arXiv subjects

Paola Caselli

Publications and source records attributed to Paola Caselli.

At least 163 records · Page 9Linked to original sources

arXiv2020

Velocity-coherent Filaments in NGC 1333: Evidence for Accretion Flow?

Recent observations of global velocity gradients across and along molecular filaments have been interpreted as signs of gas accreting onto and along these filaments, potentially feeding star-forming cores and proto-clusters. The behavior of velocity gradients in filaments, however, has not been studied in detail, particularly on small scales (< 0.1 pc). In this paper, we present MUFASA, an efficient, robust, and automatic method to fit ammonia lines with multiple velocity components, generalizable to other molecular species. We also present CRISPy, a Python package to identify filament spines in 3D images (e.g., position-position-velocity cubes), along with a complementary technique to sort fitted velocity components into velocity-coherent filaments. In NGC 1333, we find a wealth of velocity gradient structures on a beam-resolved scale of ~0.05 pc. Interestingly, these local velocity gradients are not randomly oriented with respect to filament spines and their perpendicular, i.e., radial, component decreases in magnitude towards the spine for many filaments. Together with remarkably constant velocity gradients on larger scales along many filaments, these results suggest a scenario in which gas falling onto filaments is progressively damped and redirected to flow along these filaments.

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arXiv2020

Seeds of Life in Space (SOLIS). VI. Chemical evolution of sulfuretted species along the outflows driven by the low-mass protostellar binary NGC1333-IRAS4A

Context. Low-mass protostars drive powerful molecular outflows that can be observed with mm and sub-mm telescopes. Various sulfuretted species are known to be bright in shocks and could be used to infer the physical and chemical conditions throughout the observed outflows. Aims. The evolution of sulfur chemistry is studied along the outflows driven by the NGC1333-IRAS4A protobinary system located in the Perseus cloud to constrain the physical and chemical processes at work in shocks. Methods. We observed various transitions from OCS, CS, SO, and SO$_2$ towards NGC1333-IRAS4A in the 1.3, 2, and 3mm bands using the IRAM NOEMA array and we interpreted the observations through the use of the Paris-Durham shock model. Results. The targeted species clearly show different spatial emission along the two outflows driven by IRAS4A. OCS is brighter on small and large scales along the south outflow driven by IRAS4A1, whereas SO$_2$ is detected rather along the outflow driven by IRAS4A2 that is extended along the north east - south west (NE-SW) direction. Column density ratio maps estimated from a rotational diagram analysis allowed us to confirm a clear gradient of the OCS/SO$_2$ column density ratio between the IRAS4A1 and IRAS4A2 outflows. SO is detected at extremely high radial velocity up to 25 km/s relative to the source velocity, clearly allowing us to distinguish the two outflows on small scales. Conclusions. The observed chemical differentiation between the two outflows of the IRAS4A system could be explained by a different chemical history. The outflow driven by IRAS4A1 is likely younger and more enriched in species initially formed in interstellar ices, such as OCS, and recently sputtered into the shock gas. In contrast, the longer and likely older outflow triggered by IRAS4A2 is more enriched in species that have a gas phase origin, such as SO$_2$.

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arXiv2020

Impact of magneto-rotational instability on grain growth in protoplanetary disks: I. Relevant turbulence properties

Turbulence in the protoplanetary disks induces collisions between dust grains, and thus facilitates grain growth. We investigate the two fundamental assumptions of the turbulence in obtaining grain collisional velocities -- the kinetic energy spectrum and the turbulence autocorrelation time -- in the context of the turbulence generated by the magneto-rotational instability (MRI). We carry out numerical simulations of the MRI as well as driven turbulence, for a range of physical and numerical parameters. We find that the convergence of the turbulence $α$-parameter does not necessarily imply the convergence of the energy spectrum. The MRI turbulence is largely solenoidal, for which we observe a persistent kinetic energy spectrum of $k^{-4/3}$. The same is obtained for solenoidal driven turbulence with and without magnetic field, over more than 1 dex near the dissipation scale. This power-law slope appears to be converged in terms of numerical resolution, and to be due to the bottleneck effect. The kinetic energy in the MRI turbulence peaks at the fastest growing mode of the MRI. In contrast, the magnetic energy peaks at the dissipation scale. The magnetic energy spectrum in the MRI turbulence does not show a clear power-law range, and is almost constant over approximately 1 dex near the dissipation scale. The turbulence autocorrelation time is nearly constant at large scales, limited by the shearing timescale, and shows a power-law drop close to $k^{-1}$ at small scales, with a slope steeper than that of the eddy crossing time. The deviation from the standard picture of the Kolmogorov turbulence with the injection scale at the disk scale height can potentially have a significant impact on the grain collisional velocities.

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arXiv2019

Efficient Production of S$_8$ in Interstellar Ices: The effects of cosmic ray-driven radiation chemistry and non-diffusive bulk reactions

In this work, we reexamine sulfur chemistry occurring on and in the ice mantles of interstellar dust grains, and report the effects of two new modifications to standard astrochemical models; namely, (a) the incorporation of cosmic ray-driven radiation chemistry and (b) the assumption of fast, non-diffusive reactions for key radicals in the bulk. Results from our models of dense molecular clouds show that these changes can have a profound influence on the abundances of sulfur-bearing species in ice mantles, including a reduction in the abundance of solid-phase H$_2$S and HS, and a significant increase in the abundances of OCS, SO$_2$, as well as pure allotropes of sulfur, especially S$_8$. These pure-sulfur species - though nearly impossible to observe directly - have long been speculated to be potential sulfur reservoirs and our results represent possibly the most accurate estimates yet of their abundances in the dense ISM. Moreover, the results of these updated models are found to be in good agreement with available observational data. Finally, we examine the implications of our findings with regard to the as-yet-unknown sulfur reservoir thought to exist in dense interstellar environments.

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arXiv2019

The first steps of Interstellar Phosphorus Chemistry

Phosphorus-bearing species are an essential key to form life on Earth, however they have barely been detected in the interstellar medium. Since only PN and PO have been identified so far towards star-forming regions, the chemical formation pathways of P-bearing molecules are not easy to constrain and are thus highly debatable. An important factor still missing in the chemical models is the initial elemental abundance of phosphorus, i.e. the depletion level of P. In order to overcome this problem, we study P-bearing species in diffuse/translucent clouds. In these objects phosphorus is mainly in the gas phase and therefore the elemental initial abundance needed in our chemical simulations corresponds to the cosmic one and is thus well constrained. An advanced chemical model with an updated P-chemistry network has been used. Single-pointing observations were performed with the IRAM 30m telescope towards the line of sight to the blazar B0355+508 aiming for the (2-1) transitions of PN, PO, HCP and CP. This line of sight incorporates five diffuse/translucent clouds. The (2-1) transitions of the PN, PO, HCP and CP were not detected. We report detections of the (1-0) lines of $\mathrm{^{13}CO}$, HNC and CN along with a first detection of $\mathrm{C^{34}S}$. We have reproduced the observations of HNC, CN, CS and CO in every cloud by applying typical conditions for diffuse/translucent clouds. According to our best-fit model, the most abundant P-bearing species are HCP and CP ($\sim10^{-10}$), followed by PN, PO and $\mathrm{PH_3}$ ($\sim10^{-11}$). We show that the production of P-bearing species is favoured towards translucent rather than diffuse clouds, where the environment provides a stronger shielding from the interstellar radiation. Based on our improved model, the (1-0) transitions of HCP, CP, PN and PO are expected to be detectable with estimated intensities up to $\sim200$ mK.

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arXiv2019

The magnetic properties of the protostellar core IRAS 15398-3359

Context. Magnetic fields can affect significantly the star formation process. The theory of the magnetically-driven collapse in a uniform field predicts that initially the contraction happens along the field lines. When the gravitational pull grows strong enough, the magnetic field lines pinch inwards, giving rise to a characteristic hourglass shape. Aims. We investigate the magnetic field structure of a young Class 0 object, IRAS 15398-3359, embedded in the Lupus I cloud. Previous observations at large scales suggest that this source evolved in an highly magnetised environment. This object thus appears an ideal candidate to study the magnetically driven core collapse in the low-mass regime. Methods. We have performed polarisation observations of IRAS 15398-3359 at 214$μ$m using the SOFIA/HAWC+ instrument, thus tracing the linearly polarised thermal emission of cold dust. Results. Our data unveil a significant bend of the magnetic field lines due to the gravitational pull. The magnetic field appears ordered and aligned with the large-scale B-field of the cloud and with the outflow direction. We estimate a magnetic field strength of $B= 78 μ$G, expected to be accurate within a factor of two. The measured mass-to-flux parameter is $λ= 0.95$, indicating that the core is in a transcritical regime.

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arXiv2019

Search for H$_3^+$ isotopologues toward CRL 2136 IRS 1

Deuterated interstellar molecules frequently have abundances relative to their main isotopologues much higher than the overall elemental D-to-H ratio in the cold dense interstellar medium. The H$_3^+$ and its isotopologues play a key role in the deuterium fractionation; however, the abundances of these isotopologues have not been measured empirically with respect to H$_3^+$ to date. Our aim was to constrain the relative abundances of H$_2$D$^+$ and D$_3^+$ in the cold outer envelope of the hot core CRL 2136 IRS 1. We carried out three observations targeting H$_3^+$ and its isotopologues using the spectrographs CRIRES at the VLT, iSHELL at IRTF, and EXES on board SOFIA. In addition, the CO overtone band at 2.3 $μ$m was observed by iSHELL to characterize the gas on the line of sight. The H$_3^+$ ion was detected toward CRL 2136 IRS 1 as in previous observations. Spectroscopy of lines of H$_2$D$^+$ and D$_3^+$ resulted in non-detections. The 3$σ$ upper limits of $N({\rm H_2D^+})/N({\rm H_3^+})$ and $N({\rm D_3^+})/N({\rm H_3^+})$ are 0.24 and 0.13, respectively. The population diagram for CO is reproduced by two components of warm gas with the temperatures 58 K and 530 K, assuming a local thermodynamic equilibrium (LTE) distribution of the rotational levels. Cold gas ($<$20 K) makes only a minor contribution to the CO molecular column toward CRL 2136 IRS 1. The critical conditions for deuterium fractionation in a dense cloud are low temperature and CO depletion. Given the revised cloud properties, it is no surprise that H$_3^+$ isotopologues are not detected toward CRL 2136 IRS 1. The result is consistent with our current understanding of how deuterium fractionation proceeds.

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arXiv2019

Gas flow and accretion via spiral streamers and circumstellar disks in a young binary protostar

The majority of stars are part of gravitationally bound stellar systems, such as binaries. Observations of protobinary systems constrain the conditions that lead to stellar multiplicity and subsequent orbital evolution. We report high-angular resolution observations of the circumbinary disk around [BHB2007] 11, a young binary protostar system. The two protostars are embedded in circumstellar disks that have radii of 2 to 3 astronomical units and probably contain a few Jupiter masses. These systems are surrounded by a complex structure of filaments connecting to the larger circumbinary disk. We also observe accretion and radio jets associated with the protobinary system. The accretion is preferentially onto the lower-mass protostar, consistent with theoretical predictions.

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arXiv2019

Gas and dust temperature in pre-stellar cores revisited: New limits on cosmic-ray ionization rate

We develop a self-consistent model for the equilibrium gas temperature and size-dependent dust temperature in cold, dense pre-stellar cores, assuming an arbitrary power-law size distribution of dust grains. Compact analytical expressions applicable to a broad range of physical parameters are derived and compared with predictions of the commonly used standard model. It is suggested that combining the theoretical results with observations should allow us to constrain the degree of dust evolution and the cosmic-ray ionization rate in dense cores, and to help in discriminating between different regimes of cosmic-ray transport in molecular clouds. In particular, assuming a canonical MRN distribution of grain sizes, our theory demonstrates that the gas temperature measurements in the pre-stellar core L1544 are consistent with an ionization rate as high as $\sim 10^{-16}$ s$^{-1}$, an order of magnitude higher than previously thought.

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arXiv2019

KFPA Examinations of Young STellar Object Natal Environments (KEYSTONE): Hierarchical Ammonia Structures in Galactic Giant Molecular Clouds

We present initial results from the K-band focal plane array Examinations of Young STellar Object Natal Environments (KEYSTONE) survey, a large project on the 100-m Green Bank Telescope mapping ammonia emission across eleven giant molecular clouds at distances of $0.9-3.0$ kpc (Cygnus X North, Cygnus X South, M16, M17, MonR1, MonR2, NGC2264, NGC7538, Rosette, W3, and W48). This data release includes the NH$_3$ (1,1) and (2,2) maps for each cloud, which are modeled to produce maps of kinetic temperature, centroid velocity, velocity dispersion, and ammonia column density. Median cloud kinetic temperatures range from $11.4\pm2.2$ K in the coldest cloud (MonR1) to $23.0\pm6.5$ K in the warmest cloud (M17). Using dendrograms on the NH$_3$ (1,1) integrated intensity maps, we identify 856 dense gas clumps across the eleven clouds. Depending on the cloud observed, $40-100\%$ of the clumps are aligned spatially with filaments identified in H$_2$ column density maps derived from SED-fitting of dust continuum emission. A virial analysis reveals that 523 of the 835 clumps ($\sim63\%$) with mass estimates are bound by gravity alone. We find no significant difference between the virial parameter distributions for clumps aligned with the dust-continuum filaments and those unaligned with filaments. In some clouds, however, hubs or ridges of dense gas with unusually high mass and low virial parameters are located within a single filament or at the intersection of multiple filaments. These hubs and ridges tend to host water maser emission, multiple 70$μ$m-detected protostars, and have masses and radii above an empirical threshold for forming massive stars.

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arXiv2019

Interstellar Plunging Waves: ALMA resolves the physical structure of non-stationary MHD shocks

Magneto-hydrodynamic (MHD) shocks are violent events that inject large amounts of energy in the interstellar medium (ISM) dramatically modifying its physical properties and chemical composition. Indirect evidence for the presence of such shocks has been reported from the especial chemistry detected toward a variety of astrophysical shocked environments. However, the internal physical structure of these shocks remains unresolved since their expected spatial scales are too small to be measured with current instrumentation. Here we report the first detection of a fully spatially resolved, MHD shock toward the Infrared Dark Cloud (IRDC) G034.77-00.55. The shock, probed by Silicon Monoxide (SiO) and observed with the Atacama Large Millimetre/sub-millimetre Array (ALMA), is associated with the collision between the dense molecular gas of the cloud and a molecular gas flow pushed toward the IRDC by the nearby supernova remnant (SNR) W44. The interaction is occurring on sub-parsec spatial scales thanks to the enhanced magnetic field of the SNR, making the dissipation region of the MHD shock large enough to be resolved with ALMA. Our observations suggest that molecular flow-flow collisions can be triggered by stellar feedback, inducing shocked molecular gas densities compatible with those required for massive star formation.

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arXiv2019

Searches for Interstellar HCCSH and H$_2$CCS

A long standing problem in astrochemistry is the inability of many current models to account for missing sulfur content. Many relatively simple species that may be good candidates to sequester sulfur have not been measured experimentally at the high spectral resolution necessary to enable radioastronomical identification. On the basis of new laboratory data, we report searches for the rotational lines in the microwave, millimeter, and sub-millimeter regions of the sulfur-containing hydrocarbon HCCSH. This simple species would appear to be a promising candidate for detection in space owing to the large dipole moment along its $b$-inertial axis, and because the bimolecular reaction between two highly abundant astronomical fragments (CCH and SH radicals) may be rapid. An inspection of multiple line surveys from the centimeter to the far-infrared toward a range of sources from dark clouds to high-mass star-forming regions, however, resulted in non-detections. An analogous search for the lowest-energy isomer, H$_2$CCS, is presented for comparison, and also resulted in non-detections. Typical upper limits on the abundance of both species relative to hydrogen are $10^{-9}$-$10^{-10}$. We thus conclude that neither isomer is a major reservoir of interstellar sulfur in the range of environments studied. Both species may still be viable candidates for detection in other environments or at higher frequencies, providing laboratory frequencies are available.

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arXiv2019

High sensitivity maps of molecular ions in L1544: I. Deuteration of N2H+ and HCO+ and first evidence of N2D+ depletion

Context. The deuterium fraction in low-mass prestellar cores is a good diagnostic indicator of the initial phases of star formations, and it is also a fundamental quantity to infer the ionisation degree in these objects. Aims. With the analysis of multiple transitions of $\rm N_2H^+$, $\rm N_2D^+$, $\rm HC^{18}O^+$ and $\rm DCO^+$ we are able to determine the molecular column density maps and the deuterium fraction in $\rm N_2H^+$ and $\rm HCO^+$ toward the prototypical prestellar core L1544. This is the preliminary step to derive the ionisation degree in the source. Methods. We use a non-local thermodynamic equilibrium (non-LTE) radiative transfer code, combined with the molecular abundances derived from a chemical model, to infer the excitation conditions of all the observed transitions, which allows us to derive reliable maps of each molecule's column density. The ratio between the column density of a deuterated species and its non-deuterated counterpart gives the searched deuteration level. Results. The non-LTE analysis confirms that, for the analysed molecules, higher-J transitions are characterised by excitation temperatures $\approx 1-2\,$K lower than the lower-J ones. The chemical model that provides the best fit to the observational data predict the depletion of $\rm N_2H^+$ and to a lesser extent of $\rm N_2D^+$ in the innermost region. The peak values for the deuterium fraction that we find are $\mathrm{D/H_{N_2H^+}} = 0.26^{+0.15}_{-0.14}$ and $\mathrm{D/H_{HCO^+}} = 0.035^{+0.015}_{-0.012}$, in good agreement with previous estimates in the source.

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arXiv2019

Cyanopolyyne Chemistry around Massive Young Stellar Objects

Recent radio astronomical observations have revealed that HC$_{5}$N, the second shortest cyanopolyyne (HC$_{2n+1}$N), is abundant around some massive young stellar objects (MYSOs), which is not predicted by classical carbon-chain chemistry. For example, the observed HC$_{5}$N abundance toward the G28.28$-$0.36 MYSO is higher than that in L1527, which is one of the warm carbon chain chemistry (WCCC) sources, by more than one order of magnitude (Taniguchi et al., 2017). In this paper, we present chemical simulations of hot-core models with a warm-up period using the astrochemical code Nautilus. We find that the cyanopolyynes are formed initially in the gas phase and accreted onto the bulk and surface of granular ice mantles during the lukewarm phase, which occurs at $25 < T < 100$ K. In slow warm-up period models, the peak abundances occur as the cyanopolyynes desorb from dust grains after the temperature rises above 100 K. The lower limits of the abundances of HC$_{5}$N, CH$_{3}$CCH, and CH$_{3}$OH observed in the G28.28$-$0.36 MYSO can be reproduced in our hot-core models, after their desorption from dust grains. Moreover, previous observations suggested chemical diversity in envelopes around different MYSOs. We discuss possible interpretations of relationships between stages of the star-formation process and such chemical diversity, such as the different warm-up timescales. This timescale depends not only on the mass of central stars but also on the relationship between the size of warm regions and their infall velocity.

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arXiv2019

The specific angular momentum radial profile in dense cores: improved initial conditions for disk formation

The determination of the specific angular momentum radial profile, $j(r)$, in the early stages of star formation is crucial to constrain star and circumstellar disk formation theories. The specific angular momentum is directly related to the largest Keplerian disk possible, and it could constrain the angular momentum removal mechanism. We determine $j(r)$ towards two Class 0 objects and a first hydrostatic core candidate in the Perseus cloud, which is consistent across all three sources and well fit with a single power-law relation between 800 and 10,000\,au: $j_{fit}(r)=10^{-3.60\pm0.15}\left(r/\textrm{1,000au}\right)^{1.80\pm0.04}$ km s$^{-1}$ pc. This power-law relation is in between solid body rotation ($\propto r^2$) and pure turbulence ($\propto r^{1.5}$). This strongly suggests that even at 1,000\,au, the influence of the dense core's initial level of turbulence or the connection between core and the molecular cloud is still present. The specific angular momentum at 10,000\,au is $\approx3\times$ higher than previously estimated, while at 1,000\,au it is lower by $2\times$. We do not find a region of conserved specific angular momentum, although it could still be present at a smaller radius. We estimate an upper limit to the largest Keplerian disk radius of 60\,au, which is small but consistent with published upper limits. Finally, these results suggest that more realistic initial conditions for numerical simulations of disk formation are needed. Some possible solutions include: a) use a larger simulation box to include some level of driven turbulence or connection to the parental cloud, or b) incorporate the observed $j(r)$ to setup the dense core kinematics initial conditions.

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arXiv2019

Deuterated forms of H${_3^+}$ and their importance in astrochemistry

At the low temperatures ($\sim$10 K) and high densities ($\sim$100,000 H$_2$ molecules per cc) of molecular cloud cores and protostellar envelopes, a large amount of molecular species (in particular those containing C and O) freeze-out onto dust grain surfaces. It is in these regions that the deuteration of H$_3^+$ becomes very efficient, with a sharp abundance increase of H$_2$D$^+$ and D$_2$H$^+$. The multi-deuterated forms of H$_3^+$ participate in an active chemistry: (i) their collision with neutral species produces deuterated molecules such as the commonly observed N$_2$D$^+$, DCO$^+$ and multi-deuterated NH$_3$; (ii) their dissociative electronic recombination increases the D/H atomic ratio by several orders of magnitude above the D cosmic abundance, thus allowing deuteration of molecules (e.g. CH$_3$OH and H$_2$O) on the surface of dust grains. Deuterated molecules are the main diagnostic tools of dense and cold interstellar clouds, where the first steps toward star and protoplanetary disk formation take place. Recent observations of deuterated molecules are reviewed and discussed in view of astrochemical models inclusive of spin-state chemistry. We present a new comparison between models based on complete scrambling (to calculate branching ratio tables for reactions between chemical species that include protons and/or deuterons) and models based on non-scrambling (proton hop) methods, showing that the latter best agree with observations of NH$_3$ deuterated isotopologues and their different nuclear spin symmetry states.

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arXiv2019

Droplets I: Pressure-Dominated Sub-0.1 pc Coherent Structures in L1688 and B18

We present the observation and analysis of newly discovered coherent structures in the L1688 region of Ophiuchus and the B18 region of Taurus. Using data from the Green Bank Ammonia Survey (GAS), we identify regions of high density and near-constant, almost-thermal, velocity dispersion. Eighteen coherent structures are revealed, twelve in L1688 and six in B18, each of which shows a sharp "transition to coherence" in velocity dispersion around its periphery. The identification of these structures provides a chance to study the coherent structures in molecular clouds statistically. The identified coherent structures have a typical radius of 0.04 pc and a typical mass of 0.4 Msun, generally smaller than previously known coherent cores identified by Goodman et al. (1998), Caselli et al. (2002), and Pineda et al. (2010). We call these structures "droplets." We find that unlike previously known coherent cores, these structures are not virially bound by self-gravity and are instead predominantly confined by ambient pressure. The droplets have density profiles shallower than a critical Bonnor-Ebert sphere, and they have a velocity (VLSR) distribution consistent with the dense gas motions traced by NH3 emission. These results point to a potential formation mechanism through pressure compression and turbulent processes in the dense gas. We present a comparison with a magnetohydrodynamic simulation of a star-forming region, and we speculate on the relationship of droplets with larger, gravitationally bound coherent cores, as well as on the role that droplets and other coherent structures play in the star formation process.

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arXiv2019

TRAO Survey of Nearby Filamentary Molecular clouds, the Universal Nursery of Stars (TRAO FUNS) I. Dynamics and Chemistry of L1478 in the California Molecular Cloud

"TRAO FUNS" is a project to survey Gould Belt's clouds in molecular lines. This paper presents its first results on the central region of the California molecular cloud, L1478. We performed On-The-Fly mapping observations using the Taedeok Radio Astronomy Observatory (TRAO) 14m single dish telescope equipped with a 16 multi-beam array covering $\sim$1.0 square degree area of this region using C$^{18}$O (1-0) mainly tracing low density cloud and about 460 square arcminute area using N$_{2}$H$^{+}$ (1-0) mainly tracing dense cores. CS (2-1) and SO $(3_{2}-2_{1})$ were also used simultaneously to map $\sim$440 square arcminute area of this region. We identified 10 filaments by applying the dendrogram technique to the C$^{18}$O data-cube and 8 dense N$_{2}$H$^{+}$ cores by using {\sc FellWalker}. Basic physical properties of filaments such as mass, length, width, velocity field, and velocity dispersion are derived. It is found that L1478 consists of several filaments with slightly different velocities. Especially the filaments which are supercritical are found to contain dense cores detected in N$_{2}$H$^{+}$. Comparison of non-thermal velocity dispersions derived from C$^{18}$O and N$_{2}$H$^{+}$ for the filaments and dense cores indicates that some of dense cores share similar kinematics with those of the surrounding filaments while several dense cores have different kinematics with those of their filaments. This suggests that the formation mechanism of dense cores and filaments can be different in individual filaments depending on their morphologies and environments.

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