arXiv subjects

Kohji Tomisaka

Publications and source records attributed to Kohji Tomisaka.

At least 19 recordsLinked to original sources

arXiv2026

Evolution of compressed clouds formed by filament coalescence. I. Oblique collisions

Stars are thought to form predominantly within filamentary molecular clouds. Recent studies have suggested that active star formation, including the formation of stellar clusters and massive stars, occurs within so-called "hub" structures, where multiple filaments converge. Understanding the formation and evolution of such hub-filament systems is therefore essential for unveiling the physical processes responsible for cluster and massive star formation, although the full picture remains incomplete. To address this, we have focused on filament-filament collisions as a potential formation mechanism of the hubs. In this study, we investigate the fundamental evolutionary processes of oblique collisions between two magnetized filaments using three-dimensional ideal magnetohydrodynamical simulations. As a model of initial filaments, we consider two identical finite-length magnetized filaments, varying the collision angle between their long axes, the collision velocity, which is set perpendicular to the long axes, and the initial line mass. We find that as the collision angle decreases from orthogonal to parallel, the compressed cloud becomes more prone to gravitational collapse. In addition, the instability of the post-collision compressed cloud can be explained by its energy balance. Specifically, if the absolute value of the gravitational energy exceeds the sum of the kinetic, thermal, and magnetic energies immediately after the collision, the cloud undergoes gravitational collapse. Conversely, if the gravitational energy is smaller, the cloud expands. In addition, we estimate the upper limit of the collision velocity that enables hub-filament formation and identify the collision conditions favorable for massive star formation.

astro-ph.GA↗

arXiv2026

Hub Formation and Filament-Filament Collision: An Analytical Model

Filaments are ubiquitous throughout the Galaxy. Massive star formation is often observed in hub-filament systems, where multiple filaments appear to be interconnected and merging. Filament-filament collisions are therefore a likely triggering mechanism for massive star formation. We derive basic physical properties of filament-filament collisions, such as the collision cross section (CCS), the hub mass, and its mass function, based on a simple cylindrical filament model. We assume a cylindrical filament with length $2p$, full width $2q$, and line-mass $\lambda_0$, and consider the CCS between two identical filaments. The collision is specified by three vectors: the directions of the colliding filaments ($n_1$ and $n_2$) and the direction of the relative velocity between the two filaments ($n_v=v/|v|$). For the thin filament, $p\gg q$, the CCS is expressed as $S=4p^2|n'_1\times n'_2|$, where $n'_1$ and $n'_2$ represent the directional vectors projected onto a plane perpendicular to the relative velocity $n_v$. As the angle between $n'_1$ and $n'_2$ becomes smaller, the cross section proportional to $p\cdot q$ becomes relatively important. We propose a simple model in which the hub mass is estimated by the overlapping portion of the two colliding filaments. The hub mass function is derived using the CCSs and the geometrically estimated overlapping mass. When the directions and relative velocities of the filaments are isotropically distributed, the mass function expected from a single species of filaments fits well to a power law and the power exponent is $\gamma_M\simeq -2.96$ ~ $-3.78$. The power exponent of the global hub mass function is the same as that of the line-mass distribution function, $\gamma_\lambda\simeq -1.5$. This means that a massive hub is formed by the collision of two massive filaments.

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arXiv2024

Instability and Evolution of Shocked Clouds Formed by Orthogonal Collisions between Magnetized Filamentary Molecular Clouds

Filamentary molecular clouds are recognized as primary sites for the formation of stars. Specifically, regions characterized by the overlapping point of multiple filaments, known as hub regions, often associated with active star formation. However, the formation mechanism of this hub structure is not well understood. Therefore, to understand the formation mechanism and star formation in hub structures, as a first step, we investigate the orthogonal collisions between two filaments using three-dimensional ideal magnetohydrodynamical simulations. As a model of initial filaments, we use an infinitely long filament in magnetohydrostatic equilibrium under a global magnetic field running perpendicular to the filament axis. Two identical equilibrium filaments, sharing the same magnetic flux, are arranged with their long axes perpendicular to each other and given an initial velocity perpendicular to their long axes to replicate an orthogonal collision. We find three types of evolution after the shocked cloud is formed: collapse, stable, and expansion modes. The energy balance just after the filaments completely collide explains the future evolution of the shocked cloud. If the magnitude of gravitational energy is larger than the sum of the kinetic, thermal, and magnetic energies, the shocked cloud evolves in collapse mode. If the magnitude of gravitational energy is less than the sum of these energies, the cloud evolves in stable mode when the kinetic energy is relatively small and in expansion mode when the kinetic energy is sufficiently large.

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arXiv2024

An Extremely Young Protostellar Core, MMS 1/ OMC-3: Episodic Mass Ejection History Traced by the Micro SiO Jet

We present ${\sim}0.2$ arcsec ($\sim$80 au) resolution observations of the CO (2-1) and SiO (5-4) lines made with the Atacama large millimeter/submillimeter array toward an extremely young intermediate-mass protostellar source (t$_{\rm dyn}<$1000 years), MMS 1 located in the Orion Molecular Cloud-3 region. We have successfully imaged a very compact CO molecular outflow associated with MMS 1, having deprojected lobe sizes of $\sim$18000 au (red-shifted lobe) and $\sim$35000 au (blue-shifted lobe). We have also detected an extremely compact ($\lesssim$1000 au) and collimated SiO protostellar jet within the CO outflow. The maximum deprojected jet speed is measured to be as high as 93 km s$^{-1}$. The SiO jet wiggles and displays a chain of knots. Our detection of the molecular outflow and jet is the first direct evidence that MMS 1 already hosts a protostar. The position-velocity diagram obtained from the SiO emission shows two distinct structures: (i) bow-shocks associated with the tips of the outflow, and (ii) a collimated jet, showing the jet velocities linearly increasing with the distance from the driving source. Comparisons between the observations and numerical simulations quantitatively share similarities such as multiple-mass ejection events within the jet and Hubble-like flow associated with each mass ejection event. Finally, while there is a weak flux decline seen in the 850 $μ$m light curve obtained with JCMT/SCUBA 2 toward MMS 1, no dramatic flux change events are detected. This suggests that there has not been a clear burst event within the last 8 years.

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arXiv2023

Dust Polarization of Prestellar and Protostellar Sources in OMC-3

We present the Atacama Large Millimeter/submillimeter Array (ALMA) observations of linearly polarized 1.1 mm continuum emission at $\sim$0.14" (55 au) resolution and CO ($J$=2$-$1) emission at $\sim$1.5" (590 au) resolution towards one prestellar (MMS 4), four Class 0 (MMS$\,$1, MMS$\,$3, MMS$\,$5, and MMS$\,$6), one Class I (MMS$\,$7), and one flat-spectrum (MMS$\,$2) sources in the Orion Molecular Cloud$\,$3 region. The dust disk-like structures and clear CO outflows are detected towards all sources except for MMS$\,$4. The diameters of these disk-like structures, ranging from 16 au to 97 au, are estimated based on the deconvolved full width half maximum (FWHM) values obtained from the multi-Gaussian fitting. Polarized emissions are detected towards MMS$\,$2, MMS$\,$5, MMS$\,$6, and MMS$\,$7, while no polarized emission is detected towards MMS$\,$1, MMS$\,$3, and MMS$\,$4. MMS$\,$2, MMS$\,$5, and MMS$\,$7 show organized polarization vectors aligned with the minor axes of the disk-like structures, with mean polarization fractions ranging from 0.6$\%$ to 1.2$\%$. The strongest millimeter source, MMS$\,$6, exhibits complex polarization orientations and a remarkably high polarization fraction of $\sim$10$\%$ around the Stokes $I$ peak, and 15$-$20$\%$ on the arm-like structure, as reported by Takahashi et al. (2019). The origins of the polarized emission, such as self-scattering and dust alignment due to the magnetic field or radiative torque, are discussed for individual sources. Some disk-like sources exhibit a polarized intensity peak shift towards the nearside of the disk, which supports that the polarized emission originates from self-scattering.

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arXiv2023

Simulation of Head-on Collisions Between Filamentary Molecular Clouds Threaded by a Lateral Magnetic Field and Subsequent Evolution

Filamentary molecular clouds are regarded as the place where newborn stars are formed. In particular, a hub region, a place where it appears as if several filaments are colliding, often indicates active star formation. To understand the star formation in filament structures, we investigate the collisions between two filaments using two-dimensional magnetohydrodynamical simulations. As a model of filaments, we assume that the filaments are in magnetohydrostatic equilibrium under a global magnetic field perpendicular to the filament axis. We set two identical filaments with an infinite length and collided them with a zero-impact parameter (head-on). When the two filaments collide while sharing the same magnetic flux, we found two types of evolution after a merged filament is formed: runaway radial collapse and stable oscillation with a finite amplitude. The condition for the radial collapse is independent of the collision velocity and is given by the total line mass of the two filaments exceeding the magnetically critical line mass for which no magnetohydrostatic solution exists. The radial collapse proceeds in a self-similar manner, resulting in a unique distribution irrespective of the various initial line masses of the filament, as the collapse progresses. When the total line mass is less massive than the magnetically critical line mass, the merged filament oscillates, and the density distribution is well-fitted by a magnetohydrostatic equilibrium solution. The condition necessary for the radial collapse is also applicable to the collision whose direction is perpendicular to the global magnetic field.

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arXiv2022

JCMT BISTRO Observations: Magnetic Field Morphology of Bubbles Associated with NGC 6334

We study the HII regions associated with the NGC 6334 molecular cloud observed in the sub-millimeter and taken as part of the B-fields In STar-forming Region Observations (BISTRO) Survey. In particular, we investigate the polarization patterns and magnetic field morphologies associated with these HII regions. Through polarization pattern and pressure calculation analyses, several of these bubbles indicate that the gas and magnetic field lines have been pushed away from the bubble, toward an almost tangential (to the bubble) magnetic field morphology. In the densest part of NGC 6334, where the magnetic field morphology is similar to an hourglass, the polarization observations do not exhibit observable impact from HII regions. We detect two nested radial polarization patterns in a bubble to the south of NGC 6334 that correspond to the previously observed bipolar structure in this bubble. Finally, using the results of this study, we present steps (incorporating computer vision; circular Hough Transform) that can be used in future studies to identify bubbles that have physically impacted magnetic field lines.

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arXiv2022

The JCMT BISTRO Survey: A Spiral Magnetic Field in a Hub-filament Structure, Monoceros R2

We present and analyze observations of polarized dust emission at 850 $μ$m towards the central 1 pc $\times$ 1 pc hub-filament structure of Monoceros R2 (Mon R2). The data are obtained with SCUBA-2/POL-2 on the James Clerk Maxwell Telescope (JCMT) as part of the BISTRO (B-fields in Star-forming Region Observations) survey. The orientations of the magnetic field follow the spiral structure of Mon R2, which are well-described by an axisymmetric magnetic field model. We estimate the turbulent component of the magnetic field using the angle difference between our observations and the best-fit model of the underlying large-scale mean magnetic field. This estimate is used to calculate the magnetic field strength using the Davis-Chandrasekhar-Fermi method, for which we also obtain the distribution of volume density and velocity dispersion using a column density map derived from $Herschel$ data and the C$^{18}$O ($J$ = 3-2) data taken with HARP on the JCMT, respectively. We make maps of magnetic field strengths and mass-to-flux ratios, finding that magnetic field strengths vary from 0.02 to 3.64 mG with a mean value of 1.0 $\pm$ 0.06 mG, and the mean critical mass-to-flux ratio is 0.47 $\pm$ 0.02. Additionally, the mean Alfvén Mach number is 0.35 $\pm$ 0.01. This suggests that in Mon R2, magnetic fields provide resistance against large-scale gravitational collapse, and magnetic pressure exceeds turbulent pressure. We also investigate the properties of each filament in Mon R2. Most of the filaments are aligned along the magnetic field direction and are magnetically sub-critical.

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arXiv2022

Twisted magnetic field in star formation processes of L1521 F revealed by submillimeter dual band polarimetry using James Clerk Maxwell Telescope

Understanding the initial conditions of star formation requires both observational studies and theoretical works taking into account the magnetic field, which plays an important role in star formation processes. Herein, we study the young nearby dense cloud core L1521 F ($n$(H$_2$) $\sim 10^{4-6}$ cm$^{-3}$) in the Taurus Molecular Cloud. This dense core hosts a 0.2 $M_\odot$ protostar, categorized as a Very Low Luminosity Objects with complex velocity structures, particularly in the vicinity of the protostar. To trace the magnetic field within the dense core, we conducted high sensitivity submillimeter polarimetry of the dust continuum at $λ$= 850 $μ$m and 450 $μ$m using the POL-2 polarimeter situated in front of the SCUBA-2 submillimeter bolometer camera on James Clerk Maxwell Tetescope. This was compared with millimeter polarimetry taken at $λ$= 3.3 mm with ALMA. The magnetic field was detected at $λ$= 850 $μ$m in the peripheral region, which is threaded in a north-south direction, while the central region traced at $λ$= 450 $μ$m shows a magnetic field with an east-west direction, i.e., orthogonal to that of the peripheral region. Magnetic field strengths are estimated to be $\sim$70 $μ$G and 200 $μ$G in the peripheral- and central-regions, respectively, using the Davis-Chandrasekhar-Fermi method. The resulting mass-to-flux ratio of 3 times larger than that of magnetically critical state for both regions indicates that L1521 F is magnetically supercritical, i.e., gravitational forces dominate over magnetic turbulence forces. Combining observational data with MHD simulations, detailed parameters of the morphological properties of this puzzling object are derived for the first time.

astro-ph.SR↗

arXiv2022

Mushroom-instability-driven Magnetic Reconnections in Collisionless Relativistic Jets

We study the kinetic plasma dynamics in collisionless relativistic jets with velocity shear, by carrying out particle-in-cell simulations in the transverse plane of a jet. It is discovered that intermittent magnetic reconnections (MRs) are driven by Mushroom instability (MI), which is an important kinetic-scale plasma instability in the plasma shear-flows with relativistic bulk speed. We refer to this sequence of kinetic plasma phenomena as "MI-driven MR". The MI-driven MRs intermittently occur with moving the location of the reconnection points from the vicinity of the initial velocity-shear surface towards the center of the jet. As a consequence, the number density of high energy electrons, which are accelerated by MI-driven MRs, increases with time in the region inside the initial velocity-shear surface with accompanying the generation and subsequent amplification of magnetic fields by MI. The maximum Lorentz factor of electrons increases with initial bulk Lorentz factor of the jet. A possible relation of MI-driven MR to the bright synchrotron emission in jet-spine of active galactic nucleus jets is also discussed.

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arXiv2021

The JCMT BISTRO Survey: Evidence for Pinched Magnetic Fields in Quiescent Filaments of NGC 1333

We investigate the internal 3D magnetic structure of dense interstellar filaments within NGC 1333 using polarization data at $850 μ\mathrm{m}$ from the $B$-fields In STar-forming Region Observations survey at the James Clerk Maxwell Telescope. Theoretical models predict that the magnetic field lines in a filament will tend to be dragged radially inward (i.e., pinched) toward the central axis due to the filament's self-gravity. We study the cross-sectional profiles of the total intensity ($I$) and polarized intensity (PI) of dust emission in four segments of filaments unaffected by local star formation that are expected to retain a pristine magnetic field structure. We find that the filaments' FWHM in PI are not the same as those in $I$, with two segments being appreciably narrower in PI (FWHM ratio $\simeq 0.7-0.8$) and one segment being wider (FWHM ratio $\simeq 1.3$). The filament profiles of the polarization fraction ($P$) do not show a minimum at the spine of the filament, which is not in line with an anticorrelation between $P$ and $I$ normally seen in molecular clouds and protostellar cores. Dust grain alignment variation with density cannot reproduce the observed $P$ distribution. We demonstrate numerically that the $I$ and PI cross-sectional profiles of filaments in magnetohydrostatic equilibrium will have differing relative widths depending on the viewing angle. The observed variations of FWHM ratios in NGC 1333 are therefore consistent with models of pinched magnetic field structures inside filaments, and especially if they are magnetically near-critical or supercritical.

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arXiv2021

Super-fast Rotation in the OMC 2/FIR 6b Jet

We present ALMA CO ($J$=2--1) and 1.3 mm continuum observations of the high-velocity jet associated with the FIR 6b protostar located in the Orion Molecular Cloud-2. We detect a velocity gradient along the short axis of the jet in both the red- and blue-shifted components. The position-velocity diagrams along the short axis of the red-shifted jet show a typical characteristic of a rotating cylinder. We attribute the velocity gradient in the red-shifted component to rotation of the jet. The rotation velocity ($>20\,\ \rm{km s^{-1}}$) and specific angular momentum ($>10^{22}\, \rm{cm^{2}\, s^{-1}}$) of the jet around FIR 6b are the largest among all jets in which rotation has been observed. By combining disk wind theory with our observations, the jet launching radius is estimated to be in the range of $2.18-2.96$\,au. The rapid rotation, large specific angular momentum, and a launching radius far from the central protostar can be explained by a magnetohydrodynamic disk wind that contributes to the angular momentum transfer in the late stages of protostellar accretion.

astro-ph.GA↗

arXiv2021

Magnetohydrostatic Equilibrium Structure and Mass of Polytropic Filamentary Cloud Threaded by Lateral Magnetic Field

Filamentary structures are recognized as a fundamental component of interstellar molecular clouds in observations by the Herschel satellite. These filaments, especially massive filaments, often extend in a direction perpendicular to the interstellar magnetic field. Furthermore, the filaments sometimes have an apparently negative temperature gradient, that is, their temperature decreases towards the center. In this paper, we study the magnetohydrostatic equilibrium state of negative-indexed polytropic gas with the magnetic field running perpendicular to the axis of the filament. The model is controlled by four parameters: center-to-surface density ratio ($ρ_c/ρ_s$), plasma $β$ of the surrounding gas, radius of the parent cloud $R'_0$ normalized by the scale height, and the polytropic index $N$. The steepness of the temperature gradient is represented by $N$. We found that the envelope of the column density profile becomes shallow when the temperature gradient is large. This reconciles the inconsistency between the observed profiles and those expected from the isothermal models. We compared the maximum line-mass (mass per unit length), above which there is no equilibrium, with that of the isothermal non-magnetized filament. We obtained an empirical formula to express the maximum line-mass of a magnetized polytropic filament as $λ_{max}\simeq\left[{\left(λ_{0,max}(N)/M_\odot{\rm pc^{-1}}\right)^2+\left[5.9(1.0+1.2/N)^{1/2}({Φ_{cl}}/{1μ{\rm G\,pc}})\right]^2}\right]^{1/2}M_\odot {\rm pc^{-1}}$, where $λ_{0,max}(N)$ represents the maximum line-mass of the non-magnetized filament and $Φ_{cl}$ indicates one-half of the magnetic flux threading the filament per unit length. Although the negative-indexed polytrope makes the maximum line-mass decrease compared with that of the isothermal model, a magnetic field threading the filament increases the line-mass.

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arXiv2020

Distortion of Magnetic Fields in the Dense Core SL42 (CrA-E) in the Corona Australis Molecular Cloud Complex

Detailed magnetic field structure of the dense core SL42 (CrA-E) in the Corona Australis molecular cloud complex was investigated based on near-infrared polarimetric observations of background stars to measure dichroically polarized light produced by magnetically aligned dust grains. The magnetic fields in and around SL42 were mapped using 206 stars and curved magnetic fields were identified. On the basis of simple hourglass (parabolic) magnetic field modeling, the magnetic axis of the core on the plane of sky was estimated to be $40^{\circ} \pm 3^{\circ}$. The plane-of-sky magnetic field strength of SL42 was found to be $22.4 \pm 13.9$ $\mu$G. Taking into account the effects of thermal/turbulent pressure and the plane-of-sky magnetic field component, the critical mass of SL42 was obtained to be $M_{\rm cr} = 21.2 \pm 6.6$ M$_{\odot}$, which is close to the observed core mass of $M_{\rm core} \approx 20$ M$_{\odot}$. We thus conclude that SL42 is in a condition close to the critical state if the magnetic fields lie near the plane of the sky. Since there is a very low luminosity object (VeLLO) toward the center of SL42, it is unlikely this core is in a highly subcritical condition (i.e., magnetic inclination angle significantly deviated from the plane of sky). The core probably started to collapse from a nearly kinematically critical state. In addition to the hourglass magnetic field modeling, the Inoue \& Fukui (2013) mechanism may explain the origin of the curved magnetic fields in the SL42 region.

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arXiv2020

The JCMT BISTRO Survey: Magnetic Fields Associated with a Network of Filaments in NGC 1333

We present new observations of the active star-formation region NGC 1333 in the Perseus molecular cloud complex from the James Clerk Maxwell Telescope B-Fields In Star-forming Region Observations (BISTRO) survey with the POL-2 instrument. The BISTRO data cover the entire NGC 1333 complex (~1.5 pc x 2 pc) at 0.02 pc resolution and spatially resolve the polarized emission from individual filamentary structures for the first time. The inferred magnetic field structure is complex as a whole, with each individual filament aligned at different position angles relative to the local field orientation. We combine the BISTRO data with low- and high- resolution data derived from Planck and interferometers to study the multiscale magnetic field structure in this region. The magnetic field morphology drastically changes below a scale of ~1 pc and remains continuous from the scales of filaments (~0.1 pc) to that of protostellar envelopes (~0.005 pc or ~1000 au). Finally, we construct simple models in which we assume that the magnetic field is always perpendicular to the long axis of the filaments. We demonstrate that the observed variation of the relative orientation between the filament axes and the magnetic field angles are well reproduced by this model, taking into account the projection effects of the magnetic field and filaments relative to the plane of the sky. These projection effects may explain the apparent complexity of the magnetic field structure observed at the resolution of BISTRO data toward the filament network.

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arXiv2020

Disk structure around the Class I protostar L1489 IRS revealed by ALMA: a warped disk system

We have observed the Class I protostar L1489 IRS with the Atacama Millimeter/submillimeter Array (ALMA) in Band 6. The C$^{18}$O $J=$2-1 line emission shows flattened and non-axisymmetric structures in the same direction as its velocity gradient due to rotation. We discovered that the C$^{18}$O emission shows dips at a radius of ~200-300 au while the 1.3 mm continuum emission extends smoothly up to r~400 au. At the radius of the C$^{18}$O dips, the rotational axis of the outer portion appears to be tilted by ~15 degrees from that of the inner component. Both the inner and outer components with respect to the C$^{18}$O dips exhibit the $r^{-0.5}$ Keplerian rotation profiles until r~600 au. These results not only indicate that a Keplerian disk extends up to ~600 au but also that the disk is warped. We constructed a three dimensional warped disk model rotating at the Keplerian velocity, and demonstrated that the warped disk model reproduces main observed features in the velocity channel maps and the PV diagrams. Such a warped disk system can form by mass accretion from a misaligned envelope. We also discuss a possible disk evolution scenario based on comparisons of disk radii and masses between Class I and Class II sources.

astro-ph.SR↗

arXiv2020

Distortion of Magnetic Fields in BHR 71

The magnetic field structure of a star-forming Bok globule BHR 71 was determined based on near-infrared polarimetric observations of background stars. The magnetic field in BHR 71 was mapped from 25 stars. By using a simple 2D parabolic function, the plane-of-sky magnetic axis of the core was found to be $θ_{\rm mag} = 125^{\circ} \pm 11^{\circ}$. The plane-of-sky mean magnetic field strength of BHR 71 was found to be $B_{\rm pos} = 8.8 - 15.0$ $μ$G, indicating that the BHR 71 core is magnetically supercritical with $λ= 1.44 - 2.43$. Taking into account the effect of thermal/turbulent pressure and the plane-of-sky magnetic field component, the critical mass of BHR 71 was $M_{\rm cr} = 14.5-18.7$ M$_{\odot}$, which is consistent with the observed core mass of $M_{\rm core} \approx 14.7$ M$_{\odot}$ (Yang et al. 2017). We conclude that BHR 71 is in a condition close to a kinematically critical state, and the magnetic field direction lies close to the plane of sky. Since BHR 71 is a star-forming core, a significantly subcritical condition (i.e., the magnetic field direction deviating from the plane of sky) is unlikely, and collapsed from a condition close to a kinematically critical state. There are two possible scenarios to explain the curved magnetic fields of BHR 71, one is an hourglass-like field structure due to mass accumulation and the other is the Inoue \& Fukui (2013) mechanism, which proposes the interaction of the core with a shock wave to create curved magnetic fields wrapping around the core.

astro-ph.GA↗

arXiv2020

Distortion of Magnetic Fields in Barnard 335

In this study, the detailed magnetic field structure of the dense protostellar core Barnard 335 (B335) was revealed based on near-infrared polarimetric observations of background stars to measure dichroically polarized light produced by magnetically aligned dust grains in the core. Magnetic fields pervading B335 were mapped using 24 stars after subtracting unrelated ambient polarization components, for the first time revealing that they have an axisymmetrically distorted hourglass-shaped structure toward the protostellar core. On the basis of simple two- and three-dimensional magnetic field modeling, magnetic inclination angles in the plane-of-sky and line-of-sight directions were determined to be $90^{\circ} \pm 7^{\circ}$ and $50^{\circ} \pm 10^{\circ}$, respectively. The total magnetic field strength of B335 was determined to be $30.2 \pm 17.7$ $\mu {\rm G}$. The critical mass of B335, evaluated using both magnetic and thermal/turbulent support against collapse, was determined to be $M_{\rm cr} = 3.37 \pm 0.94$ ${\rm M}_{\odot}$, which is identical to the observed core mass of $M_{\rm core}=3.67$ M$_{\odot}$. We thus concluded that B335 started its contraction from a condition near equilibrium. We found a linear relationship in the polarization versus extinction diagram, up to $A_V \sim 15$ mag toward the stars with the greatest obscuration, which verified that our observations and analysis provide an accurate depiction of the core.

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