inTable 3 was corrected using the corresponding dust opacity. Theflux error is evaluated by considering the contributions of the rmsnoise of the dust continuum map close to the intense sources, ≈ − , and the ALMA flux calibration uncertaintyof 5%, as recently estimated from the analysis of calibrators inbands 3 and 6 by Bonato et al. (2018, see also references therein).The uncertainty in the mass of the mm sources is derived by tak-ing into account both the flux and gas temperature uncertainties. We now focus on the gas kinematics around the massive YSOinside the mm source B. In the following we refer to this YSOas Bm. This is probably the most massive object in source B.A well-defined, SW-NE V LSR gradient is detected at the posi-tion of Bm in all the observed high-density gas tracers. Fig-ures 4, 5, and 6 present results from low-E u lines of CH OH,CH CN, and C S, respectively. We note that the JVLA 22-GHzcontinuum, pinpointing the YSO, falls exactly between the SWblue-shifted and the NE red-shifted line emission, and that thedirection of the V LSR gradient forms a large ( ≈ ◦ ) angle withthe radio jet traced by the extended JVLA 13-GHz continuum.These findings suggest that the V LSR gradient could be due torotation of the gas in an envelope and / or disk surrounding theYSO.The P-V plots produced along the axis (at PA = ◦ ) of the V LSR gradient confirm that we are observing envelope–disk rota-tion. The plots have a butterfly-like shape (mostly clear in Fig. 6for the C S line), with well-defined spurs at high absolute veloc-ities and small o ff sets in the second and fourth quadrants. Thesespurs correspond to gas whose line-of-sight velocity increaseswith decreasing radius and could be consistent with Keplerianrotation. In Sect. 4, we fit the velocity profile and estimate thedisk radius and mass, and the YSO mass. Here, we constrain theYSO V LSR and position by inspecting the P-V plots. The posi-tional o ff set (along the axis at PA = ◦ ) of the YSO is delimitedby the o ff sets of the high-velocity spurs in the second and fourthquadrants of the P-V plots, falling inside the interval 0 (cid:48)(cid:48) –0 (cid:48)(cid:48) . ff sets are less clear, because they are contaminated by emis-sion of the ambient gas at the systemic velocity. We make useof the P-V plot of the C S line (see Fig. 6) to confidently set a
Article number, page 3 of 16 & A proofs: manuscript no. 34366corr
Fig. 1.
The gray-scale map and white contours reproduce the ALMA 1.2-mm continuum. The color scale at the top gives the intensity of the map.The plotted levels are from 10 to 90% of 0.032 Jy beam − in steps of 10%. The main continuum sources are indicated with their correspondinglabels. The level at 10% of the peak around each source is plotted in magenta. The velocity-integrated intensity of the CH OH 5 , –4 , line isshown with dashed cyan contours, plotting levels from 20 to 90% of 1.1 Jy beam − km s − in steps of 10%. The ALMA beams for the continuumand the CH OH 5 , –4 , line are reported on the bottom left and right corners, respectively. The big white star marks the position of source “a”(Moscadelli et al. 2013). range of values for the YSO V LSR within 60–61 km s − . Theseconstraints for the YSO position and the V LSR are used in thefollowing analysis.Looking at Figs. 4, 5, and 6 (left panels), in all the threemolecular tracers the blue-shifted emission extends over an areasignificantly smaller than that of the red-shifted emission. More-over, while the red-shifted emission is distributed approximatelysymmetrically about the major axis of the envelope–disk, thebarycenter of the blue-shifted gas is o ff set to W. These asymme-tries in the velocity distribution of the gas around Bm are furtherdiscussed in Sects. 5.1 and 5.2. We now consider a larger region encompassing the jet emergingfrom Bm. Figures 7 and 8 show the channel maps of two intenseCH CN lines with quite di ff erent excitations, the J K = –13 with E u / k =
121 K and the J K = –13 with E u / k =
442 K.These two lines are representative of the velocity distribution ofthe large majority of the low- and high-excitation molecular tran-sitions detected towards Bm. At high velocities (channels with V LSR ≤
56 km s − or ≥
63 km s − ) both low- and high-excitationmolecular lines trace the compact disk close to the high-massYSO. At V LSR ≈
55 km s − , a compact source is detected only inlow-excitation lines at ≈ (cid:48)(cid:48) . Article number, page 4 of 16. Moscadelli et al.: A Keplerian disk around a 10 M (cid:12) YSO
Fig. 2.
Spectra of the prominent lines of CH CN (J = left panels ) and CH OH ( right panels ) extracted at the position of the 1.2-mm peakfor each of the four continuum sources B, A1, A2 and A3 (from top to bottom, respectively). The spectra are shown as brightness temperature vs.rest frequency. The transitions of the two molecular species (see Table 2) are labeled in the upper panels. source B, in proximity to the weak continuum emission and thecluster of water masers located at the largest distance from theradio jet. In the following, we refer to this compact source as B-NW. At central velocities (56 km s − ≤ V LSR ≤
63 km s − ), low-excitation lines show extended emission emerging from (only)the western side of the jet at blue-shifted velocity, and from an arc-like / linear bridge at blue- / red-shifted velocities connectingthe massive YSO Bm with the compact source B-NW. High-excitation lines have a quasi-compact structure also at centralvelocities, with some notable features: 1) at V LSR ≈
59 km s − ,a slightly resolved funnel-like structure is traced on top of thewestern lobe of the jet near Bm, and 2) at V LSR ≈ − , Article number, page 5 of 16 & A proofs: manuscript no. 34366corr
Table 2.
List of the molecular transitions considered in this work. Thetransitions given in boldface characters have been fitted with MAD-CUBA to determine the gas physical conditions.
Mol. Species Frequency Resolved QNs E u / k (MHz) (K)CH OH 241590.115 25 , –25 , , –4 , − , –4 − , , –4 , , –4 , , –4 , , –4 , , –18 , , –20 , CN 257127.035 J K = –13 K = –13 K = –13 K = –13 K = –13 K = –13 K = –13 S 241016.089 J = CH OCH , –4 , , –4 , , –4 , , –4 , , –4 , , –4 , , –4 , , –4 , , –20 , , –20 , , –20 , , –20 , , –17 , , –17 , , –17 , , –17 , , –19 , , –19 , , –19 , , –19 , , –16 , , –16 , , –16 , , –16 , , –25 , , –25 , , –25 , , –25 , an emission spot is observed adjacent to the radio jet towards N.This latter feature is referred to as HS in the following.The radio jet from Bm is one of the few known cases ofnonthermal jets from high-mass YSOs. In particular, the easternlobe of the radio jet is well detected with the JVLA at 6 GHz,and is very weak and / or undetected at frequencies ≥
10 GHz(Moscadelli et al. 2013, see their Figs. 1 and 2). Our ALMAobservations confirm the presence of a strong asymmetry be-tween the eastern and western lobes of the jet, with the westernlobe being much more intense in both continuum and molecularlines. Considering also the distribution of the dust emission (see Fig. 1), predominant towards W-NW of Bm, the simplest expla-nation for all these facts is an E-W density gradient at the posi-tion of Bm. Integrating the ALMA 1.2-mm continuum inside thearea of each jet lobe, we estimate that the average gas density inthe western lobe is about one order of magnitude larger than inthe eastern lobe.
4. The Keplerian disk around the high-mass YSOBm
In this section, we derive the properties of the YSO Bm andits disk. The angular resolution of the P-V plots shown inFigs. 4, 5, and 6 varies in the range 0 (cid:48)(cid:48) . (cid:48)(cid:48) .
17, reflecting theFWHM of the observing beam at the frequency of the molecu-lar line employed to produce the P-V plot. The emission at highblue- ( ≤
56 km s − ) and red-shifted ( ≥
63 km s − ) velocities isapproximatively compact (see Figs. 7 and 8), which allows us tofit a 2D Gaussian profile and determine the peak position at eachvelocity channel. The positional accuracy is equal to FWHM2 . σ I (see, e.g., Reid et al. 1988), where I and σ are the peak in-tensity and the rms noise, respectively, of a given channel. Withtypical values of the ratio I σ ≈
30, the error on the position of thefitted channel peaks is as small as a few mas. For channels wherethe emission is su ffi ciently compact, this method increases the(relative) positional accuracy by a large factor, while retainingthe essential information of the P-V plots.In Fig. 9 we show that the spatial distribution of the high-velocity emission of CH OH and CH CN is elongated along thesame PA = ± ◦ , which we take as the direction of the ma-jor axis of the molecular disk around the high-mass YSO Bm.As already noted in Sect. 3.2 for the SW-NE V LSR gradient, thered-shifted side of the disk is significantly longer than the blue-shifted side. Along the red-shifted side, ≈ (cid:48)(cid:48) .
15 or ≈
500 au inextent, the gas V LSR increases monotonically approaching theYSO, ranging from ≈
62 km s − up to ≈
69 km s − . On the con-trary, the blue-shifted side of the disk is traced only at the lowestvelocities, 50–55 km s − ; the mildly blue-shifted channels, in therange 55–60 km s − , show more extended structure, which tendsto be elongated to the W of Bm along the radio jet (see Fig. 7).Comparing the two molecular tracers in Fig. 9, the red-shifted side of the disk appears to be better traced by the CH OHlines, whose spatial distribution is flatter and more extended thanthat of the CH CN lines. Table 2 shows that the upper energylevel (E u ) of the CH OH transitions is on average lower thanthat of the CH CN lines. Since the gas temperature in the centrallayers of the disk is expected to be relatively low, it is reason-able that the CH OH transitions are found to be better tracers ofthe disk midplane. Accordingly, examining the di ff erent CH OHtransitions (see Table 2), we find that the ones with E u ≤
150 Kpresent a significantly flatter and more elongated spatial distri-bution. Considering only the CH OH transitions with 20 ≤ E u ≤
150 K, Fig. 10 plots V LSR versus positions projected along thedisk major-axis. While the radial profile of the red-shifted veloc-ities is well reproduced with a Keplerian curve (as described be-low), the blue-shifted emission concentrates within a small o ff setrange ( ≤ (cid:48)(cid:48) .
04) and cannot be adequately fitted. However, the av-erage position and V LSR of the blue-shifted emission is useful toconstrain the position and the V LSR of the YSO.The free parameters of the Keplerian fit are the YSO’s posi-tional o ff set, S (cid:63) , LSR velocity, V (cid:63) , and mass, M (cid:63) sin ( i ). Indi-cating with i the inclination of the disk rotation axis with theline of sight, the formulation of the latter parameter takes intoaccount that the disk plane is actually seen at an angle 90 − i Article number, page 6 of 16. Moscadelli et al.: A Keplerian disk around a 10 M (cid:12) YSO
Table 3.
Physical parameters of the mm sources mm source Flux log(N col ) T ex V LSR
FWHM Mass(mJy) (cm − ) (K) (km s − ) (km s − ) ( M (cid:12) )B 70 ± ± ±
11 62.3 ± ± ± ±
18 17.2 ± ±
18 62.4 ± ± ± ± ± ±
16 61.1 ± ± ± ± ± ± ± ± ± Notes.
Column 1 indicates the mm source; column 2 lists the 1.2-mm flux calculated by integrating inside the contour at 10% of the peak aroundeach source (see Fig. 1); column 3 reports the column density of the molecular species fitted with MADCUBA: (1) CH OCH for sources B, A1,and A2, and (2) CH OH for A3; columns 4, 5, and 6 give, respectively, the excitation temperature, velocity, and line width of the fitted molecularlines; column 6 lists the estimated mass of the mm source. from the line of sight, and the fitted V LSR correspond to the ac-tual rotation velocities multiplied by the factor sin( i ). We haveminimized the following χ expression: χ = (cid:88) j [ V j − ( V (cid:63) ± . M (cid:63) sin ( i )) . | S j − S (cid:63) | − . )] ( ∆ V j ) , (1)where V j and S j are the channel V LSR (in km s − ) andcorresponding peak positions (in arcsecond), the index j runsover all the fitted channels, and the + and − symbols hold forred- and blue-shifted velocities, respectively. The YSO mass M (cid:63) is given in M (cid:12) . In order to take into account both the uncer-tainty on the velocity and that on the position, the global ve-locity error ∆ V j was obtained by summing in quadrature twoerrors: that on the velocity (taken equal to half of the channelwidth) and that obtained by converting the error on the o ff setinto a velocity error through the function fitted to the data. InSect. 3.2, based on the symmetrical patterns of the P-V plots, weconstrained the ranges for the YSO positional o ff set and V LSR to: 0 (cid:48)(cid:48) ≤ S (cid:63) ≤ (cid:48)(cid:48) .
15, 60.0 km s − ≤ V (cid:63) ≤ − . Themass of the YSO is searched over the range 5–15 M (cid:12) , consistentwith the estimated bolometric luminosity of 10 L (cid:12) . Figure 11reports the plots of the distribution of the χ as a function ofthe free parameters. The white contour in these two plots drawsthe 1- σ confidence level for the three free parameters, follow-ing Lampton et al. (1976). These plots show that we do findan absolute minimum of the χ , and the determined 1- σ inter-vals for the parameter values are: S (cid:63) = − (cid:48)(cid:48) . ± (cid:48)(cid:48) . V (cid:63) = . ± . − , and M (cid:63) sin ( i ) = ± M (cid:12) .Following the analysis by Moscadelli et al. (2013, see in par-ticular their Fig. 5), source B, the HMC, dominates the IR emis-sion of the region, suggesting that our estimate of 10 L (cid:12) for thebolometric luminosity of B is reasonable and not too high. Thisluminosity corresponds to a single ZAMS star of ≈ M (cid:12) (seeDavies et al. 2011), which is an upper limit for the mass of Bm.Comparing this upper limit with the YSO mass from the Ke-plerian fit, the value of the disk inclination angle is constrainedwithin the interval 60 ◦ ≤ i ≤ ◦ , that is, the plane of the disk iswithin 30 ◦ of the line of sight. However, if a sizeable fraction ofthe bolometric luminosity is due to gravitational energy releasedin the accretion process rather than nuclear burning, the mass ofBm could be less than 13 M (cid:12) , and the disk would be almostedge-on. Inside the disk radius of ≈ (cid:48)(cid:48) .
15, the 1.2-mm continuumflux is 42 mJy, corresponding to ≈ M (cid:12) (making the same as-sumptions as in Sect. 3.1). Since this value is much less than theYSO mass ≈ M (cid:12) , our choice of fitting a Keplerian velocityprofile appears to be well justified a posteriori .Figure 12 (lower panel) compares the kinematics of the disk,traced with thermal CH OH, with that of the 6.7-GHz CH OH masers observed with VLBI by Sanna et al. (2010). The 6.7-GHz masers trace a slightly elongated structure oriented along aPA ( ≈ − ◦ ) quite di ff erent from that (18 ◦ ) of the YSO disk. Themaser bipolar V LSR distribution (red-(blue-)shifted to NW(SE))and the proper motion pattern were interpreted by Sanna et al.(2010) in terms of rotation, and the 6.7-GHz masers were thefirst indication of the existence of a rotating disk around Bm.However, the new ALMA data indicate now that the 6.7-GHzmasers are not tracing the disk midplane, as originally assumed.While the positions and V LSR of the NW red-shifted 6.7-GHzcluster are in reasonable agreement with the red-shifted side ofthe YSO disk, the SE blue-shifted cluster is placed 0 (cid:48)(cid:48) . (cid:48)(cid:48) . ff set from the disk midplane.
5. The YSO, the disk, and the jet
In this section, we discuss in more detail the interactions amongthe YSO, the disk, and the jet.
Looking at Fig. 9, one can note that, near Bm, the slightly re-solved 13-GHz continuum is elongated to NW along a directionroughly perpendicular to the disk. As shown in Figs. 7 and 8,the axis of the funnel-like structure on top of the radio jet tracedby the CH CN emission at V LSR ≈
59 km s − also has a similarNW orientation. This structure can be interpreted in terms of thejet cavity, and together with the shape of the 13-GHz emissionnear Bm, could mark the direction of ejection of the jet close tothe YSO. At larger separation from the YSO, the 13-GHz con-tinuum seems to bend and approach the E-W direction, whichcould suggest that precession or recollimation is taking place.The nonthermal continuum emission in the two lobes of theradio jet, shown in the upper panel of Fig. 12, emerges fromshocks responsible for the acceleration of the electrons to rel-ativistic velocities. These shocks originate near Bm where thejet impinges on high-density material and propagate away alongthe jet direction at a speed, assuming momentum conservation,of V sh = (cid:112) n jet / n amb V jet , where n jet and V jet are the jet den-sity and ejection velocity, respectively, and n amb is the ambi-ent density (see, e.g., Masson & Chernin 1993). Looking at theupper panel of Fig. 12, one can note that the western lobe is Article number, page 7 of 16 & A proofs: manuscript no. 34366corr significantly closer to Bm, which could indicate that the non-thermal shock has moved more slowly towards W because of thehigher ambient density, as already discussed in Sect. 3.3. Fromthe JVLA 6-GHz map we derive that the eastern lobe is aboutthree times more distant from Bm than the western lobe, which,assuming the jet is ejected symmetrically, agrees well with ourprevious estimate of a density contrast in the ambient gas bya factor of approximately ten between the western and easternside. We denote with ∆ S W and ∆ S E the separations (pro-jected onto the line connecting the lobes – see Fig. 12) betweenthe position of Bm and the emission peaks of the western andeastern lobes, respectively, and with V Wsh and V Esh the shockpropagation velocities towards W and E, respectively. The timeelapsed since the episode of ejection responsible for the presentemission in the jet lobes is then ∆ T = ∆ S W / V Wsh = ∆ S E / V Esh .From the 6-GHz map we obtain ∆ S W ≈ (cid:48)(cid:48) .
33 or ≈ ∆ T ≈ / V Wsh yr, where V Wsh is expressed in km s − . Comparing the upper to the lower panel of Fig. 12, it is clearthat the line connecting the 6-GHz lobes of the radio jet crossessource B near the 1.2-mm peak but is displaced from Bm (pin-pointed by the 22-GHz emission) by > ∼
100 mas towards N. Thiso ff set is significantly larger than the expected positional error ofa few tens of milliarcseconds between the 6- and 22-GHz JVLAimages (Moscadelli et al. 2013, 2016). In Sect. 3.2 we notedthe clear asymmetry between the NE red-shifted and SW blue-shifted sides of the YSO envelope–disk, with the NE side beingmuch more extended than the SE one (see Figs. 4 and 12). Weargue now that both the displacement of Bm from the jet axisand the disk asymmetry could result from the relative motion ofBm with respect to the disk. We assume that Bm has moved fromits original position, at the disk center, towards S-SW, along thedisk plane.What is causing the motion of Bm? One possibility is thatBm is orbiting in a gravitationally bound, multiple stellar sys-tem. This would naturally explain its motion relative to the disk.In this case, the observed disk would rotate around the multiplesystem and mediate the accretion onto it. Recent observations ofbound systems of low-mass YSOs surrounded by a disk showthat the regular distribution in mass and velocity of the disk istruncated at an inner radius comparable to the separation amongthe most massive stellar members (Tobin et al. 2016; Artur de laVillarmois et al. 2018). At radii comparable to these stellar or-bits, the disk fragments and gaps, rings, and spirals appear, likethose observed in protoplanetary disks. Looking at Fig. 9, onecan note that the disk around Bm presents a regular (Keplerian)velocity pattern until reaching the position of the YSO, markedby the compact 22-GHz continuum. The mass responsible for theobserved velocity pattern appears to be confined inside a radius ≤
200 au from Bm, which implies that other (putative) YSOsembedded in the parental mm source B are not dynamically rel-evant for the disk or the motion of Bm.An alternative explanation for the motion of Bm is that theYSO has been ejected from its original position at the disk cen-ter by dynamical interaction with one or more companions. TheYSO moved through the disk plane until it reached the currentposition, traced by the 22-GHz continuum. The distribution ofthe gas in the disk remained essentially una ff ected by the move- We note that the same phase calibrator, J1832-1035, was used forboth the 6- and 22-GHz JVLA observations, which guarantees a goodrelative astrometry between the images at the two frequencies. ment of the YSO. The fact that we see Keplerian rotation aroundBm implies that the material of the disk has been rotating fastenough to re-adjust its velocity field to the new position of theYSO. This sets a lower limit to the crossing time, T cr , neededfor the star to go from the original position to the current po-sition. For a stellar mass of 10 M (cid:12) and a radius of the Keple-rian disk of 0 (cid:48)(cid:48) .
15 (540 au), we derive a rotational period T rot = T cr ≥ T rot = T cr and the distance of ∼ (cid:48)(cid:48) . ≤ − .This is in agreement with the result that the LSR velocity of Bmof V (cid:63) = . ± . − determined from the Keplerian fit(see Sect. 4) corresponds to the systemic velocity of the molec-ular cloud, V sys = ± .
04 km s − , obtained from single-dishobservations (see, e.g., Hill et al. 2010).For a plausible mass accretion rate of ∼ − M (cid:12) yr − , T cr issu ffi ciently long that most of the mass of Bm could be accretedafter its ejection from the original position. In this scenario, thestructure of the disk has not been significantly a ff ected by themotion of the YSO through it, because the star has become su ffi -ciently massive to dominate the gravitational field of the region,only when it was already close to the current position.We still have to explain why the jet is o ff set from the currentposition of the YSO. One possibility is that the jet was ejectedbefore the YSO left its original position (marked by the inter-section between the jet axis and the disk). Following the analy-sis of Sect. 5.1 and assuming ∆ T ∼ T cr ≥ ≤ − . Such alow velocity, much less than the typical jet speeds ≥
100 km s − (see, e.g., Masqué et al. 2015), implies a very high density ra-tio ( ∼ ) between the ambient gas and the jet. Another possi-bility is that the jet is ejected from the present location of Bm,but is then recollimated on a larger scale along the axis of themagnetic field, which, on that scale, has not been a ff ected bythe movement of the YSO. This latter interpretation is supportedby the morphology of the 13-GHz continuum and the funnel-like molecular emission observed near Bm, which, as noted inSect. 5.1, suggests that the jet emerges from Bm perpendicularto the Keplerian disk.Looking at Fig. 12, it is also interesting to note that the 1.2-mm peak is slightly o ff set from the jet axis in the direction ofthe 22-GHz continuum. This o ff set, 0 (cid:48)(cid:48) . (cid:48)(cid:48) .
04, is comparablewith the error in the relative astrometry between the JVLA andALMA images, but it could have a physical explanation, too. Infact, it could result from a combination of two components ofdust emission with similar intensities: one characterized by hightemperature and low column density at the position of the 22-GHz continuum, the other with low temperature and large col-umn density at the disk center. In order to resolve these two puta-tive components, we have redone the 1.2-mm continuum imageuniformly weighting the visibilities, thus increasing the angularresolution from 0 (cid:48)(cid:48) .
15 to 0 (cid:48)(cid:48) .
12, but the image still presents asingle peak. We conclude that, if two components are present,their separation must be ≤ (cid:48)(cid:48) .
6. Conclusions
The main results of our Cycle 3 high-angular resolution (beamFWHM ≈ (cid:48)(cid:48) .
15) ALMA observations towards the high-massSFR G16.59 − ∼ (cid:48)(cid:48) ) mm sources, among which the one (source B) harbor-ing the high-mass YSO (Bm) is the most prominent in molecularemission. Fitting unblended, optically thin lines of CH OCH Article number, page 8 of 16. Moscadelli et al.: A Keplerian disk around a 10 M (cid:12) YSO and CH OH, we determined temperatures for the gas inside themm sources in the range 42–131 K, and estimated masses ofbetween 1 and 5 M (cid:12) .A well-defined V LSR gradient (prominent in CH OH,CH CN and C S) is traced in many high-density moleculartracers at the position of the high-mass YSO Bm, and is ori-ented along a direction forming a large ( ≈ ◦ ) angle with the ra-dio jet previously revealed through sensitive JVLA observations.The P-V plots of this gradient present butterfly-like shapes, andthe emission peaks of the molecular lines at high velocity drawlinear patterns, indicating that we are observing rotation of thedisk–envelope surrounding Bm. The disk radius is estimated tobe ≈
500 au, and the V LSR radial distribution is well reproducedby Keplerian rotation around a central mass of 10 ± M (cid:12) .The position of Bm, pinpointed by the compact 22-GHzemission, is found to be o ff set by > ∼ (cid:48)(cid:48) . ff ected by the movement of the YSO. Acknowledgements.
V.M.R. is funded by the European Union’s Horizon 2020research and innovation programme under the Marie Skłodowska-Curie grantagreement No 664931. We thank the referee Todd Hunter for useful comments,which improved the paper. This paper makes use of the following ALMA data:ADS / JAO.ALMA / NRAO and NAOJ.
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Article number, page 9 of 16 & A proofs: manuscript no. 34366corr
Fig. 3.
In each panel, the observed spectrum and the MADCUBA LTE best fit are shown in black and red, respectively. The spectra are shown asbrightness temperature vs. rest frequency. In the upper-left corner and at the bottom of each panel, the molecular species and the corresponding lineemployed in the fit are indicated (see Table 2). Each raw refers to one of the four mm sources: B, A1, A2 and A3, from top to bottom, respectively.Article number, page 10 of 16. Moscadelli et al.: A Keplerian disk around a 10 M (cid:12) YSO
Fig. 4.
Gas kinematics towards the high-mass YSO Bm.
Left panel:
Black contours and the color map show, respectively, the velocity-integratedintensity and the intensity-averaged velocity of the CH OH 5 , –4 , line (E u =
35 K). Plotted contours are from 10 to 90% of 1.1 Jy beam − km s − in steps of 10% and the scale on the right gives the color-velocity conversion. The gray-scale filled and white contours show the JVLA 22-GHzand 13-GHz continuum emission, respectively. Contours are from 50 to 90% of 0.28 mJy beam − in steps of 10% at 22 GHz, and from 20 to90% of 0.1 mJy beam − in steps of 10% at 13 GHz. The JVLA beams at 22 and 13 GHz are reported in the bottom-left and bottom-right corners,respectively. Right panel:
P-V plot of the CH OH 5 , –4 , line. The cut (at PA = ◦ ) along which positions are evaluated is indicated withthe dashed black line in the left panel. To produce the P-V plot, we averaged the emission inside a strip parallel to the cut and 0. (cid:48)(cid:48) V LSR and positional o ff set, respectively, estimated with a Keplerian fit (see Sect. 4). The yellow dashed vertical line indicates the positionalo ff set of the peak of the 1.2-mm continuum emission of source B. The four quadrants are labeled. Fig. 5.
As in Fig. 4 but for the CH CN J K = –13 line (E u =
121 K).
Left panel:
Black contours show the velocity-integrated intensity withlevels ranging from 10 to 90% of 0.9 Jy beam − km s − in steps of 10%. Article number, page 11 of 16 & A proofs: manuscript no. 34366corr
Fig. 6.
As in Fig. 4 but for the C S J = u =
28 K).
Left panel:
Black contours show the velocity-integrated intensity with levels rangingfrom 10 to 90% of 0.8 Jy beam − km s − in steps of 10%. Right panel:
Horizontal and vertical white continuous lines, and the blue curves mark,respectively, the V LSR and positional o ff set of the YSO, and the Keplerian profile around a YSO of 10 M (cid:12) . The two horizontal and vertical, whitedashed lines indicate the maximum interval of variation for the YSO V LSR and positional o ff set, respectively, estimated by eye whilst looking atthe symmetrical patterns of the P-V plot. We note that the plotted o ff set range is larger than for the P-V plots of Figs. 4 and 5. Fig. 7.
Each panel presents a color map of the intensity of the CH CN J K = –13 line (E u =
121 K) at a di ff erent V LSR (km s − ), indicated inthe upper-left corner. The color-intensity scale is shown on the right. The grayscale-filled and white contours show the JVLA 22-GHz and 13-GHzcontinuum, respectively, plotting the same levels as in Fig. 4. The green contours reproduce the ALMA 1.2-mm continuum, showing levels at10%, 20%, 40%, and 80% of the peak emission of 0.032 Jy beam − . The magenta-edged white triangles mark the positions of the 22-GHz watermasers derived through VLBI observations by Sanna et al. (2010). In the upper first and second panels, the high-mass YSO Bm, and the compactmolecular source B-NW are labeled.Article number, page 12 of 16. Moscadelli et al.: A Keplerian disk around a 10 M (cid:12) YSO
Fig. 8.
As in Fig. 7 but for the CH CN J K = –13 line (E u =
442 K). In the upper-last and middle-first panels, the emission spot HS, adjacentto the radio jet, is labeled.
Fig. 9.
The disk around the high-mass YSO Bm. Colored dots indicate the peak positions of the most blue- and red-shifted velocity channels forthe emission of the nine CH OH ( left panel ) and seven CH CN ( right panel ) lines listed in Table 2. Colors represent V LSR as coded on the right ofeach panel. The dashed black lines, at PA = ◦ and 17 ◦ for CH OH and CH CN, respectively, show the linear fits to the spatial distribution of thechannel peaks. The grayscale-filled and black contours represent the JVLA 22-GHz and 13-GHz continuum, respectively, with the same levels asin Fig. 4. Article number, page 13 of 16 & A proofs: manuscript no. 34366corr
Fig. 10.
Black and red error bars give major-axis projected positions and V LSR (together with the corresponding errors), respectively, for thehighest-velocity emission peaks of the six CH OH lines with 20 K ≤ E u ≤
150 K listed in Table 2. The blue curve is the best Keplerian fit to thedata. The horizontal and vertical dashed lines indicate the fitted YSO V LSR and position, respectively.Article number, page 14 of 16. Moscadelli et al.: A Keplerian disk around a 10 M (cid:12) YSO
Fig. 11.
Plots of the χ distribution from the Keplerian fit (see Fig. 10) as a function of the free parameters YSO mass and position ( left panel ), andYSO V LSR and mass ( right panel ). To produce these plots, the third free parameter of the Keplerian fit, that is, the YSO V LSR and position in theleft and right plot, respectively, is taken equal to the best-fit value. The color scale at the top of each panel gives the value of the χ in a logarithmicscale. In each of the two plots, the position of the minimum χ , χ min = χ min + = σ confidence level for three free parameters (Lampton et al. 1976). Article number, page 15 of 16 & A proofs: manuscript no. 34366corr
Fig. 12.
Lower panel:
Colored dots represent positions and V LSR of the thermal CH OH emission as in Fig. 9, with the black dashed line markingthe major axis of the disk around the high-mass YSO Bm. The grayscale map and the white contours reproduce the ALMA 1.2-mm continuum.The intensity scale for the map is shown on the top, and the plotted contours are the same as in Fig. 1. The JVLA 22-GHz continuum is shownwith cyan contours (same levels as in Fig. 4). Colored squares denote positions and V LSR of the 6.7-GHz CH OH masers (Sanna et al. 2010). Themaser proper motions are represented by black arrows, with the amplitude scale given in the bottom-right corner. The black dotted line marks themajor axis of the distribution of the CH OH masers. The dashed magenta line has the same meaning as in the upper panel.
Upper panel:
Theblack contours represent the JVLA 6-GHz continuum with levels from 20 to 90%, in steps of 10%, and 95% of 0.17 mJy beam −1