arXiv subjects

Qizhou Zhang

Publications and source records attributed to Qizhou Zhang.

At least 127 records · Page 7Linked to original sources

arXiv2022

Digging into the Interior of Hot Cores with ALMA (DIHCA). II. Exploring the Inner Binary (Multiple) System Embedded in G335 MM1 ALMA1

We observed the high-mass protostellar core G335.579-0.272 ALMA1 at ${\sim}200$ au (0.05") resolution with the Atacama Large Millimeter/submillimeter Array (ALMA) at 226 GHz (with a mass sensitivity of $5σ=0.2$ M$_\odot$ at 10 K). We discovered that at least a binary system is forming inside this region, with an additional nearby bow-like structure (${\lesssim}1000$ au) that could add an additional member to the stellar system. These three sources are located at the center of the gravitational potential well of the ALMA1 region and the larger MM1 cluster. The emission from CH$_3$OH (and many other tracers) is extended ($>1000$ au), revealing a common envelope toward the binary system. We use CH$_2$CHCN line emission to estimate an inclination angle of the rotation axis of $26^\circ$ with respect to the line of sight based on geometric assumptions and derive a kinematic mass of the primary source (protostar+disk) of 3.0 M$_\odot$ within a radius of 230 au. Using SiO emission, we find that the primary source drives the large scale outflow revealed by previous observations. Precession of the binary system likely produces a change in orientation between the outflow at small scales observed here and large scales observed in previous works. The bow structure may have originated by entrainment of matter into the envelope due to widening or precession of the outflow, or, alternatively, an accretion streamer dominated by the gravity of the central sources. An additional third source, forming due to instabilities in the streamer, cannot be ruled out as a temperature gradient is needed to produce the observed absorption spectra.

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arXiv2022

ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- VIII. A search for hot cores by using C$_2$H$_5$CN, CH$_3$OCHO and CH$_3$OH lines

Hot cores characterized by rich lines of complex organic molecules are considered as ideal sites for investigating the physical and chemical environments of massive star formation. We present a search for hot cores by using typical nitrogen- and oxygen-bearing complex organic molecules (C$_2$H$_5$CN, CH$_3$OCHO and CH$_3$OH), based on ALMA Three-millimeter Observations of Massive Star-forming regions (ATOMS). The angular resolutions and line sensitivities of the ALMA observations are better than 2 arcsec and 10 mJy/beam, respectively. A total of 60 hot cores are identified with 45 being newly detected, in which the complex organic molecules have high gas temperatures ($>$ 100 K) and small source sizes ($<$ 0.1 pc). So far this is the largest sample of hot cores observed with similar angular resolution and spectral coverage. The observations have also shown nitrogen and oxygen differentiation in both line emission and gas distribution in 29 hot cores. Column densities of CH$_3$OH and CH$_3$OCHO increase as rotation temperatures rise. The column density of CH$_3$OCHO correlates tightly with that of CH$_3$OH. The pathways for production of different species are discussed. Based on the spatial position difference between hot cores and UC~H{\sc ii} regions, we conclude that 24 hot cores are externally heated while the other hot cores are internally heated. The observations presented here will potentially help establish a hot core template for studying massive star formation and astrochemistry.

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arXiv2021

The DR21(OH) Trident -- Resolving the Massive Ridge into Three Entangled Fibers As the Initial Condition of Cluster Formation

DR21(OH) ridge, the central part of a high-mass star and cluster forming hub-filament system, is resolved spatially and kinematically into three nearly parallel fibers (f1, f2, and f3) with a roughly north-south orientation, using the observations of molecular transitions of H$^{13}$CO$^+$ (1-0), N$_2$H$^+$ (1-0), and NH$_2$D (1$_{1,1}$-1$_{0,1}$) with the Combined Array for Research in Millimeter Astronomy. These fibers are all mildly supersonic ($σ_{\rm V}$ about 2 times the sound speed), having lengths around 2 pc and widths about 0.1 pc, and they entangle and conjoin in the south where the most active high-mass star formation takes place. They all have line masses 1 - 2 orders of magnitude higher than their low-mass counterparts and are gravitationally unstable both radially and axially. However, only f1 exhibits high-mass star formation all the way along the fiber, yet f2 and f3 show no signs of significant star formation in their northern parts. A large velocity gradient increasing from north to south is seen in f3, and can be well reproduced with a model of free-fall motion toward the most massive and active dense core in the region, which corroborates the global collapse of the ridge and suggests that the disruptive effects of the tidal forces may explain the inefficiency of star formation in f2 and f3. On larger scales, some of the lower-density, peripheral filaments are likely to be the outer extensions of the fibers, and provide hints on the origin of the ridge.

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arXiv2021

Magnetic fields in star formation: a complete compilation of all the DCF estimations

The Davis-Chandrasekhar-Fermi (DCF) method provides an indirect way to estimate the magnetic field strength from statistics of magnetic field orientations. We compile all the previous DCF estimations from polarized dust emission observations and re-calculate the magnetic field strength of the selected samples with the new DCF correction factors in Liu et al. (2021). We find the magnetic field scales with the volume density as $B \propto n^{0.57}$. However, the estimated power-law index of the observed $B-n$ relation has large uncertainties and may not be comparable to the $B-n$ relation of theoretical models. A clear trend of decreasing magnetic viral parameter (i.e., increasing mass-to-flux ratio in units of critical value) with increasing column density is found in the sample, which suggests the magnetic field dominates the gravity at lower densities but cannot compete with the gravity at higher densities. This finding also indicates that the magnetic flux is dissipated at higher column densities due to ambipolar diffusion or magnetic recennection, and the accumulation of mass at higher densities may be by mass flows along the magnetic field lines. Both sub-Alfvénic and super-Alfvénic states are found in the sample, with the average state being approximately trans-Alfvénic.

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arXiv2021

The ALMA Survey of 70 $μ$m Dark High-mass Clumps in Early Stages (ASHES). V. Deuterated Molecules in the 70 $μ$m dark IRDC G14.492-00.139

We have observed the 70 $μ$m dark infrared dark cloud (IRDC) G14.492-00.139 in the N$_2$D$^+$ $J$=3--2, DCO$^+$ $J$=3--2, DCN $J$=3--2, and C$^{18}$O $J$=2--1 lines, using the Atacama Large Millimeter/submillimeter Array (ALMA) as part of the ALMA Survey of 70 $μ$m Dark High-mass Clumps in Early Stages (ASHES). We find that the spatial distribution is different among the observed emission from the deuterated molecular lines. The N$_2$D$^+$ emission traces relatively quiescent regions, while both the DCO$^+$ and DCN emission emanates mainly from regions with signs of active star-formation. In addition, the DCO$^+$/N$_2$D$^+$ ratio is found to be lower in several dense cores than in starless cores embedded in low-mass star-forming regions. By comparing the observational results with chemical model calculations, we discuss the origin of the low DCO$^+$/N$_2$D$^+$ ratio in this IRDC clump. The low DCO$^+$/N$_2$D$^+$ ratio can be explained if the temperature of the dense cores is in the range between the sublimation temperature of N$_2$ ($\sim$20 K) and CO ($\sim$25 K). The results suggest that the dense cores in G14.492-00.139 are warmer and denser than the dense cores in low-mass star-forming regions.

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arXiv2021

ALMA observations of NGC 6334S. II. Subsonic and Transonic Narrow Filaments in a High-mass Star Formation Cloud

We present a study of narrow filaments toward a massive infrared dark cloud, NGC 6334S, using the Atacama Large Millimeter/submillimeter Array (ALMA). Thirteen gas filaments are identified using the H$^{13}$CO$^{+}$ line, while a single continuum filament is revealed by the continuum emission. The filaments present a compact radial distribution with a median filament width of $\sim$0.04 pc narrower than the previously proposed `quasi-universal' 0.1~pc filament width. The higher spatial resolution observations and higher-density gas tracer tend to identify even narrower and lower mass filaments. The filament widths are roughly twice the size of embedded cores. The gas filaments are largely supported by thermal motions. The nonthermal motions are predominantly subsonic and transonic in both identified gas filaments and embedded cores, which may imply that stars are likely born in environments of low turbulence. A fraction of embedded objects show a narrower velocity dispersion compared with their corresponding natal filaments, which may indicate that the turbulent dissipation is taking place in these embedded cores. The physical properties (mass, mass per unit length, gas kinematics, and width) of gas filaments are analogous to those of narrow filaments found in low- to high-mass star-forming regions. The more evolved sources are found to be farther away from the filaments, a situation that may have resulted from the relative motions between the YSOs and their natal filaments.

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arXiv2021

ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions -- V. Hierarchical fragmentation and gas dynamics in IRDC G034.43+00.24

We present new 3-mm continuum and molecular lines observations from the ATOMS survey towards the massive protostellar clump, MM1, located in the filamentary infrared dark cloud (IRDC), G034.43+00.24 (G34). The lines observed are the tracers of either dense gas (e.g. HCO+/H13CO+ J = 1-0) or outflows (e.g. CS J = 2-1). The most complete picture to date of seven cores in MM1 is revealed by dust continuum emission. These cores are found to be gravitationally bound, with virial parameter, $α_{vir}<2$. At least four outflows are identified in MM1 with a total outflowing mass of $\sim 45 M_\odot$, and a total energy of $\sim 1\times 10^{47}$ erg, typical of outflows from a B0-type star. Evidence of hierarchical fragmentation, where turbulence dominates over thermal pressure, is observed at both the cloud and the clump scales. This could be linked to the scale-dependent, dynamical mass inflow/accretion on clump and core scales. We therefore suggest that the G34 cloud could be undergoing a dynamical mass inflow/accretion process linked to the multiscale fragmentation, which leads to the sequential formation of fragments of the initial cloud, clumps, and ultimately dense cores, the sites of star formation.

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arXiv2021

Magnetic fields in the early stages of massive star formation as revealed by ALMA

We present 1.3 mm ALMA dust polarization observations at a resolution of $\sim$0.02 pc of three massive molecular clumps, MM1, MM4, and MM9, in the infrared dark cloud G28.34+0.06. With the sensitive and high-resolution continuum data, MM1 is resolved into a cluster of condensations. The magnetic field structure in each clump is revealed by the polarized emission. We found a trend of decreasing polarized emission fraction with increasing Stokes $I$ intensities in MM1 and MM4. Using the angular dispersion function method (a modified Davis-Chandrasekhar-Fermi method), the plane-of-sky magnetic field strength in two massive dense cores, MM1-Core1 and MM4-Core4, are estimated to be $\sim$1.6 mG and $\sim$0.32 mG, respectively. \textbf{The ordered magnetic energy is found to be smaller than the turbulent energy in the two cores, while the total magnetic energy is found to be comparable to the turbulent energy.} The total virial parameters in MM1-Core1 and MM4-Core4 are calculated to be $\sim$0.76 and $\sim$0.37, respectively, suggesting that massive star formation does not start in equilibrium. Using the polarization-intensity gradient-local gravity method, we found that the local gravity is closely aligned with intensity gradient in the three clumps, and the magnetic field tends to be aligned with the local gravity in MM1 and MM4 except for regions near the emission peak, which suggests that the gravity plays a dominant role in regulating the gas collapse. Half of the outflows in MM4 and MM9 are found to be aligned within 10$^{\circ}$ of the condensation-scale ($<$0.05 pc) magnetic field, indicating that the magnetic field could play an important role from condensation to disk scale in the early stage of massive star formation. We also found that the fragmentation in MM1-Core1 cannot be solely explained by thermal Jeans fragmentation or turbulent Jeans fragmentation.

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arXiv2021

Magnetic Fields in Massive Star-Forming Regions (MagMaR) II. Tomography Through Dust and Molecular Line Polarization in NGC 6334I(N)

Here, we report ALMA detections of polarized emission from dust, CS($J=5 \rightarrow 4$), and C$^{33}$S($J=5 \rightarrow 4$) toward the high-mass star-forming region NGC6334I(N). A clear ``hourglass'' magnetic field morphology was inferred from the polarized dust emission which is also directly seen from the polarized CS emission across velocity, where the polarization appears to be parallel to the field. By considering previous findings, the field retains a pinched shape which can be traced to clump length-scales from the envelope scales traced by ALMA, suggesting that the field is dynamically important across multiple length-scales in this region. The CS total intensity emission is found to be optically thick ($τ_{\mathrm{CS}} = 32 \pm 12$) while the C$^{33}$S emission appears to be optically thin ($τ_{\mathrm{C^{33}S}} = 0.1 \pm 0.01$). This suggests that sources of anisotropy other than large velocity gradients, i.e. anisotropies in the radiation field are required to explain the polarized emission from CS seen by ALMA. By using four variants of the Davis-Chandrasekhar-Fermi technique and the angle dispersion function methods (ADF), we obtain an average of estimates for the magnetic field strength onto the plane of the sky of $\left< \mathrm{B}_{\mathrm{pos}} \right> = 16$ mG from the dust and $\left< \mathrm{B}_{\mathrm{pos}} \right> \sim 2$ mG from the CS emission, where each emission traces different molecular hydrogen number densities. This effectively enables a tomographic view of the magnetic field within a single ALMA observation.

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arXiv2021

The ALMA Survey of 70 $μ$m Dark High-mass Clumps in Early Stages (ASHES). IV. Star formation signatures in G023.477

With a mass of $\sim$1000 $M_\odot$ and a surface density of $\sim$0.5 g cm$^{-2}$, G023.477+0.114 also known as IRDC 18310-4 is an infrared dark cloud (IRDC) that has the potential to form high-mass stars and has been recognized as a promising prestellar clump candidate. To characterize the early stages of high-mass star formation, we have observed G023.477+0.114 as part of the ALMA Survey of 70 $μ$m Dark High-mass Clumps in Early Stages (ASHES). We have conducted $\sim$1."2 resolution observations with the Atacama Large Millimeter/submillimeter Array (ALMA) at 1.3 mm in dust continuum and molecular line emission. We identified 11 cores, whose masses range from 1.1 $M_\odot$ to 19.0 $M_\odot$. Ignoring magnetic fields, the virial parameters of the cores are below unity, implying that the cores are gravitationally bound. However, when magnetic fields are included, the prestellar cores are close to virial equilibrium, while the protostellar cores remain sub-virialized. Star formation activity has already started in this clump. Four collimated outflows are detected in CO and SiO. H$_2$CO and CH$_3$OH emission coincide with the high-velocity components seen in the CO and SiO emission. The outflows are randomly oriented for the natal filament and the magnetic field. The position-velocity diagrams suggest that episodic mass ejection has already begun even in this very early phase of protostellar formation. The masses of the identified cores are comparable to the expected maximum stellar mass that this IRDC could form (8-19 $M_\odot$). We explore two possibilities on how IRDC G023.477+0.114 could eventually form high-mass stars in the context of theoretical scenarios.

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arXiv2021

Core mass function of a single giant molecular cloud complex with ~10^4 cores

Similarity in shape between the initial mass function (IMF) and the core mass functions (CMFs) in star-forming regions prompts the idea that the IMF originates from the CMF through a self-similar core-to-star mass mapping process. To accurately determine the shape of the CMF, we create a sample of 8,431 cores with the dust continuum maps of the Cygnus X giant molecular cloud complex, and design a procedure for deriving the CMF considering the mass uncertainty, binning uncertainty, sample incompleteness, and the statistical errors. The resultant CMF coincides well with the IMF for core masses from a few $M_{\odot}$ to the highest masses of 1300 $M_{\odot}$ with a power-law of ${\rm d}N/{\rm d}M\propto M^{-2.30\pm0.04}$, but does not present an obvious flattened turnover in the low-mass range as the IMF does. More detailed inspection reveals that the slope of the CMF steepens with increasing mass. Given the numerous high-mass star-forming activities of Cygnus X, this is in stark contrast with the existing top-heavy CMFs found in high-mass star-forming clumps. We also find that the similarity between the IMF and the mass function of cloud structures is not unique at core scales, but can be seen for cloud structures of up to several pc scales. Finally, our SMA observations toward a subset of the cores do not present evidence for the self-similar mapping. The latter two results indicate that the shape of the IMF may not be directly inherited from the CMF.

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arXiv2021

Planck Galactic Cold Clumps at High Galactic Latitude-A Study with CO Lines

Gas at high Galactic latitude is a relatively little-noticed component of the interstellar medium. In an effort to address this, forty-one Planck Galactic Cold Clumps at high Galactic latitude (HGal; $|b|>25^{\circ}$) were observed in $^{12}$CO, $^{13}$CO and C$^{18}$O J=1-0 lines, using the Purple Mountain Observatory 13.7-m telescope. $^{12}$CO (1-0) and $^{13}$CO (1-0) emission was detected in all clumps while C$^{18}$O (1-0) emission was only seen in sixteen clumps. The highest and average latitudes are $71.4^{\circ}$ and $37.8^{\circ}$, respectively. Fifty-one velocity components were obtained and then each was identified as a single clump. Thirty-three clumps were further mapped at 1$^\prime$ resolution and 54 dense cores were extracted. Among dense cores, the average excitation temperature $T_{\mathrm{ex}}$ of $^{12}$CO is 10.3 K. The average line widths of thermal and non-thermal velocity dispersions are $0.19$ km s$^{-1}$ and $0.46$ km s$^{-1}$ respectively, suggesting that these cores are dominated by turbulence. Distances of the HGal clumps given by Gaia dust reddening are about $120-360$ pc. The ratio of $X_{13}$/$X_{18}$ is significantly higher than that in the solar neighbourhood, implying that HGal gas has a different star formation history compared to the gas in the Galactic disk. HGal cores with sizes from $0.01-0.1$ pc show no notable Larson's relation and the turbulence remains supersonic down to a scale of slightly below $0.1$ pc. None of the HGal cores which bear masses from 0.01-1 $M_{\odot}$ are gravitationally bound and all appear to be confined by outer pressure.

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arXiv2021

Calibrating the Davis-Chandrasekhar-Fermi method with numerical simulations: uncertainties in estimating the magnetic field strength from statistics of field orientations

The Davis-Chandrasekhar-Fermi (DCF) method is widely used to indirectly estimate the magnetic field strength from the plane-of-sky field orientation. In this work, we present a set of 3D MHD simulations and synthetic polarization images using radiative transfer of clustered massive star-forming regions. We apply the DCF method on the synthetic polarization maps to investigate its reliability in high-density molecular clumps and dense cores where self-gravity is significant. We investigate the validity of the assumptions of the DCF method step by step and compare the model and estimated field strength to derive the correction factors for the estimated uniform and total (rms) magnetic field strength at clump and core scales. The correction factors in different situations are catalogued. We find the DCF method works well in strong field cases. However, the magnetic field strength in weak field cases could be significantly overestimated by the DCF method when the turbulent magnetic energy is smaller than the turbulent kinetic energy. We investigate the accuracy of the angular dispersion function (ADF, a modified DCF method) method on the effects that may affect the measured angular dispersion and find that the ADF method correctly accounts for the ordered field structure, the beam-smoothing, and the interferometric filtering, but may not be applicable to account for the signal integration along the line of sight in most cases. Our results suggest that the DCF methods should be avoided to be applied below $\sim$0.1 pc scales if the effect of line-of-sight signal integration is not properly addressed.

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arXiv2021

An ALMA study of outflow parameters of protoclusters: outflow feedback to maintain the turbulence

With the aim of understanding the role of outflows in star formation, we performed a statistical study of the physical parameters of outflows in eleven massive protoclusters associated with ultra-compact HII regions. A total of 106 outflow lobes are identified in these protoclusters using the ALMA CO (3-2), HCN (4-3) and HCO+ (4-3) line observations. Although the position angles of outflow lobes do not differ in these three tracers, HCN and HCO+ tend to detect lower terminal velocity of the identified outflows compared to CO. The majority of the outflows in our targets are young with typical dynamical time-scales of 10^2-10^4 years, and are mostly composed of low-mass outflows along with at least one high-mass outflow in each target. An anti-correlation of outflow rate with dynamical time-scale indicates that the outflow rate possibly decreases with time. Also, a rising trend of dynamical time-scale with the mass of the associated core hints that the massive cores might have longer accretion histories than the low mass cores. Estimation of different energies in these protoclusters shows that outflows studied here cannot account for the generation of the observed turbulence, but can sustain the turbulence at the current epoch as the energy injection rate from the outflows is similar to the estimated dissipation rate.

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arXiv2021

Gravity Driven Magnetic Field at ~1000 au Scales in High-mass Star Formation

A full understanding of high-mass star formation requires the study of one of the most elusive components of the energy balance in the interstellar medium: magnetic fields. We report ALMA 1.2 mm, high-resolution (700 au) dust polarization and molecular line observations of the rotating hot molecular core embedded in the high-mass star-forming region IRAS 18089-1732. The dust continuum emission and magnetic field morphology present spiral-like features resembling a whirlpool. The velocity field traced by the H13CO+ (J=3-2) transition line reveals a complex structure with spiral filaments that are likely infalling and rotating, dragging the field with them. We have modeled the magnetic field and find that the best model corresponds to a weakly magnetized core with a mass-to-magnetic-flux ratio (lambda) of 8.38. The modeled magnetic field is dominated by a poloidal component, but with an important contribution from the toroidal component that has a magnitude of 30% of the poloidal component. Using the Davis-Chandrasekhar-Fermi method, we estimate a magnetic field strength of 3.5 mG. At the spatial scales accessible to ALMA, an analysis of the energy balance of the system indicates that gravity overwhelms turbulence, rotation, and the magnetic field. We show that high-mass star formation can occur in weakly magnetized environments, with gravity taking the dominant role.

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arXiv2021

A Low-mass Cold and Quiescent Core Population in a Massive Star Protocluster

Pre-stellar cores represent the initial conditions of star formation. Although these initial conditions in nearby low-mass star-forming regions have been investigated in detail, such initial conditions remain vastly unexplored for massive star-forming regions. We report the detection of a cluster of low-mass starless and pre-stellar core candidates in a massive star protocluster forming cloud, NGC6334S. With the ALMA observations at a $\sim$0.02 pc spatial resolution, we identified 17 low-mass starless core candidates that do not show any evidence of protostellar activity. These candidates present small velocity dispersions, high fractional abundances of NH$_{2}$D, high NH$_{3}$ deuterium fractionations, and are completely dark in the infrared wavelengths from 3.6 up to 70~$μ$m. Turbulence is significantly dissipated and the gas kinematics are dominated by thermal motions toward these candidates. Nine out of the 17 cores are gravitationally bound, and therefore are identified as pre-stellar core candidates. The embedded cores of NGC6334S show a wide diversity in masses and evolutionary stages.

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arXiv2021

Convergent Filaments Contracting Towards an Intermediate-mass Prestellar Core

Filamentary structures are closely associated with star-forming cores, but their detailed physical connections are still not clear. We studied the dense gas in the region of OMC-3 MMS-7 in Orion A molecular cloud using the molecular lines observed with the Atacama Large Millimeter/submillimeter Array (ALMA) and the Submillimeter Array (SMA). The ALMA N$_2$H$^+$ (1-0) emission has revealed three dense filaments intersected at the center, coincident with the central core MMS-7, which has a mass of $3.6\,M_\odot$. The filaments and cores are embedded in a parental clump with total mass of $29\,M_\odot$. The N$_2$H$^+$ velocity field exhibits a noticeable increasing trend along the filaments towards the central core MMS-7 with a scale of $v-v_{\rm lsr} \simeq 1.5$ ${\rm km\, s^{-1}}$ over a spatial range of $\sim$20 arcsec ($8\times 10^3$ AU), corresponding to a gradient of $40\,{\rm km\, s^{-1}}\,{\rm pc}^{-1}$. This feature is most likely to indicate an infall motion towards the center. The derived infall rate ($8\times 10^{-5}\,M_\odot$ year$^{-1}$) and timescale ($3.6\times 10^5$ years) are much lower than that in a spherical free-fall collapse and more consistent with the contraction of filament structures. The filaments also exhibit a possible fragmentation, but it does not seem to largely interrupt the gas structure or the infall motion towards the center. MMS-7 thus provides an example of filamentary infall into an individual prestellar core. The filament contraction could be less intense but more steady than the global spherical collapse, and may help generate an intermediate- or even high-mass star.

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arXiv2021

Does the magnetic field suppress fragmentation in massive dense cores?

Theoretical and numerical works indicate that a strong magnetic field should suppress fragmentation in dense cores. However, this has never been tested observationally in a relatively large sample of fragmenting massive dense cores. Here we use the polarization data obtained in the Submillimeter Array Legacy Survey of Zhang et al. to build a sample of 18 massive dense cores where both fragmentation and magnetic field properties are studied in a uniform way. We measured the fragmentation level, Nmm, within the field of view common to all regions, of 0.15 pc, with a mass sensitivity of about 0.5 Msun, and a spatial resolution of about 1000 au. In order to obtain the magnetic field strength using the Davis-Chandrasekhar-Fermi method, we estimated the dispersion of the polarization position angles, the velocity dispersion of the H13CO+(4-3) gas, and the density of each core, all averaged within 0.15 pc. A strong correlation is found between Nmm and the average density of the parental core, although with significant scatter. When large-scale systematic motions are separated from the velocity dispersion and only the small-scale (turbulent) contribution is taken into account, a tentative correlation is found between Nmm and the mass-to-flux ratio, as suggested by numerical and theoretical works.

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