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Ian W. Stephens

Publications and source records attributed to Ian W. Stephens.

At least 55 records · Page 3Linked to original sources

The Twisted Magnetic Field of the Protobinary L483

We present H-band (1.65 $μ$m) and SOFIA HAWC+ 154 $μ$m polarization observations of the low-mass core L483. Our H-band observations reveal a magnetic field that is overwhelmingly in the E-W direction, which is approximately parallel to the bipolar outflow that is observed in scattered IR light and in single-dish $^{12}$CO observations. From our 154 $μ$m data, we infer a $\sim$ 45$^{\circ}$ twist in the magnetic field within the inner 5" (1000 au) of L483. We compare these new observations with published single-dish 350 $μ$m polarimetry and find that the 10,000 au scale H-band data match the smaller scale 350 $μ$m data, indicating that the collapse of L483 is magnetically regulated on these larger scales. We also present high-resolution 1.3 mm ALMA data of L483 which reveals it is a close binary star with a separation of 34 au. The plane of the binary of L483 is observed to be approximately parallel to the twisted field in the inner 1000 au. Comparing this result to the $\sim$ 1000 au protostellar envelope, we find that the envelope is roughly perpendicular to the 1000 au HAWC+ field. Using the data presented, we speculate that L483 initially formed as a wide binary and the companion star migrated to its current position, causing an extreme shift in angular momentum thereby producing the twisted magnetic field morphology observed. More observations are needed to further test this scenario.

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The Magnetic Field in the Milky Way Filamentary Bone G47

Star formation primarily occurs in filaments where magnetic fields are expected to be dynamically important. The largest and densest filaments trace spiral structure within galaxies. Over a dozen of these dense ($\sim$10$^4$\,cm$^{-3}$) and long ($>$10\,pc) filaments have been found within the Milky Way, and they are often referred to as "bones." Until now, none of these bones have had their magnetic field resolved and mapped in their entirety. We introduce the SOFIA legacy project FIELDMAPS which has begun mapping $\sim$10 of these Milky Way bones using the HAWC+ instrument at 214\,$μ$m and 18$\farcs$2 resolution. Here we present a first result from this survey on the $\sim$60\,pc long bone G47. Contrary to some studies of dense filaments in the Galactic plane, we find that the magnetic field is often not perpendicular to the spine (i.e., the center-line of the bone). Fields tend to be perpendicular in the densest areas of active star formation and more parallel or random in other areas. The average field is neither parallel or perpendicular to the Galactic plane nor the bone. The magnetic field strengths along the spine typically vary from $\sim$20 to $\sim$100\,$μ$G. Magnetic fields tend to be strong enough to suppress collapse along much of the bone, but for areas that are most active in star formation, the fields are notably less able to resist gravitational collapse.

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Evolution and Kinematics of Protostellar Envelopes in the Perseus Molecular Cloud

We present a comprehensive analysis on the evolution of envelopes surrounding protostellar systems in the Perseus molecular cloud using data from the MASSES survey. We focus our attention to the C$^{18}$O(2--1) spectral line, and we characterize the shape, size, and orientation of 54 envelopes and measure their fluxes, velocity gradients, and line widths. To look for evolutionary trends, we compare these parameters to the bolometric temperature Tbol, a tracer of protostellar age. We find evidence that the angular difference between the elongation angle of the C$^{18}$O envelope and the outflow axis direction generally becomes increasingly perpendicular with increasing Tbol, suggesting the envelope evolution is directly affected by the outflow evolution. We show that this angular difference changes at Tbol = $53 \pm 20$ K, which includes the conventional delineation between Class 0 and I protostars of 70K. We compare the C$^{18}$O envelopes with larger gaseous structures in other molecular clouds and show that the velocity gradient increases with decreasing radius ($|\mathcal{G}| \sim R^{-0.72 \pm 0.06}$). From the velocity gradients we show that the specific angular momentum follows a power law fit $J/M \propto R^{1.83 \pm 0.05}$ for scales from 1pc down to $\sim$500 au, and we cannot rule out a possible flattening out at radii smaller than $\sim$1000 au.

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Discovery of Molecular Line Polarization in the Disk of TW Hya

We report observations of polarized line and continuum emission from the disk of TW~Hya using the Atacama Large Millimeter/submillimeter Array. We target three emission lines, $^{12}$CO (3-2), $^{13}$CO (3-2) and CS (7-6), to search for linear polarization due to the Goldreich-Kylafis effect, while simultaneously tracing the continuum polarization morphology at 332\,GHz (900\,\micron{}), achieving a spatial resolution of 0.5\arcsec{} (30~au). We detect linear polarization in the dust continuum emission; the polarization position angles show an azimuthal morphology, and the median polarization fraction is $\sim$\,0.2\%, comparable to previous, lower frequency observations. Adopting a `shift-and-stack' technique to boost the sensitivity of the data, combined with a linear combination of the $Q$ and $U$ components to account for their azimuthal dependence, we detect weak linear polarization of $^{12}$CO and $^{13}$CO line emission at a $\sim 10σ$ and $\sim 5σ$ significance, respectively. The polarization was detected in the line wings, reaching a peak polarization fraction of $\sim 5\%$ and $\sim 3\%$ for the two molecules between disk radii of 0.5" and 1". The sign of the polarization was found to flip from the blue-shifted side of the emission to the red-shifted side, suggesting a complex, asymmetric polarization morphology. Polarization is not robustly detected for the CS emission; however, a tentative signal, comparable in morphology to that found for the $^{12}$CO and $^{13}$CO emission, is found at a $\lesssim 3σ$ significance. We are able to reconstruct a polarization morphology, consistent with the azimuthally averaged profiles, under the assumption that this is also azimuthally symmetric, which can be compared with future higher-sensitivity observations.

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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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ALMA CN Zeeman Observations of AS 209: Limits on Magnetic Field Strength and Magnetically Driven Accretion Rate

While magnetic fields likely play an important role in driving the evolution of protoplanetary disks through angular momentum transport, observational evidence of magnetic fields has only been found in a small number of disks. Although dust continuum linear polarization has been detected in an increasing number of disks, its pattern is more consistent with that from dust scattering than from magnetically aligned grains in the vast majority of cases. Continuum linear polarization from dust grains aligned to a magnetic field can reveal information about the magnetic field's direction, but not its strength. On the other hand, observations of circular polarization in molecular lines produced by Zeeman splitting offer a direct measure of the line-of-sight magnetic field strength in disks. We present upper limits on the net toroidal and vertical magnetic field strengths in the protoplanetary disk AS 209 derived from Zeeman splitting observations of the CN 2-1 line. The 3$σ$ upper limit on the net line-of-sight magnetic field strength in AS 209 is 5.0 mG on the redshifted side of the disk and 4.2 mG on the blueshifted side of the disk. Given the disk's inclination angle, we set a 3$σ$ upper limit on the net toroidal magnetic field strength of 8.7 and 7.3 mG for the red and blue sides of the disk, respectively, and 6.2 and 5.2 mG on the net vertical magnetic field on the red and blue sides of the disk. If magnetic disk winds are a significant mechanism of angular momentum transport in the disk, magnetic fields of a strength close to the upper limits would be sufficient to drive accretion at the rate previously inferred for regions near the protostar.

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Dust Polarization in Four Protoplanetary Disks at 3 mm: Further Evidence of Multiple Origins

We present polarimetric observations of four Class II protoplanetary disks (DG Tau, Haro 6-13, RY Tau, and MWC 480) taken with the Atacama Large Millimeter/submillimeter Array (ALMA) at 3 mm. The polarization morphologies observed fall into two distinct categories: azimuthal polarization (DG Tau and Haro 6-13) and polarization parallel to the disk minor axis (RY Tau and MWC 480). The mechanisms responsible for disk polarization at millimeter and submillimeter wavelengths are currently under debate. In this Letter, we investigate two mechanisms capable of producing polarized dust emission in disks: self-scattering and grain alignment to the radiation anisotropy. The polarization morphologies of DG Tau and Haro 6-13 are broadly consistent with that expected from radiation alignment (though radiative alignment still does not account for all of the features seen in these disks), while RY Tau and MWC 480 are more consistent with self-scattering. Such a variation in the polarized morphology may provide evidence of dust grain size differences between the sources.

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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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Four annular structures in a protostellar disk less than 500,000 years old

Annular structures, or rings and gaps, in disks around pre-main sequence stars have been detected in abundance towards Class II objects ~1,000,000 years in age. These structures are often interpreted as evidence of planet formation, with planet-mass bodies carving rings and gaps in the disk. This implies that planet formation may already be underway in even younger disks in the Class I phase, when the protostar is still embedded in a larger scale dense envelope of gas and dust. While younger disks likely play an important role in the onset of planet formation, only within the past decade have detailed properties of disks in the youngest star-forming phases begun to be observed. Here we present 1.3 mm dust emission observations with 5 au resolution that show four annular substructures in the disk of the young (<500,000 years) protostar IRS 63. IRS 63, a single Class I source located in the nearby Ophiuchus molecular cloud (at a distance of 144 pc), is one of the brightest Class I protostars at (sub)millimeter wavelengths that also has a relatively large disk (>50 au). Multiple annular substructures observed towards disks at young times can act as an early foothold for dust grain growth, a prerequisite of planet formation. Whether planets already exist or not in the disk of IRS 63, it is clear that the planet formation process begins in the young protostellar phases, earlier than predicted by current planet formation theories.

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Characterizing [C II] Line Emission In Massive Star Forming Clumps

Because the 157.74 micron [C II] line is the dominant coolant of star-forming regions, it is often used to infer the global star-formation rates of galaxies. By characterizing the [C II] and far-infrared emission from nearby Galactic star-forming molecular clumps, it is possible to determine whether extragalactic [C II] emission arises from a large ensemble of such clumps, and whether [C II] is indeed a robust indicator of global star formation. We describe [C II] and far-infrared observations using the FIFI-LS instrument on the SOFIA airborne observatory toward four dense, high-mass, Milky Way clumps. Despite similar far-infrared luminosities, the [C II] to far-infrared luminosity ratio, L([C II])/L(FIR) varies by a factor of at least 140 among these four clumps. In particular, for AGAL313.576+0.324, no [C II] line emission is detected despite a FIR luminosity of 24,000 L_sun. AGAL313.576+0.324 lies a factor of more than 100 below the empirical correlation curve between L([C II])/L(FIR) and S_ν(63 micron)/S_ν(158 micron) found for galaxies. AGAL313.576+0.324 may be in an early evolutionary "protostellar" phase with insufficient ultraviolet flux to ionize carbon, or in a deeply embedded ``hypercompact' H II region phase where dust attenuation of UV flux limits the region of ionized carbon to undetectably small volumes. Alternatively, its apparent lack of \cii\, emission may arise from deep absorption of the \cii\, line against the 158 micron continuum, or self-absorption of brighter line emission by foreground material, which might cancel or diminish any emission within the FIFI-LS instrument's broad spectral resolution element (~250 km/s)

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HAWC+ Far-Infrared Observations of the Magnetic Field Geometry in M51 and NGC 891

SOFIA HAWC+ polarimetry at $154~\micron$ is reported for the face-on galaxy M51 and the edge-on galaxy NGC 891. For M51, the polarization vectors generally follow the spiral pattern defined by the molecular gas distribution, the far-infrared (FIR) intensity contours, and other tracers of star formation. The fractional polarization is much lower in the FIR-bright central regions than in the outer regions, and we rule out loss of grain alignment and variations in magnetic field strength as causes. When compared with existing synchrotron observations, which sample different regions with different weighting, we find the net position angles are strongly correlated, the fractional polarizations are moderately correlated, but the polarized intensities are uncorrelated. We argue that the low fractional polarization in the central regions must be due to significant numbers of highly turbulent segments across the beam and along lines of sight in the beam in the central 3 kpc of M51. For NGC 891, the FIR polarization vectors within an intensity contour of 1500 $\rm{MJy~sr^{-1}}$ are oriented very close to the plane of the galaxy. The FIR polarimetry is probably sampling the magnetic field geometry in NGC 891 much deeper into the disk than is possible with NIR polarimetry and radio synchrotron measurements. In some locations in NGC 891 the FIR polarization is very low, suggesting we are preferentially viewing the magnetic field mostly along the line of sight, down the length of embedded spiral arms. There is tentative evidence for a vertical field in the polarized emission off the plane of the disk.

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Low Level Carbon Monoxide Line Polarization in two Protoplanetary Disks: HD 142527 and IM Lup

Magnetic fields are expected to play an important role in accretion processes for circumstellar disks. Measuring the magnetic field morphology is difficult, especially since polarimetric (sub)millimeter continuum observations may not trace fields in most disks. The Goldreich-Kylafis (GK) effect suggests that line polarization is perpendicular or parallel to the magnetic field direction. We attempt to observe CO(2-1), $^{13}$CO(2-1), and C$^{18}$O(2-1) line polarization toward HD 142527 and IM Lup, which are large, bright protoplanetary disks. We use spatial averaging and spectral integration to search for signals in both disks, and detect a potential CO(2-1) Stokes $Q$ signal toward both disks. The total CO(2-1) polarization fractions are 1.57 $\pm$ 0.18% and 1.01 $\pm$ 0.10% for HD 142527 and IM Lup, respectively. Our Monte Carlo simulations indicate that these signals are marginal. We also stack Stokes parameters based on the Keplerian rotation, but no signal was found. Across the disk traced by dust of HD 142527, the 3$σ$ upper limits for $P_{\text{frac}}$ at 0.5$^{\prime\prime}$ ($\sim$80 au) resolution are typically less than 3% for CO(2-1) and $^{13}$CO(2-1) and 4% for C$^{18}$O(2-1). For IM Lup, the 3$σ$ upper limits for these three lines are typically less than 3%, 4%, and 12%, respectively. Upper limits based on our stacking technique are up to a factor of $\sim$10 lower, though stacking areas can potentially average out small-scale polarization structure. We also compare our continuum polarization at 1.3 mm to observations at 870 $μ$m from previous studies. The polarization in the northern dust trap of HD 142527 shows a significant change in morphology and an increase in $P_{\text{frac}}$ as compared to 870 $μ$m. For IM Lup, the 1.3 mm polarization may be more azimuthal and has a higher $P_{\text{frac}}$ than at 870 $μ$m.

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Magnetic Field Structure in Spheroidal Star-Forming Clouds. II. Estimating Field Structure from Observed Maps

This paper presents models to estimate the structure of density and magnetic field strength in spheroidal condensations, from maps of their column density and their polarization of magnetically aligned dust grains. The density model is obtained by fitting a column density map with an embedded p = 2 Plummer spheroid of any aspect ratio and inclination. The magnetic properties are based on the density model, on the Davis-Chandrasekhar-Fermi (DCF) model of Alfvénic fluctuations, and on the Spheroid Flux Freezing (SFF) model of mass and flux conservation in Paper I. The field strength model has the resolution of the column density map, which is finer than the resolution of the DCF estimate of field strength. The models are applied to ALMA observations of the envelope of the protostar BHR71 IRS1. Column density fits give the density model, from (2.0 +- 0.4) x 10^5 cm^-3 to (7 +- 1) x 10^7 cm^-3 . The density model predicts the field directions map, which fits the polarization map best within 1100 au, with standard deviation of angle differences 17°. In this region the DCF mean field strength is 0.7 +- 0.2 mG and the envelope mass is supercritical, with ratio of mass to magnetic critical mass 1.5 +- 0.4. The SFF field strength profile scales with the DCF field strength, from 60 x 10μG to 4+-1 mG. The spatial resolution of the SFF field strength estimate is finer than the DCF resolution by a factor ~7, and the peak SFF field strength exceeds the DCF field strength by a factor ~5.

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Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES) -- Full Data Release

We present and release the full dataset for the Mass Assembly of Stellar Systems and their Evolution with the SMA (MASSES) survey. This survey used the Submillimeter Array (SMA) to image the 74 known protostars within the Perseus molecular cloud. The SMA was used in two array configurations to capture outflows for scales $>$30$^{\prime\prime}$ ($>$9000 au) and to probe scales down to $\sim$1$^{\prime\prime}$ ($\sim$300 au). The protostars were observed with the 1.3 mm and 850 $μ$m receivers simultaneously to detect continuum at both wavelengths and molecular line emission from CO(2-1), $^{13}$CO(2-1), C$^{18}$O(2-1), N$_2$D$^+$(3-2), CO(3-2), HCO$^+$(4-3), and H$^{13}$CO$^+$(4-3). Some of the observations also used the SMA's recently upgraded correlator, SWARM, whose broader bandwidth allowed for several more spectral lines to be observed (e.g., SO, H$_2$CO, DCO$^+$, DCN, CS, CN). Of the main continuum and spectral tracers observed, 84% of the images and cubes had emission detected. The median C$^{18}$O(2-1) linewidth is $\sim$1.0 km s$^{-1}$, which is slightly higher than those measured with single-dish telescopes at scales of 3000-20000 au. Of the 74 targets, six are suggested to be first hydrostatic core candidates, and we suggest that L1451-mm is the best candidate. We question a previous continuum detection toward L1448 IRS2E. In the SVS13 system, SVS13A certainly appears to be the most evolved source, while SVS13C appears to be hotter and more evolved than SVS13B. The MASSES survey is the largest publicly available interferometric continuum and spectral line protostellar survey to date, and is largely unbiased as it only targets protostars in Perseus. All visibility ($uv$) data and imaged data are publicly available at https://dataverse.harvard.edu/dataverse/full_MASSES/.

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The Interaction Between the Supernova Remnant W41 and the Filamentary Infrared Dark Cloud G23.33-0.30

G23.33-0.30 is a 600 $M_{\odot}$ infrared dark molecular filament that exhibits large NH$_3$ velocity dispersions ($σ\sim 8 \ \rm{km \ s^{-1}}$) and bright, narrow NH$_3$(3,3) line emission. We have probed G23.33-0.30 at the $<0.1$ pc scale and confirmed that the narrow NH$_3$(3,3) line is emitted by four rare NH$_3$(3,3) masers, which are excited by a large-scale shock impacting the filament. G23.33-0.30 also displays a velocity gradient along its length, a velocity discontinuity across its width, shock-tracing SiO(5-4) emission extended throughout the filament, broad turbulent line widths in NH$_3$(1,1) through (6,6), CS(5-4), and SiO(5-4), as well as an increased NH$_3$ rotational temperature ($T_{\rm{rot}}$) and velocity dispersion ($σ$) associated with the shocked, blueshifted component. The correlations among $T_{\rm{rot}}$, $σ$, and $V_{\rm{LSR}}$ implies that the shock is accelerating, heating, and adding turbulent energy to the filament gas. Given G23.33-0.30's location within the giant molecular cloud G23.0-0.4, we speculate that the shock and NH$_3$(3,3) masers originated from the supernova remnant W41, which exhibits additional evidence of an interaction with G23.0-0.4. We have also detected the 1.3 mm dust continuum emission from at least three embedded molecular cores associated with G23.33-0.30. Although the cores have moderate gas masses ($M = 7-10$ M$_{\odot}$), their large virial parameters ($α=4-9$) suggest that they will not collapse to form stars. The turbulent line widths of the cores may indicate negative feedback due to the SNR shock.

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Formation of Massive Protostellar Clusters -- Observations of Massive 70 $μ$m Dark Molecular Clouds

We present Submillimeter Array (SMA) observations of seven massive molecular clumps which are dark in the far-infrared for wavelengths up to 70 $μ$m. Our 1.3 mm continuum images reveal 44 dense cores, with gas masses ranging from 1.4 to 77.1 M$_{\odot}$. Twenty-nine dense cores have masses greater than 8 M$_{\odot}$ and the other fifteen dense cores have masses between 1.4 and 7.5 M$_{\odot}$. Assuming the core density follows a power-law in radius $ρ\propto r^{-b}$, the index $b$ is found to be between 0.6 and 2.1 with a mean value of 1.3. The virial analysis reveals that the dense cores are not in virial equilibrium. CO outflow emission was detected toward 6 out of 7 molecular clumps and associated with 17 dense cores. For five of these cores, CO emissions appear to have line-wings at velocities of greater than 30 km s$^{-1}$ with respect to the source systemic velocity, which indicates that most of the clumps harbor protostars and thus are not quiescent in star formation. The estimated outflow timescale increase with core mass, which likely indicates that massive cores have longer accretion timescale than that of the less massive ones. The fragmentation analysis shows that the mass of low-mass and massive cores are roughly consistent with thermal and turbulent Jeans masses, respectively.

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Dust Polarization Toward Embedded Protostars in Ophiuchus with ALMA. III. Survey Overview

We present 0.25 arcsec resolution (35 au) ALMA 1.3 mm dust polarization observations for 37 young stellar objects (YSOs) in the Ophiuchus cloud. These data encompass all the embedded protostars in the cloud and several Flat and Class II objects to produce the largest, homogeneous study of dust polarization on disk scales to date. The goal of this study is to study dust polarization down to disk scales. We find that 14/37 (38%) of the YSOs are detected in polarization. Nine of these sources have uniform polarization angles and four sources have azimuthal polarization. The sources with uniform polarization tend to have steeper inclinations (> 60 degree) than those with azimuthal polarization (< 60 degree). The majority (9/14) of the detected sources have polarization morphologies and disk properties consistent with dust self-scattering in optically thick disks. The remaining sources may be instead tracing magnetic fields. Their inferred field directions from rotating the polarization vectors by 90 degree are mainly poloidal or hourglass shaped. We find no evidence of a strong toroidal field component toward any of our disks. For the 23 YSOs that are undetected in polarization, roughly half of them have 3-sigma upper limits of < 2%. These sources also tend to have inclinations < 60 degree and they are generally compact. Since lower inclination sources tend to have azimuthal polarization, these YSOs may be undetected in polarization due to unresolved polarization structure within our beam. We propose that disks with inclinations > 60 degree are the best candidates for future polarization studies of dust self-scattering as these systems will generally show uniform polarization vectors that do not require very high resolution to resolve. We release the continuum and polarization images for all the sources with this publication. Data from the entire survey can be obtained from Dataverse.

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The far-infrared polarization spectrum of Rho Ophiuchi A from HAWC+/SOFIA observations

We report on polarimetric maps made with HAWC+/SOFIA toward Rho Oph A, the densest portion of the Rho Ophiuchi molecular complex. We employed HAWC+ bands C (89 $μ$m) and D (154 $μ$m). The slope of the polarization spectrum was investigated by defining the quantity R_DC = p_D/p_C, where p_C and p_D represent polarization degrees in bands C and D, respectively. We find a clear correlation between R_DC and the molecular hydrogen column density across the cloud. A positive slope (R_DC > 1) dominates the lower density and well illuminated portions of the cloud, that are heated by the high mass star Oph S1, whereas a transition to a negative slope (R_DC < 1) is observed toward the denser and less evenly illuminated cloud core. We interpret the trends as due to a combination of: (1) Warm grains at the cloud outskirts, which are efficiently aligned by the abundant exposure to radiation from Oph S1, as proposed in the radiative torques theory; and (2) Cold grains deep in the cloud core, which are poorly aligned due to shielding from external radiation. To assess this interpretation, we developed a very simple toy model using a spherically symmetric cloud core based on Herschel data, and verified that the predicted variation of R_DC is consistent with the observations. This result introduces a new method that can be used to probe the grain alignment efficiency in molecular clouds, based on the analysis of trends in the far-infrared polarization spectrum.

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