arXiv subjects

Rafael Bachiller

Publications and source records attributed to Rafael Bachiller.

At least 19 recordsLinked to original sources

arXiv2026

Jets and Outflows in Young Stellar Objects with the SKAO

Jets and outflows are ubiquitous phenomena associated with the formation of young stellar objects (YSOs). They play a crucial role in removing angular momentum from the accreting system and in regulating star-formation efficiency. Theoretical studies and observations with ALMA and VLA have shown that jets and winds may have a crucial role in promoting dust growth in the envelope-disc system and in shaping the physical and chemical properties of the surrounding environment. Despite these significant advances, many fundamental questions remain unanswered regarding the acceleration, collimation, and chemical impact of jets and outflows from YSOs. The SKA-project will overcome the limitations of current mm/cm-facilities by enabling high-angular resolution and high-sensitivity cm-observations, crucial for probing jets/outflows near YSOs. Radio recombination lines, combined with proper motions, offer a unique opportunity to study the 3D-kinematics of jets. Non-thermal linearly polarised synchrotron emission will allow measuring magnetic field strength and morphology at unprecedented scales of a few au. Observations of dust emission in outflow cavities will allow studying how dust grows and is eventually transported from the disc to the envelope and back. Finally, the SKA-project will allow exploring the dust composition and chemical enrichment in shocks, where sputtering/shattering of grains cause the release of their mantles and refractory cores in the gas-phase. Complementary to ALMA's detection of simple and complex organic molecules, the SKAO will probe, for the first time, long carbon chains/rings, several Cl-, Al-, Mg-, and other metal-bearing species (missed by current sub-mm facilities).

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arXiv2023

Gas phase Elemental abundances in Molecular cloudS (GEMS). IX. Deuterated compounds of H2S in starless cores

H2S is thought to be the main sulphur reservoir in the ice, being therefore a key molecule to understand sulphur chemistry in the star formation process and to solve the missing sulphur problem. The H2S deuterium fraction can be used to constrain its formation pathways. We investigate for the first time the H2S deuteration in a large sample of starless cores (SC). We use observations of the GEMS IRAM 30m Large Program and complementary IRAM 30m observations. We consider a sample of 19 SC in Taurus, Perseus, and Orion, detecting HDS in 10 and D2S in five. The H2S single and double deuterium fractions are analysed with regard to their relation with the cloud physical parameters, their comparison with other interstellar sources, and their comparison with deuterium fractions in early stage star-forming sources of c-C3H2, H2CS, H2O, H2CO, and CH3OH. We obtain a range of X(HDS)/X(H2S)~0.025-0.2 and X(D2S)/X(HDS)~0.05-0.3. H2S single deuteration shows an inverse relation with the cloud kinetic temperature. H2S deuteration values in SC are similar to those observed in Class 0. Comparison with other molecules in other sources reveals a general trend of decreasing deuteration with increasing temperature. In SC and Class 0 objects H2CS and H2CO present higher deuteration fractions than c-C3H2, H2S, H2O, and CH3OH. H2O shows single and double deuteration values one order of magnitude lower than those of H2S and CH3OH. Differences between c-C3H2, H2CS and H2CO deuterium fractions and those of H2S, H2O, and CH3OH are related to deuteration processes produced in gas or solid phases, respectively. We interpret the differences between H2S and CH3OH deuterations and that of H2O as a consequence of differences on the formation routes in the solid phase, particularly in terms of the different occurrence of the D-H and H-D substitution reactions in the ice, together with the chemical desorption processes.

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arXiv2023

Streamers feeding the SVS13-A protobinary system: astrochemistry reveals accretion shocks?

We report ALMA high-angular resolution (~ 50 au) observations of the binary system SVS13-A. More specifically, we analyse deuterated water (HDO) and sulfur dioxide (SO2) emission. The molecular emission is associated with both the components of the binary system, VLA4A and VLA4B. The spatial distribution is compared to that of formamide (NH2CHO), previously analysed in the system. Deuterated water reveals an additional emitting component spatially coincident with the dust accretion streamer, at a distance larger than 120 au from the protostars, and at blue-shifted velocities (> 3 km/s from the systemic velocities). We investigate the origin of the molecular emission in the streamer, in light of thermal sublimation temperatures calculated using updated binding energies (BE) distributions. We propose that the observed emission is produced by an accretion shock at the interface between the accretion streamer and the disk of VLA4A. Thermal desorption is not completely excluded in case the source is actively experiencing an accretion burst.

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arXiv2022

CH$_3$CN deuteration in the SVS13-A Class I hot-corino. SOLIS XV

We studied the line emission from CH3CN and its deuterated isotopologue CH$_2$DCN towards the prototypical Class I object SVS13-A, where the deuteration of a large number of species has already been reported. Our goal is to measure the CH$_3$CN deuteration in a Class I protostar, for the first time, in order to constrain the CH$_3$CN formation pathways and the chemical evolution from the early prestellar core and Class 0 to the evolved Class I stages. We imaged CH2DCN towards SVS13-A using the IRAM NOEMA interferometer at 3mm in the context of the Large Program SOLIS (with a spatial resolution of 1.8"x1.2"). The NOEMA images have been complemented by the CH$_3$CN and CH$_2$DCN spectra collected by the IRAM-30m Large Program ASAI, that provided an unbiased spectral survey at 3mm, 2mm, and 1.3mm. The observed line emission has been analysed using LTE and non-LTE LVG approaches. The NOEMA/SOLIS images of CH2DCN show that this species emits in an unresolved area centered towards the SVS13-A continuum emission peak, suggesting that methyl cyanide and its isotopologues are associated with the hot corino of SVS13-A, previously imaged via other iCOMs. In addition, we detected 41 and 11 ASAI transitions of CH$_3$CN and CH2DCN, respectively, which cover upper level energies (Eup) from 13 to 442 K and from 18 K to 200 K, respectively. The derived [CH2DCN]/[CH3CN] ratio is $\sim$9\%. This value is consistent with those measured towards prestellar cores and a factor 2-3 higher than those measured in Class 0 protostars. Contrarily to what expected for other molecular species, the CH3CN deuteration does not show a decrease in SVS13-A with respect to measurements in younger prestellar cores and Class 0 protostars. Finally, we discuss why our new results suggest that CH3CN was likely synthesised via gas-phase reactions and frozen onto the dust grain mantles during the cold prestellar phase.

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arXiv2020

AB Aur, a Rosetta stone for studies of planet formation (I): chemical study of a planet-forming disk

AB Aur is a Herbig Ae star that hosts a prototypical transition disk. The disk shows a plethora of features connected with planet formation mechanisms. Understanding the physical and chemical characteristics of these features is crucial to advancing our knowledge of planet formation. We aim to characterize the gaseous disk around the Herbig Ae star AB Aur. A complete spectroscopic study was performed using NOEMA to determine the physical and chemical conditions. We present new observations of the continuum and 12CO, 13CO, C18O, H2CO, and SO lines. We used the integrated intensity maps and stacked spectra to derive estimates of the disk temperature. By combining our 13CO and C18O observations, we computed the gas-to-dust ratio along the disk. We also derived column density maps for the different species and used them to compute abundance maps. The results of our observations were compared with Nautilus astrochemical models. We detected continuum emission in a ring that extends from 0.6 to 2.0 arcsec, peaking at 0.97 and with a strong azimuthal asymmetry. The molecules observed show different spatial distributions, and the peaks of the distributions are not correlated with the binding energy. Using H2CO and SO lines, we derived a mean disk temperature of 39 K. We derived a gas-to-dust ratio that ranges from 10 to 40. The comparison with Nautilus models favors a disk with a low gas-to-dust ratio (40) and prominent sulfur depletion. From a very complete spectroscopic study of the prototypical disk around AB Aur, we derived, for the first time, the gas temperature and the gas-to-dust ratio along the disk, providing information that is essential to constraining hydrodynamical simulations.Moreover, we explored the gas chemistry and, in particular, the sulfur depletion. The derived sulfur depletion is dependent on the assumed C/O ratio. Our data are better explained with C/O ~ 0.7 and S/H=8e-8.

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arXiv2019

Gas accretion within the dust cavity in AB Aur

AB Aur is a Herbig Ae star hosting a well-known transitional disk. Because of its proximity and low inclination angle, it is an excellent object to study planet formation. Our goal is to investigate the chemistry and dynamics of the molecular gas component in the AB Aur disk, and its relation with the prominent horseshoe shape observed in continuum mm emission. We used the NOEMA interferometer to map with high angular resolution the J = 3-2 lines of HCO+ and HCN. By combining both, we can gain insight into the AB Aur disk structure. Chemical segregation is observed in the AB Aur disk: HCO+ shows intense emission toward the star position, at least one bright molecular bridge within the dust cavity, and ring-like emission at larger radii, while HCN is only detected in an annular ring that is coincident with the dust ring and presents an intense peak close to the dust trap. We use HCO+ to investigate the gas dynamics inside the cavity. The observed bright HCO+ bridge connects the compact central source with the outer dusty ring. This bridge can be interpreted as an accretion flow from the outer ring to the inner disk/jet system proving gas accretion through the cavity.

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arXiv2019

Sulfur Chemistry in L1157-B1

The main carrier of sulfur in dense clouds, where it is depleted from the gas phase, remains a mystery. Shock waves in young molecular outflows disrupt the ice mantles and allow us to directly probe the material that is ejected into the gas phase. A comprehensive study of sulfur-bearing species towards L1157-B1, a shocked region along a protostellar outflow, has been carried out as part of the IRAM-30m large program ASAI. The dataset contains over 100 lines of CCS, H$_2$CS, OCS, SO, SO$_2$ and isotopologues. The results of these observations are presented, complementing previous studies of sulfur-bearing species in the region. The column densities and fractional abundances of these species are measured and together these species account for 10\% of the cosmic sulfur abundance in the region. The gas properties derived from the observations are also presented, demonstrating that sulfur bearing species trace a wide range of different gas conditions in the region.

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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

Chemical survey toward young stellar objects in the Perseus molecular cloud complex

Chemical diversity of the gas in low-mass protostellar cores is widely recognized. In order to explore its origin, a survey of chemical composition toward 36 Class 0/I protostars in the Perseus molecular cloud complex, which are selected in an unbiased way under certain physical conditions, has been conducted with IRAM 30 m and NRO 45 m telescope. Multiple lines of C2H, c-C3H2 and CH3OH have been observed to characterize the chemical composition averaged over a 1000 au scale around the protostar. The derived beam-averaged column densities show significant chemical diversity among the sources, where the column density ratios of C2H/CH3OH are spread out by 2 orders of magnitude. From previous studies, the hot corino sources have abundant CH3OH but deficient C2H, their C2H/CH3OH column density ratios being relatively low. In contrast, the warm-carbon-chain chemistry (WCCC) sources are found to reveal the high C2H/CH3OH column density ratios. We find that the majority of the sources have intermediate characters between these two distinct chemistry types. A possible trend is seen between the C2H/CH3OH ratio and the distance of the source from the edge of a molecular cloud. The sources located near cloud edges or in isolated clouds tend to have a high C2H/CH3OH ratio. On the other hand, the sources having a low C2H/CH3OH ratio tend to be located in inner regions of the molecular cloud complex. This result gives an important clue to an understanding of the origin of the chemical diversity of protostellar cores in terms of environmental effects.

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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

Laboratory measurements and astronomical search for cyanomethanimine

C-cyanomethanimine (HNCHCN), existing in the two $Z$ and $E$ isomeric forms, is a key prebiotic molecule, but, so far, only the $E$ isomer has been detected toward the massive star-forming region. Sagittarius B2(N) using transitions in the radio wavelength domain. With the aim of detecting HNCHCN in Sun-like-star forming regions, the laboratory investigation of its rotational spectrum has been extended to the millimeter-/submillimeter-wave (mm-/submm-) spectral window in which several unbiased spectral surveys have been already carried out. High-resolution laboratory measurements of the rotational spectrum of C-cyanomethanimine were carried out in the 100-420 GHz range using a frequency-modulation absorption spectrometer. We then searched for the C-cyanomethanimine spectral features in the mm-wave range using the high-sensitivity and unbiased spectral surveys obtained with the IRAM 30-m antenna in the ASAI context, the earliest stages of star formation from starless to evolved Class I objects being sampled. For both the $Z$ and $E$ isomers, the spectroscopic work has led to an improved and extended knowledge of the spectroscopic parameters, thus providing accurate predictions of the rotational signatures up to $\sim$700 GHz. So far, no C-cyanomethanimine emission has been detected toward the ASAI targets, and upper limits of the column density of $\sim$ 10$^{11}$--10$^{12}$ cm$^{-2}$ could only be derived. Consequently, the C-cyanomethanimine abundances have to be less than a few 10$^{-10}$ for starless and hot-corinos. A less stringent constraint, $\leq$ 10$^{-9}$, is obtained for shocks sites. The combination of the upper limits of the abundances of C-cyanomethanimine together with accurate laboratory frequencies up to $\sim$ 700 GHz poses the basis for future higher sensitivity searches around Sun-like-star forming regions.

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arXiv2017

Probing the cold dust emission in the AB Aur disk: a dust trap in a decaying vortex?

One serious challenge for planet formation is the rapid inward drift of pebble-sized dust particles in protoplanetary disks. Dust trapping at local maxima in the disk gas pressure has received much theoretical attention but still lacks observational support. The cold dust emission in the AB Aur disk forms an asymmetric ring at a radius of about 120 au, which is suggestive of dust trapping in a gas vortex. We present high spatial resolution (0".58x0".78 ~ 80x110 au) NOEMA observations of the 1.12 mm and 2.22 mm dust continuum emission from the AB Aur disk. Significant azimuthal variations of the flux ratio at both wavelengths indicate a size segregation of the large dust particles along the ring. Our continuum images also show that the intensity variations along the ring are smaller at 2.22 mm than at 1.12 mm, contrary to what dust trapping models with a gas vortex have predicted. Our two-fluid (gas+dust) hydrodynamical simulations demonstrate that this feature is well explained if the gas vortex has started to decay due to turbulent diffusion, and dust particles are thus losing the azimuthal trapping on different timescales depending on their size. The comparison between our observations and simulations allows us to constrain the size distribution and the total mass of solid particles in the ring, which we find to be of the order of 30 Earth masses, enough to form future rocky planets.

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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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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

H2S in the L1157-B1 Bow shock

Sulfur-bearing molecules are highly reactive in the gas phase of the ISM. However, the form in which most of the sulfur is locked onto interstellar dust grains is unknown. By taking advantage of the short time-scales of shocks in young molecular outflows, one could track back the main form of sulfur in the ices. In this paper, six transitions of H$_2$S and its isotopologues in the L1157-B1 bowshock have been detected using data from the Herschel-CHESS survey and the IRAM-30m ASAI large program. These detections are used to calculate the properties of H$_2$S gas in L1157-B1 through use of a rotation diagram and to explore the possible carriers of sulfur on the grains. The isotopologue detections allow the first calculation of the H$_2$S deuteration fraction in an outflow from a low mass protostar. The fractional abundance of H$_2$S in the region is found to be 6.0$\times$10$^{-7}$ and the deuteration fraction is 2$\times$10$^{-2}$. In order to investigate the form of sulfur on the grains, a chemical model is run with four different networks, each with different branching ratios for the freeze out of sulfur bearing species into molecules such as OCS and H$_2$S. It is found that the model best fits the data when at least half of each sulfur bearing species hydrogenates when freezing. We therefore conclude that a significant fraction of sulfur in L1157-B1 is likely to be locked in H$_2$S on the 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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arXiv2015

The radio continuum spectrum of Mira A and Mira B up to submillimeter wavelengths

We present new measurements of the flux densities at submillimeter wavelengths based on ALMA band 7 (338 GHz) and band 9 (679 GHz) observations to better constrain the origin of the continuum emission of the Mira AB binary system and to check its orbit. We have measured the Mira A and Mira B continuum in ALMA band 7, with a resolution of ~0"31, and for the first time in ALMA band 9, with a resolution of ~0"18. We resolved the binary system at both bands, and derived the continuum spectral index of the stars and their relative position. We also analyzed ALMA SciVer data obtained in bands 6 and 3. Measurements at centimeter wavelengths obtained by other authors have been included in our study of the spectral energy distribution of the Mira components. The Mira A continuum emission has a spectral index of 1.98+-0.04 extending from submillimeter down to centimeter wavelengths. The spectral index of the Mira B continuum emission is 1.93+-0.06 at wavelengths ranging from submillimeter to ~3.1 mm, and a shallower spectral index of 1.22+-0.09 at longer wavelengths. The Mira A continuum emission up to submillimeter wavelengths is consistent with that of a radio photosphere surrounding the evolved star for which models predict a spectral index close to 2. The Mira B continuum emission cannot be described with a single ionized component. An extremely compact and dense region around the star can produce the nearly thermal continuum measured in the 0.4-3.1 mm wavelength range, and an inhomogeneous, less dense, and slightly larger ionized envelope could be responsible for the emission at longer wavelengths. Our results illustrate the potential of ALMA for high precision astrometry of binary systems. We have found a significant discrepancy of ~14 milliarcsec between the ALMA measurements and the predicted orbit positions.

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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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