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J. Brand

Publications and source records attributed to J. Brand.

At least 19 recordsLinked to original sources

Odd-frequency pair correlations in the trapped fermionic Tonks-Girardeau gas

The fermionic Tonks-Girardeau gas is an exactly solvable model realizing a conventional macroscopic condensate of p-wave Cooper pairs. Here we demonstrate that, when confined by a trapping potential, it also hosts unconventional odd-frequency pairing, i.e., pair correlations with s-wave symmetry that are only present with a finite time delay t between fermions forming a pair. Quantitative results for fixed particle number are obtained using a generalization of Yang's theory of off-diagonal long-range order to define a t-dependent order parameter that is antisymmetric under combined t inversion and exchange of fermion-pair indices. Odd-frequency pairing in the fermionic Tonks-Girardeau gas is found to be a mesoscopic effect, localized at the system's boundary and therefore nonextensive thermodynamically. Our results show that this elusive hidden order is accessible in systems having fixed particle number, suggesting new avenues towards its experimental realization and further detailed study.

cond-mat.quant-gas

OGHReS: Star formation in the Outer Galaxy II ($\ell = 180^\circ$-$280^\circ$)

The Outer Galaxy High-Resolution Survey (OGHReS) covers 100 square degrees ($180^\circ < \ell < 280^\circ$) in the (2--1) transitions of three CO-isotopologues. We use the spectra to refine the velocities and physical properties to 6706 \higal\ clumps located in the OGHReS region. In a previous paper, we analysed 3584 clumps between $\ell = 250^\circ$ and $280^\circ$. Here, we cover a further 3122 clumps ($180^\circ < \ell < 250^\circ$) and determine reliable velocities for \withVLSR\ of these, finding good agreement with the previously assigned velocities ($\sim$80 percent within 5 \kms). We update velocities for 288 clumps and provide new values for an additional 411. Combining these with the previous results, we have velocities and physical properties for 6193 clumps (92.3 percent). The \allnonDetections\ non-detections are low surface density clumps or likely contamination by evolved stars and galaxies. Key findings: i) improved correlation between clumps and spiral arm loci, and the discovery of clumps beyond the outer arm supports the existence of a new spiral structure; ii) decreasing trend in the $L/M$-ratio consistent with less high-mass star formation in the outer Galaxy; iii) increase in the star formation fraction (SFF) in the outer Galaxy, suggesting that more clumps are forming stars despite their lower mass; iv) discrepancies in velocity assignments across different surveys that could affect $\sim$10000 clumps, especially in the fourth quadrant.

astro-ph.GA

Time evolution of o-H$_2$D$^+$, N$_2$D$^+$, and N$_2$H$^+$ during the high-mass star formation process

Deuterium fractionation is a well-established evolutionary tracer in low-mass star formation, but its applicability to the high-mass regime remains an open question. The abundances and ratios of deuterated species have often been proposed as reliable evolutionary indicators for different stages of the high-mass star formation. We investigate the role of N$_2$H$^+$ and key deuterated molecules as tracers of the different stages of the high-mass star formation, and test whether their abundance ratios can serve as reliable evolutionary indicators. We conducted APEX observations of o-H$_2$D$^+$ (1$_{10}$-1$_{11}$), N$_2$H$^+$ (4-3), and N$_2$d$^+$ (3-2) in 40 high-mass clumps at different evolutionary stages, selected from the ATLASGAL survey. Molecular column densities ($N$) and abundances ($X$), were derived through spectral line modelling, both under local thermodynamic equilibrium (LTE) and non-LTE conditions. The $N$(o-H$_2$D$^+$) show the smallest deviation from LTE results when derived under non-LTE assumptions. In contrast, N$_2$D$^+$ shows the largest discrepancy between the $N$ derived from LTE and non-LTE. In all the cases discussed, we found that $X$(o-H$_2$D$^+$) decreases more significantly with time than in the case of $X$(N$_2$D$^+$); whereas $X$(N$_2$H$^+$) increases slightly. Therefore, the validity of the recently proposed $X$(o-H$_2$D$^+$)/$X$(N$_2$D$^+$) ratio as a reliable evolutionary indicator was not observed for this sample. While the deuteration fraction derived from N$_2$D$^+$ and N$_2$H$^+$ clearly decreases with clump evolution, the interpretation of this trend is complex, given the different distribution of the two tracers. Our results suggest that a careful consideration of the observational biases and beam-dilution effects are crucial for an accurate interpretation of the evolution of the deuteration process during the high-mass star formation process.

astro-ph.GA

Odd-frequency superfluidity from a particle-number-conserving perspective

We investigate odd-in-time - or odd-frequency - pairing of fermions in equilibrium systems within the particle-number-conserving framework of Penrose, Onsager and Yang, where superfluid order is defined by macroscopic eigenvalues of reduced density matrices. We show that odd-frequency pair correlations are synonymous with even fermion-exchange symmetry in a time-dependent correlation function that generalises the two-body reduced density matrix. Macroscopic even-under-fermion-exchange pairing is found to emerge from conventional Penrose-Onsager-Yang condensation in two-body or higher-order reduced density matrices through the symmetry-mixing properties of the Hamiltonian. We identify and characterise a transformer matrix responsible for producing macroscopic even fermion-exchange correlations that coexist with a conventional Cooper-pair condensate, while a generator matrix is shown to be responsible for creating macroscopic even fermion-exchange correlations from hidden orders such as a multi-particle condensate. The transformer scenario is illustrated using the spin-balanced s-wave superfluid with Zeeman splitting as an example. The generator scenario is demonstrated by the composite-boson condensate arising for itinerant electrons coupled to magnetic excitations. Structural analysis of the transformer and generator matrices is shown to provide general conditions for odd-frequency pairing order to arise in a given system. Our formalism facilitates a fully general derivation of the Meissner effect for odd-frequency superconductors that holds also beyond the regime of validity for mean-field theory.

cond-mat.supr-con

Water vapour masers in long-period variable stars III. Mira variables U Her and RR Aql

Within the 'Medicina/Effelsberg H2O maser monitoring program' we observed U Her and RR Aql at 22-GHz for about two decades between 1990 and 2011, with a gap between 1997 and 2000 in the case of RR Aql. In addition, maps were obtained in the period 1990-1992 of U Her with the Very Large Array. We find that the strongest emission in U Her is located in a shell with boundaries 11-25 AU. The gas crossing time is 8.5 years. We derive lifetimes for individual maser clouds of less than 4 years, based on the absence of detectable line-of-sight velocity drifts of the maser emission. The shell is not evenly filled, and its structure is maintained on timescales much longer than those of individual maser clouds. Both stars show brightness variability on several timescales. The prevalent variation is periodic, following the optical variability of the stars with a lag of 2-3 months. Superposed are irregular fluctuations, of a few months' duration, of increased or decreased excitation at particular locations, and long-term systematic variations on timescales of a decade or more. The properties of the maser emission are governed by those of the stellar wind while traversing the water maser shell. Inhomogeneities in the wind affecting the excitation conditions and prevalent beaming directions likely cause the variations seen on timescales longer than the stellar pulsation period. We propose the existence of long-living regions in the shells, which maintain favourable excitation conditions on timescales of the wind crossing times through the shells or orbital periods of (sub-)stellar companions.

astro-ph.GA

OGHReS: Star formation in the Outer Galaxy ($\ell = 250^\circ$-$280^\circ$)

We have used data from the Outer Galaxy High-Resolution Survey (OGHReS) to refine the velocities, distances, and physical properties of a large sample of 3584 clumps detected in far infrared/submillimetre emission in the HiGAL survey located in the $\ell = 250^\circ-280^\circ$ region of the Galactic plane. Using $^{12}$CO and $^{13}$CO spectra, we have determined reliable velocities to 3412 clumps (95% of the sample). In comparison to the velocities from the HiGAL catalogue, we find good agreement for 80% of the sample (within 5 km/s). Using the higher resolution and sensitivity of OGHReS has allowed us to correct the velocity for 632 clumps and provide velocities for 687 clumps for which no velocity had been previously allocated. The velocities are used with a rotation curve to refine the distances to the clumps and to calculate the clumps' properties using a distance-dependent gas-to-dust ratio. We have determined reliable physical parameters for 3200 outer Galaxy dense clumps (~90% of the HiGAL sources in the region). We find a trend of decreasing luminosity-to-mass ratio with increasing Galactocentric distance, suggesting the star formation efficiency is lower in the outer Galaxy or that it is resulting in more lower mass stars than in the inner Galaxy. We also find a similar surface density for protostellar clumps located in the inner and outer Galaxy, revealing that the surface density requirements for star formation are the same across the Galactic disc.

astro-ph.GA

A Keplerian disk with a four-arm spiral birthing an episodically accreting high-mass protostar

High-mass protostars (M$_{\star} >$ 8 M$_{\odot}$) are thought to gain the majority of their mass via short, intense bursts of growth. This episodic accretion is thought to be facilitated by gravitationally unstable and subsequently inhomogeneous accretion disks. Limitations of observational capabilities, paired with a lack of observed accretion burst events has withheld affirmative confirmation of the association between disk accretion, instability and the accretion burst phenomenon in high-mass protostars. Following its 2019 accretion burst, a heat-wave driven by a burst of radiation propagated outward from the high-mass protostar G358.93-0.03-MM1. Six VLBI (very long baseline interferometry) observations of the raditively pumped 6.7 GHz methanol maser were conducted during this period, tracing ever increasing disk radii as the heat-wave propagated outward. Concatenating the VLBI maps provided a sparsely sampled, milliarcsecond view of the spatio-kinematics of the accretion disk covering a physical range of $\sim$ 50 - 900 AU. We term this observational approach `heat-wave mapping'. We report the discovery of a Keplerian accretion disk with a spatially resolved four-arm spiral pattern around G358.93-0.03-MM1. This result positively implicates disk accretion and spiral arm instabilities into the episodic accretion high-mass star formation paradigm.

astro-ph.SR

OGHReS: Large-scale filaments in the outer Galaxy

Filaments are a ubiquitous morphological feature of the molecular interstellar medium and are identified as sites of star formation. In recent years, more than 100 large-scale filaments (with a length $>10$\,pc) have been observed in the inner Milky Way. As they appear linked to Galactic dynamics, studying those structures represents an opportunity to link kiloparsec-scale phenomena to the physics of star formation, which operates on much smaller scales. In this letter, we use newly acquired Outer Galaxy High Resolution Survey (OGHReS) $^{12}$CO(2-1) data to demonstrate that a significant number of large-scale filaments are present in the outer Galaxy as well. The 37 filaments identified appear tightly associated with inter-arm regions. In addition, their masses and linear masses are, on average, one order of magnitude lower than similar-sized molecular filaments located in the inner Galaxy, showing that Milky Way dynamics is able to create very elongated features in spite of the lower gas supply in the Galactic outskirts.

astro-ph.GA

Establishing the evolutionary timescales of the massive star formation process through chemistry

(Abridged) Understanding the details of the formation process of massive (i.e. M<8-10M$_\odot$) stars is a long-standing problem in astrophysics. [...] We present a method to derive accurate timescales of the different evolutionary phases of the high-mass star formation process. We model a representative number of massive clumps of the ATLASGAL-TOP100 sample which cover all the evolutionary stages. The models describe an isothermal collapse and the subsequent warm-up phase, for which we follow their chemical evolution. The timescale of each phase is derived by comparing the results of the models with the properties of the sources of the ATLASGAL-TOP100 sample, taking into account the mass and luminosity of the clumps, and the column densities of methyl acetylene (CH$_3$CCH), acetonitrile (CH$_3$CN), formaldehyde (H$_2$CO) and methanol (CH$_3$OH). We find that the chosen molecular tracers are affected by the thermal evolution of the clumps, showing steep ice evaporation gradients from 10$^3$ to 10$^5$ AU during the warm-up phase. We succeed in reproducing the observed column densities of CH$_3$CCH and CH$_3$CN, while H$_2$CO and CH$_3$OH show a poorer agreement with the observed values. The total (massive) star formation time is found to be $\sim5.2\times10^5$ yr, which is defined by the timescales of the individual evolutionary phases of the ATLASGAL-TOP100 sample: $\sim5\times10^4$ yr for 70-$μ$m weak, $\sim1.2\times10^5$ yr for mid-IR weak, $\sim2.4\times10^5$ yr for mid-IR bright and $\sim1.1\times10^5$ yr for HII-regions phases. Our models, with an appropriate selection of molecular tracers that can act as chemical clocks, allow to get robust estimates of the duration of the individual phases of the high-mass star formation process, with the advantage of being capable to include additional tracers aimed at increasing the accuracy of the estimated timescales.

astro-ph.GA

Molecular cloud catalogue from $^{13}$CO(1-0) data of the Forgotten Quadrant Survey

New-generation spectroscopic surveys of the Milky Way plane have been revealing the structure of the interstellar medium, allowing the simultaneous study of dense structures from single star-forming objects or systems to entire spiral arms. We present the catalogue of molecular clouds extracted from the $^{13}$CO(1-0) data cubes of the Forgotten Quadrant Survey, which mapped the Galactic plane in the range 220°<l<240°, and -2.5°<b<0°in $^{12}$CO(1-0) and $^{13}$CO(1-0).The catalogue contains 87 molecular clouds for which the main physical parameters such as area, mass, distance, velocity dispersion, and virial parameter were derived. These structures are overall less extended and less massive than the molecular clouds identified in the $^{12}$CO(1-0) data-set because they trace the brightest and densest part of the $^{12}$CO(1-0) clouds. Conversely, the distribution of aspect ratio, equivalent spherical radius, velocity dispersion, and virial parameter in the two catalogues are similar. The mean value of the mass surface density of molecular clouds is 87$\pm$55 M$_{\odot}$ pc$^{-2}$ and is almost constant across the galactocentric radius, indicating that this parameter, which is a proxy of star formation, is mostly affected by local conditions.In data of the Forgotten Quadrant Survey, we find a good agreement between the total mass and velocity dispersion of the clouds derived from $^{12}$CO(1-0) and $^{13}$CO(1-0). This is likely because in the surveyed portion of the Galactic plane, the H$_2$ column density is not particularly high, leading to a CO emission with a not very high optical depth. This mitigates the effects of the different line opacities between the two tracers on the derived physical parameters. This is a common feature in the outer Galaxy, but our result cannot be readily generalised to the entire Milky Way.

astro-ph.GA

The Additional Representative Images for Legacy (ARI-L) project for the ALMA Science Archive

The Additional Representative Images for Legacy (ARI-L) project is a European Development project for ALMA Upgrade approved by the Joint ALMA Observatory (JAO) and the European Southern Observatory (ESO), started in June 2019. It aims to increase the legacy value of the ALMA Science Archive (ASA) by bringing the reduction level of ALMA data from Cycles 2-4 close to that of data from more recent Cycles processed for imaging with the ALMA Pipeline. As of mid-2021 more than 150000 images have been returned to the ASA for public use. At its completion in 2022, the project will have provided enhanced products for at least 70% of the observational data from Cycles 2-4 processable with the ALMA Pipeline. In this paper we present the project rationale, its implementation, and the new opportunities offered to ASA users by the ARI-L products. The ARI-L cubes and images complement the much limited number of archival image products generated during the data quality assurance stages (QA2), which cover only a small fraction of the available data for those Cycles. ARI-L imaging products are highly relevant for many science cases and significantly enhance the possibilities for exploiting archival data. Indeed, ARI-L products facilitate archive access and data usage for science purposes even for non-expert data miners, provide a homogeneous view of all data for better dataset comparisons and download selections, make the archive more accessible to visualization and analysis tools, and enable the generation of preview images and plots similar to those possible for subsequent Cycles.

astro-ph.IM

Coexistence of topological and nontopological Fermi-superfluid phases

The two-dimensional spin-imbalanced Fermi gas subject to s-wave pairing and spin-orbit coupling is considered a promising platform for realizing a topological chiral-p-wave superfluid. In the BCS limit of s-wave pairing, i.e., when Cooper pairs are only weakly bound, the system enters the topological phase via a second-order transition driven by increasing the Zeeman spin-splitting energy. Stronger attractive two-particle interactions cause the system to undergo the BCS-BEC crossover, in the course of which the topological transition becomes first-order. As a result, topological and nontopological superfluids coexist in spatially separated domains in an extended region of phase space spanned by the strength of s-wave interactions and the Zeeman energy. Here we investigate this phase-coexistence region theoretically using a zero-temperature mean-field approach. Exact numerical results are presented to illustrate basic physical characteristics of the coexisting phases and to validate an approximate analytical description derived for weak spin-orbit coupling. Besides extending our current understanding of spin-imbalanced superfluid Fermi systems, the present approach also provides a platform for future studies of unconventional Majorana excitations that, according to topology, should be present at the internal interface between coexisting topological and nontopological superfluid parts of the system.

cond-mat.quant-gas

Physical conditions in the warped accretion disk of a massive star. 349 GHz ALMA observations of G023.01$-$00.41

Young massive stars warm up the large amount of gas and dust which condenses in their vicinity, exciting a forest of lines from different molecular species. Their line brightness is a diagnostic tool of the gas physical conditions locally, which we use to set constraints on the environment where massive stars form. We made use of the Atacama Large Millimeter/submillimeter Array at frequencies near 349 GHz, with an angular resolution of $0.1''$, to observe the methyl cyanide (CH$_3$CN) emission which arises from the accretion disk of a young massive star. We sample the disk midplane with twelve distinct beams, where we get an independent measure of the gas (and dust) physical conditions. The accretion disk extends above the midplane showing a double-armed spiral morphology projected onto the plane of the sky, which we sample with ten additional beams: along these apparent spiral features, gas undergoes velocity gradients of about $\rm 1 km s^{-1}$ per 2000 au. The gas temperature (T) rises symmetrically along each side of the disk, from about 98 K at 3000 au to 289 K at 250 au, following a power law with radius, R$^{-0.43}$. The CH$_3$CN column density (N) increases from $\rm 9.2\times10^{15} cm^{-2}$ to $\rm 8.7\times10^{17} cm^{-2}$ at the same radii, following a power law with radius, R$^{-1.8}$. In the framework of a circular gaseous disk observed approximately edge-on, we infer an H$_2$ volume density in excess of $\rm 4.8\times10^9 cm^{-3}$ at a distance of 250 au from the star. We study the disk stability against fragmentation following the methodology by Kratter et al. (2010), appropriate under rapid accretion, and we show that the disk is marginally prone to fragmentation along its whole extent.

astro-ph.GA

A possible far-ultraviolet flux-dependent core mass function in NGC 6357

To derive the properties of the dense cores in the galactic star-forming complex NGC6357 and to investigate the effects of an intense far-UV radiation field on their properties, we mapped the region at 450 and 850 micron, and in the CO(3-2) line with the JCMT. We also made use of the Herschel Hi-GAL data at 70 and 160 micron. We used Gaussclumps to retrieve 686 compact cores embedded in the diffuse sub-mm emission and constructed their SED from 70 to 850 micron, from which we derived mass and temperature. The estimated mass completeness limit is ~5Mo. We divided the observed area in an 'active' region, exposed to the far-UV radiation from the more massive members of three star clusters (411 cores), and a 'quiescent' region, less affected by far-UV radiation (275 cores). We also attempted to select a sample of pre-stellar cores based on cross-correlation with 70 micron emission and red WISE point sources. Most of the cores above the mass completeness limit are likely to be gravitationally bound. The fraction of gas in dense cores is very low, 1.4%. We found a mass-size relation log(M/Mo) ~ (2.0-2.4) x log (D/arcsec), depending on the precise selection of the sample. The temperature distributions in the two sub-regions are clearly different, peaking at ~25K in the quiescent region and at ~35K in the active region. The core mass functions are different as well, at a 2sigma level, consistent with a Salpeter IMF in the quiescent region and flatter than that in the active region. The dense cores lying close to the HII regions are consistent with pre-existing cores being gradually engulfed by a PDR and photoevaporating. We attribute the different global properties of dense cores in the two sub-regions to the influence of the far-UV radiation field.

astro-ph.GA

Water vapour masers in long-period variable stars II. The semi-regular variables R Crt and RT Vir

Within the 'Medicina/Effelsberg H2O maser monitoring program' we have observed the maser emission of R Crt and RT Vir for more than two decades. To get insight in the distribution and longevity of maser spots in the circumstellar envelopes, we have collected interferometric data, taken in the same period, from the literature. We confirm short-time variations of individual maser features on timescales of months to up to 1.5 years. Also decade-long variations of the general brightness level independent from individual features were seen in both stars. These are due to brightness variations occurring independently from each other in selected velocity ranges, and are independent of the optical lightcurves. Expected drifts in velocity of individual features are usually masked by blending. However, in RT Vir we found an exceptional case of a feature with a constant velocity over 7.5 years (<0.06 km/s/yr). We attribute the long-term brightness variations to the presence of regions with higher-than-average density in the stellar wind, which host several clouds which emit maser radiation on the short time scales. These regions typically need ~20 years to cross the H2O maser shell, where the right conditions to excite H2O masers are present. The constant velocity feature (11 km/s) is likely to come from a single maser cloud, which moved through about half of RT Vir's H2O maser shell without changing velocity. From this we infer that its path was located in the outer part of the H2O maser shell, where RT Vir's stellar wind apparently has already reached its terminal outflow velocity. This conclusion is corroborated by the observation that the highest H2O maser outflow velocity in RT Vir approaches the terminal outflow velocity as given by OH and CO observations. This is generally not observed in other semi-regular variable stars.

astro-ph.GA

Square Kilometre Array Science Data Challenge 1: analysis and results

As the largest radio telescope in the world, the Square Kilometre Array (SKA) will lead the next generation of radio astronomy. The feats of engineering required to construct the telescope array will be matched only by the techniques developed to exploit the rich scientific value of the data. To drive forward the development of efficient and accurate analysis methods, we are designing a series of data challenges that will provide the scientific community with high-quality datasets for testing and evaluating new techniques. In this paper we present a description and results from the first such Science Data Challenge (SDC1). Based on SKA MID continuum simulated observations and covering three frequencies (560 MHz, 1400MHz and 9200 MHz) at three depths (8 h, 100 h and 1000 h), SDC1 asked participants to apply source detection, characterization and classification methods to simulated data. The challenge opened in November 2018, with nine teams submitting results by the deadline of April 2019. In this work we analyse the results for 8 of those teams, showcasing the variety of approaches that can be successfully used to find, characterise and classify sources in a deep, crowded field. The results also demonstrate the importance of building domain knowledge and expertise on this kind of analysis to obtain the best performance. As high-resolution observations begin revealing the true complexity of the sky, one of the outstanding challenges emerging from this analysis is the ability to deal with highly resolved and complex sources as effectively as the unresolved source population.

astro-ph.IM

Direct Measurements of Collisional Dynamics in Cold Atom Triads

The introduction of optical tweezers for trapping atoms has opened remarkable opportunities for manipulating few-body systems. Here, we present the first bottom-up assembly of atom triads. We directly observe atom loss through inelastic collisions at the single event level, overcoming the substantial challenge in many-atom experiments of distinguishing one-, two-, and three-particle processes. We measure a strong suppression of three-body loss, which is not fully explained by the presently availably theory for three-body processes. The suppression of losses could indicate the presence of local anti-correlations due to the interplay of attractive short range interactions and low dimensional confinement. Our methodology opens a promising pathway in experimental few-body dynamics.

quant-ph

The Forgotten Quadrant Survey. $^{12}$CO and $^{13}$CO (1-0) survey of the Galactic Plane in the range 220°$<l<$240° -2.5°$<b<$0°

We present the Forgotten Quadrant Survey (FQS), an ESO large project that used the 12m antenna of the Arizona Radio Observatory to map the Galactic Plane in the range 220°$<l<$240°and -2.5°$<b<$0°, both in $^{12}$CO(1-0) and $^{13}$CO(1-0), at a spectral resolution of 0.65 km s$^{-1}$ and 0.26 km s$^{-1}$. Our dataset allows us to easily identify how the molecular dense gas is organised at different spatial scales: from the giant clouds with their denser filamentary networks, down to the clumps and cores that host the newborn stars and to obtain reliable estimates of their key physical parameters. We present the first release of the FQS data and discuss their quality. Spectra with 0.65 km s$^{-1}$ velocity channels have a noise ranging from 0.8 K to 1.3 K for $^{12}$CO(1-0) and from 0.3 K to 0.6 K for $^{13}$CO(1-0). In this paper, we used the $^{12}$CO(1-0) spectral cubes to produce a catalogue of 263 molecular clouds. This is the first selfconsistent, statistical catalogue of molecular clouds of the outer Galaxy, obtained with a subarcminute spatial resolution and therefore able to detect not only the classical giant molecular clouds, but also the small clouds and to resolve the cloud structure at the subparsec scale up to a distance of a few kpc. We found two classes of objects: structures with size above a few parsecs that are typical molecular clouds and may be self-gravitating, and subparsec structures that cannot be in gravitational equilibrium and are likely transient or confined by external pressure. We used the ratio between the Herschel H$_2$ column density and the integrated intensity of the CO lines to calculate the CO conversion factor and we found mean values of (3.3$\pm$1.4)$\times 10^{20}$ cm$^{-2}$(K km s$^{-1})^{-1}$ and (1.2$\pm$0.4)$\times 10^{21}$ cm$^{-2}$(K km s$^{-1})^{-1}$, for $^{12}$CO(1-0) and $^{13}$CO(1-0), respectively.

astro-ph.GA