arXiv subjects

Zhi-Yun Li

Publications and source records attributed to Zhi-Yun Li.

At least 199 records · Page 11Linked to original sources

arXiv2017

Modeling Dust Polarization Observations of Molecular Clouds through MHD Simulations

The BLASTPol observations of Vela C have provided the most detailed characterization of the polarization fraction $p$ and dispersion in polarization angles $S$ for a molecular cloud. We compare the observed distributions of $p$ and $S$ with those obtained in synthetic observations of simulations of molecular clouds, assuming homogeneous grain alignment. We find that the orientation of the mean magnetic field relative to the observer has a significant effect on the $p$ and $S$ distributions. These distributions for Vela C are most consistent with synthetic observations where the mean magnetic field is close to the line-of-sight. Our results point to apparent magnetic disorder in the Vela C molecular cloud, although it can be due to either an inclination effect (i.e., observing close to the mean field direction) or significant field tangling from strong turbulence/low magnetization. The joint correlations of $p$ with column density and of $S$ with column density for the synthetic observations generally agree poorly with the Vela C joint correlations, suggesting that understanding these correlations require a more sophisticated treatment of grain alignment physics.

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arXiv2017

Decoupling of Magnetic Fields in Collapsing Protostellar Envelopes and Disk Formation and Fragmentation

Efficient magnetic braking is a formidable obstacle to the formation of rotationally supported disks (RSDs) around protostars in magnetized dense cores. We have previously shown, through 2D (axisymmetric) non-ideal MHD simulations, that removing very small grains (VSGs: ~10 Å$~$to few 100 Å) can greatly enhance ambipolar diffusion and enable the formation of RSDs. Here we extend the simulations of disk formation enabled by VSG removal to 3D. We find that the key to this scenario of disk formation is that the drift velocity of the magnetic field almost cancels out the infall velocity of the neutrals in the $10^2$-$10^3$ AU-scale "pseudo-disk" where the field lines are most severely pinched and most of protostellar envelope mass infall occurs. As a result, the bulk neutral envelope matter can collapse without dragging much magnetic flux into the disk-forming region, which lowers the magnetic braking efficiency. We find that the initial disks enabled by VSG removal tend to be Toomre-unstable, which leads to the formation of prominent spiral structures that function as centrifugal barriers. The piling-up of infall material near the centrifugal barrier often produces dense fragments of tens of Jupiter masses, especially in cores that are not too strongly magnetized. Some fragments accrete onto the central stellar object, producing bursts in mass accretion rate. Others are longer lived, although whether they can survive long-term to produce multiple systems remains to be ascertained. Our results highlight the importance of dust grain evolution in determining the formation and properties of protostellar disks and potentially multiple systems.

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arXiv2017

The VLA Nascent Disk And Multiplicity Survey of Perseus Protostars (VANDAM). III. Extended Radio Emission from Protostars in Perseus

Centimeter continuum emission from protostars offers insight into the innermost part of the outflows, as shock-ionized gas produces free-free emission. We observed a complete population of Class 0 and I protostars in the Perseus molecular cloud at 4.1 cm and 6.4 cm with resolution and sensitivity superior to previous surveys. From a total of 71 detections, 8 sources exhibit resolved emission at 4.1 cm and/or 6.4 cm. In this paper we focus on this sub-sample, analyzing their spectral indices along the jet, and their alignment with respect to the large-scale molecular outflow. Spectral indices for fluxes integrated toward the position of the protostar are consistent with free-free thermal emission. The value of the spectral index along a radio jet decreases with distance from the protostar. For six sources, emission is well aligned with the outflow central axis, showing that we observe the ionized base of the jet. This is not the case for two sources, where we note misalignment of the emission with respect to the large-scale outflow. This might indicate that the emission does not originate in the radio jet, but rather in an ionized outflow cavity wall or disk surface. For five of the sources, the spectral indices along the jet decrease well below the thermal free-free limit of -0.1 with $>2σ$ significance. This is indicative of synchrotron emission, meaning that high energy electrons are being produced in the outflows close to the disk. This result can have far-reaching implications for the chemical composition of the embedded disks.

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arXiv2017

A Model of the H$α$ and Na Transmission Spectrum of HD 189733b

This paper presents a detailed hydrostatic model of the upper atmosphere of HD 189733b, with the goal of constraining its temperature, particle densities, and radiation field over the pressure range $10^{-4}-10\, μ\rm bar$, where the observed H$α$ transmission spectrum is produced. The atomic hydrogen level population is computed including both collisional and radiative transition rates. The Ly$α$ resonant scattering is computed using a Monte-Carlo simulation. The model transmission spectra are in broad agreement with the data. Excitation of the H(2$\ell$) population is mainly by Ly$α$ radiative excitation due to the large Ly$α$ intensity. The density of H(2$\ell$) is nearly flat over two decades in pressure, and is optically thick to H$α$. Additional models computed for a range of the stellar Lyman continuum (LyC) flux suggest that the variability in H$α$ transit depth may be due to the variability in the stellar LyC. Since metal lines provide the dominant cooling of this part of the atmosphere, the atmosphere structure is sensitive to the density of species such as Mg and Na which may themselves be constrained by observations. Since the H$α$ and Na D lines have comparable absorption depths, we argue that the center of the Na D lines are also formed in the atomic layer where the H$α$ line is formed.

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arXiv2017

Protoplanetary Disks in $ρ$ Ophiuchus as Seen From ALMA

We present a high angular resolution ($\sim 0.2^{\prime\prime}$), high sensitivity ($σ\sim 0.2$ mJy) survey of the 870 $μ$m continuum emission from the circumstellar material around 49 pre-main sequence stars in the $ρ$ Ophiuchus molecular cloud. Because most millimeter instruments have resided in the northern hemisphere, this represents the largest high-resolution, millimeter-wave survey of the circumstellar disk content of this cloud. Our survey of 49 systems comprises 63 stars; we detect disks associated with 29 single sources, 11 binaries, 3 triple systems and 4 transition disks. We present flux and radius distributions for these systems; in particular, this is the first presentation of a reasonably complete probability distribution of disk radii at millimeter-wavelengths. We also compare the flux distribution of these protoplanetary disks with that of the disk population of the Taurus-Auriga molecular cloud. We find that disks in binaries are both significantly smaller and have much less flux than their counterparts around isolated stars. We compute truncation calculations on our binary sources and find that these disks are too small to have been affected by tidal truncation and posit some explanations for this. Lastly, our survey found 3 candidate gapped disks, one of which is a newly identified transition disk with no signature of a dip in infrared excess in extant observations.

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arXiv2017

Scattering-Produced (Sub)millimeter Polarization in Inclined Disks: Optical Depth Effects, Near-Far Side Asymmetry, and Dust Settling

Disk polarization at (sub)millimeter wavelengths is being revolutionized by ALMA observationally, but its origin remains uncertain. Dust scattering was recently recognized as a potential contributor to polarization, although its basic properties have yet to be thoroughly explored. Here, we quantify the effects of optical depth on the scattering-induced polarization in inclined disks through a combination of analytical illustration, approximate semi-analytical modeling using formal solution to the radiative transfer equation, and Monte Carlo simulations. We find that the near-side of the disk is significantly brighter in polarized intensity than the far-side, provided that the disk is optically thick and that the scattering grains have yet to settle to the midplane. This asymmetry is the consequence of a simple geometric effect: the near-side of the disk surface is viewed more edge-on than the far-side. It is a robust signature that may be used to distinguish the scattering-induced polarization from that by other mechanisms, such as aligned grains. The asymmetry is weaker for a geometrically thinner dust disk. As such, it opens an exciting new window on dust settling. We find anecdotal evidence from dust continuum imaging of edge-on disks that large grains are not yet settled in the youngest (Class 0) disks, but become more so in older disks. This trend is corroborated by the polarization data in inclined disks showing that younger disks have more pronounced near-far side asymmetry and thus less grain settling. If confirmed, the trend would have far-reaching implications for grain evolution and, ultimately, the formation of planetesimals and planets.

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arXiv2017

ALMA observations of dust polarization and molecular line emission from the Class 0 protostellar source Serpens SMM1

We present high angular resolution dust polarization and molecular line observations carried out with the Atacama Large Millimeter/submillimeter Array (ALMA) toward the Class 0 protostar Serpens SMM1. By complementing these observations with new polarization observations from the Submillimeter Array (SMA) and archival data from the Combined Array for Research in Millimeter-wave Astronomy (CARMA) and the James Clerk Maxwell Telescopes (JCMT), we can compare the magnetic field orientations at different spatial scales. We find major changes in the magnetic field orientation between large (~0.1 pc) scales -- where the magnetic field is oriented E-W, perpendicular to the major axis of the dusty filament where SMM1 is embedded -- and the intermediate and small scales probed by CARMA (~1000 AU resolution), the SMA (~350 AU resolution), and ALMA (~140 AU resolution). The ALMA maps reveal that the redshifted lobe of the bipolar outflow is shaping the magnetic field in SMM1 on the southeast side of the source; however, on the northwestern side and elsewhere in the source, low velocity shocks may be causing the observed chaotic magnetic field pattern. High-spatial-resolution continuum and spectral-line observations also reveal a tight (~130 AU) protobinary system in SMM1-b, the eastern component of which is launching an extremely high-velocity, one-sided jet visible in both CO(2-1) and SiO(5-4); however, that jet does not appear to be shaping the magnetic field. These observations show that with the sensitivity and resolution of ALMA, we can now begin to understand the role that feedback (e.g., from protostellar outflows) plays in shaping the magnetic field in very young, star-forming sources like SMM1.

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arXiv2017

First Observation of the Submillimeter Polarization Spectrum in a Translucent Molecular Cloud

Polarized emission from aligned dust is a crucial tool for studies of magnetism in the ISM and a troublesome contaminant for studies of CMB polarization. In each case, an understanding of the significance of the polarization signal requires well-calibrated physical models of dust grains. Despite decades of progress in theory and observation, polarized dust models remain largely underconstrained. During its 2012 flight, the balloon-borne telescope BLASTPol obtained simultaneous broad-band polarimetric maps of a translucent molecular cloud at 250, 350, and 500 microns. Combining these data with polarimetry from the Planck 850 micron band, we have produced a submillimeter polarization spectrum for a cloud of this type for the first time. We find the polarization degree to be largely constant across the four bands. This result introduces a new observable with the potential to place strong empirical constraints on ISM dust polarization models in a previously inaccessible density regime. Comparing with models by Draine and Fraisse (2009), our result disfavors two of their models for which all polarization arises due only to aligned silicate grains. By creating simple models for polarized emission in a translucent cloud, we verify that extinction within the cloud should have only a small effect on the polarization spectrum shape compared to the diffuse ISM. Thus we expect the measured polarization spectrum to be a valid check on diffuse ISM dust models. The general flatness of the observed polarization spectrum suggests a challenge to models where temperature and alignment degree are strongly correlated across major dust components.

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arXiv2017

A Rotating Protostellar Jet Launched from the Innermost Disk of HH 212

The central problem in forming a star is the angular momentum in the circumstellar disk which prevents material from falling into the central stellar core. An attractive solution to the "angular momentum problem" appears to be the ubiquitous (low-velocity and poorly-collimated) molecular outflows and (high-velocity and highly-collimated) protostellar jets accompanying the earliest phase of star formation that remove angular momentum at a range of disk radii. Previous observations suggested that outflowing material carries away the excess angular momentum via magneto-centrifugally driven winds from the surfaces of circumstellar disks down to ~ 10 AU scales, allowing the material in the outer disk to transport to the inner disk. Here we show that highly collimated protostellar jets remove the residual angular momenta at the ~ 0.05 AU scale, enabling the material in the innermost region of the disk to accrete toward the central protostar. This is supported by the rotation of the jet measured down to ~ 10 AU from the protostar in the HH 212 protostellar system. The measurement implies a jet launching radius of ~ 0.05_{-0.02}^{+0.05} AU on the disk, based on the magneto-centrifugal theory of jet production, which connects the properties of the jet measured at large distances to those at its base through energy and angular momentum conservation.

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arXiv2017

Formation and Atmosphere of Complex Organic Molecules of the HH 212 Protostellar Disk

HH 212 is a nearby (400 pc) Class 0 protostellar system recently found to host a "hamburger"-shaped dusty disk with a radius of ~ 60 AU, deeply embedded in an infalling-rotating flattened envelope. We have spatially resolved this envelope-disk system with the Atacama Large Millimeter/submillimeter Array at up to ~ 16 AU (0.04") resolution. The envelope is detected in HCO+ J=4-3 down to the dusty disk. Complex organic molecules (COMs) and doubly deuterated formaldehyde (D2CO) are detected above and below the dusty disk within ~ 40 AU of the central protostar. The COMs are methanol (CH3OH), deuterated methanol (CH2DOH), methyl mercaptan (CH3SH), and formamide (NH2CHO, a prebiotic precursor). We have modeled the gas kinematics in HCO+ and COMs, and found a centrifugal barrier at a radius of ~ 44 AU, within which a Keplerian rotating disk is formed. This indicates that HCO+ traces the infalling-rotating envelope down to centrifugal barrier and COMs trace the atmosphere of a Keplerian rotating disk within the centrifugal barrier. The COMs are spatially resolved for the first time, both radially and vertically, in the atmosphere of a disk in the earliest, Class 0 phase of star formation. Our spatially resolved observations of COMs favor their formation in the disk rather than a rapidly infalling (warm) inner envelope. The abundances and spatial distributions of the COMs provide strong constraints on models of their formation and transport in low-mass star formation.

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arXiv2017

Fantastic Striations and Where to Find Them: Origin of Magnetically Aligned Striations in Interstellar Clouds

Thin, magnetically aligned striations of relatively moderate contrast with the background are commonly observed in both atomic and molecular clouds. They are also prominent in MHD simulations with turbulent converging shocks. The simulated striations develop within a dense, stagnated sheet in the mid plane of the post-shock region where magnetically-induced converging flows collide. We show analytically that the secondary flows are an inevitable consequence of the jump conditions of oblique MHD shocks. They produce the stagnated, sheet-like sub-layer through a secondary shock when, roughly speaking, the Alfvénic speed in the primary converging flows is supersonic, a condition that is relatively easy to satisfy in interstellar clouds. The dense sub-layer is naturally threaded by a strong magnetic field that lies close to the plane of the sub-layer. The substantial magnetic field makes the sheet highly anisotropic, which is the key to the striation formation. Specifically, perturbations of the primary inflow that vary spatially perpendicular to the magnetic field can easily roll up the sheet around the field lines without bending them, creating corrugations that appear as magnetically-aligned striations in column density maps. On the other hand, perturbations that vary spatially along the field lines curve the sub-layer and alter its orientation relative to the magnetic field locally, seeding special locations that become slanted overdense filaments and prestellar cores through enhanced mass accumulation along field lines. In our scenario, the dense sub-layer unique to magnetized oblique shocks is the birthplace for both magnetically-aligned diffuse striations and massive star-forming structures.

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arXiv2017

Unveiling the Role of the Magnetic Field at the Smallest Scales of Star Formation

We report ALMA observations of polarized dust emission from the protostellar source Ser-emb 8 at a linear resolution of 140 au. Assuming models of dust-grain alignment hold, the observed polarization pattern gives a projected view of the magnetic field structure in this source. Contrary to expectations based on models of strongly magnetized star formation, the magnetic field in Ser-emb 8 does not exhibit an hourglass morphology. Combining the new ALMA data with previous observational studies, we can connect magnetic field structure from protostellar core (~80,000 au) to disk (~100 au) scales. We compare our observations with four magnetohydrodynamic gravo-turbulence simulations made with the AREPO code that have initial conditions ranging from super-Alfvénic (weakly magnetized) to sub-Alfvénic (strongly magnetized). These simulations achieve the spatial dynamic range necessary to resolve the collapse of protostars from the parsec scale of star-forming clouds down to the ~100 au scale probed by ALMA. Only in the very strongly magnetized simulation do we see both the preservation of the field direction from cloud to disk scales and an hourglass-shaped field at < 1000 au scales. We conduct an analysis of the relative orientation of the magnetic field and the density structure in both the Ser-emb 8 ALMA observations and the synthetic observations of the four AREPO simulations. We conclude that the Ser-emb 8 data are most similar to the weakly magnetized simulations, which exhibit random alignment, in contrast to the strongly magnetized simulation, where the magnetic field plays a role in shaping the density structure in the source. In the weak-field case, it is turbulence -- not the magnetic field -- that shapes the material that forms the protostar, highlighting the dominant role that turbulence can play across many orders of magnitude in spatial scale.

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arXiv2017

First Detection of Equatorial Dark Dust Lane in a Protostellar Disk at Submillimeter Wavelength

In the earliest (so-called "Class 0") phase of sunlike (low-mass) star formation, circumstellar disks are expected to form, feeding the protostars. However, such disks are difficult to resolve spatially because of their small sizes. Moreover, there are theoretical difficulties in producing such disks in the earliest phase, due to the retarding effects of magnetic fields on the rotating, collapsing material (so-called "magnetic braking"). With the Atacama Large Millimeter/submillimeter Array (ALMA), it becomes possible to uncover such disks and study them in detail. HH 212 is a very young protostellar system. With ALMA, we not only detect but also spatially resolve its disk in dust emission at submillimeter wavelength. The disk is nearly edge-on and has a radius of ~ 60 AU. Interestingly, it shows a prominent equatorial dark lane sandwiched between two brighter features, due to relatively low temperature and high optical depth near the disk midplane. For the first time, this dark lane is seen at submillimeter wavelength, producing a "hamburger"-shaped appearance that is reminiscent of the scattered-light image of an edge-on disk in optical and near infrared. Our observations open up an exciting possibility of directly detecting and characterizing small disks around the youngest protostars through high-resolution imaging with ALMA, which provides strong constraints on theories of disk formation.

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arXiv2017

Rings and gaps produced by variable magnetic disk winds and avalanche accretion streams: I. Axisymmetric resistive MHD simulations

Rings and gaps are being observed in an increasing number of disks around young stellar objects. We illustrate the formation of such radial structures through idealized, 2D (axisymmetric) resistive MHD simulations of coupled disk-wind systems threaded by a relatively weak poloidal magnetic field (plasma-$β\sim 10^3$). We find two distinct modes of accretion depending on the resistivity and field strength. A small resistivity or high field strength promotes the development of rapidly infalling `avalanche accretion streams' in a vertically extended disk envelope that dominates the dynamics of the system, especially the mass accretion. The streams are suppressed in simulations with larger resistivities or lower field strengths, where most of the accretion instead occurs through a laminar disk. In these simulations, the disk accretion is driven mainly by a slow wind that is typically accelerated by the pressure gradient from a predominantly toroidal magnetic field. Both wind-dominated and stream-dominated modes of accretion create prominent features in the surface density distribution of the disk, including rings and gaps, with a strong spatial variation of the magnetic flux relative to the mass. Regions with low mass-to-flux ratios accrete quickly, leading to the development of gaps, whereas regions with higher mass-to-flux ratios tend to accrete more slowly, allowing matter to accumulate and form dense rings. In some cases, avalanche accretion streams are observed to produce dense rings directly through continuous feeding. We discuss the implications of ring and gap formation driven by winds and streams on grain growth and planet formation.

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arXiv2017

Comparing submillimeter polarized emission with near-infrared polarization of background stars for the Vela C molecular cloud

We present a large-scale combination of near-infrared (near-IR) interstellar polarization data from background starlight with polarized emission data at submillimeter (sub-mm) wavelengths for the Vela C molecular cloud. The near-IR data consist of more than 6700 detections probing a range of visual extinctions between $2$ and $20\,$mag in and around the cloud. The sub-mm data was collected in Antartica by the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol). This is the first direct combination of near-IR and sub-mm polarization data for a molecular cloud aimed at measuring the "polarization efficiency ratio" ($R_{\mathrm{eff}}$), a quantity that is expected to depend only on grain intrinsic physical properties. It is defined as $p_{500}/(p_{I}/τ_{V})$, where $p_{500}$ and $p_{I}$ are polarization fractions at $500\,μ$m and $I$-band, respectively, and $τ_{V}$ is the optical depth. To ensure that the same column density of material is producing both polarization from emission and from extinction, we conducted a careful selection of near-background stars using 2MASS, $Herschel$ and $Planck$ data. This selection excludes objects contaminated by the Galactic diffuse background material as well as objects located in the foreground. Accounting for statistical and systematic uncertainties, we estimate an average $R_{\mathrm{eff}}$ value of $2.4\pm0.8$, which can be used to test the predictions of dust grain models designed for molecular clouds when such predictions become available. $R_{\mathrm{eff}}$ appears to be relatively flat as a function of the cloud depth for the range of visual extinctions probed.

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arXiv2016

A Triple Protostar System Formed via Fragmentation of a Gravitationally Unstable Disk

Binary and multiple star systems are a frequent outcome of the star formation process, and as a result, almost half of all sun-like stars have at least one companion star. Theoretical studies indicate that there are two main pathways that can operate concurrently to form binary/multiple star systems: large scale fragmentation of turbulent gas cores and filaments or smaller scale fragmentation of a massive protostellar disk due to gravitational instability. Observational evidence for turbulent fragmentation on scales of $>$1000~AU has recently emerged. Previous evidence for disk fragmentation was limited to inferences based on the separations of more-evolved pre-main sequence and protostellar multiple systems. The triple protostar system L1448 IRS3B is an ideal candidate to search for evidence of disk fragmentation. L1448 IRS3B is in an early phase of the star formation process, likely less than 150,000 years in age, and all protostars in the system are separated by $<$200~AU. Here we report observations of dust and molecular gas emission that reveal a disk with spiral structure surrounding the three protostars. Two protostars near the center of the disk are separated by 61 AU, and a tertiary protostar is coincident with a spiral arm in the outer disk at a 183 AU separation. The inferred mass of the central pair of protostellar objects is $\sim$1 M$_{sun}$, while the disk surrounding the three protostars has a total mass of $\sim$0.30 M$_{\sun}$. The tertiary protostar itself has a minimum mass of $\sim$0.085 M$_{sun}$. We demonstrate that the disk around L1448 IRS3B appears susceptible to disk fragmentation at radii between 150~AU and 320~AU, overlapping with the location of the tertiary protostar. This is consistent with models for a protostellar disk that has recently undergone gravitational instability, spawning one or two companion stars.

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arXiv2016

Instrumental performance and results from testing of the BLAST-TNG receiver, submillimeter optics, and MKID arrays

Polarized thermal emission from interstellar dust grains can be used to map magnetic fields in star forming molecular clouds and the diffuse interstellar medium (ISM). The Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol) flew from Antarctica in 2010 and 2012 and produced degree-scale polarization maps of several nearby molecular clouds with arcminute resolution. The success of BLASTPol has motivated a next-generation instrument, BLAST-TNG, which will use more than 3000 linear polarization sensitive microwave kinetic inductance detectors (MKIDs) combined with a 2.5m diameter carbon fiber primary mirror to make diffraction-limited observations at 250, 350, and 500 $μ$m. With 16 times the mapping speed of BLASTPol, sub-arcminute resolution, and a longer flight time, BLAST-TNG will be able to examine nearby molecular clouds and the diffuse galactic dust polarization spectrum in unprecedented detail. The 250 $μ$m detector array has been integrated into the new cryogenic receiver, and is undergoing testing to establish the optical and polarization characteristics of the instrument. BLAST-TNG will demonstrate the effectiveness of kilo-pixel MKID arrays for applications in submillimeter astronomy. BLAST-TNG is scheduled to fly from Antarctica in December 2017 for 28 days and will be the first balloon-borne telescope to offer a quarter of the flight for "shared risk" observing by the community.

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arXiv2016

Change of Magnetic Field$-$Gas Alignment at Gravity-Driven Alfvénic Transition in Molecular Clouds: Implications for Dust Polarization Observations

Diffuse striations in molecular clouds are preferentially aligned with local magnetic fields whereas dense filaments tend to be perpendicular to them. When and why this transition occurs remain uncertain. To explore the physics behind this transition, we compute the histogram of relative orientation (HRO) between the density gradient and the magnetic field in 3D MHD simulations of prestellar core formation in shock-compressed regions within GMCs. We find that, in the magnetically-dominated (sub-Alfvénic) post-shock region, the gas structure is preferentially aligned with the local magnetic field. For overdense sub-regions with super-Alfvénic gas, their elongation becomes preferentially perpendicular to the local magnetic field instead. The transition occurs when self-gravitating gas gains enough kinetic energy from the gravitational acceleration to overcome the magnetic support against the cross-field contraction, which results in a power-law increase of the field strength with density. Similar results can be drawn from HROs in projected 2D maps with integrated column densities and synthetic polarized dust emission. We quantitatively analyze our simulated polarization properties, and interpret the reduced polarization fraction at high column densities as the result of increased distortion of magnetic field directions in trans- or super-Alfvénic gas. Furthermore, we introduce measures of the inclination and tangledness of the magnetic field along the line of sight as the controlling factors of the polarization fraction. Observations of the polarization fraction and angle dispersion can therefore be utilized in studying local magnetic field morphology in star-forming regions.

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