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Chun-Fan Liu

Publications and source records attributed to Chun-Fan Liu.

At least 19 recordsLinked to original sources

ALMASOP. A Rotating Feature Rich in Complex Organic Molecules in a Protostellar Core

Interstellar complex organic molecules (COMs) in solar-like young stellar objects (YSOs), particularly within protostellar disks, are of significant interest due to their potential connection to prebiotic chemistry in emerging planetary systems. We report the discovery of a rotating feature enriched in COMs, including CH3OH, CH3CHO, and NH2CHO, in the protostellar core G192.12-11.10. By constructing a YSO model, we find that the COM-rich feature is likely located within or near the boundary of the Keplerian disk. The image synthesis results suggest that additional heating mechanisms leading to a warm ring or a warm inner disk are required to reproduce the observed emission. We discuss possible origins of the COM-rich feature, particularly accretion shocks as a plausible cause for a warm ring. Additionally, molecules such as C18O, H2CO, DCS, H2S, and OCS exhibit distinct behavior compared to CH3OH, indicating a range of physical and chemical conditions within the region. The observed kinematics of H2S and OCS suggest that OCS resides in regions closer to the central protostar than H2S, consistent with previous experimental studies.

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A Spectroastrometric Study of the Low-velocity Wind from DG Tau A

We obtained high spectral resolution spectra ($\Delta v$ $\sim$ 2.5 km s$^{-1}$) for DG Tau A from 4800 \r{A} to 7500 \r{A} using Subaru High Dispersion Spectrograph (HDS) for the first time. The low-velocity components (LVCs, |$v$| < 100 km s$^{-1}$) were observed in the [O I] 5577, 6300, 6364 \r{A}, [S II] 6716, 6731 \r{A} lines. The offset position spectra observed in the LVCs show a "negative velocity gradient", supporting the presence of a wide-angled wind associated with the LVC emission. The offset position spectra observed in a component within the LVC velocity range between -16 km s$^{-1}$ to -41 km s$^{-1}$, namely, LVC-M, show a "negative velocity gradient'', supporting the presence of a wide-angled wind. With 12-70 au wind lengths measured using spectroastrometry, we estimate a lower limit to the wind mass-loss rate of $\sim$10$^{-8}$ M$_\odot$ yr$^{-1}$. In addition to the LVCs, we identify two high-velocity components (HVCs, |$v$| > 100 km s$^{-1}$) associated with the collimated jet in 26 lines ([N I], [N II], [O I], [O II], [O III], [S II], [Ca II], [Fe II], H$\alpha$, H$\beta$, He I). The one with a clear spatial offset from the star ($n_e$ $\sim$10$^4$ cm$^{-3}$, HVC1) is associated with an internal shock surface of the jet, while the other at the base ($n_e$ $\sim$10$^6$ cm$^{-3}$, HVC2) may be a stationary shock component. We find that the observed line profiles and the spatial scales of the LVC emission do not agree with the existing predictions for photoevaporative or magnetohydrodynamical (MHD) disk winds. These could be explained by the X-wind model, but synthetic observations are required for detailed comparisons.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): Nested Morphological and Kinematic Structures of Outflows Revealed in SiO and CO Emission

The Atacama Large Millimeter/submillimeter Array Survey of Orion Planck Galactic Cold Clumps (ALMASOP) reveals complex nested morphological and kinematic features of molecular outflows through the CO (J = 2 - 1) and SiO (J = 5 - 4) emission. We characterize the jet and outflow kinematics of the ALMASOP sample in four representative sources (HOPS 10, 315, 358, and G203.21-11.20W2) through channel maps and position-velocity diagrams (PVDs) parallel and transverse to the outflow axes. The combined CO and SiO emission exhibits the coexistence of the conventional extremely-high-velocity (EHV) jets and shell-like low-velocity (LV) cavity walls and new features. More complex, nested bubble-like and filamentary structures in the images and channel maps, triangle-shaped regions near the base of the parallel PVDs, and regions composed of rhombus/oval shapes in the transverse PVDs, are also evident. Such features find natural explanations within the bubble structure of the unified model of jet, wind, and ambient medium. The reverse shock cavity is revealed on the PVD base regions, and other features naturally arise within the dynamic postshock region of magnetic interaction. The finer nested shells observed within the compressed wind region reveal previously unnoticed shocked emission between the jet and the conventional large cavity walls. These pseudopulse-produced filamentary features connect to the jet-like knotty blobs, creating an impression of episodicity in mass ejection. SiO emission is enhanced downstream of the reverse shock boundary, with jet-like excitation conditions. Combined, these observed features reveal the extended structures induced by the magnetic interplay between a jet-bearing magnetized wide-angle wind and its ambient magnetized surrounding medium.

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Multiple Components of the Outflow in the Protostellar System HH 212: Outer Outflow Shell, Rotating Wind, Shocked Wind, and Jet

We present the Atacama Large Millimeter/submillimeter Array Band 7 observations of the CO (J=3-2) line emission of the protostellar system HH 212 at $\sim$24 au spatial resolution and compare them to those of the SiO (J=8-7) and SO (J=8-7) line emission reported in the literature. We find that the CO line traces four distinct regions: (1) an outer outflow shell, (2) a rotating wind region between the SiO and CO shells, (3) the shocked and wide-angle inner X-wind inside a SiO shell, and (4) the jet. The origin of the CO outer outflow shell could be associated with the entrained material of the envelope, or an extended disk wind. The rotating wind, which is shocked, is launched from a radius of 9-15 au, slightly exterior to that of the previously detected SO shell, which marks the boundary where the wide-angle X-wind is interacting with and shocking the disk wind. Additionally, the SO is found to be mixed with the CO emission within the thick and extended rotating wind region. The large scale CO shocked wind coexists with the SO emission near the upper portion of the inner shocked region converged on top of the inner SiO knots. The CO jet is traced by a chain of knots with roughly equal interval, exhibiting quasi-periodicity, as reported in other jets in the literature.

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ALMASOP. The Localized and Chemically rich Features near the Bases of the Protostellar Jet in HOPS 87

HOPS 87 is a Class 0 protostellar core known to harbor an extremely young bipolar outflow and a hot corino. We report the discovery of localized, chemically rich regions near the bases of the two-lobe bipolar molecular outflow in HOPS 87 containing molecules such as H$_2$CO, $^{13}$CS, H$_2$S, OCS, and CH$_3$OH, the simplest complex organic molecule (COM). The locations and kinematics suggest that these localized features are due to jet-driven shocks rather than being part of the hot corino region encasing the protostar. The COM compositions of the molecular gas in these jet-localized regions are relatively simpler than those in the hot corino zone. We speculate that this simplicity is due to either the liberation of ice with a less complex chemical history or the effects of shock chemistry. Our study highlights the dynamic interplay between the protostellar bipolar outflow, disk, inner core environment, and the surrounding medium, contributing to our understanding of molecular complexity in solar-like young stellar objects.

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A Unified Model for Bipolar Outflows from Young Stars: Kinematic and Mixing Structures in HH 30

The young stellar source HH 30 is a textbook example of an ionic optical jet originating from a disk in an edge-on system shown by the HST. It has a remnant envelope in $^{12}$CO observed by ALMA. The optical jet is characterized by its narrow appearance, large line width at the base, and high temperature inferred from line diagnostics. Three featured structures can be identified, most evident in the transverse position--velocity diagrams: an extremely--high-velocity (EHV) wide-angle wind component with large spectral widths in the optical, a very--low-velocity (VLV) ambient surrounding medium seen in $^{12}$CO, and a low-velocity (LV) region traced by $^{12}$CO nested both in velocity and location between the primary wind and ambient environment. A layered cavity with multiple shells forms nested morphological and kinematic structures around the optical jet. The atomic gas originating from the innermost region of the disk attains a sufficient temperature and ionization to emit brightly in forbidden lines as an optical jet. The wide-angle portion expands, forming a low-density cavity. The filamentary $^{12}$CO encompassing the wind cavity is mixed and advected inward through the action of the magnetic interplay of the wide-angle wind with the molecular ambient medium. The magnetic interplay results in the layered shells penetrating deeply into the vast cavity of tenuous atomic wind material. The HH 30 system is an ideal manifestation of the unified wind model of \citet{Shang_2020,Shang_2023}, with clearly distinguishable atomic and molecular species mixed through the atomic lightly ionized magnetized wind and the surrounding cold molecular ambient material.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): The Warm-Envelope Origin of Hot Corinos

Hot corinos are of great interest due to their richness in interstellar complex organic molecules (COMs) and the consequent potential prebiotic connection to solar-like planetary systems. Recent surveys have reported an increasing number of hot corino detections in Class 0/I protostars; however, the relationships between their physical properties and the hot-corino signatures remain elusive. In this study, our objective is to establish a general picture of the detectability of the hot corinos by identifying the origin of the hot-corino signatures in the sample of young stellar objects (YSOs) obtained from the Atacama Large Millimeter/submillimeter Array Survey of Orion Planck Galactic Cold Clumps (ALMASOP) project. We apply spectral energy distribution (SED) modeling to our sample and identify the physical parameters of the modeled YSOs directly, linking the detection of hot-corino signatures to the envelope properties of the YSOs. Imaging simulations of the methanol emission further support this scenario. We, therefore, posit that the observed COM emission originates from the warm inner envelopes of the sample YSOs, based on both the warm region size and the envelope density profile. The former is governed by the source luminosity and is additionally affected by the disk and cavity properties, while the latter is related to the evolutionary stages. This scenario provides a framework for detecting hot-corino signatures toward luminous Class 0 YSOs, with fewer detections observed toward similarly luminous Class I sources.

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A Unified Model for Bipolar Outflows from Young Stars: Apparent Magnetic Jet Acceleration

We explore a new, efficient mechanism that can power toroidally magnetized jets up to two to three times their original terminal velocity after they enter a self-similar phase of magnetic acceleration. Underneath the elongated outflow lobe formed by a magnetized bubble, a wide-angle free wind, through the interplay with its ambient toroid, is compressed and accelerated around its axial jet. The extremely magnetic bubble can inflate over its original size, depending on the initial Alfvén Mach number $M_A$ of the launched flow. The shape-independent slope $\partial{}v_r/\partial{}r=2/3t$ is a salient feature of the self-similarity in the acceleration phase. Peculiar kinematic signatures are observable in the position--velocity (PV) diagrams and can combine with other morphological signatures as probes for the density-collimated jets arising in toroidally dominated magnetized winds. The apparent second acceleration is powered by the decrease of the toroidal magnetic field but operates far beyond the scales of the primary magnetocentrifugal launch region and the free asymptotic terminal state. Rich implications may connect the jets arising from the youngest protostellar outflows such as HH 211 and HH 212 and similar systems with parsec-scale jets across the mass and evolutionary spectra.

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A Unified Model for Bipolar Outflows from Young Stars: Kinematic Signatures of Jets, Winds, and Their Magnetic Interplay with the Ambient Toroids

Kinematic signatures of the jet, winds, multicavities, and episodic shells arising in the unified model of bipolar outflows developed in Shang et al.\ (2020), in which an outflow forms by radially directed, wide-angle toroidally magnetized winds interacting with magnetized isothermal toroids, are extracted in the form of position--velocity diagrams. Elongated outflow lobes, driven by magnetized winds and their interplay with the environment, are dominated by extended bubble structures with mixing layers beyond the conventional thin-shell models. The axial cylindrically stratified density jet carries a broad profile near the base, across the projected velocity of the wide-angle wind, and narrows down along the axis with the collimated flow. The reverse shock encloses the magnetized free wind, forms an innermost cavity, and deflects the flow pattern. Shear, Kelvin--Helmholtz instabilities, and pseudopulses add fine and distinctive features between the jet--shell components, and the fluctuating jet velocities. The broad webbed velocity features connect the extremely high and the low velocities across the multicavities, mimicking nested outflowing slower-wind components. Rings and ovals in the perpendicular cuts trace multicavities at different heights, and the compressed ambient gap regions enrich the low-velocity features with protruding spikes. Our kinematic signatures capture the observed systematics of the high-, intermediate-, and low-velocity components from Class 0 to II jet--outflow systems in molecular and atomic lines. The nested shells observed in HH 212, HH 30, and DG Tau B are naturally explained. Outflows as bubbles are ubiquitous and form an inevitable integrative outcome of the interaction between wind and ambient media.

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Time-Variable Jet Ejections from RW Aur A, RY Tau and DG Tau

We present Gemini-NIFS, VLT-SINFONI and Keck-OSIRIS observations of near-infrared [Fe II] emission associated with the well-studied jets from three active T Tauri stars; RW Aur A, RY Tau and DG Tau taken from 2012-2021. We primarily covered the redshifted jet from RW Aur A, and the blueshifted jets from RY Tau and DG Tau, to investigate long-term time variabilities potentially related to the activities of mass accretion and/or the stellar magnetic fields. All of these jets consist of several moving knots with tangential velocities of 70-240 km s-1, ejected from the star with different velocities and at irregular time intervals. Via comparison with literature, we identify significant differences in tangential velocities for the DG Tau jet between 1985-2008 and 2008-2021. The sizes of the individual knots appear to increase with time, and in turn, their peak brightnesses in the 1.644-micron emission decreased up to a factor of ~30 during the epochs of our observations. A variety of the decay timescales measured in the [Fe II] 1.644 micron emission can be attributed to different pre-shock conditions if the moving knots are unresolved shocks. However, our data do not exclude the possibility that these knots are due to non-uniform density/temperature distributions with another heating mechanism, or in some cases due to stationary shocks without proper motions. Spatially resolved observations of these knots with significantly higher angular resolutions are necessary to better understand their physical nature.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): Deriving Inclination Angle and Velocity of the Protostellar Jets from their SiO Knots

We have selected six sources (G209.55-19.68S2, G205.46-14.56S1$_{-}$A, G203.21-11.20W2, G191.90-11.21S, G205.46-14.56S3, and G206.93-16.61W2) from the Atacama Large Millimeter/submillimeter Array Survey of Orion Planck Galactic Cold Clumps (ALMASOP), in which these sources have been mapped in the CO (J=2-1), SiO (J=5-4), and C$^{18}$O (J=2-1) lines. These sources have high-velocity SiO jets surrounded by low-velocity CO outflows. The SiO jets consist of a chain of knots. These knots have been thought to be produced by semi-periodical variations in jet velocity. Therefore, we adopt a shock-forming model, which uses such variations to estimate the inclination angle and velocity of the jets. We also derive the inclination angle of the CO outflows using the wide-angle wind-driven shell model, and find it to be broadly consistent with that of the associated SiO jets. In addition, we apply this shock-forming model to another three protostellar sources with SiO jets in the literature -- HH 211, HH 212, and L1448C(N) -- and find that their inclination angle and jet velocity are consistent with those previously estimated from proper motion and radial velocity studies.

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ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP): A Hot Corino Survey toward Protostellar Cores in the Orion Cloud

The presence of complex organic molecules (COMs) in the interstellar medium (ISM) is of great interest since it may link to the origin and prevalence of life in the universe. Aiming to investigate the occurrence of COMs and their possible origins, we conducted a chemical census toward a sample of protostellar cores as part of the ALMA Survey of Orion Planck Galactic Cold Clumps (ALMASOP) project. We report the detection of 11 hot corino sources, which exhibit compact emissions from warm and abundant COMs, among 56 Class 0/I protostellar cores. All the hot corino sources discovered are likely Class 0 and their sizes of the warm region ($>$ 100 K) are comparable to 100 au. The luminosity of the hot corino sources exhibits positive correlations with the total number of methanol and the extent of its emissions. Such correlations are consistent with the thermal desorption picture for the presence of hot corino and suggest that the lower luminosity (Class 0) sources likely have a smaller region with COMs emissions. With the same sample selection method and detection criteria being applied, the detection rates of the warm methanol in the Orion cloud (15/37) and the Perseus cloud (28/50) are statistically similar when the cloud distances and the limited sample size are considered. Observing the same set of COM transitions will bring a more informative comparison between the cloud properties.

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Detection of a dense SiO jet in the evolved protostellar phase

Jets and outflows trace the accretion history of protostars. High-velocity molecular jets have been observed from several protostars in the early Class\,0 phase of star formation, detected with the high-density tracer SiO. Until now, no clear jet has been detected with SiO emission from isolated evolved Class\,I protostellar systems. We report a prominent dense SiO jet from a Class\,I source G205S3 (HOPS\,315: T$_{bol}$ $\sim$ 180 K, spectral index $\sim$ 0.417), with a moderately high mass-loss rate ($\sim$ 0.59 $\times$ 10$^{-6}$ M$_\odot$ yr$^{-1}$) estimated from CO emission. Together, these features suggest that G205S3 is still in a high accretion phase, similar to that expected of Class\,0 objects. We compare G205S3 to a representative Class\,0 system G206W2 (HOPS\,399) and literature Class\,0/I sources to explore the possible explanations behind the SiO emission seen at the later phase. We estimate a high inclination angle ($\sim$ 40$^\circ$) for G205S3 from CO emission, which may expose the infrared emission from the central core and mislead the spectral classification. However, the compact 1.3\,mm continuum, C$^{18}$O emission, location in the bolometric luminosity to sub-millimeter fluxes diagram, outflow force ($\sim$ 3.26 $\times$ 10$^{-5}$ M$_\odot$km s$^{-1}$/yr) are also analogous to that of Class\,I systems. We thus consider G205S3 to be at the very early phase of Class\,I, and in the late phase of ``high-accretion". The episodic ejection could be due to the presence of an unknown binary, a planetary companion, or dense clumps, where the required mass for such high accretion could be supplied by a massive circumbinary disk.

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Revealing Ionization Conditions of Sz 102 with Spatially Resolved [Ne III] Microjets

Forbidden neon emission lines from small-scale microjets can probe high-energy processes in low-mass young stellar systems. We obtained spatially resolved [Ne III] spectra of the microjets from the classical T Tauri Star Sz 102 using the Hubble Space Telescope Imaging Spectrograph (HST/STIS) at a spatial resolution of ~0".1. The blueshifted and redshifted [Ne III] emission both peak in intensity within ~0".1 of the star and gradually decay along the flow outward to ~0".24. The spatial distribution and extent of the [Ne III] microjet is consistent with a jet that is ionized close to the base and subsequently recombines on a longer timescale than the flow time. Ca II H and K lines are also detected from the redshifted microjet with a line full-width at half-maximum of ~170 km/s, consistent with those of other forbidden emission lines, atop a 300-km/s wide stellar component. The launching radius of the Sz 102 jet, inferred from the observed line centroids and the range of inclination angles and stellar masses from the literature, is on the order of ~0.03 au. The possible proximity of the launching region to the star allows immediate ionization without distance dilution from the circumstellar ionization sources, most likely keV X-ray flares generated by magnetic reconnection events in the star-disk system, to sustain the observed [Ne III] flux.

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Possible Time Correlation Between Jet Ejection and Mass Accretion for RW Aur A

For the active T-Taur star RW Aur A we have performed long-term (~10 yr) monitoring observations of (1) jet imaging in the [Fe II] 1.644-micron emission line using Gemini-NIFS and VLT-SINFONI; (2) optical high-resolution spectroscopy using CFHT-ESPaDOnS; and (3) V-band photometry using the CrAO 1.25-m telescope and AAVSO. The latter two observations confirm the correlation of time variabilities between (A) the Ca II 8542 A and O I 7772 A line profiles associated with magnetospheric accretion, and (B) optical continuum fluxes. The jet images and their proper motions show that four knot ejections occurred at the star over the past ~15 years with an irregular interval of 2-6 years. The time scale and irregularity of these intervals are similar to those of the dimming events seen in the optical photometry data. Our observations show a possible link between remarkable (Delta_V < -1 mag.) photometric rises and jet knot ejections. Observations over another few years may confirm or reject this trend. If confirmed, this would imply that the location of the jet launching region is very close to the star (r <<0.1 au) as predicted by some jet launching models. Such a conclusion would be crucial for understanding disk evolution within a few au of the star, and therefore possible ongoing planet formation at these radii.

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Placing the spotted T Tauri star LkCa 4 on an HR diagram

Ages and masses of young stars are often estimated by comparing their luminosities and effective temperatures to pre-main sequence stellar evolution tracks, but magnetic fields and starspots complicate both the observations and evolution. To understand their influence, we study the heavily-spotted weak-lined T-Tauri star LkCa 4 by searching for spectral signatures of radiation originating from the starspot or starspot groups. We introduce a new methodology for constraining both the starspot filling factor and the spot temperature by fitting two-temperature stellar atmosphere models constructed from Phoenix synthetic spectra to a high-resolution near-IR IGRINS spectrum. Clearly discernable spectral features arise from both a hot photospheric component $T_{\mathrm{hot}} \sim4100$ K and to a cool component $T_{\mathrm{cool}} \sim2700-3000$ K, which covers $\sim80\%$ of the visible surface. This mix of hot and cool emission is supported by analyses of the spectral energy distribution, rotational modulation of colors and of TiO band strengths, and features in low-resolution optical/near-IR spectroscopy. Although the revised effective temperature and luminosity make LkCa 4 appear much younger and lower mass than previous estimates from unspotted stellar evolution models, appropriate estimates will require the production and adoption of spotted evolutionary models. Biases from starspots likely afflict most fully convective young stars and contribute to uncertainties in ages and age spreads of open clusters. In some spectral regions starspots act as a featureless veiling continuum owing to high rotational broadening and heavy line-blanketing in cool star spectra. Some evidence is also found for an anti-correlation between the velocities of the warm and cool components.

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The [Ne III] Jet of DG Tau and its Ionization Scenarios

Forbidden neon emission from jets of low-mass young stars can be used to probe the underlying high-energy processes in these systems. We analyze spectra of the jet of DG Tau obtained with the Very Large Telescope/X-Shooter spectrograph in 2010. [Ne III] $λ$3869 is clearly detected in the innermost 3" microjet and the outer knot located at $\sim$6".5. The velocity structure of the inner microjet can be decomposed into the low-velocity component (LVC) at $\sim -70$ km/s and the high-velocity component (HVC) at $\sim -180$ km/s. Based on the observed [Ne III] flux and its spatial extent, we suggest the origins of the [Ne III] emission regions and their relation with known X-ray sources along the jet. The flares from the hard X-ray source close to the star may be the main ionization source of the innermost microjet. The fainter soft X-ray source at 0".2 from the star may provide sufficient heating to help to sustain the ionization fraction against the recombination in the flow. The outer knot may be reionized by shocks faster than 100 km/s such that [Ne III] emission reappears and that the soft X-ray emission at 5".5 is produced. Velocity decomposition of the archival Hubble Space Telescope spectra obtained in 1999 shows that the HVC had been faster, with a velocity centroid of $\sim -260$ km/s. Such a decrease in velocity may potentially be explained by the expansion of the stellar magnetosphere, changing the truncation radius and thus the launching speed of the jet. The energy released by magnetic reconnections during relaxation of the transition can heat the gas up to several tens of megakelvin and provide the explanation for on-source keV X-ray flares that ionize the neon microjet.

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Velocity-Resolved [Ne III] from X-Ray Irradiated Sz 102 Microjets

Neon emission lines are good indicators of high-excitation regions close to a young stellar system because of their high ionization potentials and large critical densities. We have discovered [Ne III]λ3869 emission from the microjets of Sz 102, a low-mass young star in Lupus III. Spectroastrometric analyses of two-dimensional [Ne III] spectra obtained from archival high-dispersion ($R\approx 33,000$) Very Large Telescope/UVES data suggest that the emission consists of two velocity components spatially separated by ~ 0."3, or a projected distance of ~ 60 AU. The stronger redshifted component is centered at ~ +21 km/s with a line width of ~ 140 km/s, and the weaker blueshifted component at ~ -90 km/s with a line width of ~ 190 km/s. The two components trace velocity centroids of the known microjets and show large line widths that extend across the systemic velocity, suggesting their potential origins in wide-angle winds that may eventually collimate into jets. Optical line ratios indicate that the microjets are hot ($T\lesssim1.6\times10^4$ K) and ionized ($n_e\gtrsim5.7\times10^4$ cm$^{-3}$). The blueshifted component has ~ 13% higher temperature and ~ 46% higher electron density than the redshifted counterpart, forming a system of asymmetric pair of jets. The detection of the [Ne III]λ3869 line with the distinct velocity profile suggests that the emission originates in flows that may have been strongly ionized by deeply embedded hard X-ray sources, most likely generated by magnetic processes. The discovery of [Ne III]λ3869 emission along with other optical forbidden lines from Sz 102 support the picture of wide-angle winds surrounding magnetic loops in the close vicinity of the young star. Future high sensitivity X-ray imaging and high angular-resolution optical spectroscopy may help confirm the picture proposed.

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