arXiv subjects

Kate Pattle

Publications and source records attributed to Kate Pattle.

At least 37 records · Page 2Linked to original sources

arXiv2025

The JCMT Gould Belt Survey: First results from the Corona Australis molecular cloud and evidence of variable dust emissivity indices in the Coronet region

We present 450$μ$m and 850$μ$m James Clerk Maxwell Telescope (JCMT) observations of the Corona Australis (CrA) molecular cloud taken as part of the JCMT Gould Belt Legacy Survey (GBLS). We present a catalogue of 39 starless and protostellar sources, for which we determine source temperatures and masses using SCUBA-2 450$μ$m/850$μ$m flux density ratios for sources with reliable 450$μ$m detections, and compare these to values determined using temperatures measured by the Herschel Gould Belt Survey (HGBS). In keeping with previous studies, we find that SCUBA-2 preferentially detects high-volume-density starless cores, which are most likely to be prestellar (gravitationally bound). We do not observe any anti-correlation between temperature and volume density in the starless cores in our sample. Finally, we combine our SCUBA-2 and Herschel data to perform SED fitting from 160-850$μ$m across the central Coronet region, thereby measuring dust temperature $T$, dust emissivity index $β$ and column density $N({\rm H}_2)$ across the Coronet. We find that $β$ varies across the Coronet, particularly measuring $β= 1.55 \pm 0.35$ in the colder starless SMM-6 clump to the north of the B star R CrA. This relatively low value of $β$ is suggestive of the presence of large dust grains in SMM-6, even when considering the effects of $T-β$ fitting degeneracy and $^{12}$CO contamination of SCUBA-2 850$μ$m data on the measured $β$ values.

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arXiv2024

A Tale of Three: Magnetic Fields along the Orion Integral-Shaped Filament as Revealed by JCMT BISTRO survey

As part of the BISTRO survey, we present JCMT 850 $μ$m polarimetric observations towards the Orion Integral-Shaped Filament (ISF) that covers three portions known as OMC-1, OMC-2, and OMC-3. The magnetic field threading the ISF seen in the JCMT POL-2 map appears as a tale of three: pinched for OMC-1, twisted for OMC-2, and nearly uniform for OMC-3. A multi-scale analysis shows that the magnetic field structure in OMC-3 is very consistent at all the scales, whereas the field structure in OMC-2 shows no correlation across different scales. In OMC-1, the field retains its mean orientation from large to small scales, but shows some deviations at small scales. Histograms of relative orientations between the magnetic field and filaments reveal a bimodal distribution for OMC-1, a relatively random distribution for OMC-2, and a distribution with a predominant peak at 90$^\circ$ for OMC-3. Furthermore, the magnetic fields in OMC-1 and OMC-3 both appear to be aligned perpendicular to the fibers, which are denser structures within the filament, but the field in OMC-2 is aligned along with the fibers. All these suggest that gravity, turbulence, and magnetic field are each playing a leading role in OMC-1, 2, and 3, respectively. While OMC-2 and 3 have almost the same gas mass, density, and non-thermal velocity dispersion, there are on average younger and fewer young stellar objects in OMC-3, providing evidence that a stronger magnetic field will induce slower and less efficient star formation in molecular clouds.

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arXiv2024

Magnetic Fields in Massive Star-forming Regions (MagMaR). V. The Magnetic Field at the Onset of High-mass Star Formation

A complete understanding of the initial conditions of high-mass star formation and what processes determine multiplicity require the study of the magnetic field (B-field) in young, massive cores. Using ALMA 250 GHz polarization (0.3" = 1000 au) and ALMA 220 GHz high-angular resolution observations (0.05" = 160 au), we have performed a full energy analysis including the B-field at core scales and have assessed what influences the multiplicity inside a massive core previously believed to be in the prestellar phase. With 31 Msun, the G11.92 MM2 core has a young CS outflow with a dynamical time scale of a few thousand years. At high-resolution, the MM2 core fragments into a binary system with a projected separation of 505 au and a binary mass ratio of 1.14. Using the DCF method with an ADF analysis, we estimate in this core a B-field strength of 6.2 mG and a mass-to-flux ratio of 18. The MM2 core is strongly subvirialized with a virial parameter of 0.064, including the B-field. The high mass-to-flux ratio and low virial parameter indicate that this massive core is very likely undergoing runaway collapse, which is in direct contradiction with the core-accretion model. The MM2 core is embedded in a filament that has a velocity gradient consistent with infall. In line with clump-fed scenarios, the core can grow in mass at a rate of 1.9--5.6 x 10^-4 Msun/yr. In spite of the B-field having only a minor contribution to the total energy budget at core scales, it likely plays a more important role at smaller scales by setting the binary properties. Considering energy ratios and a fragmentation criterion at the core scale, the binary could have been formed by core fragmentation. The binary properties (separation and mass ratio), however, are also consistent with radiation-magnetohydrodynamic simulations with super-Alfvenic, supersonic (or sonic) turbulence that form binaries by disk fragmentation.

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arXiv2024

The JCMT BISTRO Survey: The magnetised evolution of star-forming cores in the Ophiuchus Molecular Cloud interpreted using Histograms of Relative Orientation

The relationship between B-field orientation and density structure in molecular clouds is often assessed using the Histogram of Relative Orientations (HRO). We perform a plane-of-the-sky geometrical analysis of projected B-fields, by interpreting HROs in dense, spheroidal, prestellar and protostellar cores. We use James Clerk Maxwell Telescope (JCMT) POL-2 850 $μ$m polarisation maps and Herschel column density maps to study dense cores in the Ophiuchus molecular cloud complex. We construct two-dimensional core models, assuming Plummer column density profiles and modelling both linear and hourglass B-fields. We find high-aspect-ratio ellipsoidal cores produce strong HRO signals, as measured using the shape parameter $ξ$. Cores with linear fields oriented $< 45^{\circ}$ from their minor axis produce constant HROs with $-1 < ξ< 0$, indicating fields are preferentially parallel to column density gradients. Fields parallel to the core minor axis produce the most negative value of $ξ$. For low-aspect-ratio cores, $ξ\approx 0$ for linear fields. Hourglass fields produce a minimum in $ξ$ at intermediate densities in all cases, converging to the minor-axis-parallel linear field value at high and low column densities. We create HROs for six dense cores in Ophiuchus. $ρ$ Oph A and IRAS 16293 have high aspect ratios and preferentially negative HROs, consistent with moderately strong-field behaviour. $ρ$ Oph C, L1689A and L1689B have low aspect ratios, and $ξ\approx 0$. $ρ$ Oph B is too complex to be modelled using a simple spheroidal field geometry. We see no signature of hourglass fields, agreeing with previous findings that dense cores generally exhibit linear fields on these size scales.

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arXiv2024

The magnetic field in quiescent star-forming filament G16.96+0.27

We present 850 μm thermal dust polarization observations with a resolution of 14.4"(~ 0.13 pc) towards an infrared dark cloud G16.96+0.27 using JCMT/POL-2. The average magnetic field orientation, which roughly agrees with the larger-scale magnetic field orientation traced by the Planck 353 GHz data, is approximately perpendicular to the filament structure. The estimated plane-of-sky magnetic field strength is ~ 96 μG and ~ 60 μG using two variants of the Davis-Chandrasekhar-Fermi methods. We calculate the virial and magnetic critical parameters to evaluate the relative importance of gravity, the magnetic field, and turbulence. The magnetic field and turbulence are both weaker than gravity, but magnetic fields and turbulence together are equal to gravity, suggesting that G16.96+0.27 is in a quasi-equilibrium state. The cloud-magnetic-field alignment is found to have a trend moving away from perpendicularity in the dense regions, which may serve as a tracer of potential fragmentation in such quiescent filaments.

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arXiv2024

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

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

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arXiv2024

Magnetic Fields Under Feedback: A Case Study of the Massive Star-Forming Hub G34.26+0.15

We present 850$μ$m polarized observations of the molecular cloud G34.26+0.15 taken using the POL-2 polarimeter mounted on the James Clerk Maxwell Telescope (JCMT). G34.26+0.15 is a hub-filament system with ongoing high-mass star-formation, containing multiple HII regions. We extend the Histogram of Relative Orientations technique with an alternative application that considers the alignment of the magnetic field to the filaments and a HII region boundary, denoted as the filament alignment factor ($ξ_{F}$) and the ellipse alignment factor ($ξ_{E}$) respectively. Using these metrics, we find that, although in general the magnetic field aligns parallel to the filamentary structure within the system in the north-west, the magnetic field structure of G34.26+0.15 has been radically reshaped by the expansion of an evolved HII region in the south-east, which itself may have triggered further high-mass star formation in the cloud. Thus, we suggest high-mass star formation is both occurring through mass accretion as per the hub-filament model from one side, and through compression of gas under stellar feedback from the other. We also use HARP observations of C$^{18}$O from the CHIMPS survey to estimate the magnetic field strength across the cloud, finding strengths of $\sim$0.5-1.4 mG.

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arXiv2024

AtLAST Science Overview Report

Submillimeter and millimeter wavelengths provide a unique view of the Universe, from the gas and dust that fills and surrounds galaxies to the chromosphere of our own Sun. Current single-dish facilities have presented a tantalising view of the brightest (sub-)mm sources, and interferometers have provided the exquisite resolution necessary to analyse the details in small fields, but there are still many open questions that cannot be answered with current facilities. In this report we summarise the science that is guiding the design of the Atacama Large Aperture Submillimeter Telescope (AtLAST). We demonstrate how tranformational advances in topics including star formation in high redshift galaxies, the diffuse circumgalactic medium, Galactic ecology, cometary compositions and solar flares motivate the need for a 50m, single-dish telescope with a 1-2 degree field of view and a new generation of highly multiplexed continuum and spectral cameras. AtLAST will have the resolution to drastically lower the confusion limit compared to current single-dish facilities, whilst also being able to rapidly map large areas of the sky and detect extended, diffuse structures. Its high sensitivity and large field of view will open up the field of submillimeter transient science by increasing the probability of serendipitous detections. Finally, the science cases listed here motivate the need for a highly flexible operations model capable of short observations of individual targets, large surveys, monitoring programmes, target of opportunity observations and coordinated observations with other observatories. AtLAST aims to be a sustainable, upgradeable, multipurpose facility that will deliver orders of magnitude increases in sensitivity and mapping speeds over current and planned submillimeter observatories.

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arXiv2024

Magnetic Fields in Massive Star-forming Regions (MagMaR) IV: Tracing the Magnetic Fields in the O-type protostellar system IRAS 16547$-$4247

The formation of the massive stars, and in particular, the role that the magnetic fields play in their early evolutionary phase is still far from being completely understood. Here, we present Atacama Large Millimeter/Submillimeter Array (ALMA) 1.2 mm full polarized continuum, and H$^{13}$CO$^+$(3$-$2), CS(5$-$4), and HN$^{13}$C(3$-$2) line observations with a high angular resolution ($\sim$0.4$''$ or 1100 au). In the 1.2 mm continuum emission, we reveal a dusty envelope surrounding the massive protostars, IRAS16547-E and IRAS16547-W, with dimensions of $\sim$10,000 au. This envelope has a bi-conical structure likely carved by the powerful thermal radio jet present in region. The magnetic fields vectors follow very-well the bi-conical envelope. The polarization fraction is $\sim$2.0\% in this region. Some of these vectors seem to converge to IRAS 16547-E, and IRAS 16547-W, the most massive protostars. Moreover, the velocity fields revealed from the spectral lines H$^{13}$CO$^+$(3$-$2), and HN$^{13}$C(3$-$2) show velocity gradients with a good correspondence with the magnetic fields, that maybe are tracing the cavities of molecular outflows or maybe in some parts infall. We derived a magnetic field strength in some filamentary regions that goes from 2 to 6.1\,mG. We also find that the CS(5$-$4) molecular line emission reveals multiple outflow cavities or bow-shocks with different orientations, some of which seem to follow the NW-SE radio thermal jet.

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arXiv2024

Relative Alignments Between Magnetic Fields, Velocity Gradients, and Dust Emission Gradients in NGC 1333

Magnetic fields play an important role in shaping and regulating star formation in molecular clouds. Here, we present one of the first studies examining the relative orientations between magnetic ($B$) fields and the dust emission, gas column density, and velocity centroid gradients on the 0.02 pc (core) scales, using the BISTRO and VLA+GBT observations of the NGC 1333 star-forming clump. We quantified these relative orientations using the Project Rayleigh Statistic (PRS) and found preferential global parallel alignment between the $B$ field and dust emission gradients, consistent with large-scale studies with Planck. No preferential global alignments, however, are found between the $B$ field and velocity gradients. Local PRS calculated for subregions defined by either dust emission or velocity coherence further revealed that the $B$ field does not preferentially align with dust emission gradients in most emission-defined subregions, except in the warmest ones. The velocity-coherent structures, on the other hand, also showed no preferred $B$ field alignments with velocity gradients, except for one potentially bubble-compressed region. Interestingly, the velocity gradient magnitude in NGC 1333 ubiquitously features prominent ripple-like structures that are indicative of magnetohydrodynamic (MHD) waves. Finally, we found $B$ field alignments with the emission gradients to correlate with dust temperature and anticorrelate with column density, velocity dispersion, and velocity gradient magnitude. The latter two anticorrelations suggest that alignments between gas structures and $B$ fields can be perturbed by physical processes that elevate velocity dispersion and velocity gradients, such as infall, accretions, and MHD waves.

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arXiv2024

Magnetic Fields in Massive Star-forming Regions (MagMaR): Unveiling an Hourglass Magnetic Field in G333.46-0.16 using ALMA

The contribution of the magnetic field to the formation of high-mass stars is poorly understood. We report the high-angular resolution ($\sim0.3^{\prime\prime}$, 870 au) map of the magnetic field projected on the plane of the sky (B$_\mathrm{POS}$) towards the high-mass star forming region G333.46$-$0.16 (G333), obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) at 1.2 mm as part of the Magnetic Fields in Massive Star-forming Regions (MagMaR) survey. The B$_\mathrm{POS}$ morphology found in this region is consistent with a canonical ``hourglass'' which suggest a dynamically important field. This region is fragmented into two protostars separated by $\sim1740$ au. Interestingly, by analysing H$^{13}$CO$^{+}$ ($J=3-2$) line emission, we find no velocity gradient over the extend of the continuum which is consistent with a strong field. We model the B$_\mathrm{POS}$, obtaining a marginally supercritical mass-to-flux ratio of 1.43, suggesting an initially strongly magnetized environment. Based on the Davis-Chandrasekhar-Fermi method, the magnetic field strength towards G333 is estimated to be 5.7 mG. The absence of strong rotation and outflows towards the central region of G333 suggests strong magnetic braking, consistent with a highly magnetized environment. Our study shows that despite being a strong regulator, the magnetic energy fails to prevent the process of fragmentation, as revealed by the formation of the two protostars in the central region.

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arXiv2024

Magnetic Fields Observed along the E-W Outflow of IRAS 16293-2422

Magnetic fields likely play an important role in the formation of young protostars. Multiscale and multiwavelength dust polarization observations can reveal the inferred magnetic field from scales of the cloud to core to protostar. We present continuum polarization observations of the young protostellar triple system IRAS 16293-2422 at 89 $μ$m using HAWC+ on SOFIA. The inferred magnetic field is very uniform with an average field angle of 89$^\circ\pm$23$^\circ$ (E of N), which is different from the $\sim$170$^\circ$ field morphology seen at 850 $μ$m at larger scales (> 2000 au) with JCMT POL-2 and at 1.3 mm on smaller scales (< 300 au) with ALMA. The HAWC+ magnetic field direction is aligned with the known E-W outflow. This alignment difference suggests that the shorter wavelength HAWC+ data is tracing the magnetic field associated with warmer dust likely from the outflow cavity, whereas the longer wavelength data are tracing the bulk magnetic field from cooler dust. Also, we show in this source the dust emission peak is strongly affected by the observing wavelength. The dust continuum peaks closer to source B (northern source) at shorter wavelengths and progressively moves toward the southern A source with increasing wavelength (from 22 $μ$m to 850 $μ$m).

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arXiv2024

Atacama Large Aperture Submillimeter Telescope (AtLAST) Science: Our Galaxy

As we learn more about the multi-scale interstellar medium (ISM) of our Galaxy, we develop a greater understanding for the complex relationships between the large-scale diffuse gas and dust in Giant Molecular Clouds (GMCs), how it moves, how it is affected by the nearby massive stars, and which portions of those GMCs eventually collapse into star forming regions. The complex interactions of those gas, dust and stellar populations form what has come to be known as the ecology of our Galaxy. Because we are deeply embedded in the plane of our Galaxy, it takes up a significant fraction of the sky, with complex dust lanes scattered throughout the optically recognisable bands of the Milky Way. These bands become bright at (sub-)millimetre wavelengths, where we can study dust thermal emission and the chemical and kinematic signatures of the gas. To properly study such large-scale environments, requires deep, large area surveys that are not possible with current facilities. Moreover, where stars form, so too do planetary systems, growing from the dust and gas in circumstellar discs, to planets and planetesimal belts. Understanding the evolution of these belts requires deep imaging capable of studying belts around young stellar objects to Kuiper belt analogues around the nearest stars. Here we present a plan for observing the Galactic Plane and circumstellar environments to quantify the physical structure, the magnetic fields, the dynamics, chemistry, star formation, and planetary system evolution of the galaxy in which we live with AtLAST; a concept for a new, 50m single-dish sub-mm telescope with a large field of view which is the only type of facility that will allow us to observe our Galaxy deeply and widely enough to make a leap forward in our understanding of our local ecology.

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arXiv2024

Filamentary Network and Magnetic Field Structures Revealed with BISTRO in the High-Mass Star-Forming Region NGC2264 : Global Properties and Local Magnetogravitational Configurations

We report 850 $μ$m continuum polarization observations toward the filamentary high-mass star-forming region NGC 2264, taken as part of the B-fields In STar forming Regions Observations (BISTRO) large program on the James Clerk Maxwell Telescope (JCMT). These data reveal a well-structured non-uniform magnetic field in the NGC 2264C and 2264D regions with a prevailing orientation around 30 deg from north to east. Field strengths estimates and a virial analysis for the major clumps indicate that NGC 2264C is globally dominated by gravity while in 2264D magnetic, gravitational, and kinetic energies are roughly balanced. We present an analysis scheme that utilizes the locally resolved magnetic field structures, together with the locally measured gravitational vector field and the extracted filamentary network. From this, we infer statistical trends showing that this network consists of two main groups of filaments oriented approximately perpendicular to one another. Additionally, gravity shows one dominating converging direction that is roughly perpendicular to one of the filament orientations, which is suggestive of mass accretion along this direction. Beyond these statistical trends, we identify two types of filaments. The type-I filament is perpendicular to the magnetic field with local gravity transitioning from parallel to perpendicular to the magnetic field from the outside to the filament ridge. The type-II filament is parallel to the magnetic field and local gravity. We interpret these two types of filaments as originating from the competition between radial collapsing, driven by filament self-gravity, and the longitudinal collapsing, driven by the region's global gravity.

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arXiv2023

Magnetic fields of the starless core L 1512

We present JCMT POL-2 850 um dust polarization observations and Mimir H band stellar polarization observations toward the starless core L1512. We detect the highly-ordered core-scale magnetic field traced by the POL-2 data, of which the field orientation is consistent with the parsec-scale magnetic fields traced by Planck data, suggesting the large-scale fields thread from the low-density region to the dense core region in this cloud. The surrounding magnetic field traced by the Mimir data shows a wider variation in the field orientation, suggesting there could be a transition of magnetic field morphology at the envelope scale. L1512 was suggested to be presumably older than 1.4 Myr in a previous study via time-dependent chemical analysis, hinting that the magnetic field could be strong enough to slow the collapse of L1512. In this study, we use the Davis-Chandrasekhar-Fermi method to derive a plane-of-sky magnetic field strength ($B_{pos}$) of 18$\pm$7 uG and an observed mass-to-flux ratio ($λ_{obs}$) of 3.5$\pm$2.4, suggesting that L1512 is magnetically supercritical. However, the absence of significant infall motion and the presence of an oscillating envelope are inconsistent with the magnetically supercritical condition. Using a Virial analysis, we suggest the presence of a hitherto hidden line-of-sight magnetic field strength of ~27 uG with a mass-to-flux ratio ($λ_{tot}$) of ~1.6, in which case both magnetic and kinetic pressures are important in supporting the L1512 core. On the other hand, L1512 may have just reached supercriticality and will collapse at any time.

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arXiv2023

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

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

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arXiv2023

Magnetic fields in the Horsehead Nebula

We present the first polarized dust emission measurements of the Horsehead Nebula, obtained using the POL-2 polarimeter on the Submillimetre Common-User Bolometer Array 2 (SCUBA-2) camera on the James Clerk Maxwell Telescope (JCMT). The Horsehead Nebula contains two sub-millimeter sources, a photodissociation region (PDR; SMM1) and a starless core (SMM2). We see well-ordered magnetic fields in both sources. We estimated plane-of-sky magnetic field strengths of 56$\pm$9 and 129$\pm$21 $μ$G in SMM1 and SMM2, respectively, and obtained mass-to-flux ratios and Alfvén Mach numbers of less than 0.6, suggesting that the magnetic field can resist gravitational collapse and that magnetic pressure exceeds internal turbulent pressure in these sources. In SMM2, the kinetic and gravitational energies are comparable to one another, but less than the magnetic energy. We suggest a schematic view of the overall magnetic field structure in the Horsehead Nebula. Magnetic field lines in SMM1 appear have been compressed and reordered during the formation of the PDR, while the likely more-embedded SMM2 may have inherited its field from that of the pre-shock molecular cloud. The magnetic fields appear to currently play an important role in supporting both sources.

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arXiv2023

The JCMT Nearby Galaxies Legacy Survey: SCUBA-2 observations of nearby galaxies

We present 850$μ$m observations of a sample of 8 nearby spiral galaxies, made using the SCUBA-2 camera on the James Clerk Maxwell Telescope (JCMT) as part of the JCMT Nearby Galaxies Legacy Survey (NGLS). We corrected our data for the presence of the $^{12}$CO $J=3\to 2$ line in the SCUBA-2 850$μ$m bandwidth using NGLS HARP data, finding a typical $^{12}$CO contribution of $\sim 20$%. We measured dust column densities, temperatures and opacity indices by fitting spectral energy distributions constructed from SCUBA-2 and archival Herschel observations, and used archival GALEX and Spitzer data to make maps of surface density of star formation ($Σ_{\rm SFR}$). Typically, comparing SCUBA-2-derived H$_2$ surface densities ($Σ_{\rm H_2}$) to $Σ_{\rm SFR}$ gives shallow star formation law indices within galaxies, with SCUBA-2-derived values typically being sublinear and Herschel-derived values typically being broadly linear. This difference is likely due to the effects of atmospheric filtering on the SCUBA-2 data. Comparing the mean values of $Σ_{\rm H_2}$ and $Σ_{\rm SFR}$ of the galaxies in our sample returns a steeper star formation law index, broadly consistent with both the Kennicutt-Schmidt value of 1.4 and linearity. Our results show that a SCUBA-2 detection is a good predictor of star formation. We suggest that Herschel emission traces gas in regions which will form stars on timescales $\sim 5-100$ Myr, comparable to the star formation timescale traced by GALEX and Spitzer data, while SCUBA-2 preferentially traces the densest gas within these regions, which likely forms stars on shorter timescales.

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