arXiv subjects

Masafumi Matsumura

Publications and source records attributed to Masafumi Matsumura.

At least 19 recordsLinked to original sources

arXiv2024

The JCMT BISTRO Survey: The Magnetic Fields of the IC 348 Star-forming Region

We present 850 $μ$m polarization observations of the IC 348 star-forming region in the Perseus molecular cloud as part of the B-fields In STar-forming Region Observation (BISTRO) survey. We study the magnetic properties of two cores (HH 211 MMS and IC 348 MMS) and a filamentary structure of IC 348. We find that the overall field tends to be more perpendicular than parallel to the filamentary structure of the region. The polarization fraction decreases with intensity, and we estimate the trend by power-law and the mean of the Rice distribution fittings. The power indices for the cores are much smaller than 1, indicative of possible grain growth to micron size in the cores. We also measure the magnetic field strengths of the two cores and the filamentary area separately by applying the Davis-Chandrasekhar-Fermi method and its alternative version for compressed medium. The estimated mass-to-flux ratios are 0.45-2.20 and 0.63-2.76 for HH 211 MMS and IC 348 MMS, respectively, while the ratios for the filament is 0.33-1.50. This result may suggest that the transition from subcritical to supercritical conditions occurs at the core scale ($\sim$ 0.05 pc) in the region. In addition, we study the energy balance of the cores and find that the relative strength of turbulence to the magnetic field tends to be stronger for IC 348 MMS than HH 211 MMS. The result could potentially explain the different configurations inside the two cores: a single protostellar system in HH 211 MMS and multiple protostars in IC 348 MMS.

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arXiv2023

Tomographic Imaging of the Sagittarius Spiral Arm's Magnetic Field Structure

The Galactic global magnetic field is thought to play a vital role in shaping Galactic structures such as spiral arms and giant molecular clouds. However, our knowledge of magnetic field structures in the Galactic plane at different distances is limited, as measurements used to map the magnetic field are the integrated effect along the line of sight. In this study, we present the first-ever tomographic imaging of magnetic field structures in a Galactic spiral arm. Using optical stellar polarimetry over a $17' \times 10'$ field of view, we probe the Sagittarius spiral arm. Combining these data with stellar distances from the $Gaia$ mission, we can isolate the contributions of five individual clouds along the line of sight by analyzing the polarimetry data as a function of distance. The observed clouds include a foreground cloud ($d < 200$ pc) and four clouds in the Sagittarius arm at 1.23 kpc, 1.47 kpc, 1.63 kpc, and 2.23 kpc. The column densities of these clouds range from 0.5 to $2.8 \times 10^{21}~\mathrm{cm}^{-2}$. The magnetic fields associated with each cloud show smooth spatial distributions within their observed regions on scales smaller than 10 pc and display distinct orientations. The position angles projected on the plane-of-sky, measured from the Galactic north to east, for the clouds in increasing order of distance are $135^\circ$, $46^\circ$, $58^\circ$, $150^\circ$, and $40^\circ$, with uncertainties of a few degrees. Notably, these position angles deviate significantly from the direction parallel to the Galactic plane.

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arXiv2023

The JCMT BISTRO Survey: Studying the Complex Magnetic Field of L43

We present observations of polarized dust emission at 850 $μ$m from the L43 molecular cloud which sits in the Ophiuchus cloud complex. The data were taken using SCUBA-2/POL-2 on the James Clerk Maxwell Telescope as a part of the BISTRO large program. L43 is a dense ($N_{\rm H_2}\sim 10^{22}$-10$^{23}$ cm$^{-2}$) complex molecular cloud with a submillimetre-bright starless core and two protostellar sources. There appears to be an evolutionary gradient along the isolated filament that L43 is embedded within, with the most evolved source closest to the Sco OB2 association. One of the protostars drives a CO outflow that has created a cavity to the southeast. We see a magnetic field that appears to be aligned with the cavity walls of the outflow, suggesting interaction with the outflow. We also find a magnetic field strength of up to $\sim$160$\pm$30 $μ$G in the main starless core and up to $\sim$90$\pm$40 $μ$G in the more diffuse, extended region. These field strengths give magnetically super- and sub-critical values respectively and both are found to be roughly trans-Alfvénic. We also present a new method of data reduction for these denser but fainter objects like starless cores.

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arXiv2023

First BISTRO observations of the dark cloud Taurus L1495A-B10: the role of the magnetic field in the earliest stages of low-mass star formation

We present BISTRO Survey 850 μm dust emission polarisation observations of the L1495A-B10 region of the Taurus molecular cloud, taken at the JCMT. We observe a roughly triangular network of dense filaments. We detect 9 of the dense starless cores embedded within these filaments in polarisation, finding that the plane-of-sky orientation of the core-scale magnetic field lies roughly perpendicular to the filaments in almost all cases. We also find that the large-scale magnetic field orientation measured by Planck is not correlated with any of the core or filament structures, except in the case of the lowest-density core. We propose a scenario for early prestellar evolution that is both an extension to, and consistent with, previous models, introducing an additional evolutionary transitional stage between field-dominated and matter-dominated evolution, observed here for the first time. In this scenario, the cloud collapses first to a sheet-like structure. Uniquely, we appear to be seeing this sheet almost face-on. The sheet fragments into filaments, which in turn form cores. However, the material must reach a certain critical density before the evolution changes from being field-dominated to being matter-dominated. We measure the sheet surface density and the magnetic field strength at that transition for the first time and show consistency with an analytical prediction that had previously gone untested for over 50 years (Mestel 1965).

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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

B-fields in Star-Forming Region Observations (BISTRO): Magnetic Fields in the Filamentary Structures of Serpens Main

We present 850 $μ$m polarimetric observations toward the Serpens Main molecular cloud obtained using the POL-2 polarimeter on the James Clerk Maxwell Telescope (JCMT) as part of the B-fields In STar-forming Region Observations (BISTRO) survey. These observations probe the magnetic field morphology of the Serpens Main molecular cloud on about 6000 au scales, which consists of cores and six filaments with different physical properties such as density and star formation activity. Using the histogram of relative orientation (HRO) technique, we find that magnetic fields are parallel to filaments in less dense filamentary structures where $N_{H_2} < 0.93\times 10^{22}$ cm$^{-2}$ (magnetic fields perpendicular to density gradients), while being perpendicular to filaments (magnetic fields parallel to density gradients) in dense filamentary structures with star formation activity. Moreover, applying the HRO technique to denser core regions, we find that magnetic field orientations change to become perpendicular to density gradients again at $N_{H_2} \approx 4.6 \times 10^{22}$ cm$^{-2}$. This can be interpreted as a signature of core formation. At $N_{H_2} \approx 16 \times 10^{22}$ cm$^{-2}$ magnetic fields change back to being parallel to density gradients once again, which can be understood to be due to magnetic fields being dragged in by infalling material. In addition, we estimate the magnetic field strengths of the filaments ($B_{POS} = 60-300~μ$G)) using the Davis-Chandrasekhar-Fermi method and discuss whether the filaments are gravitationally unstable based on magnetic field and turbulence energy densities.

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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

Two-component Magnetic Field along the Line of Sight to the Perseus Molecular Cloud: Contribution of the Foreground Taurus Molecular Cloud

Optical stellar polarimetry in the Perseus molecular cloud direction is known to show a fully mixed bi-modal distribution of position angles across the cloud (Goodman et al. 1990). We study the Gaia trigonometric distances to each of these stars and reveal that the two components in position angles trace two different dust clouds along the line of sight. One component, which shows a polarization angle of -37.6 deg +/- 35.2 deg and a higher polarization fraction of 2.0 +/- 1.7%, primarily traces the Perseus molecular cloud at a distance of 300 pc. The other component, which shows a polarization angle of +66.8 deg +/- 19.1 deg and a lower polarization fraction of 0.8 +/- 0.6%, traces a foreground cloud at a distance of 150 pc. The foreground cloud is faint, with a maximum visual extinction of < 1 mag. We identify that foreground cloud as the outer edge of the Taurus molecular cloud. Between the Perseus and Taurus molecular clouds, we identify a lower-density ellipsoidal dust cavity with a size of 100 -- 160 pc. This dust cavity locates at l = 170 deg, b = -20 deg, and d = 240 pc, which corresponds to an HI shell generally associated with the Per OB2 association. The two-component polarization signature observed toward the Perseus molecular cloud can therefore be explained by a combination of the plane-of-sky orientations of the magnetic field both at the front and at the back of this dust cavity.

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arXiv2021

The JCMT BISTRO Survey: The Distribution of Magnetic Field Strengths towards the OMC-1 Region

Measurement of magnetic field strengths in a molecular cloud is essential for determining the criticality of magnetic support against gravitational collapse. In this paper, as part of the JCMT BISTRO survey, we suggest a new application of the Davis-Chandrasekhar-Fermi (DCF) method to estimate the distribution of magnetic field strengths in the OMC-1 region. We use observations of dust polarization emission at 450 $μ$m and 850 $μ$m, and C$^{18}$O (3-2) spectral line data obtained with the JCMT. We estimate the volume density, the velocity dispersion and the polarization angle dispersion in a box, 40$''$ $\times$ 40$''$ (5$\times$5 pixels), which moves over the OMC-1 region. By substituting three quantities in each box to the DCF method, we get magnetic field strengths over the OMC-1 region. We note that there are very large uncertainties in inferred field strengths, as discussed in detail in this paper. The field strengths vary from 0.8 to 26.4 mG and their mean value is about 6 mG. Additionally, we obtain maps of the mass-to-flux ratio in units of a critical value and the Alfv$\acute{e}$n mach number. The central parts of the BN-KL and South (S) clumps in the OMC-1 region are magnetically supercritical, so the magnetic field cannot support the clumps against gravitational collapse. However, the outer parts of the region are magnetically subcritical. The mean Alfv$\acute{e}$n mach number is about 0.4 over the region, which implies that the magnetic pressure exceeds the turbulent pressure in the OMC 1 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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arXiv2019

JCMT BISTRO Survey observations of the Ophiuchus Molecular Cloud: Dust grain alignment properties inferred using a Ricean noise model

The dependence of polarization fraction $p$ on total intensity $I$ in polarized submillimeter emission measurements is typically parameterized as $p\propto I^{-α}$ $(α\leq 1)$, and used to infer dust grain alignment efficiency in star-forming regions, with an index $α=1$ indicating near-total lack of alignment of grains with the magnetic field. In this work we demonstrate that the non-Gaussian noise characteristics of polarization fraction may produce apparent measurements of $α\sim 1$ even in data with significant signal-to-noise in Stokes $Q$, $U$ and $I$ emission, and so with robust measurements of polarization angle. We present a simple model demonstrating this behavior, and propose a criterion by which well-characterized measurements of polarization fraction may be identified. We demonstrate that where our model is applicable, $α$ can be recovered by fitting the $p-I$ relationship with the mean of the Rice distribution, without statistical debiasing of polarization fraction. We apply our model to JCMT BISTRO Survey POL-2 850$μ$m observations of three clumps in the Ophiuchus Molecular Cloud, finding that in the externally-illuminated Oph A region, $α\approx 0.34$, while in the more isolated Oph B and C, despite their differing star formation histories, $α\sim 0.6-0.7$. Our results thus suggest that dust grain alignment in dense gas is more strongly influenced by incident interstellar radiation field than by star formation history. We further find that grains may remain aligned with the magnetic field at significantly higher gas densities than has previously been believed, thus allowing investigation of magnetic field properties within star-forming clumps and cores.

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arXiv2019

The JCMT BISTRO Survey: The Magnetic Field of the Barnard 1 Star-Forming Region

We present the POL-2 850 $μ$m linear polarization map of the Barnard 1 clump in the Perseus molecular cloud complex from the B-fields In STar-forming Region Observations (BISTRO) survey at the James Clerk Maxwell Telescope. We find a trend of decreasing polarization fraction as a function of total intensity, which we link to depolarization effects towards higher density regions of the cloud. We then use the polarization data at 850 $μ$m to infer the plane-of-sky orientation of the large-scale magnetic field in Barnard 1. This magnetic field runs North-South across most of the cloud, with the exception of B1-c where it turns more East-West. From the dispersion of polarization angles, we calculate a turbulence correlation length of $5.0 \pm 2.5$ arcsec ($1500$ au), and a turbulent-to-total magnetic energy ratio of $0.5 \pm 0.3$ inside the cloud. We combine this turbulent-to-total magnetic energy ratio with observations of NH$_3$ molecular lines from the Green Bank Ammonia Survey (GAS) to estimate the strength of the plane-of-sky component of the magnetic field through the Davis-Chandrasekhar-Fermi method. With a plane-of-sky amplitude of $120 \pm 60$ $μ$G and a criticality criterion $λ_c = 3.0 \pm 1.5$, we find that Barnard 1 is a supercritical molecular cloud with a magnetic field nearly dominated by its turbulent component.

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arXiv2019

JCMT BISTRO survey: Magnetic Fields within the Hub-Filament Structure in IC 5146

We present the 850 $μ$m polarization observations toward the IC5146 filamentary cloud taken using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) and its associated polarimeter (POL-2), mounted on the James Clerk Maxwell Telescope (JCMT), as part of the B-fields In STar forming Regions Observations (BISTRO). This work is aimed at revealing the magnetic field morphology within a core-scale ($\lesssim 1.0$ pc) hub-filament structure (HFS) located at the end of a parsec-scale filament. To investigate whether or not the observed polarization traces the magnetic field in the HFS, we analyze the dependence between the observed polarization fraction and total intensity using a Bayesian approach with the polarization fraction described by the Rice likelihood function, which can correctly describe the probability density function (PDF) of the observed polarization fraction for low signal-to-noise ratio (SNR) data. We find a power-law dependence between the polarization fraction and total intensity with an index of 0.56 in $A_V\sim$ 20--300 mag regions, suggesting that the dust grains in these dense regions can still be aligned with magnetic fields in the IC5146 regions. Our polarization maps reveal a curved magnetic field, possibly dragged by the contraction along the parsec-scale filament. We further obtain a magnetic field strength of 0.5$\pm$0.2 mG toward the central hub using the Davis-Chandrasekhar-Fermi method, corresponding to a mass-to-flux criticality of $\sim$ $1.3\pm0.4$ and an Alfvénic Mach number of $<$0.6. These results suggest that gravity and magnetic field is currently of comparable importance in the HFS, and turbulence is less important.

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arXiv2019

The JCMT BISTRO Survey: The Magnetic Field In The Starless Core $ρ$ Ophiuchus C

We report 850~$μ$m dust polarization observations of a low-mass ($\sim$12 $M_{\odot}$) starless core in the $ρ$ Ophiuchus cloud, Ophiuchus C, made with the POL-2 instrument on the James Clerk Maxwell Telescope (JCMT) as part of the JCMT B-fields In STar-forming Region Observations (BISTRO) survey. We detect an ordered magnetic field projected on the plane of sky in the starless core. The magnetic field across the $\sim$0.1~pc core shows a predominant northeast-southwest orientation centering between $\sim$40$^\circ$ to $\sim$100$^\circ$, indicating that the field in the core is well aligned with the magnetic field in lower-density regions of the cloud probed by near-infrared observations and also the cloud-scale magnetic field traced by Planck observations. The polarization percentage ($P$) decreases with an increasing total intensity ($I$) with a power-law index of $-$1.03 $\pm$ 0.05. We estimate the plane-of-sky field strength ($B_{\mathrm{pos}}$) using modified Davis-Chandrasekhar-Fermi (DCF) methods based on structure function (SF), auto-correlation (ACF), and unsharp masking (UM) analyses. We find that the estimates from the SF, ACF, and UM methods yield strengths of 103 $\pm$ 46 $μ$G, 136 $\pm$ 69 $μ$G, and 213 $\pm$ 115 $μ$G, respectively. Our calculations suggest that the Ophiuchus C core is near magnetically critical or slightly magnetically supercritical (i.e. unstable to collapse). The total magnetic energy calculated from the SF method is comparable to the turbulent energy in Ophiuchus C, while the ACF method and the UM method only set upper limits for the total magnetic energy because of large uncertainties.

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arXiv2018

Magnetic fields towards Ophiuchus-B derived from SCUBA-2 polarization measurements

We present the results of dust emission polarization measurements of Ophiuchus-B (Oph-B) carried out using the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) camera with its associated polarimeter (POL-2) on the James Clerk Maxwell Telescope (JCMT) in Hawaii. This work is part of the B-fields In Star-forming Region Observations (BISTRO) survey initiated to understand the role of magnetic fields in star formation for nearby star-forming molecular clouds. We present a first look at the geometry and strength of magnetic fields in Oph-B. The field geometry is traced over $\sim$0.2 pc, with clear detection of both of the sub-clumps of Oph-B. The field pattern appears significantly disordered in sub-clump Oph-B1. The field geometry in Oph-B2 is more ordered, with a tendency to be along the major axis of the clump, parallel to the filamentary structure within which it lies. The degree of polarization decreases systematically towards the dense core material in the two sub-clumps. The field lines in the lower density material along the periphery are smoothly joined to the large scale magnetic fields probed by NIR polarization observations. We estimated a magnetic field strength of 630$\pm$410 $μ$G in the Oph-B2 sub-clump using a Davis-Chandeasekhar-Fermi analysis. With this magnetic field strength, we find a mass-to-flux ratio $λ$= 1.6$\pm$1.1, which suggests that the Oph-B2 clump is slightly magnetically supercritical.

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arXiv2018

A First Look at BISTRO Observations of The $ρ$ Oph-A core

We present 850 $μ$m imaging polarimetry data of the $ρ$ Oph-A core taken with the Submillimeter Common-User Bolometer Array-2 (SCUBA-2) and its polarimeter (POL-2), as part of our ongoing survey project, BISTRO (B-fields In STar forming RegiOns). The polarization vectors are used to identify the orientation of the magnetic field projected on the plane of the sky at a resolution of 0.01 pc. We identify 10 subregions with distinct polarization fractions and angles in the 0.2 pc $ρ$ Oph A core; some of them can be part of a coherent magnetic field structure in the $ρ$ Oph region. The results are consistent with previous observations of the brightest regions of $ρ$ Oph-A, where the degrees of polarization are at a level of a few percents, but our data reveal for the first time the magnetic field structures in the fainter regions surrounding the core where the degree of polarization is much higher ($> 5 \%$). A comparison with previous near-infrared polarimetric data shows that there are several magnetic field components which are consistent at near-infrared and submillimeter wavelengths. Using the Davis-Chandrasekhar-Fermi method, we also derive magnetic field strengths in several sub-core regions, which range from approximately 0.2 to 5 mG. We also find a correlation between the magnetic field orientations projected on the sky with the core centroid velocity components.

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arXiv2017

First results from BISTRO -- a SCUBA-2 polarimeter survey of the Gould Belt

We present the first results from the B-fields In STar-forming Region Observations (BISTRO) survey, using the Sub-millimetre Common-User Bolometer Array 2 (SCUBA-2) camera, with its associated polarimeter (POL-2), on the James Clerk Maxwell Telescope (JCMT) in Hawaii. We discuss the survey's aims and objectives. We describe the rationale behind the survey, and the questions which the survey will aim to answer. The most important of these is the role of magnetic fields in the star formation process on the scale of individual filaments and cores in dense regions. We describe the data acquisition and reduction processes for POL-2, demonstrating both repeatability and consistency with previous data. We present a first-look analysis of the first results from the BISTRO survey in the OMC 1 region. We see that the magnetic field lies approximately perpendicular to the famous 'integral filament' in the densest regions of that filament. Furthermore, we see an 'hour-glass' magnetic field morphology extending beyond the densest region of the integral filament into the less-dense surrounding material, and discuss possible causes for this. We also discuss the more complex morphology seen along the Orion Bar region. We examine the morphology of the field along the lower-density north-eastern filament. We find consistency with previous theoretical models that predict magnetic fields lying parallel to low-density, non-self-gravitating filaments, and perpendicular to higher-density, self-gravitating filaments.

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arXiv2011

Correlation between Interstellar Polarization and Dust Temperature: Alignment of Grains by Radiative Torques is Ubiquitous?

We investigate the efficiency of interstellar polarization $p_λ/A_λ$ where $p_λ$ is the fractional linear polarization and $A_λ$ is extinction, in 16 lines of sight as a function of wavelength $λ$. We have used the data obtained with the low-dispersion spectropolarimeter HBS as well as those in literature. It is found that the polarization efficiency $p_λ/A_λ$ is proportional to $\exp(-β/λ)$ in wavelength $λ\approx 0.4-0.8 \micron$, where $β$ is a parameter which varies from 0.5 to 1.2 $\micron$. We find that $β$ is negatively correlated with the dust temperature deduced from infrared data by Schlegel et al., suggesting that the polarization efficiency is higher in short wavelength for higher temperature. According to the alignment theory by radiative torques (RATs), if the radiation is stronger and bluer, RATs will make small grains align better, and the polarization efficiency will increase in short wavelength. Our finding of the correlation between $β$ and the temperature is consistent with what is expected with the alignment mechanism by RATs.

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