arXiv subjects

Charlotte Vastel

Publications and source records attributed to Charlotte Vastel.

At least 37 records · Page 2Linked to original sources

arXiv2020

Molecular Cloud Cores with High Deuterium Fraction: Nobeyama Single-Pointing Survey

We present the results of a single-pointing survey of 207 dense cores embedded in Planck Galactic Cold Clumps distributed in five different environments ($λ$ Orionis, Orion A, B, Galactic plane, and high latitudes) to identify dense cores on the verge of star formation for the study of the initial conditions of star formation. We observed these cores in eight molecular lines at 76-94 GHz using the Nobeyama 45-m telescope. We find that early-type molecules (e.g., CCS) have low detection rates and that late-type molecules (e.g., N$_2$H$^+$, c-C$_3$H$_2$) and deuterated molecules (e.g., N$_2$D$^+$, DNC) have high detection rates, suggesting that most of the cores are chemically evolved. The deuterium fraction (D/H) is found to decrease with increasing distance, indicating that it suffers from differential beam dilution between the D/H pair of lines for distant cores ($>$1 kpc). For $λ$ Orionis, Orion A, and B located at similar distances, D/H is not significantly different, suggesting that there is no systematic difference in the observed chemical properties among these three regions. We identify at least eight high D/H cores in the Orion region and two at high latitudes, which are most likely to be close to the onset of star formation. There is no clear evidence of the evolutionary change in turbulence during the starless phase, suggesting that the dissipation of turbulence is not a major mechanism for the beginning of star formation as judged from observations with a beam size of 0.04 pc.

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arXiv2020

A 3mm chemical exploration of small organics in Class I YSOs

There is mounting evidence that the composition and structure of planetary systems are intimately linked to their birth environments. During the past decade, several spectral surveys probed the chemistry of the earliest stages of star formation and of late planet-forming disks. However, very little is known about the chemistry of intermediate protostellar stages, i.e. Class I Young Stellar Objects (YSOs), where planet formation may have already begun. We present here the first results of a 3mm spectral survey performed with the IRAM-30m telescope to investigate the chemistry of a sample of seven Class I YSOs located in the Taurus star-forming region. These sources were selected to embrace the wide diversity identified for low-mass protostellar envelope and disk systems. We present detections and upper limits of thirteen small ($N_{\rm atoms}\leq3$) C, N, O, and S carriers - namely CO, HCO$^+$, HCN, HNC, CN, N$_2$H$^+$, C$_2$H, CS, SO, HCS$^+$, C$_2$S, SO$_2$, OCS - and some of their D, $^{13}$C, $^{15}$N, $^{18}$O, $^{17}$O, and $^{34}$S isotopologues. Together, these species provide constraints on gas-phase C/N/O ratios, D- and $^{15}$N-fractionation, source temperature and UV exposure, as well as the overall S-chemistry. We find substantial evidence of chemical differentiation among our source sample, some of which can be traced back to Class I physical parameters, such as the disk-to-envelope mass ratio (proxy for Class I evolutionary stage), the source luminosity, and the UV-field strength. Overall, these first results allow us to start investigating the astrochemistry of Class I objects, however, interferometric observations are needed to differentiate envelope versus disk chemistry.

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arXiv2020

Efficient methanol production on the dark side of a prestellar core

We present ALMA maps of the starless molecular cloud core Ophiuchus/H-MM1 in the lines of deuterated ammonia (ortho-NH2D), methanol (CH3OH), and sulphur monoxide (SO). The dense core is seen in NH2D emission, whereas the CH3OH and SO distributions form a halo surrounding the core. Because methanol is formed on grain surfaces, its emission highlights regions where desorption from grains is particularly efficient. Methanol and sulphur monoxide are most abundant in a narrow zone that follows the eastern side of the core. This side is sheltered from the stronger external radiation field coming from the west. We show that photodissociation on the illuminated side can give rise to an asymmetric methanol distribution, but that the stark contrast observed in H-MM1 is hard to explain without assuming enhanced desorption on the shaded side. The region of the brightest emission has a wavy structure that rolls up at one end. This is the signature of Kelvin-Helmholtz instability occurring in sheared flows. We suggest that in this zone, methanol and sulphur are released as a result of grain-grain collisions induced by shear vorticity.

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arXiv2019

Multi-scale analysis of the Monoceros OB 1 star-forming region: II. Colliding filaments in the Monoceros OB1 molecular cloud

We started a multi-scale analysis of G202.3+2.5, an intertwined filamentary region of Monoceros OB1. In Paper I, we examined the distributions of dense cores and protostars and found enhanced star formation (SF) activity in the junction region of the filaments. In this second paper, we aim to unveil the connections between the core and filament evolutions, and between the filament dynamics and the global evolution of the cloud. We characterise the gas dynamics and energy balance using Herschel and WISE observations and molecular tracers observed with the IRAM 30m and TRAO 14m telescopes. The velocity field of the cloud is examined and velocity-coherent structures are put in perspective with the cloud environment. Two main velocity components (VCs) are revealed, well separated in the north and merged around the location of intense N2H+ emission where Paper I found the peak of SF activity. The relative position of the two VCs along the sightline, and the velocity gradient in N2H+ emission imply that the VCs have been undergoing collision for ~10^5 yrs. The dense gas where N2H+ is detected is interpreted as the compressed region between the two filaments, which corresponds to a high mass inflow rate of ~1e-3 Msun/yr and possibly leads to an increase in its SF efficiency. We identify a protostar in the junction region that possibly powers two crossed intermittent outflows. We show that the HII region around the nearby cluster NCG 2264 is still expanding and its role in the collision is examined. However, we cannot rule out the idea that the collision arises mostly from the global collapse of the cloud. The (sub-)filament-scale observables examined in this paper reveal a collision between G202.3+2.5 sub-structures and its probable role in feeding the cores in the junction region. One must now characterise the cloud morphology, its fragmentation, and magnetic field, all at high resolution.

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arXiv2019

Multi-scale analysis of the Monoceros OB 1 star-forming region: I. The dense core population

Current theories and models attempt to explain star formation globally, from core scales to giant molecular cloud scales. A multi-scale observational characterisation of an entire molecular complex is necessary to constrain them. We investigate star formation in G202.3+2.5, a ~10x3 pc sub-region of the Monoceros OB1 cloud with a complex morphology harbouring interconnected filamentary structures. We aim to connect the evolution of cores and filaments in G202.3+2.5 with the global evolution of the cloud and to identify the engines of the cloud dynamics. In this first paper, the star formation activity is evaluated by surveying the distributions of dense cores and protostars, and their evolutionary state, as characterised using both infrared observations from the Herschel and WISE telescopes and molecular line observations with the IRAM 30-m telescope. We find ongoing star formation in the whole cloud, with a local peak in star formation activity around the centre of G202.3+2.5 where a chain of massive cores (10-50 Msun) forms a massive ridge (>150 Msun). All evolutionary stages from starless cores to Class II protostars are found in G202.3+2.5, including a possibly starless, large column density (8x10^{22} cm-2), and massive (52 Msun) core. All the core-scale observables examined in this paper point to an enhanced star formation activity centred on the junction between the three main branches of the ramified structure of G202.3+2.5. This suggests that the increased star-formation activity results from the convergence of these branches. To further investigate the origin of this enhancement, it is now necessary to extend the analysis to larger scales, in order to examine the relationship between cores, filaments and their environment. We address these points through the analysis of the dynamics of G202.3+2.5 in a joint paper.

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arXiv2019

Sulfur-Bearing Species Tracing the Disk/Envelope System in the Class I Protostellar Source Elias 29

We have observed the Class I protostellar source Elias 29 with Atacama Large Millimeter/submillimeter Array (ALMA). We have detected CS, SO, $^{34}$SO, SO$_2$, and SiO line emissions in a compact component concentrated near the protostar and a ridge component separated from the protostar by 4\arcsec\ ($\sim 500$ au). The former component is found to be abundant in SO and SO$_2$ but deficient in CS. The abundance ratio SO/CS is as high as $3^{+13}_{-2} \times 10^2$ at the protostar, which is even higher than that in the outflow-shocked region of L1157 B1. However, organic molecules (HCOOCH$_3$, CH$_3$OCH$_3$, CCH, and c-C$_3$H$_2$) are deficient in Elias 29. We attribute the deficiency in organic molecules and richness in SO and SO$_2$ to the evolved nature of the source or the relatively high dust temperature (\protect\raisebox{-0.7ex}{$\:\stackrel{\textstyle >}{\sim}\:$} 20 K) in the parent cloud of Elias 29. The SO and SO$_2$ emissions trace rotation around the protostar. Assuming a highly inclined configuration ($i \geq 65$\degr; 0\degr\ for a face-on configuration) and Keplerian motion for simplicity, the protostellar mass is estimated to be (0.8 -- 1.0) \Msun. The $^{34}$SO and SO$_2$ emissions are asymmetric in their spectra; the blue-shifted components are weaker than the red-shifted ones. Although this may be attributed to the asymmetric molecular distribution, other possibilities are also discussed.

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arXiv2019

Isocyanogen formation in the cold interstellar medium

Cyanogen (NCCN) is the simplest member of the dicyanopolyynes group, and has been proposed as a major source of the CN radical observed in cometary atmospheres. Although not detected through its rotational spectrum in the cold interstellar medium, this very stable species is supposed to be very abundant. The chemistry of cyanogen in the cold interstellar medium can be investigated through its metastable isomer, CNCN (isocyanogen). Its formation may provide a clue on the widely abundant CN radical observed in cometary atmospheres. We performed an unbiased spectral survey of the L1544 proto-typical prestellar core, using the IRAM-30m and have analysed, for this paper, the nitrogen chemistry that leads to the formation of isocyanogen. We report on the first detection of CNCN, NCCNH+, C3N, CH3CN, C2H3CN, and H2CN in L1544. We built a detailed chemical network for NCCN/CNCN/HC2N2+ involving all the nitrogen bearing species detected (CN, HCN, HNC, C3N, CNCN, CH3CN, CH2CN, HCCNC, HC3N, HNC3, H2CN, C2H3CN, HCNH+, HC3NH+) and the upper limits on C4N, C2N. The main cyanogen production pathways considered in the network are the CN + HNC and N + C3N reactions. The comparison between the observations of the nitrogen bearing species and the predictions from the chemical modelling shows a very good agreement, taking into account the new chemical network. The expected cyanogen abundance is greater than the isocyanogen abundance by a factor of 100. Although cyanogen cannot be detected through its rotational spectrum, the chemical modelling predicts that it should be abundant in the gas phase and hence might be traced through the detection of isocyanogen. It is however expected to have a very low abundance on the grain surfaces compared to HCN.

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arXiv2018

Sulphur chemistry in the L1544 pre-stellar core

The L1544 pre-stellar core has been observed as part of the ASAI IRAM 30m Large Program as well as follow-up programs. These observations have revealed the chemical richness of the earliest phases of low-mass star-forming regions. In this paper we focus on the twenty-one sulphur bearing species (ions, isotopomers and deuteration) that have been detected in this spectral-survey through fifty one transitions: CS, CCS, C3S, SO, SO2, H2CS, OCS, HSCN, NS, HCS+, NS+ and H2S. We also report the tentative detection (4 σ level) for methyl mercaptan (CH3SH). LTE and non-LTE radiative transfer modelling have been performed and we used the nautilus chemical code updated with the most recent chemical network for sulphur to explain our observations. From the chemical modelling we expect a strong radial variation for the abundances of these species, which mostly are emitted in the external layer where non thermal desorption of other species has previously been observed. We show that the chemical study cannot be compared to what has been done for the TMC-1 dark cloud, where the abundance is supposed constant along the line of sight, and conclude that a strong sulphur depletion is necessary to fully reproduce our observations of the prototypical pre-stellar core L1544.

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arXiv2018

Seeds of Life in Space (SOLIS). III. Zooming into the methanol peak of the pre-stellar core L1544

Towards the pre-stellar core L1544, the methanol (CH$_3$OH) emission forms an asymmetric ring around the core centre, where CH$_3$OH is mostly in solid form, with a clear peak 4000~au to the north-east of the dust continuum peak. As part of the NOEMA Large Project SOLIS (Seeds of Life in Space), the CH$_3$OH peak has been spatially resolved to study its kinematics and physical structure and to investigate the cause behind the local enhancement. We find that methanol emission is distributed in a ridge parallel to the main axis of the dense core. The centroid velocity increases by about 0.2~km~s$^{-1}$ and the velocity dispersion increases from subsonic to transonic towards the central zone of the core, where the velocity field also shows complex structure. This could be indication of gentle accretion of material onto the core or interaction of two filaments, producing a slow shock. We measure the rotational temperature and show that methanol is in local thermodynamic equilibrium (LTE) only close to the dust peak, where it is significantly depleted. The CH$_3$OH column density, $N_{tot}({\rm CH_3OH})$, profile has been derived with non-LTE radiative transfer modelling and compared with chemical models of a static core. The measured $N_{tot}({\rm CH_3OH})$ profile is consistent with model predictions, but the total column densities are one order of magnitude lower than those predicted by models, suggesting that the efficiency of reactive desorption or atomic hydrogen tunnelling adopted in the model may be overestimated; or that an evolutionary model is needed to better reproduce methanol abundance.

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arXiv2017

Detection of the HC$_3$NH$^+$ and HCNH$^+$ ions in the L1544 pre-stellar core

The L1544 pre-stellar core was observed as part of the ASAI (Astrochemical Surveys At IRAM) Large Program. We report the first detection in a pre-stellar core of the HCNH$^+$ and HC$_3$NH$^+$ ions. The high spectral resolution of the observations allows to resolve the hyperfine structure of HCNH$^+$. Local thermodynamic equilibrium analysis leads to derive a column density equal to (2.0$\pm$0.2)$\times$10$^{13}$cm$^{-2}$ for HCNH$^+$ and (1.5$\pm$0.5)$\times$10$^{11}$cm$^{-2}$ for HC$_3$NH$^+$. We also present non-LTE analysis of five transitions of HC$_3$N, three transitions of H$^{13}$CN and one transition of HN$^{13}$C, all of them linked to the chemistry of HCNH$^+$ and HC$_3$NH$^+$. We computed for HC$_3$N, HCN, and HNC a column density of (2.0$\pm$0.4)$\times$10$^{13}$cm$^{-2}$, (3.6$\pm$0.9)$\times10^{14}$cm$^{-2}$, and (3.0$\pm$1.0)$\times$10$^{14}$cm$^{-2}$, respectively. We used the gas-grain chemical code Nautilus to predict the abundances all these species across the pre-stellar core. Comparison of the observations with the model predictions suggests that the emission from HCNH$^+$ and HC$_3$NH$^+$ originates in the external layer where non-thermal desorption of other species was previously observed. The observed abundance of both ionic species ([HCNH$^+$]$\,\simeq3\times10^{-10}$ and [HC$_3$NH$^+$]$\,\simeq[1.5-3.0]\times10^{-12}$, with respect to H$_2$) cannot be reproduced at the same time by the chemical modelling, within the error bars of the observations only. We discuss the possible reasons for the discrepancy and suggest that the current chemical models are not fully accurate or complete. However, the modelled abundances are within a factor of three consistent with the observations, considering a late stage of the evolution of the pre-stellar core, compatible with previous observations.

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arXiv2017

Vertical Structure of the Transition Zone from Infalling Rotating Envelope to Disk in the Class 0 Protostar, IRAS04368+2557

We have resolved for the first time the radial and vertical structure of the almost edge-on envelope/disk system of the low-mass Class 0 protostar L1527. For that, we have used ALMA observations with a spatial resolution of 0.25$^{\prime\prime}$$\times$0.13$^{\prime\prime}$ and 0.37$^{\prime\prime}$$\times$0.23$^{\prime\prime}$ at 0.8 mm and 1.2 mm, respectively. The L1527 dust continuum emission has a deconvolved size of 78 au $\times$ 21 au, and shows a flared disk-like structure. A thin infalling-rotating envelope is seen in the CCH emission outward of about 150 au, and its thickness is increased by a factor of 2 inward of it. This radius lies between the centrifugal radius (200 au) and the centrifugal barrier of the infalling-rotating envelope (100 au). The gas stagnates in front of the centrifugal barrier and moves toward vertical directions. SO emission is concentrated around and inside the centrifugal barrier. The rotation speed of the SO emitting gas is found to be decelerated around the centrifugal barrier. A part of the angular momentum could be extracted by the gas which moves away from the mid-plane around the centrifugal barrier. If this is the case, the centrifugal barrier would be related to the launching mechanism of low velocity outflows, such as disk winds.

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arXiv2017

L483: Warm Carbon-Chain Chemistry Source Harboring Hot Corino Activity

The Class 0 protostar, L483, has been observed in various molecular lines in the 1.2 mm band at a sub-arcsecond resolution with ALMA. An infalling-rotating envelope is traced by the CS line, while a very compact component with a broad velocity width is observed for the CS, SO, HNCO, NH$_2$CHO, and HCOOCH$_3$ lines. Although this source is regarded as the warm carbon-chain chemistry (WCCC) candidate source at a 1000 au scale, complex organic molecules characteristic of hot corinos such as NH$_2$CHO and HCOOCH$_3$ are detected in the vicinity of the protostar. Thus, both hot corino chemistry and WCCC are seen in L483. Although such a mixed chemical character source has been recognized as an intermediate source in previous single-dish observations, we here report the first spatially-resolved detection. A kinematic structure of the infalling-rotating envelope is roughly explained by a simple ballistic model with the protostellar mass of 0.1--0.2 $M_\odot$ and the radius of the centrifugal barrier (a half of the centrifugal radius) of 30--200 au, assuming the inclination angle of 80\degr\ (0\degr\ for a face-on). The broad line emission observed in the above molecules most likely comes from the disk component inside the centrifugal barrier. Thus, a drastic chemical change is seen around the centrifugal barrier.

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arXiv2016

Discovery of a Hot Corino in the Bok Globule B335

We report the first evidence of a hot corino in a Bok globule. This is based on the ALMA observations in the 1.2 mm band toward the low-mass Class 0 protostar IRAS 19347+0727 in B335. Saturated complex organic molecules (COMs), CH$_3$CHO, HCOOCH$_3$, and NH$_2$CHO, are detected in a compact region within a few 10 au around the protostar. Additionally, CH$_3$OCH$_3$, C$_2$H$_5$OH, C$_2$H$_5$CN, and CH$_3$COCH$_3$ are tentatively detected. Carbon-chain related molecules, CCH and c-C$_3$H$_2$, are also found in this source, whose distributions are extended over a few 100 au scale. On the other hand, sulfur-bearing molecules CS, SO, and SO$_2$, have both compact and extended components. Fractional abundances of the COMs relative to H$_2$ are found to be comparable to those in known hot-corino sources. Though the COMs lines are as broad as 5-8 km s$^{-1}$, they do not show obvious rotation motion in the present observation. Thus, the COMs mainly exist in a structure whose distribution is much smaller than the synthesized beam (0."58 x 0."52).

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arXiv2016

The Spatial Distribution of Complex Organic Molecules in the L1544 Pre-stellar Core

The detection of complex organic molecules (COMs) toward cold sources such as pre-stellar cores (with T<10 K), has challenged our understanding of the formation processes of COMs in the interstellar medium. Recent modelling on COM chemistry at low temperatures has provided new insight into these processes predicting that COM formation depends strongly on parameters such as visual extinction and the level of CO freeze out. We report deep observations of COMs toward two positions in the L1544 pre-stellar core: the dense, highly-extinguished continuum peak with Av>=30 mag within the inner 2700 au; and a low-density shell with average Av~7.5-8 mag located at 4000 au from the core's center and bright in CH3OH. Our observations show that CH3O, CH3OCH3 and CH3CHO are more abundant (by factors ~2-10) toward the low-density shell than toward the continuum peak. Other COMs such as CH3OCHO, c-C3H2O, HCCCHO, CH2CHCN and HCCNC show slight enhancements (by factors <=3) but the associated uncertainties are large. This suggests that COMs are actively formed and already present in the low-density shells of pre-stellar cores. The modelling of the chemistry of O-bearing COMs in L1544 indicates that these species are enhanced in this shell because i) CO starts freezing out onto dust grains driving an active surface chemistry; ii) the visual extinction is sufficiently high to prevent the UV photo-dissociation of COMs by the external interstellar radiation field; and iii) the density is still moderate to prevent severe depletion of COMs onto grains.

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arXiv2016

Abundance of HOCO+ and CO2 in the outer layers of the L1544 prestellar core

The L1544 prestellar core has been observed as part of the ASAI IRAM Large Program at 3 mm. These observations led to the detection of many complex molecules. In this Letter, we report the detection of two lines, at 85.5 GHz (4,0,4-3,0,3) and 106.9 GHz (5,0,5-4,0,4), respectively, of the protonated carbon dioxide ion, HOCO+. We also report the tentative detection of the line at 100.4 GHz (5,0,5-4,0,4) of DOCO+. The non-LTE analysis of the detected lines shows that the HOCO+ emission originates in the external layer where non-thermal desorption of other species has previously been observed. Its abundance is (5 +/- 2) e-11. Modelling of the chemistry involved in the formation and destruction of HOCO+ provides a gaseous CO2 abundance of 2e-7 (with respect to H2) with an upper limit of 2e-6.

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arXiv2016

Subarcsecond Analysis of Infalling-Rotating Envelope around the Class I Protostar IRAS 04365+2535

Sub-arcsecond images of the rotational line emission of CS and SO have been obtained toward the Class I protostar IRAS 04365$+$2535 in TMC-1A with ALMA. A compact component around the protostar is clearly detected in the CS and SO emission. The velocity structure of the compact component of CS reveals infalling-rotating motion conserving the angular momentum. It is well explained by a ballistic model of an infalling-rotating envelope with the radius of the centrifugal barrier (a half of the centrifugal radius) of 50 AU, although the distribution of the infalling gas is asymmetric around the protostar. The distribution of SO is mostly concentrated around the radius of the centrifugal barrier of the simple model. Thus a drastic change in chemical composition of the gas infalling onto the protostar is found to occur at a 50 AU scale probably due to accretion shocks, demonstrating that the infalling material is significantly processed before being delivered into the disk.

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arXiv2015

Detectability of deuterated water in prestellar cores

Water is an important molecule in the chemical and thermal balance of dense molecular gas, but knowing its history through-out the various stages of the star formation is a fundamental problem. Its molecular deuteration provides us with a crucial clue to its formation history. H$_2$O has recently been detected for the first time towards the prestellar core L1544 with the Herschel Space Observatory with a high spectral resolution (HIFI instrument). Prestellar cores provide the original reservoir of material from which future planetary systems are built, but few observational constraints exist on the formation of water and none on its deuteration before the collapse starts and a protostar forms at the centre. We report on new APEX observations of the ground state 1$_{0,1}$-0$_{0,0}$ HDO transition at 464 GHz towards the prestellar core L1544. The line is undetected, and we present an extensive study of the conditions for its detectability in cold and dense cloud cores. The water and deuterated water abundances have been estimated using an advanced chemical model simplified for the limited number of reactions or processes that are active in cold regions (< 15 K). We use the LIME radiative transfer code to compute the expected intensity and profile of both H$_2$O and HDO lines and compare them with the observations. We present several ad hoc profiles that best-fit the observations and compare the profiles with results from an astrochemical modelling, coupling gas phase and grain surface chemistry. Our comparison between observations, radiative transfer, and chemical modelling shows the limits of detectability for singly deuterated water, through the ground-state transitions 1$_{0,1}$-0$_{0,0}$ and 1$_{1,1}$-0$_{0,0}$ at 464.9 and 893.6 GHz, respectively, with both single-dish telescope and interferometric observations.

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arXiv2015

Abundance Anomaly of the $^{13}$C Isotopic Species of c-C$_3$H$_2$ in the Low-Mass Star Formation Region L1527

The rotational spectral lines of c-C$_3$H$_2$ and two kinds of the $^{13}$C isotopic species, c-$^{13}$CCCH$_2$ ($C_{2v}$ symmetry) and c-CC$^{13}$CH$_2$ ($C_s$ symmetry) have been observed in the 1-3 mm band toward the low-mass star-forming region L1527. We have detected 7, 3, and 6 lines of c-C$_3$H$_2$, c-$^{13}$CCCH$_2$ , and c-CC$^{13}$CH$_2$, respectively, with the Nobeyama 45 m telescope, and 34, 6, and 13 lines, respectively, with the IRAM 30 m telescope, where 7, 2, and 2 transitions, respectively, are observed with the both telescopes. With these data, we have evaluated the column densities of the normal and $^{13}$C isotopic species. The [c-C$_3$H$_2$]/[c-$^{13}$CCCH$_2$] ratio is determined to be $310\pm80$, while the [c-C$_3$H$_2$]/[c-CC$^{13}$CH$_2$] ratio is determined to be $61\pm11$. The [c-C$_3$H$_2$]/[c-$^{13}$CCCH$_2$] and [c-C$_3$H$_2$]/[c-CC$^{13}$CH$_2$] ratios expected from the elemental $^{12}$C/$^{13}$C ratio are 60-70 and 30-35, respectively, where the latter takes into account the statistical factor of 2 for the two equivalent carbon atoms in c-C$_3$H$_2$. Hence, this observation further confirms the dilution of the $^{13}$C species in carbon-chain molecules and their related molecules, which are thought to originate from the dilution of $^{13}$C$^+$ in the gas-phase C$^+$ due to the isotope exchange reaction: $\mathrm{^{13}C^++CO\rightarrow{}^{13}CO+C^+}$. Moreover, the abundances of the two $^{13}$C isotopic species are different from each other. The ratio of c-$\mathrm{^{13}CCCH_2}$ species relative to c-$\mathrm{CC^{13}CH_2}$ is determined to be $0.20\pm0.05$. If $^{13}$C were randomly substituted for the three carbon atoms, the [c-$\mathrm{^{13}CCCH_2}$]/[c-$\mathrm{CC^{13}CH_2}$] ratio would be 0.5. Hence, the observed ratio indicates that c-$\mathrm{CC^{13}CH_2}$ exists more favorably. Possible origins of the different abundances are discussed.

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