arXiv subjects

Rowan J. Smith

Publications and source records attributed to Rowan J. Smith.

At least 37 records · Page 2Linked to original sources

arXiv2023

Magnetic fields do not suppress global star formation in low metallicity dwarf galaxies

Many studies concluded that magnetic fields suppress star formation in molecular clouds and Milky Way like galaxies. However, most of these studies are based on fully developed fields that have reached the saturation level, with little work on investigating how an initial weak primordial field affects star formation in low metallicity environments. In this paper, we investigate the impact of a weak initial field on low metallicity dwarf galaxies. We perform high-resolution AREPO simulations of five isolated dwarf galaxies. Two models are hydrodynamical, two start with a primordial magnetic field of 10$^{-6} μ$G and different sub-solar metallicities, and one starts with a saturated field of 10$^{-2} μ$G. All models include a non-equilibrium, time-dependent chemical network that includes the effects of gas shielding from the ambient ultraviolet field. Sink particles form directly from the gravitational collapse of gas and are treated as star-forming clumps that can accrete gas. We vary the ambient uniform far ultraviolet field, and cosmic ray ionization rate between 1\% and 10\% of solar values. We find that the magnetic field has little impact on the global star formation rate, which is in tension with some previously published results. We further find that the initial field strength has little impact on the global star formation rate. We show that an increase in the mass fractions of both molecular hydrogen and cold gas, along with changes in the perpendicular gas velocity dispersion and the magnetic field acting in the weak-field model, overcome the expected suppression in star formation.

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arXiv2023

PHANGS-JWST First Results: The Dust Filament Network of NGC 628 and its Relation to Star Formation Activity

PHANGS-JWST mid-infrared (MIR) imaging of nearby spiral galaxies has revealed ubiquitous filaments of dust emission in intricate detail. We present a pilot study to systematically map the dust filament network (DFN) at multiple scales between 25-400 pc in NGC 628. MIRI images at 7.7, 10, 11.3 and 21$μ$m of NGC 628 are used to generate maps of the filaments in emission, while PHANGS-HST B-band imaging yields maps of dust attenuation features. We quantify the correspondence between filaments traced by MIR thermal continuum / polycyclic aromatic hydrocarbon (PAH) emission and filaments detected via extinction / scattering of visible light; the fraction of MIR flux contained in the DFN; and the fraction of HII regions, young star clusters and associations within the DFN. We examine the dependence of these quantities with the physical scale at which the DFN is extracted. With our highest resolution DFN maps (25 pc filament width), we find that filaments in emission and attenuation are co-spatial in 40% of sight lines, often exhibiting detailed morphological agreement; that ~30% of the MIR flux is associated with the DFN; and that 75-80% of HII regions and 60% of star clusters younger than 5 Myr are contained within the DFN. However, the DFN at this scale is anti-correlated with looser associations of stars younger than 5 Myr identified using PHANGS-HST near-UV imaging. We discuss the impact of these findings for studies of star formation and the ISM, and the broad range of new investigations enabled with multi-scale maps of the DFN.

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arXiv2022

PHANGS-JWST First Results: Tracing the Diffuse ISM with JWST Imaging of Polycyclic Aromatic Hydrocarbon Emission in Nearby Galaxies

JWST observations of polycyclic aromatic hydrocarbon (PAH) emission provide some of the deepest and highest resolution views of the cold interstellar medium (ISM) in nearby galaxies. If PAHs are well mixed with the atomic and molecular gas and illuminated by the average diffuse interstellar radiation field, PAH emission may provide an approximately linear, high resolution, high sensitivity tracer of diffuse gas surface density. We present a pilot study that explores using PAH emission in this way based on MIRI observations of IC 5332, NGC 628, NGC 1365, and NGC 7496 from the PHANGS-JWST Treasury. Using scaling relationships calibrated in Leroy et al. (2022), scaled F1130W provides 10--40 pc resolution and 3$σ$ sensitivity of $Σ_{\rm gas} \sim 2$ M$_\odot$ pc$^{-2}$. We characterize the surface densities of structures seen at $< 7$ M$_\odot$ pc$^{-2}$ in our targets, where we expect the gas to be HI-dominated. We highlight the existence of filaments, inter-arm emission, and holes in the diffuse ISM at these low surface densities. Below $\sim 10$ M$_\odot$ pc$^{-2}$ for NGC 628, NGC 1365, and NGC 7496 the gas distribution shows a ``Swiss cheese''-like topology due to holes and bubbles pervading the relatively smooth distribution of diffuse ISM. Comparing to recent galaxy simulations, we observe similar topology for the low surface density gas, though with notable variations between simulations with different setups and resolution. Such a comparison of high resolution, low surface density gas with simulations is not possible with existing atomic and molecular gas maps, highlighting the unique power of JWST maps of PAH emission.

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arXiv2022

PHANGS--JWST First Results: ISM structure on the turbulent Jeans scale in four disk galaxies observed by JWST and ALMA

JWST/MIRI imaging of the nearby galaxies IC 5332, NGC 628, NGC 1365 and NGC 7496 from PHANGS reveals a richness of gas structures that in each case form a quasi-regular network of interconnected filaments, shells and voids. We examine whether this multi-scale network of structure is consistent with the fragmentation of the gas disk through gravitational instability. We use FilFinder to detect the web of filamentary features in each galaxy and determine their characteristic radial and azimuthal spacings. These spacings are then compared to estimates of the most Toomre-unstable length (a few kpc), the turbulent Jeans length (a few hundred pc) and the disk scale height (tens of pc) reconstructed using PHANGS-ALMA observations of the molecular gas as a dynamical tracer. Our analysis of the four galaxies targeted in this work indicates that Jeans-scale structure is pervasive. Future work will be essential for determining how the structure observed in gas disks impacts not only the rate and location of star formation but also how stellar feedback interacts positively or negatively with the surrounding multi-phase gas reservoir.

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arXiv2022

PHANGS-JWST First Results: Duration of the early phase of massive star formation in NGC628

The earliest stages of star formation, when young stars are still deeply embedded in their natal clouds, represent a critical phase in the matter cycle between gas clouds and young stellar regions. Until now, the high-resolution infrared observations required for characterizing this heavily obscured phase (during which massive stars have formed, but optical emission is not detected) could only be obtained for a handful of the most nearby galaxies. One of the main hurdles has been the limited angular resolution of the Spitzer Space Telescope. With the revolutionary capabilities of the JWST, it is now possible to investigate the matter cycle during the earliest phases of star formation as a function of the galactic environment. In this Letter, we demonstrate this by measuring the duration of the embedded phase of star formation and the implied time over which molecular clouds remain inert in the galaxy NGC628 at a distance of 9.8Mpc, demonstrating that the cosmic volume where this measurement can be made has increased by a factor of $>100$ compared to Spitzer. We show that young massive stars remain embedded for $5.1_{-1.4}^{+2.7}$Myr ($2.3_{-1.4}^{+2.7}$Myr of which being heavily obscured), representing $\sim20\%$ of the total cloud lifetime. These values are in broad agreement with previous measurements in five nearby ($D < 3.5$Mpc) galaxies and constitute a proof of concept for the systematic characterization of the early phase of star formation across the nearby galaxy population with the PHANGS-JWST survey.

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arXiv2022

The PHANGS-JWST Treasury Survey: Star Formation, Feedback, and Dust Physics at High Angular resolution in Nearby GalaxieS

The PHANGS collaboration has been building a reference dataset for the multi-scale, multi-phase study of star formation and the interstellar medium in nearby galaxies. With the successful launch and commissioning of JWST, we can now obtain high-resolution infrared imaging to probe the youngest stellar populations and dust emission on the scales of star clusters and molecular clouds ($\sim$5-50 pc). In Cycle 1, PHANGS is conducting an 8-band imaging survey from 2-21$μ$m of 19 nearby spiral galaxies. CO(2-1) mapping, optical integral field spectroscopy, and UV-optical imaging for all 19 galaxies have been obtained through large programs with ALMA, VLT/MUSE, and Hubble. PHANGS-JWST enables a full inventory of star formation, accurate measurement of the mass and age of star clusters, identification of the youngest embedded stellar populations, and characterization of the physical state of small dust grains. When combined with Hubble catalogs of $\sim$10,000 star clusters, MUSE spectroscopic mapping of $\sim$20,000 HII regions, and $\sim$12,000 ALMA-identified molecular clouds, it becomes possible to measure the timescales and efficiencies of the earliest phases of star formation and feedback, build an empirical model of the dependence of small dust grain properties on local ISM conditions, and test our understanding of how dust-reprocessed starlight traces star formation activity, all across a diversity of galactic environments. Here we describe the PHANGS-JWST Treasury survey, present the remarkable imaging obtained in the first few months of science operations, and provide context for the initial results presented in the first series of PHANGS-JWST publications.

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arXiv2022

PHANGS-JWST First Results: Multi-wavelength view of feedback-driven bubbles (The Phantom Voids) across NGC 628

We present a high-resolution view of bubbles within The Phantom Galaxy (NGC 628); a nearby (~10Mpc), star-forming (~2Msun/yr), face-on (i~9deg) grand-design spiral galaxy. With new data obtained as part of the PHANGS-JWST treasury program, we perform a detailed case-study of two regions of interest, one of which contains the largest and most prominent bubble in the galaxy (The Phantom Void; over 1kpc in diameter), and the other being a smaller region that may be the precursor to such a large bubble (The Precursor Phantom Void). When comparing to matched resolution Halpha observations from the Hubble Space Telescope (HST), we see that the ionized gas is brightest in the shells of both bubbles, and is coincident with the youngest (~1Myr) and most massive (~100,000Msun) stellar associations. We also find an older generation (~20Myr) of stellar associations is present within the bubble of The Phantom Void. From our kinematic analysis of the HI, H2 (CO) and HII gas across The Phantom Void, we infer a high expansion speed of around 15 to 50km/s. The large size and high expansion speed of The Phantom Void suggest that the driving mechanism is sustained stellar feedback due to multiple mechanisms, where early feedback first cleared a bubble (as we observe now in The Precursor Phantom Void), and since then SNe have been exploding within the cavity, and have accelerated the shell. Finally, comparison to simulations shows a striking resemblance to our JWST observations, and suggests that such large-scale stellar feedback-driven bubbles should be common within other galaxies.

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arXiv2022

Filament Formation via Collision-induced Magnetic Reconnection -- Formation of a Star Cluster

A collision-induced magnetic reconnection (CMR) mechanism was recently proposed to explain the formation of a filament in the Orion A molecular cloud. In this mechanism, a collision between two clouds with antiparallel magnetic fields produces a dense filament due to the magnetic tension of the reconnected fields. The filament contains fiber-like sub-structures and is confined by a helical magnetic field. To show whether the dense filament is capable of forming stars, we use the \textsc{Arepo} code with sink particles to model star formation following the formation of the CMR-filament. First, the CMR-filament formation is confirmed with \textsc{Arepo}. Second, the filament is able to form a star cluster after it collapses along its main axis. Compared to the control model without magnetic fields, the CMR model shows two distinctive features. First, the CMR-cluster is confined to a factor of $\sim4$ smaller volume. The confinement is due to the combination of the helical field and gravity. Second, the CMR model has a factor of $\sim2$ lower star formation rate. The slower star formation is again due to the surface helical field that hinders gas inflow from larger scales. Mass is only supplied to the accreting cluster through streamers.

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arXiv2022

The Galactic dynamics revealed by the filamentary structure in atomic hydrogen emission

We present a study of the filamentary structure in the atomic hydrogen (HI) emission at the 21 cm wavelength toward the Galactic plane using the observations in the HI4PI survey. Using the Hessian matrix method across radial velocity channels, we identified the filamentary structures and quantified their orientations using circular statistics. We found that the regions of the Milky Way's disk beyond 10 kpc and up to roughly 18 kpc from the Galactic center display HI filamentary structures predominantly parallel to the Galactic plane. For regions at lower Galactocentric radii, we found that the HI filaments are mostly perpendicular or do not have a preferred orientation with respect to the Galactic plane. We interpret these results as the imprint of supernova feedback in the inner Galaxy and Galactic rotation in the outer Milky Way. We found that the HI filamentary structures follow the Galactic warp and that they highlight some of the variations interpreted as the effect of the gravitational interaction with satellite galaxies. In addition, the mean scale height of the filamentary structures is lower than that sampled by the bulk of the HI emission, thus indicating that the cold and warm atomic hydrogen phases have different scale heights in the outer galaxy. Finally, we found that the fraction of the column density in HI filaments is almost constant up to approximately 18 kpc from the Galactic center. This is possibly a result of the roughly constant ratio between the cold and warm atomic hydrogen phases inferred from the HI absorption studies. Our results indicate that the HI filamentary structures provide insight into the dynamical processes shaping the Galactic disk. Their orientations record how and where the stellar energy input, the Galactic fountain process, the cosmic ray diffusion, and the gas accretion have molded the diffuse interstellar medium in the Galactic plane.

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arXiv2021

Is the molecular KS relationship universal down to low metallicities?

In recent years it has been speculated that in extreme low metallicity galactic environments, stars form in regions that lack H2. In this paper we investigate how changing the metallicity and UV-field strength of a galaxy affects the star formation within, and the molecular gas Kennicutt-Schmidt relation. Using extremely high resolution arepo simulations of isolated dwarf galaxies, we independently vary the metallicity and UV-field to between 1% and 10% solar neighbourhood values. We include a non-equilibrium, time-dependant chemical network to model the molecular composition of the ISM, and include the effects of gas shielding from an ambient UV field. Crucially our simulations directly model the gravitational collapse of gas into star-forming clumps and cores and their subsequent accretion using sink particles. In this first publication we find that reducing the metallicity and UV-field by a factor of 10 has no effect on star formation, and minimal effect on the cold, dense star forming gas. The cold gas depletion times are almost an order of magnitude longer than the molecular gas depletion time due to the presence of star formation in HI dominated cold gas. We study the H2 Kennicutt-Schmidt relationship that arises naturally within the simulations and find a near linear power law index of N = 1.09 +/- 0.014 in our fiducial 10% solar metallicity model. As the metallicity and UV-field are reduced this becomes moderately steeper, with a slope of N = 1.24 +/- 0.022 for our 1% solar metallicity and 1% solar UV field model.

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arXiv2021

SIGAME v3: Gas Fragmentation in Post-processing of Cosmological Simulations for More Accurate Infrared Line Emission Modeling

We present an update to the framework called SImulator of GAlaxy Millimeter/submillimeter Emission (SÍGAME). SÍGAME derives line emission in the far-infrared (FIR) for galaxies in particle-based cosmological hydrodynamics simulations by applying radiative transfer and physics recipes via a post-processing step after completion of the simulation. In this version, a new technique is developed to model higher gas densities by parametrizing the gas density probability distribution function (PDF) in higher resolution simulations for use as a look-up table, allowing for more adaptive PDFs than in previous work. SÍGAME v3 is tested on redshift z = 0 galaxies drawn from the SIMBA cosmological simulation for eight FIR emission lines tracing vastly different interstellar medium phases. Including dust radiative transfer with SKIRT and high resolution photo-ionization models with Cloudy, this new method is able to self-consistently reproduce observed relations between line luminosity and star formation rate in all cases, except for [NII]122, [NII]205 and [OI]63, the luminosities of which are overestimated by median factors of 1.6, 1.2 and 1.2 dex, respectively. We attribute the remaining disagreement with observations to the lack of precise attenuation of the interstellar light on subgrid scales (<200 pc).

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arXiv2021

Dynamically Driven Inflow onto the Galactic Center and its Effect upon Molecular Clouds

The Galactic bar plays a critical role in the evolution of the Milky Way's Central Molecular Zone (CMZ), driving mass inward toward the Galactic Center via gas flows known as dust lanes. To explore the interaction between the CMZ and the dust lanes, we run hydrodynamic simulations in AREPO, modeling the potential of the Milky Way's bar in the absence of gas self-gravity and star formation physics, and we study the flows of mass using Monte Carlo tracer particles. We estimate the efficiency of the inflow via the dust lanes, finding that only about a third (30$\pm$12%) of the dust lanes' mass initially accretes onto the CMZ, while the rest overshoots and accretes later. Given observational estimates of the amount of gas within the Milky Way's dust lanes, this suggests that the true total inflow rate onto the CMZ is 0.8$\pm$0.6 M$_\odot$~yr$^{-1}$. Clouds in this simulated CMZ have sudden peaks in their average density near the apocenter, where they undergo violent collisions with inflowing material. While these clouds tend to counter-rotate due to shear, co-rotating clouds occasionally occur due to the injection of momentum from collisions with inflowing material (~52% are strongly counter-rotating, and ~7% are strongly co-rotating of the 44 cloud sample). We investigate the formation and evolution of these clouds, finding that they are fed by many discrete inflow events, providing a consistent source of gas to CMZ clouds even as they collapse and form stars

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arXiv2021

ALMA observations of the Extended Green Object G19.01$-$0.03: I. A Keplerian disc in a massive protostellar system

Using the Atacama Large Millimetre/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA), we observed the Extended Green Object (EGO) G19.01$-$0.03 with sub-arcsecond resolution from 1.05 mm to 5.01 cm wavelengths. Our $\sim0.4''\sim1600$ AU angular resolution ALMA observations reveal a velocity gradient across the millimetre core MM1, oriented perpendicular to the previously known bipolar molecular outflow, that is consistently traced by 20 lines of 8 molecular species with a range of excitation temperatures, including complex organic molecules (COMs). Kinematic modelling shows the data are well described by models that include a disc in Keplerian rotation and infall, with an enclosed mass of $40-70 \mathrm{M}_{\odot}$ (within a 2000 AU outer radius) for a disc inclination angle of $i=40^{\circ}$, of which $5.4-7.2 \mathrm{M}_{\odot}$ is attributed to the disc. Our new VLA observations show that the 6.7 GHz Class II methanol masers associated with MM1 form a partial ellipse, consistent with an inclined ring, with a velocity gradient consistent with that of the thermal gas. The disc-to-star mass ratio suggests the disc is likely to be unstable and may be fragmenting into as-yet-undetected low mass stellar companions. Modelling the centimetre--millimetre spectral energy distribution of MM1 shows the ALMA 1.05 mm continuum emission is dominated by dust, whilst a free-free component, interpreted as a hypercompact HII region, is required to explain the VLA $\sim$5 cm emission. The high enclosed mass derived for a source with a moderate bolometric luminosity ($\sim$10$^{4} \mathrm{L}_{\odot}$) suggests that the MM1 disc may feed an unresolved high-mass binary system.

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arXiv2021

Simulations of the star-forming molecular gas in an interacting M51-like galaxy: cloud population statistics

To investigate how molecular clouds react to different environmental conditions at a galactic scale, we present a catalogue of giant molecular clouds resolved down to masses of $\sim 10$~M$_{\odot}$ from a simulation of the entire disc of an interacting M51-like galaxy and a comparable isolated galaxy. Our model includes time-dependent gas chemistry, sink particles for star formation and supernova feedback, meaning we are not reliant on star formation recipes based on threshold densities and can follow the physics of the cold molecular phase. We extract giant molecular clouds at a given timestep of the simulations and analyse their properties. In the disc of our simulated galaxies, spiral arms seem to act merely as snowplows, gathering gas and clouds without dramatically affecting their properties. In the centre of the galaxy, on the other hand, environmental conditions lead to larger, more massive clouds. While the galaxy interaction has little effect on cloud masses and sizes, it does promote the formation of counter-rotating clouds. We find that the identified clouds seem to be largely gravitationally unbound at first glance, but a closer analysis of the hierarchical structure of the molecular interstellar medium shows that there is a large range of virial parameters with a smooth transition from unbound to mostly bound for the densest structures. The common observation that clouds appear to be virialised entities may therefore be due to CO bright emission highlighting a specific level in this hierarchical binding sequence. The small fraction of gravitationally bound structures found suggests that low galactic star formation efficiencies may be set by the process of cloud formation and initial collapse.

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arXiv2021

High-resolution CARMA Observation of Molecular Gas in the North America and Pelican Nebulae

We present the first results from a CARMA high-resolution $^{12}$CO(1-0), $^{13}$CO(1-0), and C$^{18}$O(1-0) molecular line survey of the North America and Pelican (NAP) Nebulae. CARMA observations have been combined with single-dish data from the Purple Mountain 13.7m telescope to add short spacings and produce high-dynamic-range images. We find that the molecular gas is predominantly shaped by the W80 HII bubble that is driven by an O star. Several bright rims are probably remnant molecular clouds heated and stripped by the massive star. Matching these rims in molecular lines and optical images, we construct a model of the three-dimensional structure of the NAP complex. Two groups of molecular clumps/filaments are on the near side of the bubble, one being pushed toward us, whereas the other is moving toward the bubble. Another group is on the far side of the bubble and moving away. The young stellar objects in the Gulf region reside in three different clusters, each hosted by a cloud from one of the three molecular clump groups. Although all gas content in the NAP is impacted by feedback from the central O star, some regions show no signs of star formation, while other areas clearly exhibit star formation activity. Other molecular gas being carved by feedback includes the cometary structures in the Pelican Head region and the boomerang features at the boundary of the Gulf region. The results show that the NAP complex is an ideal place for the study of feedback effects on star formation.

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arXiv2021

The Core Mass Function in the Orion Nebula Cluster Region: What Determines the Final Stellar Masses?

Applying dendrogram analysis to the CARMA-NRO C$^{18}$O ($J$=1--0) data having an angular resolution of $\sim$ 8", we identified 692 dense cores in the Orion Nebula Cluster (ONC) region. Using this core sample, we compare the core and initial stellar mass functions in the same area to quantify the step from cores to stars. About 22 \% of the identified cores are gravitationally bound. The derived core mass function (CMF) for starless cores has a slope similar to Salpeter's stellar initial mass function (IMF) for the mass range above 1 $M_\odot$, consistent with previous studies. Our CMF has a peak at a subsolar mass of $\sim$ 0.1 $M_\odot$, which is comparable to the peak mass of the IMF derived in the same area. We also find that the current star formation rate is consistent with the picture in which stars are born only from self-gravitating starless cores. However, the cores must gain additional gas from the surroundings to reproduce the current IMF (e.g., its slope and peak mass), because the core mass cannot be accreted onto the star with a 100\% efficiency. Thus, the mass accretion from the surroundings may play a crucial role in determining the final stellar masses of stars.

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arXiv2020

The Cloud Factory II: Gravoturbulent Kinematics of Resolved Molecular Clouds in a Galactic Potential

We present a statistical analysis of the gravoturbulent velocity fluctuations in molecular cloud complexes extracted from our "Cloud Factory" galactic-scale ISM simulation suite. For this purpose, we produce non-LTE $^{12}$CO J=1-0 synthetic observations and apply the Principal Component Analysis (PCA) reduction technique on a representative sample of cloud complexes. The velocity fluctuations are self-consistently generated by different physical mechanisms at play in our simulations, which include galactic-scale forces, gas self-gravity, and supernova feedback. The statistical analysis suggests that, even though purely gravitational effects are necessary to reproduce standard observational laws, they are not sufficient in most cases. We show that the extra injection of energy from supernova explosions plays a key role in establishing the global turbulent field and the local dynamics and morphology of molecular clouds. Additionally, we characterise structure function scaling parameters as a result of cloud environmental conditions: some of the complexes are immersed in diffuse (inter-arm) or dense (spiral-arm) environments, and others are influenced by embedded or external supernovae. In quiescent regions, we obtain time-evolving trajectories of scaling parameters driven by gravitational collapse and supersonic turbulent flows. Our findings suggests that a PCA-based statistical study is a robust method to diagnose the physical mechanisms that drive the gravoturbulent properties of molecular clouds. Also, we present a new open source module, the PCAFACTORY, which smartly performs PCA to extract velocity structure functions from simulated or real data of the ISM in a user-friendly way. Software DOI: 10.5281/zenodo.3822718

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arXiv2020

The CARMA-NRO Orion Survey: Filament Formation via Collision-Induced Magnetic Reconnection -- The Stick in Orion A

A unique filament is identified in the {\it Herschel} maps of the Orion A giant molecular cloud. The filament, which, we name the Stick, is ruler-straight and at an early evolutionary stage. Transverse position-velocity diagrams show two velocity components closing in on the Stick. The filament shows consecutive rings/forks in C$^{18}$O(1-0) channel maps, which is reminiscent of structures generated by magnetic reconnection. We propose that the Stick formed via collision-induced magnetic reconnection (CMR). We use the magnetohydrodynamics (MHD) code Athena++ to simulate the collision between two diffuse molecular clumps, each carrying an anti-parallel magnetic field. The clump collision produces a narrow, straight, dense filament with a factor of $>$200 increase in density. The production of the dense gas is seven times faster than free-fall collapse. The dense filament shows ring/fork-like structures in radiative transfer maps. Cores in the filament are confined by surface magnetic pressure. CMR can be an important dense-gas-producing mechanism in the Galaxy and beyond.

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