arXiv subjects

Jennifer Hatchell

Publications and source records attributed to Jennifer Hatchell.

At least 19 recordsLinked to original sources

arXiv2024

Submillimeter and Mid-Infrared Variability of Young Stellar Objects in the M17SWex Intermediate-Mass Star-Forming Region

We present a comprehensive analysis of young stellar object (YSO) variability within the M17 Southwest Extension (M17 SWex), using 3.5 years of monitoring data from the JCMT Transient Survey at sub-millimeter (sub-mm) and 9 years from the NEOWISE mission at mid-infrared (mid-IR). Our study encompasses observations of 147 bright sub-mm peaks identified within our deep JCMT co-added map as well as 156 YSOs in NEOWISE W1 and 179 in W2 that were previously identified in Spitzer surveys. We find three robust sub-mm variables: two are candidate YSOs and one is a likely extragalactic source. At mid-IR wavelengths, our analysis reveals secular and stochastic variability in 47 YSOs, with the highest fraction of secular variability occurring at the earliest evolutionary stage. This is similar to what has previously been observed for low-mass YSO variability within the Gould Belt. However, we observe less overall variability in M17SWex at both the sub-mm and mid-IR. We suspect that this lower fraction is due to the greater distance to M17 SWex. Our findings showcase the utility of multi-wavelength observations to better capture the complex variability phenomena inherent to star formation processes and demonstrate the importance of years-long monitoring of a diverse selection of star-forming environments.

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arXiv2024

The JCMT Transient Survey: Six-Year Summary of 450/850\,$\mu$m Protostellar Variability and Calibration Pipeline Version 2.0

The JCMT Transient Survey has been monitoring eight Gould Belt low-mass star-forming regions since December 2015 and six somewhat more distant intermediate-mass star-forming regions since February 2020 with SCUBA-2 on the JCMT at \ShortS and \LongS and with an approximately monthly cadence. We introduce our Pipeline v2 relative calibration procedures for image alignment and flux calibration across epochs, improving on our previous Pipeline v1 by decreasing measurement uncertainties and providing additional robustness. These new techniques work at both \LongS and \ShortNS, where v1 only allowed investigation of the \LongS data. Pipeline v2 achieves better than $0.5^{\prime\prime}$ relative image alignment, less than a tenth of the submillimeter beam widths. The v2 relative flux calibration is found to be 1\% at \LongS and $<5$\% at \ShortNS. The improvement in the calibration is demonstrated by comparing the two pipelines over the first four years of the survey and recovering additional robust variables with v2. Using the full six years of the Gould Belt survey the number of robust variables increases by 50\,\%, and at \ShortS we identify four robust variables, all of which are also robust at \LongNS. The multi-wavelength light curves for these sources are investigated and found to be consistent with the variability being due to dust heating within the envelope in response to accretion luminosity changes from the central source.

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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

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

We present 850 $\mu$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 ($B_{POS} = 60-300~\mu$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

Spatial Statistics in Star Forming Regions: Is Star Formation Driven By Column Density Alone?

Star formation is known to occur more readily where more raw materials are available. This is often expressed by a 'Kennicutt-Schmidt' relation where the surface density of Young Stellar Objects (YSOs) is proportional to column density to some power, $\mu$. The aim of this work was to determine if column density alone is sufficient to explain the locations of Class 0/I YSOs within Serpens South, Serpens Core, Ophiuchus, NGC1333 and IC348, or if there is clumping or avoidance that would point to additional influences on the star formation. Using the O-ring test as a summary statistic, 95 per cent confidence envelopes were produced for different values of $\mu$ from probability models made using the Herschel column density maps. The YSOs were tested against four distribution models: the best-estimate of $\mu$ for the region, $\mu=0$ above a minimum column density threshold and zero probability elsewhere, $\mu=1$, and the power-law that best represents the five regions as a collective, $\mu=2.05 \pm 0.20$. Results showed that $\mu=2.05$ model was consistent with the majority of regions and, for those regions, the spatial distribution of YSOs at a given column density is consistent with being random. Serpens South and NGC1333 rejected the $\mu = 2.05$ model on small scales of $\sim 0.15 \mathrm{pc}$ which implies that small-scale interactions may be necessary to improve the model. On scales above 0.15 pc, the positions of YSOs in all five regions can be well described using column density alone.

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arXiv2021

The JCMT Transient Survey: Four Year Summary of Monitoring the Submillimeter Variability of Protostars

We present the four-year survey results of monthly submillimeter monitoring of eight nearby ($< 500 $pc) star-forming regions by the JCMT Transient Survey. We apply the Lomb-Scargle Periodogram technique to search for and characterize variability on 295 submillimeter peaks brighter than 0.14 Jy beam$^{-1}$, including 22 disk sources (Class II), 83 protostars (Class 0/I), and 190 starless sources. We uncover 18 secular variables, all of them protostars. No single-epoch burst or drop events and no inherently stochastic sources are observed. We classify the secular variables by their timescales into three groups: Periodic, Curved, and Linear. For the Curved and Periodic cases, the detectable fractional amplitude, with respect to mean peak brightness, is $\sim4$ % for sources brighter than $\sim$ 0.5 Jy beam$^{-1}$. Limiting our sample to only these bright sources, the observed variable fraction is 37 % (16 out of 43). Considering source evolution, we find a similar fraction of bright variables for both Class 0 and Class I. Using an empirically motivated conversion from submillimeter variability to variation in mass accretion rate, six sources (7 % of our full sample) are predicted to have years-long accretion events during which the excess mass accreted reaches more than 40 % above the total quiescently accreted mass: two previously known eruptive Class I sources, V1647 Ori and EC 53 (V371 Ser), and four Class 0 sources, HOPS 356, HOPS 373, HOPS 383, and West 40. Considering the full protostellar ensemble, the importance of episodic accretion on few years timescale is negligible, only a few percent of the assembled mass. However, given that this accretion is dominated by events of order the observing time-window, it remains uncertain as to whether the importance of episodic events will continue to rise with decades-long monitoring.

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arXiv2021

The JCMT Gould Belt Survey: radiative heating by OB stars

Radiative feedback can influence subsequent star formation. We quantify the heating from OB stars in the local star-forming regions in the JCMT Gould Belt survey. Dust temperatures are calculated from 450/850 micron flux ratios from SCUBA-2 observations at the JCMT assuming a fixed dust opacity spectral index $\beta=1.8$. Mean dust temperatures are calculated for each submillimetre clump along with projected distances from the main OB star in the region. Temperature vs. distance is fit with a simple model of dust heating by the OB star radiation plus the interstellar radiation field and dust cooling through optically thin radiation. Classifying the heating sources by spectral type, O-type stars produce the greatest clump average temperature rises and largest heating extent, with temperatures over 40 K and significant heating out to at least 2.4 pc. Early-type B stars (B4 and above) produce temperatures of over 20 K and significant heating over 0.4 pc. Late-type B stars show a marginal heating effect within 0.2 pc. For a given projected distance, there is a significant scatter in clump temperatures that is due to local heating by other luminous stars in the region, projection effects, or shadowing effects. Even in these local, `low-mass' star-forming regions, radiative feedback is having an effect on parsec scales, with 24% of the clumps heated to at least 3 K above the 15 K base temperature expected from heating by only the interstellar radiation field, and a mean dust temperature for heated clumps of 24 K.

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arXiv2021

Revealing the diverse magnetic field morphologies in Taurus dense cores with sensitive sub-millimeter polarimetry

We have obtained sensitive dust continuum polarization observations at 850 $\mu$m in the B213 region of Taurus using POL-2 on SCUBA-2 at the James Clerk Maxwell Telescope (JCMT), as part of the BISTRO (B-fields in STar-forming Region Observations) survey. These observations allow us to probe magnetic field (B-field) at high spatial resolution ($\sim$2000 au or $\sim$0.01 pc at 140 pc) in two protostellar cores (K04166 and K04169) and one prestellar core (Miz-8b) that lie within the B213 filament. Using the Davis-Chandrasekhar-Fermi method, we estimate the B-field strengths in K04166, K04169, and Miz-8b to be 38$\pm$14 $\mu$G, 44$\pm$16 $\mu$G, and 12$\pm$5 $\mu$G, respectively. These cores show distinct mean B-field orientations. B-field in K04166 is well ordered and aligned parallel to the orientations of the core minor axis, outflows, core rotation axis, and large-scale uniform B-field, in accordance with magnetically regulated star formation via ambipolar diffusion taking place in K04166. B-field in K04169 is found to be ordered but oriented nearly perpendicular to the core minor axis and large-scale B-field, and not well-correlated with other axes. In contrast, Miz-8b exhibits disordered B-field which show no preferred alignment with the core minor axis or large-scale field. We found that only one core, K04166, retains a memory of the large-scale uniform B-field. The other two cores, K04169 and Miz-8b, are decoupled from the large-scale field. Such a complex B-field configuration could be caused by gas inflow onto the filament, even in the presence of a substantial magnetic flux.

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arXiv2020

Observations of magnetic fields surrounding LkH$\alpha$ 101 taken by the BISTRO survey with JCMT-POL-2

We report the first high spatial resolution measurement of magnetic fields surrounding LkH$\alpha$ 101, a part of the Auriga-California molecular cloud. The observations were taken with the POL-2 polarimeter on the James Clerk Maxwell Telescope within the framework of the B-fields In Star-forming Region Observations (BISTRO) survey. Observed polarization of thermal dust emission at 850 $\mu$m is found to be mostly associated with the red-shifted gas component of the cloud. The magnetic field displays a relatively complex morphology. Two variants of the Davis-Chandrasekhar-Fermi method, unsharp masking and structure function, are used to calculate the strength of magnetic fields in the plane of the sky, yielding a similar result of $B_{\rm POS}\sim 115$ $\mathrm{\mu}$G. The mass-to-magnetic-flux ratio in critical value units, $\lambda\sim0.3$, is the smallest among the values obtained for other regions surveyed by POL-2. This implies that the LkH$\alpha$ 101 region is sub-critical and the magnetic field is strong enough to prevent gravitational collapse. The inferred $\delta B/B_0\sim 0.3$ implies that the large scale component of the magnetic field dominates the turbulent one. The variation of the polarization fraction with total emission intensity can be fitted by a power-law with an index of $\alpha=0.82\pm0.03$, which lies in the range previously reported for molecular clouds. We find that the polarization fraction decreases rapidly with proximity to the only early B star (LkH$\alpha$ 101) in the region. The magnetic field tangling and the joint effect of grain alignment and rotational disruption by radiative torques are potential of explaining such a decreasing trend.

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arXiv2020

The JCMT BISTRO survey: alignment between outflows and magnetic fields in dense cores/clumps

We compare the directions of molecular outflows of 62 low-mass Class 0 and I protostars in nearby (<450 pc) star-forming regions with the mean orientations of the magnetic fields on 0.05-0.5 pc scales in the dense cores/clumps where they are embedded. The magnetic field orientations were measured using the JCMT POL-2 data taken by the BISTRO-1 survey and from the archive. The outflow directions were observed with interferometers in the literature. The observed distribution of the angles between the outflows and the magnetic fields peaks between 15 and 35 degrees. After considering projection effects, our results could suggest that the outflows tend to be misaligned with the magnetic fields by 50+/-15 degrees in three-dimensional space and are less likely (but not ruled out) randomly oriented with respect to the magnetic fields. There is no correlation between the misalignment and the bolometric temperatures in our sample. In several sources, the small-scale (1000-3000 au) magnetic fields is more misaligned with the outflows than their large-scale magnetic fields, suggesting that the small-scale magnetic field has been twisted by the dynamics. In comparison with turbulent MHD simulations of core formation, our observational results are more consistent with models in which the energy densities in the magnetic field and the turbulence of the gas are comparable. Our results also suggest that the misalignment alone cannot sufficiently reduce the efficiency of magnetic braking to enable formation of the observed number of large Keplerian disks with sizes larger than 30-50 au.

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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

Probing the initial conditions of high-mass star formation. III. Fragmentation and triggered star formation

Massive clumps tend to fragment into clusters of cores and condensations, some of which form high-mass stars. In this work, we study the structure of massive clumps at different scales, analyze the fragmentation process, and investigate the possibility that star formation is triggered by nearby HII regions. We present a high angular resolution study of a sample of 8 massive proto-cluster clumps. Combining infrared data, we use few-arcsecond resolution radio- and millimeter interferometric data to study their fragmentation and evolution. Our sample is unique in the sense that all the clumps have neighboring HII regions. Taking advantage of that, we test triggered star formation using a novel method where we study the alignment of the centres of mass traced by dust emission at multiple scales. The eight massive clumps have masses ranging from 228 to 2279 $M_\odot$. The brightest compact structures within infrared bright clumps are typically associated with embedded compact radio continuum sources. The smaller scale structures of $R_{\rm eff}$ $\sim$ 0.02 pc observed within each clump are mostly gravitationally bound and massive enough to form at least a B3-B0 type star. Many condensations have masses larger than 8 $M_\odot$ at small scale of $R_{\rm eff}$ $\sim$ 0.02 pc. Although the clumps are mostly infrared quiet, the dynamical movements are active at clump scale ($\sim$ 1 pc). We studied the spatial distribution of the gas conditions detected at different scales. For some sources we find hints of external triggering, whereas for others we find no significant pattern that indicates triggering is dynamically unimportant. This probably indicates that the different clumps go through different evolutionary paths. In this respect, studies with larger samples are highly desired.

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arXiv2019

Spatial Statistics in Star Forming Regions: Testing the Limits of Randomness

Observational studies of star formation reveal spatial distributions of Young Stellar Objects (YSOs) that are `snapshots' of an ongoing star formation process. Using methods from spatial statistics it is possible to test the likelihood that a given distribution process could produce the observed patterns of YSOs. The aim of this paper is to determine the usefulness of the spatial statistics tests Diggle's G function (G), the `free-space' function (F), Ripley's K and O-ring for application to astrophysical data. The spatial statistics tests were applied to simulated data containing 2D Gaussian clusters projected on random distributions of stars. The number of stars within the Gaussian cluster and number of background stars were varied to determine the tests' ability to reject complete spatial randomness (CSR) with changing signal-to-noise. The best performing test was O-ring optimised with overlapping logarithmic bins, closely followed by Ripley's K. The O-ring test is equivalent to the 2-point correlation function. Both F and G (and the minimum spanning tree, of which G is a subset) performed significantly less well, requiring a cluster with a factor of two higher signal-to-noise in order to reject CSR consistently. We demonstrate the tests on example astrophysical datasets drawn from the Spitzer catalogue.

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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 $\mu$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 $\mu$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 $120 \pm 60$ $\mu$G and a criticality criterion $\lambda_c = 3.0 \pm 1.5$, 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

An initial overview of the extent and structure of recent star formation within the Serpens Molecular Cloud using Gaia Data Release 2

The dense clusters within the Serpens Molecular Cloud are among the most active regions of nearby star formation. In this paper, we use Gaia DR2 parallaxes and proper motions to statistically measure 1167 kinematic members of Serpens, few of which were previously identified, to evaluate the star formation history of the complex. The optical members of Serpens are concentrated in three distinct groups located at 380 to 480 pc; the densest clusters are still highly obscured by optically-thick dust and have few optical members. The total population of young stars and protostars in Serpens is at least 2000 stars, including past surveys that were most sensitive to protostars and disks, and may be far higher. Distances to dark clouds measured from deficits in star counts are consistent with the distances to the optical star clusters. The Serpens Molecular Cloud is seen in the foreground of the Aquila Rift, dark clouds located at 600 to 700 pc, and behind patchy extinction, here called the Serpens Cirrus, located at ~250 pc. Based on the lack of a distributed population of older stars, the star formation rate throughout the Serpens Molecular Cloud increased by at least a factor of 20 within the past ~5 Myr. The optically bright stars in Serpens Northeast are visible because their natal molecular cloud has been eroded and not because they were flung outwards from a central factory of star formation. The separation between subclusters of 20 to 100 pc and the absence of an older population leads to speculation that an external forcing was needed to trigger the active star formation.

astro-ph.SR↗

arXiv2019

Variability in the Assembly of Protostellar Systems

Understanding the collapse of clouds and the formation of protoplanetary disks is essential to understanding the formation of stars and planets. Infall and accretion, the mass-aggregation processes that occur at envelope and disk scales, drive the dynamical evolution of protostars. While the observations of protostars at different stages constrain their evolutionary tracks, the impact of variability due to accretion bursts on dynamical and chemical evolution of the source is largely unknown. The lasting effects on protostellar envelopes and disks are tracked through multi-wavelength and time domain observational campaigns, requiring deep X-ray, infrared, and radio imaging and spectroscopy, at a sufficient level of spatial detail to distinguish contributions from the various substructures (i.e., envelope from disk from star from outflow). Protostellar models derived from these campaigns will illuminate the initial chemical state of protoplanetary disks during the epoch of giant planet formation. Insight from individual star formation in the Milky Way is also necessary to understand star formation rates in extragalactic sources. This cannot be achieved with ground-based observatories and is not covered by currently approved instrumentation. Requirements: High (v < 10 km/s for survey; v < 1 km/s for followup) spectral resolution capabilities with relatively rapid response times in the IR (3-500 um), X-ray (0.1-10 keV), and radio (cm) are critical to follow the course of accretion and outflow during an outburst. Complementary, AU-scale radio observations are needed to probe the disk accretion zone, and 10 AU-scale to probe chemical and kinematic structures of the disk-forming regions, and track changes in the dust, ice, and gas within protostellar envelopes.

astro-ph.SR↗

arXiv2019

The warm and dense Galaxy - tracing the formation of dense cloud structures out to the Galactic Center

The past two decades have seen extensive surveys of the far-infrared to submillimeter continuum emission in the plane of our Galaxy. We line out prospects for the coming decade for corresponding molecular and atomic line surveys which are needed to fully understand the formation of the dense structures that give birth to clusters and stars out of the diffuse interstellar medium. We propose to work towards Galaxy wide surveys in mid-J CO lines to trace shocks from colliding clouds, Galaxy-wide surveys for atomic Carbon lines in order to get a detailed understanding of the relation of atomic and molecular gas in clouds, and to perform extensive surveys of the structure of the dense parts of molecular clouds to understand the importance of filaments/fibers over the full range of Galactic environments and to study how dense cloud cores are formed from the filaments. This work will require a large (50m) Single Dish submillimeter telescope equipped with massively multipixel spectrometer arrays, such as envisaged by the AtLAST project.

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arXiv2019

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

We report 850~$\mu$m dust polarization observations of a low-mass ($\sim$12 $M_{\odot}$) starless core in the $\rho$ 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 $\mu$G, 136 $\pm$ 69 $\mu$G, and 213 $\pm$ 115 $\mu$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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