arXiv subjects

F. Bigiel

Publications and source records attributed to F. Bigiel.

At least 73 records · Page 4Linked to original sources

arXiv2020

Cloud formation in the atomic and molecular phase: HI self absorption (HISA) towards a Giant Molecular Filament

Molecular clouds form from the atomic phase of the interstellar medium. However, characterizing the transition between the atomic and the molecular interstellar medium (ISM) is a difficult observational task. Here we address cloud formation processes by combining HSIA with molecular line data. One scenario proposed by numerical simulations is that the column density probability density functions (N-PDF) evolves from a log-normal shape at early times to a power-law-like shape at later times. In this paper, we study the cold atomic component of the giant molecular filament GMF38a (d=3.4 kpc, length$\sim230$ pc). We identify an extended HISA feature, which is partly correlated with the 13CO emission. The peak velocities of the HISA and 13CO observations agree well on the eastern side of the filament, whereas a velocity offset of approximately 4 km s$^{-1}$ is found on the western side. The sonic Mach number we derive from the linewidth measurements shows that a large fraction of the HISA, which is ascribed to the cold neutral medium (CNM), is at subsonic and transonic velocities. The column density of the CNM is on the order of 10$^{20}$ to 10$^{21}$ cm$^{-2}$. The column density of molecular hydrogen is an order of magnitude higher. The N-PDFs from HISA (CNM), HI emission (WNM+CNM), and 13CO (molecular component) are well described by log-normal functions, which is in agreement with turbulent motions being the main driver of cloud dynamics. The N-PDF of the molecular component also shows a power law in the high column-density region, indicating self-gravity. We suggest that we are witnessing two different evolutionary stages within the filament. The eastern subregion seems to be forming a molecular cloud out of the atomic gas, whereas the western subregion already shows high column density peaks, active star formation and evidence of related feedback processes.

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arXiv2019

The HI/OH/Recombination line survey of the inner Milky Way (THOR): data release 2 and HI overview

With the $Karl~G.~Jansky$ Very Large Array (VLA) in C-configuration, we observed a large portion of the first Galactic quadrant ($l=14.0-67.4^\circ $ and $\lvert b \rvert \leq 1.25^\circ $) achieving an angular resolution of $\leq 40^{\prime\prime}$. At $L$ Band, the WIDAR correlator at the VLA was set to cover the 21~cm HI line, four OH transitions, a series of H$nα$ radio recombination lines (RRLs; $n=151$ to 186), and eight 128~MHz wide continuum spectral windows (SPWs) simultaneously. The HI emission shows clear filamentary substructures at negative velocities with low velocity crowding. The emission at positive velocities is more smeared-out likely due to higher spatial and velocity crowding of structures at the positive velocities. Comparing to the spiral arm model of the Milky Way, the atomic gas follows the Sagittarius and Perseus Arm well but with significant material in the inter-arm regions. With the C-configuration-only HI+continuum data, we produced a HI optical depth map of the THOR areal coverage from 228 absorption spectra with the nearest-neighbor method. With this $τ$ map, we corrected the HI emission for optical depth and the derived column density is 38% higher than the column density with optically thin assumption. The total HI mass with optical depth correction in the survey region is 4.7$\times10^8~M_\odot$, 31% more than the mass derived assuming the emission is optically thin. If we apply this 31% correction to the whole Milky Way, the total atomic gas mass would be 9.4-10.5$\times 10^9~M_\odot$. Comparing the HI with existing CO data, we find a significant increase in the atomic-to-molecular gas ratio from the spiral arms to the inter-arm regions.

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arXiv2019

Strong excess Faraday rotation on the Inside of the Sagittarius spiral arm

We present first results for Faraday rotation of compact polarized sources (1 to 2 GHz continuum) in The HI/OH/Recombination line (THOR) survey of the inner Galaxy. In the Galactic longitude range 39 degr < l < 52 degr, we find rotation measures in the range -310 rad/m2 < RM < +4219 rad/m2, with the highest values concentrated within a degree of l = 48 degrees at the Sagittarius arm tangent. Most of the high RMs arise in diffuse plasma, along lines of sight that do not intersect HII regions. For l > 49 degr, RM drops off rapidly, while at l < 47 degr, the mean RM is higher with a larger standard deviation than at l > 49 degr. We attribute the RM structure to the compressed diffuse Warm Ionized Medium in the spiral arm, upstream of the major star formation regions. The Sagittarius arm acts as a significant Faraday screen inside the Galaxy. This has implications for models of the Galactic magnetic field and the expected amount of Faraday rotation of Fast Radio Bursts from their host galaxies. We emphasize the importance of sensitivity to high Faraday depth in future polarization surveys.

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arXiv2019

Mapping metallicity variations across nearby galaxy disks

The distribution of metals within a galaxy traces the baryon cycle and the buildup of galactic disks, but the detailed gas phase metallicity distribution remains poorly sampled. We have determined the gas phase oxygen abundances for 7,138 HII regions across the disks of eight nearby galaxies using VLT/MUSE optical integral field spectroscopy as part of the PHANGS-MUSE survey. After removing the first order radial gradients present in each galaxy, we look at the statistics of the metallicity offset (Delta O/H) and explore azimuthal variations. Across each galaxy, we find low (sigma=0.03-0.05 dex) scatter at any given radius, indicative of efficient mixing. We compare physical parameters for those HII regions that are 1 sigma outliers towards both enhanced and reduced abundances. Regions with enhanced abundances have high ionization parameter, higher Halpha luminosity, lower Halpha velocity dispersion, younger star clusters and associated molecular gas clouds show higher molecular gas densities. This indicates recent star formation has locally enriched the material. Regions with reduced abundances show increased Halpha velocity dispersions, suggestive of mixing introducing more pristine material. We observe subtle azimuthal variations in half of the sample, but can not always cleanly associate this with the spiral pattern. Regions with enhanced and reduced abundances are found distributed throughout the disk, and in half of our galaxies we can identify subsections of spiral arms with clearly associated metallicity gradients. This suggests spiral arms play a role in organizing and mixing the ISM.

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arXiv2019

OH maser emission in the THOR survey of the northern Milky Way

Context: OH masers trace diverse physical processes, from the expanding envelopes around evolved stars to star-forming regions or supernovae remnants. Aims: We identify the ground-state OH masers at 18cm wavelength in the area covered by ``The HI/OH/Recombination line survey of the Milky Way (THOR)''. We present a catalogue of all OH maser features and their possible associated environments. Methods: The THOR survey covers longitude and latitude ranges of 14.3<l<66.8 and b<1.25 deg. All OH ground state lines at 1612, 1665, 1667 and 1720MHz have been observed, employing the Very Large Array. The spatial resolution of the data varies between 12.5'' and 19'', the spectral resolution is 1.5km/s, and the rms sensitivity of the data is ~10mJy/beam per channel. Results: We identify 1585 individual maser spots distributed over 807 maser sites. Based on different criteria from spectral profiles to literature comparison, we try to associate the maser sites with astrophysical source types. Approximately 51\% of the sites exhibit the double-horned 1612MHz spectra typically emitted from the expanding shells of evolved stars. The separations of the two main velocity features of the expanding shells typically vary between 22 and 38km/s. In addition to this, at least 20% of the maser sites are associated with star-forming regions. While the largest fraction of 1720MHz maser spots (21 out of 53) is associated with supernova remnants, a significant fraction of the 1720MHz maser spots (17) are also associated with star-forming regions. We present comparisons to the thermal 13CO(1-0) emission as well as to other surveys of class II CH3OH and H2O maser emission. The catalogue attempts to present associations to astrophysical sources where available, and the full catalogue is available in electronic form.

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arXiv2019

Feedback in W49A diagnosed with radio recombination lines and models

We present images of radio recombination lines (RRLs) at wavelengths around 17 cm from the star-forming region W49A to determine the kinematics of ionized gas in the THOR survey (The HI/OH/Recombination line survey of the inner Milky Way) at an angular resolution of 16.8"x13.8". The distribution of ionized gas appears to be affected by feedback processes from the star clusters in W49A. The velocity structure of the RRLs shows a complex behavior with respect to the molecular gas. We find a shell-like distribution of ionized gas as traced by RRL emission surrounding the central cluster of OB stars in W49A. We describe the evolution of the shell with the recent feedback model code WARPFIELD that includes the important physical processes and has previously been applied to the 30 Doradus region in the Large Magellanic Cloud. The cloud structure and dynamics of W49A are in agreement with a feedback-driven shell that is re-collapsing. The shell may have triggered star formation in other parts of W49A. We suggest that W49A is a potential candidate for star formation regulated by feedback-driven and re-collapsing shells.

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arXiv2019

EMPIRE: The IRAM 30-m Dense Gas Survey of Nearby Galaxies

We present EMPIRE, an IRAM 30-m large program that mapped $λ= 3{-}4$ mm dense gas tracers at $\sim 1{-}2\,$kpc resolution across the whole star-forming disk of nine nearby, massive, spiral galaxies. We describe the EMPIRE observing and reduction strategies and show new whole-galaxy maps of HCN(1-0), HCO$^+$(1-0), HNC(1-0) and CO(1-0). We explore how the HCN-to-CO and IR-to-HCN ratios, observational proxies for the dense gas fraction and dense gas star formation efficiency, depend on host galaxy and local environment. We find that the fraction of dense gas correlates with stellar surface density, gas surface density, molecular-to-atomic gas ratio, and dynamical equilibrium pressure. In EMPIRE, the star formation rate per unit dense gas anti-correlates with these same environmental parameters. Thus, although dense gas appears abundant the central regions of many spiral galaxies, this gas appears relatively inefficient at forming stars. These results qualitatively agree with previous work on nearby galaxies and the Milky Way's Central Molecular Zone. To first order, EMPIRE demonstrates that the conditions in a galaxy disk set the gas density distribution and that the dense gas traced by HCN shows an environment-dependent relation to star formation. However, our results also show significant ($\pm 0.2$ dex) galaxy-to-galaxy variations. We suggest that gas structure below the scale of our observations and dynamical effects likely also play an important role.

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arXiv2019

Dense gas is not enough: environmental variations in the star formation efficiency of dense molecular gas at 100pc scales in M51

It remains unclear what sets the efficiency with which molecular gas transforms into stars. Here we present a new VLA map of the spiral galaxy M51 in 33GHz radio continuum, an extinction-free tracer of star formation, at 3" scales (~100pc). We combined this map with interferometric PdBI/NOEMA observations of CO(1-0) and HCN(1-0) at matched resolution for three regions in M51 (central molecular ring, northern and southern spiral arm segments). While our measurements roughly fall on the well-known correlation between total infrared and HCN luminosity, bridging the gap between Galactic and extragalactic observations, we find systematic offsets from that relation for different dynamical environments probed in M51, e.g. the southern arm segment is more quiescent due to low star formation efficiency (SFE) of the dense gas, despite having a high dense gas fraction. Combining our results with measurements from the literature at 100pc scales, we find that the SFE of the dense gas and the dense gas fraction anti-correlate and correlate, respectively, with the local stellar mass surface density. This is consistent with previous kpc-scale studies. In addition, we find a significant anti-correlation between the SFE and velocity dispersion of the dense gas. Finally, we confirm that a correlation also holds between star formation rate surface density and the dense gas fraction, but it is not stronger than the correlation with dense gas surface density. Our results are hard to reconcile with models relying on a universal gas density threshold for star formation and suggest that turbulence and galactic dynamics play a major role in setting how efficiently dense gas converts into stars.

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arXiv2019

Histogram of oriented gradients: a technique for the study of molecular cloud formation

We introduce the histogram of oriented gradients (HOG), a tool developed for machine vision that we propose as a new metric for the systematic characterization of observations of atomic and molecular gas and the study of molecular cloud formation models. In essence, the HOG technique takes as input extended spectral-line observations from two tracers and provides an estimate of their spatial correlation across velocity channels. We characterize HOG using synthetic observations of HI and $^{13}$CO(J=1-0) emission from numerical simulations of MHD turbulence leading to the formation of molecular gas after the collision of two atomic clouds. We find a significant spatial correlation between the two tracers in velocity channels where $v_{HI}\approx v_{^{13}CO}$, independent of the orientation of the collision with respect to the line of sight. We use HOG to investigate the spatial correlation of the HI, from the THOR survey, and the $^{13}$CO(J=1-0) emission, from the GRS, toward the portion of the Galactic plane 33.75$\lt l\lt$35.25$^{o}$ and $|b|\lt$1.25$^{o}$. We find a significant spatial correlation between the tracers in extended portions of the studied region. Although some of the regions with high spatial correlation are associated with HI self-absorption features, suggesting that it is produced by the cold atomic gas, the correlation is not exclusive to this kind of region. The HOG results also indicate significant differences between individual regions: some show spatial correlation in channels around $v_{HI}\approx v_{^{13}CO}$ while others present this correlation in velocity channels separated by a few km/s. We associate these velocity offsets to the effect of feedback and to the presence of physical conditions that are not included in the atomic-cloud-collision simulations, such as more general magnetic field configurations, shear, and global gas infall.

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arXiv2018

OH absorption in the first quadrant of the Milky Way as seen by THOR

The hydroxyl radical (OH) is present in the diffuse molecular and partially atomic phases of the interstellar medium (ISM), but its abundance relative to hydrogen is not clear. We aim to evaluate the abundance of OH with respect to molecular hydrogen using OH absorption against cm-continuum sources over the first Galactic quadrant. This OH study is part of the HI/OH/Recombination line survey (THOR). THOR is a Karl G. Jansky Very Large Array large program of atomic, molecular and ionized gas in the range 15°$\leq$l$\leq$67° and |b|$\leq$1°. It is the highest-resolution unbiased OH absorption survey to date towards this region. We combine the derived optical depths with literature 13CO(1-0) and HI observations to determine the OH abundance. We detect absorption in the 1665 and 1667 MHz transitions for continuum sources stronger than $F_{\rm cont}\geq$0.1 Jy/beam. OH absorption is found against $\sim$15% of these continuum sources with increasing fractions for stronger sources. Most of the absorption is associated with Galactic HII regions. We find OH and 13CO gas to have similar kinematic properties. The OH abundance decreases with increasing hydrogen column density. The OH abundance with respect to the total hydrogen nuclei column density (atomic and molecular phase) is in agreement with a constant abundance for $A_V$ < 10-20. Towards the lowest column densities, we find sources that exhibit OH absorption but no 13CO emission, indicating that OH is a well suited tracer of the low column density molecular gas. We present spatially resolved OH absorption towards W43. The unbiased nature of the THOR survey opens a new window onto the gas properties of the ISM. The characterization of the OH abundance over a large range of hydrogen gas column densities contributes to the understanding of OH as a molecular gas tracer and provides a starting point for future investigations.

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arXiv2018

Radio continuum emission in the northern Galactic plane: Sources and spectral indices from the THOR survey

Radio continuum surveys of the Galactic plane can find and characterize HII regions, supernova remnants (SNRs), planetary nebulae (PNe), and extragalactic sources. A number of surveys at high angular resolution (<25") at different wavelengths exist to study the interstellar medium (ISM), but no comparable high-resolution and high-sensitivity survey exists at long radio wavelengths around 21cm. We observed a large fraction of the Galactic plane in the first quadrant of the Milky Way (l=14.0-67.4deg and |b| < 1.25deg) with the Karl G. Jansky Very Large Array (VLA) in the C-configuration covering six continuum spectral windows. These data provide a detailed view on the compact as well as extended radio emission of our Galaxy and thousands of extragalactic background sources. We used the BLOBCAT software and extracted 10916 sources. After removing spurious source detections caused by the sidelobes of the synthesised beam, we classified 10387 sources as reliable detections. We smoothed the images to a common resolution of 25" and extracted the peak flux density of each source in each spectral window (SPW) to determine the spectral indices $α$ (assuming $I(ν)\proptoν^α$). By cross-matching with catalogs of HII regions, SNRs, PNe, and pulsars, we found radio counterparts for 840 HII regions, 52 SNRs, 164 PNe, and 38 pulsars. We found 79 continuum sources that are associated with X-ray sources. We identified 699 ultra-steep spectral sources ($α< -1.3$) that could be high-redshift galaxies. Around 9000 of the sources we extracted are not classified specifically, but based on their spatial and spectral distribution, a large fraction of them is likely to be extragalactic background sources. More than 7750 sources do not have counterparts in the SIMBAD database, and more than 3760 sources do not have counterparts in the NED database.

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arXiv2018

A 50 pc scale view of star formation efficiency across NGC 628

Star formation is a multi-scale process that requires tracing cloud formation and stellar feedback within the local ( 1 Gyr, significantly longer than previously reported for individual star-forming clouds in the Milky Way. Finally, we find no clear trends that relate variations in the depletion time observed on 500 pc scales to physical drivers (metallicity, molecular and stellar mass surface density, molecular gas boundedness) on 50 pc scales.

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arXiv2018

Full-disc $^{13}$CO(1-0) mapping across nearby galaxies of the EMPIRE survey and the CO-to-H$_2$ conversion factor

Carbon monoxide (CO) provides crucial information about the molecular gas properties of galaxies. While $^{12}$CO has been targeted extensively, isotopologues such as $^{13}$CO have the advantage of being less optically thick and observations have recently become accessible across full galaxy discs. We present a comprehensive new dataset of $^{13}$CO(1-0) observations with the IRAM 30-m telescope of the full discs of 9 nearby spiral galaxies from the EMPIRE survey at a spatial resolution of $\sim$1.5kpc. $^{13}$CO(1-0) is mapped out to $0.7-1r_{25}$ and detected at high signal-to-noise throughout our maps. We analyse the $^{12}$CO(1-0)-to-$^{13}$CO(1-0) ratio ($\Re$) as a function of galactocentric radius and other parameters such as the $^{12}$CO(2-1)-to-$^{12}$CO(1-0) intensity ratio, the 70-to-160$μ$m flux density ratio, the star-formation rate surface density, the star-formation efficiency, and the CO-to-H$_2$ conversion factor. We find that $\Re$ varies by a factor of 2 at most within and amongst galaxies, with a median value of 11 and larger variations in the galaxy centres than in the discs. We argue that optical depth effects, most likely due to changes in the mixture of diffuse/dense gas, are favored explanations for the observed $\Re$ variations, while abundance changes may also be at play. We calculate a spatially-resolved $^{13}$CO(1-0)-to-H$_2$ conversion factor and find an average value of $1.0\times10^{21}$ cm$^{-2}$ (K.km/s)$^{-1}$ over our sample with a standard deviation of a factor of 2. We find that $^{13}$CO(1-0) does not appear to be a good predictor of the bulk molecular gas mass in normal galaxy discs due to the presence of a large diffuse phase, but it may be a better tracer of the mass than $^{12}$CO(1-0) in the galaxy centres where the fraction of dense gas is larger.

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arXiv2017

A new approach for short-spacing correction of radio interferometric data sets

The short-spacing problem describes the inherent inability of radio-interferometric arrays to measure the integrated flux and structure of diffuse emission associated with extended sources. New interferometric arrays, such as SKA, require solutions to efficiently combine interferometer and single-dish data. We present a new and open source approach for merging single-dish and cleaned interferometric data sets requiring a minimum of data manipulation while offering a rigid flux determination and full high angular resolution. Our approach combines single-dish and cleaned interferometric data in the image domain. This approach is tested for both Galactic and extragalactic HI data sets. Furthermore, a quantitative comparison of our results to commonly used methods is provided. Additionally, for the interferometric data sets of NGC4214 and NGC5055, we study the impact of different imaging parameters as well as their influence on the combination for NGC4214. The approach does not require the raw data (visibilities) or any additional special information such as antenna patterns. This is advantageous especially in the light of upcoming radio surveys with heterogeneous antenna designs.

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arXiv2017

An Overview of the MHONGOOSE Survey: Observing Nearby Galaxies with MeerKAT

MHONGOOSE is a deep survey of the neutral hydrogen distribution in a representative sample of 30 nearby disk and dwarf galaxies with HI masses from 10^6 to ~10^{11} M_sun, and luminosities from M_R ~ -12 to M_R ~ -22. The sample is selected to uniformly cover the available range in log(M_HI). Our extremely deep observations, down to HI column density limits of well below 10^{18} cm^{-2} - or a few hundred times fainter than the typical HI disks in galaxies - will directly detect the effects of cold accretion from the intergalactic medium and the links with the cosmic web. These observations will be the first ever to probe the very low-column density neutral gas in galaxies at these high resolutions. Combination with data at other wavelengths, most of it already available, will enable accurate modelling of the properties and evolution of the mass components in these galaxies and link these with the effects of environment, dark matter distribution, and other fundamental properties such as halo mass and angular momentum. MHONGOOSE can already start addressing some of the SKA-1 science goals and will provide a comprehensive inventory of the processes driving the transformation and evolution of galaxies in the nearby universe at high resolution and over 5 orders of magnitude in column density. It will be a Nearby Galaxies Legacy Survey that will be unsurpassed until the advent of the SKA, and can serve as a highly visible, lasting statement of MeerKAT's capabilities.

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arXiv2017

Galactic Supernova Remnant Candidates Discovered by THOR

There is a considerable deficiency in the number of known supernova remnants (SNRs) in the Galaxy compared to that expected. Searches for extended low-surface brightness radio sources may find new Galactic SNRs, but confusion with the much larger population of HII regions makes identifying such features challenging. SNRs can, however, be separated from HII regions using their significantly lower mid-infrared (MIR) to radio continuum intensity ratios. We use the combination of high-resolution 1-2 GHz continuum data from The HI, OH, Recombination line survey of the Milky Way (THOR) and lower-resolution VLA 1.4 GHz Galactic Plane Survey (VGPS) continuum data, together with MIR data from the Spitzer GLIMPSE, Spitzer MIPSGAL, and WISE surveys to identify SNR candidates. To ensure that the candidates are not being confused with HII regions, we exclude radio continuum sources from the WISE Catalog of Galactic HII Regions, which contains all known and candidate H II regions in the Galaxy. We locate 76 new Galactic SNR candidates in the THOR and VGPS combined survey area of 67.4deg>l>17.5deg, |b|<1.25deg and measure the radio flux density for 52 previously-known SNRs. The candidate SNRs have a similar spatial distribution to the known SNRs, although we note a large number of new candidates near l=30deg, the tangent point of the Scutum spiral arm. The candidates are on average smaller in angle compared to the known regions, 6.4'+/-4.7' versus 11.0'+/-7.8', and have lower integrated flux densities. If the 76 candidates are confirmed as true SNRs, for example using radio polarization measurements or by deriving radio spectral indices, this would more than double the number of known Galactic SNRs in the survey area. This large increase would still, however, leave a discrepancy between the known and expected SNR populations of about a factor of two.

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arXiv2017

New ALMA constraints on the star-forming ISM at low metallicity: A 50 pc view of the blue compact dwarf galaxy SBS0335-052

Properties of the cold interstellar medium of low-metallicity galaxies are not well-known due to the faintness and extremely small scale on which emission is expected. We present deep ALMA band 6 (230GHz) observations of the nearby, low-metallicity (12 + log(O/H) = 7.25) blue compact dwarf galaxy SBS0335-052 at an unprecedented resolution of 0.2 arcsec (52 pc). The 12CO J=2-1 line is not detected and we report a 3-sigma upper limit of LCO(2-1) = 3.6x10^4 K km/s pc^2. Assuming that molecular gas is converted into stars with a given depletion time, ranging from 0.02 to 2 Gyr, we find lower limits on the CO-to-H2 conversion factor alpha_CO in the range 10^2-10^4 Msun pc^-2 (K km/s)^-1. The continuum emission is detected and resolved over the two main super star clusters. Re-analysis of the IR-radio spectral energy distribution suggests that the mm-fluxes are not only free-free emission but are most likely also associated with a cold dust component coincident with the position of the brightest cluster. With standard dust properties, we estimate its mass to be as large as 10^5 Msun. Both line and continuum results suggest the presence of a large cold gas reservoir unseen in CO even with ALMA.

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arXiv2017

$^{13}$CO/C$^{18}$O Gradients Across the Disks of Nearby Spiral Galaxies

We use the IRAM Large Program EMPIRE and new high-resolution ALMA data to measure 13CO(1-0)/C18O(1-0) intensity ratios across nine nearby spiral galaxies. These isotopologues of CO are typically optically thin across most of the area in galaxy disks, and this ratio allows us to gauge their relative abundance due to chemistry or stellar nucleosynthesis effects. Resolved 13CO/C18O gradients across normal galaxies have been rare due to the faintness of these lines. We find a mean 13CO/C18O ratio of 6.0$\pm$0.9 for the central regions of our galaxies. This agrees well with results in the Milky Way, but differs from results for starburst galaxies (3.4$\pm$0.9) and ultraluminous infrared galaxies (1.1$\pm$0.4). In our sample, the 13CO/C18O ratio consistently increases with increasing galactocentric radius and decreases with increasing star formation rate surface density. These trends qualitatively agree with expectations for carbon and oxygen isotopic abundance variations due to stellar nucleosynthesis, with a possible effect of fractionation.

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