arXiv subjects

Thiem Hoang

Publications and source records attributed to Thiem Hoang.

At least 91 records · Page 5Linked to original sources

arXiv2021

Alignment of irregular grains by radiative torques: efficiency study

We study the efficiency of grain alignment by radiative torques (RATs) for an ensemble of irregular grains. The grains are modeled as ensembles of oblate and prolate spheroids, deformed as Gaussian random ellipsoids, and their scattering interactions are solved using numerically exact methods. We define the fraction of the grains that both rotate fast and demonstrate perfect alignment with grain long axes perpendicular to the magnetic field. We demonstrate that for typical interstellar conditions the degree of alignment arising from the RAT mechanism is significantly larger than that arising from the Davis-Greenstein (DG) mechanism based on paramagnetic relaxation. We quantify a factor related to the efficacy of alignment and show that it is related to a $q_\mathrm{max}$-factor of analytical model (AMO) of the RAT theory. Our results indicate that the RAT alignment can potentially be sufficiently strong and to explain observations even if grains do not have magnetic inclusions.

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arXiv2021

The JCMT BISTRO-2 Survey: The Magnetic Field in the Center of the Rosette Molecular Cloud

We present the first 850 $μ$m polarization observations in the most active star-forming site of the Rosette Molecular Cloud (RMC, $d\sim$1.6 kpc) in the wall of the Rosette Nebula, imaged with the SCUBA-2/POL-2 instruments of the JCMT, as part of the B-Fields In Star-Forming Region Observations 2 (BISTRO-2) survey. From the POL-2 data we find that the polarization fraction decreases with the 850 $μ$m continuum intensity with $α$ = 0.49 $\pm$ 0.08 in the $p \propto I^{\rm -α}$ relation, which suggests that some fraction of the dust grains remain aligned at high densities. The north of our 850 $μ$m image reveals a "gemstone ring" morphology, which is a $\sim$1 pc-diameter ring-like structure with extended emission in the "head" to the south-west. We hypothesize that it might have been blown by feedback in its interior, while the B-field is parallel to its circumference in most places. In the south of our SCUBA-2 field the clumps are apparently connected with filaments which follow Infrared Dark Clouds (IRDCs). Here, the POL-2 magnetic field orientations appear bimodal with respect to the large-scale Planck field. The mass of our effective mapped area is $\sim$ 174 $M_\odot$ that we calculate from 850 $μ$m flux densities. We compare our results with masses from large-scale emission-subtracted Herschel 250 $μ$m data, and find agreement within 30%. We estimate the POS B-field strength in one typical subregion using the Davis-Chandrasekhar-Fermi (DCF) technique and find 80 $\pm$ 30 $μ$G toward a clump and its outskirts. The estimated mass-to-flux ratio of $λ$ = 2.3 $\pm$ 1.0 suggests that the B-field is not sufficiently strong to prevent gravitational collapse in this subregion.

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arXiv2021

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

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

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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 $μ$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 $μ$G, 44$\pm$16 $μ$G, and 12$\pm$5 $μ$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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arXiv2021

OMC-1 dust polarisation in ALMA Band 7: Diagnosing grain alignment mechanisms in the vicinity of Orion Source I

We present ALMA Band 7 polarisation observations of the OMC-1 region of the Orion molecular cloud. We find that the polarisation pattern observed in the region is likely to have been significantly altered by the radiation field of the $>10^{4}$ L$_{\odot}$ high-mass protostar Orion Source I. In the protostar's optically thick disc, polarisation is likely to arise from dust self-scattering. In material to the south of Source I - previously identified as a region of 'anomalous' polarisation emission - we observe a polarisation geometry concentric around Source I. We demonstrate that Source I's extreme luminosity may be sufficient to make the radiative precession timescale shorter than the Larmor timescale for moderately large grains ($> 0.005-0.1\,μ$m), causing them to precess around the radiation anisotropy vector (k-RATs) rather than the magnetic field direction (B-RATs). This requires relatively unobscured emission from Source I, supporting the hypothesis that emission in this region arises from the cavity wall of the Source I outflow. This is one of the first times that evidence for k-RAT alignment has been found outside of a protostellar disc or AGB star envelope. Alternatively, the grains may remain aligned by B-RATs and trace gas infall onto the Main Ridge. Elsewhere, we largely find the magnetic field geometry to be radial around the BN/KL explosion centre, consistent with previous observations. However, in the Main Ridge, the magnetic field geometry appears to remain consistent with the larger-scale magnetic field, perhaps indicative of the ability of the dense Ridge to resist disruption by the BN/KL explosion.

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arXiv2021

Understanding polarized dust emission from $ρ$ Ophiuchi A in light of grain alignment and disruption by radiative torques

The alignment of dust grains with the ambient magnetic field produces polarization of starlight as well as thermal dust emission. Using the archival SOFIA/HAWC+ polarimetric data observed toward $ρ$ Ophiuchus (Oph) A cloud hosted by a B association star at 89 $μ$m and 154 $μ$m, we find that the fractional polarization of thermal dust emission first increases with the grain temperature and then decreases once the grain temperature exceeds $\simeq$ 25-32 K. The latter trend differs from the prediction of the popular RAdiative Torques (RATs) alignment theory which implies a monotonic increase of the polarization fraction with the grain temperature. We perform numerical modeling of polarized dust emission for the $ρ$ Oph-A cloud and calculate the degree of dust polarization by simultaneously considering the dust grain alignment and rotational disruption by RATs. Our modeling results could successfully reproduce both the rising and declining trends of the observational data. Moreover, we show that the alignment of only silicate grains or a mixture of silicate-carbon grains within a composite structure can reproduce the observational trends, assuming that all dust grains follow a power-law size distribution. Although there are a number of simplifications and limitations to our modeling, our results suggest grains in $ρ$ Oph-A cloud have a composite structure, and the grain size distribution has steeper slope than the standard size distribution for the interstellar medium. Combination of SOFIA/HAWC+ data with JCMT observations 450 $μ$m and 850 $μ$m would be useful to test the proposed scenario based on grain alignment and disruption by RATs.

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arXiv2020

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

We report the first high spatial resolution measurement of magnetic fields surrounding LkH$α$ 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 $μ$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 $B_{\rm POS}\sim 115$ $\mathrmμ$G. The mass-to-magnetic-flux ratio in critical value units, $λ\sim0.3$, is the smallest among the values obtained for other regions surveyed by POL-2. This implies that the LkH$α$ 101 region is sub-critical and the magnetic field is strong enough to prevent gravitational collapse. The inferred $δB/B_0\sim 0.3$ 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 $α=0.82\pm0.03$, 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$α$ 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

Alignment and rotational disruption of dust

We reveal a deep connection between alignment of dust grains by RAdiative torques (RATs) and MEchanical Torques (METs) and rotational disruption of grains introduced by Hoang et al. (2019). The disruption of grains happens if they have attractor points corresponding to high angular momentum (high-J). We introduce {\it fast disruption} for grains that are directly driven to the high-J attractor on a timescale of spin-up, and {\it slow disruption} for grains that are first moved to the low-J attractor and gradually transported to the high-J attractor by gas collisions. The enhancement of grain magnetic susceptibility via iron inclusions expands the parameter space for high-J attractors and increases percentage of grains experiencing the disruption. The increase in the magnitude of RATs or METs can increase the efficiency of fast disruption, but counter-intuitively, decreases the effect of slow disruption by forcing grains towards low-J attractors, whereas the increase in gas density accelerates disruption by faster transporting grains to the high-J attractor. We also show that disruption induced by RATs and METs depends on the angle between the magnetic field and the anisotropic flow. We find that pinwheel torques can increase the efficiency of {\it fast disruption} but may decrease the efficiency of {\it slow disruption} by delaying the transport of grains from the low-J to high-J attractors via gas collisions. The selective nature of the rotational disruption opens a possibility of observational testing of grain composition as well as physical processes of grain alignment.

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arXiv2020

Observational evidence for rotational desorption of Complex Molecules by radiative torques from Orion BN/KL

Complex Organic Molecules (COMs) are believed to form in the ice mantle of dust grains and are released to the gas by thermal sublimation when grain mantles are heated to temperatures of $T_{\rm d}\gtrsim 100\,\rm K$. However, some COMs are detected in regions with temperatures below 100 K. Recently, a new mechanism of rotational desorption due to centrifugal stress induced by radiative torques (RATs) is proposed by Hoang & Tram 2020 that can desorb COMs at low temperatures. In this paper, we report observational evidence for rotational desorption of COMs toward the nearest massive star-forming region Orion BN/KL. We compare the abundance of three representative COMs which have very high binding energy computed by the rotational desorption mechanism with observations by ALMA, and demonstrate that the rotational desorption mechanism can explain the existence of such COMs. We also analyze the polarization data from SOFIA/HAWC+ and JCMT/SCUBA-2 and find that the polarization degree at far-infrared/submm decreases with increasing the grain temperature for $T_{\rm d}\gtrsim 71\,\rm K$. This is consistent with the theoretical prediction using the Radiative Torque (RAT) alignment theory and Radiative Torque Disruption (RATD) mechanism. Such an anti-correlation between dust polarization and dust temperature supports the rotational disruption as well as rotational desorption mechanism of COMs induced by RATs.

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arXiv2020

JCMT POL-2 and BISTRO Survey observations of magnetic fields in the L1689 molecular cloud

We present 850$μ$m polarization observations of the L1689 molecular cloud, part of the nearby Ophiuchus molecular cloud complex, taken with the POL-2 polarimeter on the James Clerk Maxwell Telescope (JCMT). We observe three regions of L1689: the clump L1689N which houses the IRAS 16293-2422 protostellar system, the starless clump SMM-16, and the starless core L1689B. We use the Davis-Chandrasekhar-Fermi method to estimate plane-of-sky field strengths of $366\pm 55$ $μ$G in L1689N, $284\pm 34$ $μ$G in SMM-16, and $72\pm 33$ $μ$G in L1689B, for our fiducial value of dust opacity. These values indicate that all three regions are likely to be magnetically trans-critical with sub-Alfvénic turbulence. In all three regions, the inferred mean magnetic field direction is approximately perpendicular to the local filament direction identified in $Herschel$ Space Telescope observations. The core-scale field morphologies for L1689N and L1689B are consistent with the cloud-scale field morphology measured by the $Planck$ Space Observatory, suggesting that material can flow freely from large to small scales for these sources. Based on these magnetic field measurements, we posit that accretion from the cloud onto L1689N and L1689B may be magnetically regulated. However, in SMM-16, the clump-scale field is nearly perpendicular to the field seen on cloud scales by $Planck$, suggesting that it may be unable to efficiently accrete further material from its surroundings.

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arXiv2020

Variation of dust properties with cosmic time implied by radiative torque disruption

Dust properties within a galaxy are known to change from the diffuse medium to dense clouds due to increased local gas density. However, the question of whether dust properties change with redshift remains elusive. In this paper, using the fact that the mean radiation intensity of the interstellar medium (ISM) of star-forming galaxies increases with redshift, we show that dust properties should change due to increasing efficiency of rotational disruption by radiative torques, an effect named RAdiative Torque Disruption (RATD). We first show that, due to RATD, the size distribution of interstellar dust varies with redshift, such as dust grains become smaller at higher $z$. We model the extinction curves and find that the curve becomes steeper with increasing redshift. The ratio of total-to-selective extinction, $R_{V}$, decreases with redshift and achieves low values of $R_{V}\sim 1.5-2.5$ for grains having a composite structure. We also find that dust properties change with the local gas density due to RATD, but the change is dominated by the radiation field for the diffuse ISM. The low values of $R_{V}$ implied by RATD of interstellar dust could reproduce anomalous dust extinction observed toward type Ia supernovae (SNe Ia) and Small Magellanic Cloud (SMC)-like extinction curves with a steep far-UV rise toward high-z galaxies. Fluctuations in $R_{V}$ due to interstellar turbulence and varying radiation intensity may resolve the tension in measurements of the Hubble constant using SNe Ia. We finally discuss the implications of evolving dust properties for high-z astrophysics.

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arXiv2020

Probing Interstellar Grain Growth Through Polarimetry in the Taurus Cloud Complex

The optical and near-infrared (OIR) polarization of starlight is typically understood to arise from the dichroic extinction of that light by dust grains whose axes are aligned with respect to a local magnetic-field. The size distribution of the aligned-grain population can be constrained by measurements of the wavelength dependence of the polarization. The leading physical model for producing the alignment is radiative alignment-torques (RAT), which predicts that the most efficiently aligned grains are those with sizes larger than the wavelengths of light composing the local radiation field. Therefore, for a given grain-size distribution, the wavelength at which the polarization reaches a maximum ($λ_\mathrm{max}$) should correlate with the characteristic reddening along the line of sight between the dust grains and the illumination source. A correlation between $λ_\mathrm{max}$ and reddening has been previously established for extinctions up to $A_V\approx4$ mag. We extend the study of this relationship to a larger sample of stars in the Taurus cloud complex, including extinctions $A_V>10$ mag. We confirm the earlier results for $A_V<4$ mag, but find that the $λ_\mathrm{max}$ vs. $A_V$ relationship bifurcates above $A_V\approx4$ mag, with part of the sample continuing the previously observed relationship and the remaining part exhibiting a significantly steeper rise. We propose that the data exhibiting the steep rise represent lines-of-sight towards high density "clumps," where grain coagulation has taken place. We present RAT-based modeling supporting these hypotheses. These results indicate that multi-band OIR polarimetry is a powerful tool for tracing grain growth in molecular clouds, independent of uncertainties in the dust temperature and emissivity.

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arXiv2020

Grain alignment and disruption by radiative torques in dense molecular clouds and implication for polarization holes

Dust polarization induced by aligned grains is widely used to study magnetic fields in various environments, including star-forming regions. However, the question of to what optical depth grain alignment still exists in a dense molecular cloud (MC) is unclear. In this paper, we aim to achieve analytical formulae for the minimum size of aligned grains ($a_{\rm align}$) and rotational disruption ($a_{\rm disr}$) by RAdiative Torques (RATs) as a function of the local physical parameters within dense MCs. We first find the analytical approximations for the radiation strength and the mean wavelength of the attenuated radiation field in a dense MC without and with embedded stars and then derive analytical formulae for $a_{\rm align}$ and $a_{\rm disr}$ as functions of the visual extinction $A_{V}$ and the gas density. We find that within a starless core of density $n_{\rm H}\sim 10^{5}\rm cm^{-3}$, grains of size $a<0.25μm$ can be aligned up to $A_{V}\sim 5$ by RATs, whereas micron-sized grains can still be aligned at $A_{V}\sim 50$. The increase in the alignment size with $A_{V}$ can explain the presence of polarization holes observed toward starless cores. For MCs with an embedded protostar, we find that the efficiency of both alignment and rotational disruption increases toward the protostar due to the increasing radiation strength. Such a disruption effect results in the decrease of the polarization degree with $A_{V}$ or emission intensity, which reproduces the popular polarization holes observed toward the location of protostars. Finally, we derive the formula for the maximum $A_{V}$ where grain alignment still exists in a starless core and discuss its potential for constraining grain growth.

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arXiv2020

Evolution of Dust and Water Ice in Cometary Comae by Radiative Torques

Comets provide unique information about the physical and chemical properties of the environment in which the Solar system was formed. Understanding how cometary dust and ice evolve under the effect of sunlight is essential for constraining nuclear structure and triggering mechanism of comet activity. In this paper, we first study rotational disruption of dust grains lifted by outgassing from comet nuclei by radiative torques (RATs). We find that composite grains could be rapidly disrupted into small fragments by the Radiative Torque Disruption (RATD) mechanism. We then study rotational desorption of ice grains by RATs and find that icy grains could be desorbed from large heliocentric distances, beyond the sublimation radius of water at $R_{\rm sub}(\H_{2}Ø)\sim 3\AU$. We also calculate the production rate of water vapor versus the heliocentric distance of comets due to rotational desorption. Our results could explain the variation of dust properties and the presence of small grains frequently observed from cometary comae. Finally, we suggest that the activity of distant comets could be triggered by rotational disruption of grains and desorption of water ice grains at large heliocentric distances.

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arXiv2020

Destruction of molecular hydrogen ice and Implications for 1I/2017 U1 (`Oumuamua)

The first interstellar object observed in our solar system, 1I/2017 U1 (`Oumuamua), exhibited a number of peculiar properties, including extreme elongation and acceleration excess. Recently, \cite{Seligman:2020vb} proposed that the object was made out of molecular hydrogen (H$_{2}$) ice. The question is whether H$_2$ objects could survive their travel from the birth sites to the solar system. Here we study destruction processes of icy H$_2$ objects through their journey from giant molecular clouds (GMCs) to the interstellar medium (ISM) and the solar system, owing to interstellar radiation, gas and dust, and cosmic rays. We find that thermal sublimation due to heating by starlight can destroy `Oumuamua-size objects in less than 10 Myr. Thermal sublimation by collisional heating in GMCs could destroy H$_2$ objects of `Oumuamua-size before their escape into the ISM. Most importantly, the formation of icy grains rich in H$_2$ is unlikely to occur in dense environments because collisional heating raises the temperature of the icy grains, so that thermal sublimation rapidly destroys the H$_2$ mantle before grain growth.

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arXiv2020

Rotational Disruption of Dust and Ice by Radiative Torques in Protoplanetary Disks and Implications for Observations

Dust and ice mantles on dust grains play an important role in various processes in protoplanetary disks (PPDs) around a young star, including planetesimal formation, surface chemistry, and being the reservoir of water in habitable zones. In this paper, we will perform two-dimensional modeling of rotational disruption of dust grains and ice mantles due to centrifugal force within suprathermally rotating grains spun-up by radiative torques for disks around T-Tauri and Herbig Ae/Be stars. We first study rotational disruption of large composite grains and find that large aggregates could be disrupted into individual nanoparticles via the RAdiative Torque Disruption (RATD) mechanism. We then study rotational desorption of ice mantles and ro-thermal desorption of molecules from the ice mantle. We will show that ice mantles in the warm surface layer and above of the disk can be disrupted into small icy fragments, followed by rapid evaporation of molecules. We suggest that the rotational disruption mechanism can replenish the ubiquitous presence of polycyclic aromatic hydrogen (PAHs)/ nanoparticles in the hot surface layers of PPDs as observed in mid-IR emission, which are presumably destroyed by extreme ultraviolet (UV) stellar photons. We show that the water snowline is more extended in the presence of rotational desorption, which would decrease the number of comets but increase the number of asteroids formed in the solar nebula. Finally, we suggest that the more efficient breakup of carbonaceous grains than silicates by RATD might resolve the carbon deficit problem measured on the Earth and rocky bodies.

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arXiv2020

Modeling rotational disruption of grains and microwave emission from spinning dust in AGB envelopes

Radio observations of some Asymptotic Giant Branch (AGB) star envelopes show the excess emission at frequencies below 100 GHz which cannot be explained by thermal dust emission (hereafter anomalous microwave emission-AME). Moreover, AGB envelopes are a common place where gas molecules condense to form nanoparticles (e.g., polycyclic aromatic hydrocarbons) and large grains. In this paper, we will study whether electric dipole emission from rapidly spinning nanoparticles can reproduce the AME observed toward AGB stars. To properly model the size distribution of nanoparticles in the AGB envelope, we take into account both the increase of nanoparticles due to rotational disruption of large grains spun-up by radiative torques and the decrease of smallest nanoparticles due to rotational disruption driven by stochastic gas collisions. We then perform detailed modeling of microwave emission from rapidly spinning nanoparticles from both C-rich and O-rich AGB envelopes using the grain size distribution constrained by rotational disruption. We find that spinning dust emission is dominant over thermal dust emission at frequencies below 100 GHz. We attempt to fit the observational data of AME using our spinning dust model and demonstrate that spinning dust can reproduce the observed AME in six AGB stars. Finally, we discuss that microwave emission from spinning dust in AGB envelopes could be observed with high-resolution upcoming radio telescopes such as ngVLA and ALMA Band 1. This would be a major leap for understanding AGB envelopes, formation, evolution, and internal structures of dust. Observations would help to distinguish the carrier of AME from comparing C-rich to O-rich stars, because PAHs are formed in C-rich AGB stars while silicates are formed in O-rich stars.

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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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