arXiv subjects

F. Walter

Publications and source records attributed to F. Walter.

At least 91 records · Page 5Linked to original sources

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

The Atacama Cosmology Telescope: CO(J = 3 - 2) mapping and lens modeling of an ACT-selected dusty star-forming galaxy

We report Northern Extended Millimeter Array (NOEMA) CO($J = 3 - 2$) observations of the dusty star-forming galaxy ACT-S\,J020941+001557 at $z = 2.5528$, which was detected as an unresolved source in the Atacama Cosmology Telescope (ACT) equatorial survey. Our spatially resolved spectral line data support the derivation of a gravitational lens model from 37 independent velocity channel maps using a pixel-based algorithm, from which we infer a velocity-dependent magnification factor $μ\approx 7-22$ with a luminosity-weighted mean $\left<μ\right>\approx 13$. The resulting source-plane reconstruction is consistent with a rotating disk, although other scenarios cannot be ruled out by our data. After correction for lensing, we derive a line luminosity $L^{\prime}_{\rm CO(3-2)}= (5.53\pm 0.69) \times 10^{10}\,{\rm \,K\,km\,s^{-1}\,pc^{2}}$, a cold gas mass $M_{\rm gas}= (3.86 \pm 0.33) \times 10^{10}\,M_{\odot}$, a dynamical mass $M_{\rm dyn}\,{\rm sin}^2\,i = 3.9^{+1.8}_{-1.5} \times 10^{10}\,M_{\odot}$, and a gas mass fraction $f_{\rm gas}\,{\rm csc}^2\,i = 1.0^{+0.8}_{-0.4}$. The line brightness temperature ratio of $r_{3,1}\approx 1.6$ relative to a Green Bank Telescope CO($J=1-0$) detection may be elevated by a combination of external heating of molecular clouds, differential lensing, and/or pointing errors.

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arXiv2019

ALMA reveals potential evidence for spiral arms, bars, and rings in high-redshift submillimeter galaxies

We present sub-kpc-scale mapping of the 870 $μ$m ALMA continuum emission in six luminous ($L_{\rm IR}~\sim~5~\times10^{12}$ L$_{\odot}$) submillimeter galaxies (SMGs) from the ALESS survey of the Extended Chandra Deep Field South. Our high-fidelity 0.07$''$-resolution imaging ($\sim$500 pc) reveals robust evidence for structures with deconvolved sizes of $\lesssim$0.5-1 kpc embedded within (dominant) exponential dust disks. The large-scale morphologies of the structures within some of the galaxies show clear curvature and/or clump-like structures bracketing elongated nuclear emission, suggestive of bars, star-forming rings, and spiral arms. In this interpretation, the ratio of the `ring' and `bar' radii (1.9$\pm$0.3) agrees with that measured for such features in local galaxies. These potential spiral/ring/bar structures would be consistent with the idea of tidal disturbances, with their detailed properties implying flat inner rotation curves and Toomre-unstable disks (Q<1). The inferred one-dimensional velocity dispersions ($σ_{\rm r}\lesssim$ 70-160 km s$^{-1}$) are marginally consistent with the limits implied if the sizes of the largest structures are comparable to the Jeans length. We create maps of the star formation rate density ($Σ_{\rm SFR}$) on $\sim$500 pc scales and show that the SMGs are able to sustain a given (galaxy-averaged) $Σ_{\rm SFR}$ over much larger physical scales than local (ultra-)luminous infrared galaxies. However, on 500 pc scales, they do not exceed the Eddington limit set by radiation pressure on dust. If confirmed by kinematics, the potential presence of non-axisymmetric structures would provide a means for net angular momentum loss and efficient star formation, helping to explain the very high star formation rates measured in SMGs.

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arXiv2019

Strong FUV fields drive the [CII]/FIR deficit in z~3 dusty, star-forming galaxies

We present 0.15-arcsec (1 kpc) resolution ALMA observations of the [CII] 157.74 um line and rest-frame 160-um continuum emission in two z~3 dusty, star-forming galaxies - ALESS 49.1 and ALESS 57.1, combined with resolved CO(3-2) observations. In both sources, the [CII] surface brightness distribution is dominated by a compact core $\leq$1 kpc in radius, a factor of 2-3 smaller than the extent of the CO(3-2) emission. In ALESS 49.1, we find an additional extended (8-kpc radius), low surface-brightness [CII] component. Based on an analysis of mock ALMA observations, the [CII] and 160-um continuum surface brightness distributions are inconsistent with a single-Gaussian surface brightness distribution with the same size as the CO(3-2) emission. The [CII] rotation curves flatten at $\simeq$2 kpc radius, suggesting the kinematics of the central regions are dominated by a baryonic disc. Both galaxies exhibit a strong [CII]/FIR deficit on 1-kpc scales, with FIR-surface-brightness to [CII]/FIR slope steeper than in local star-forming galaxies. A comparison of the [CII]/CO(3-2) observations with PDR models suggests a strong FUV radiation field ($G_0\sim10^4$) and high gas density ($n\mathrm{(H)}\sim10^4-10^5$ cm$^{-3}$) in the central regions of ALESS 49.1 and 57.1. The most direct interpretation of the pronounced [CII]/FIR deficit is a thermal saturation of the C+ fine-structure levels at temperatures $\geq$500 K, driven by the strong FUV field.

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arXiv2019

PHIBSS2: survey design and z=0.5-0.8 results. Molecular gas reservoirs during the winding-down of star formation

Following the success of the Plateau de Bure high-z Blue Sequence Survey (PHIBSS), we present the PHIBSS2 legacy program, a survey of the molecular gas properties of star-forming galaxies on and around the star formation main sequence (MS) at different redshifts using NOEMA. This survey significantly extends the existing sample of star-forming galaxies with CO molecular gas measurements, probing the peak epoch of star formation (z=1-1.6) as well as its building-up (z=2-3) and winding-down (z=0.5-0.8) phases. The targets are drawn from the GOODS, COSMOS, and AEGIS deep fields and uniformly sample the MS in the stellar mass (M*) - star formation rate (SFR) plane with log(M*/Msun) = 10-11.8. We describe the survey strategy and sample selection before focusing on the results obtained at z=0.5-0.8, where we report 60 CO(2-1) detections out of 61 targets. We determine their molecular gas masses and separately obtain disc sizes and bulge-to-total (B/T) luminosity ratios from HST I-band images. The median molecular gas-to-stellar mass ratio, gas fraction, and depletion time as well as their dependence with M* and offset from the MS follow published scaling relations for a much larger sample of galaxies spanning a wider range of redshifts. The galaxy-averaged Kennicutt-Schmidt (KS) relation between molecular gas and SFR surface densities is strikingly linear, pointing towards similar star formation timescales within galaxies at any given epoch. In terms of morphology, the molecular gas content, the SFR, the disc stellar mass, and the disc molecular gas fraction do not seem to correlate with B/T and the stellar surface density, which suggests an ongoing supply of fresh molecular gas to compensate for the build-up of the bulge. Our measurements do not yield any significant variation of the depletion time with B/T and hence no strong evidence for morphological quenching within the scatter of the MS.

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arXiv2018

Science with an ngVLA. Cold gas in High-z Galaxies: CO as redshift beacon

The goal of this science case is to address the use of a ngVLA as a CO redshift machine for dust-obscured high-redshift galaxies which lack of clear counterparts at other wavelengths. Thanks to its unprecedentedly large simultaneous bandwidth and sensitivity, the ngVLA will be able to detect low--J CO transitions at virtually any $z>1$. In particular, at $z>4.76$ two CO transitions will be covered in a single frequency setting, thus ensuring unambiguous line identification. The ngVLA capabilities fill in a redshift range where other approaches (e.g., photometric redshifts, search for optical/radio counterparts, etc) typically fail due to the combination of intrinsically faint emission and increasing luminosity distance. This will allow us to explore the formation of massive galaxies in the early cosmic times.

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arXiv2018

Science with an ngVLA. Cold gas in High-z Galaxies: The molecular gas budget

The goal of this science case is to accurately pin down the molecular gas content of high redshift galaxies. By targeting the CO ground transition, we circumvent uncertainties related to CO excitation. The ngVLA can observe the CO(1-0) line at virtually any $z>1.5$, thus exposing the evolution of gaseous reservoirs from the earliest epochs down to the peak of the cosmic history of star formation. The order-of-magnitude improvement in the number of CO detections with respect to state-of-the-art observational campaigns will provide a unique insight on the evolution of galaxies through cosmic time.

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arXiv2018

Science with an ngVLA. Cold gas in High-z Galaxies: The dense ISM

The goal of this science case is to study physical conditions of the interstellar medium (ISM) in distant galaxies. In particular, its densest component is associated with the inner cores of clouds -- this is where star formation takes place. Carbon monoxide is usually used to trace molecular gas emission; however, its transitions are practically opaque, thus preventing astronomers from piercing through the clouds, into the deepest layers that are most intimately connected with the formation of stars. Other dense gas tracers are required, although they are typically too faint and/or at too low frequencies to be effectively observed in high redshift galaxies. The ngVLA will offer for the first time the sensitivity at radio frequencies that is needed to target [CI]$_{1-0}$ (at $z>5$), as well as the ground transitions of dense gas tracers of the ISM such as HCN, HNC, HCO+ (at various redshifts $z>1$), beyond the tip of the iceberg of the hyper-luminous sources that could be studied up to now. These new tools will critically contribute to our understanding of the intimate interplay between gas clouds and star formation in different environments and cosmic epochs.

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arXiv2018

Science with an ngVLA: Neutral Atomic Hydrogen in the Local Universe

One of the outstanding questions in astronomy today is how gas flows from the circumgalactic medium (CGM) onto the disks of galaxies and then transitions from the diffuse atomic medium into molecular star-forming cores. For studies of the CGM, the Next Generation Very Large Array (ngVLA) will have the sensitivity and resolution to measure the sizes of the neutral atomic hydrogen (HI) disks of galaxies and complete a census of the HI content around galaxies. Within galaxies, the ngVLA will be able to resolve HI clouds in large numbers of galaxies beyond the Local Group providing measurements of the physical conditions of gas across a wide range of galaxy types. Finally, within our own Milky Way, the ngVLA will provide a dense grid of HI absorption spectra in the cold and warm neutral medium constraining the temperature and density of atomic gas as it transitions into molecular gas. Combined with radio continuum and molecular line data from the ngVLA plus multi-wavelength data from other planned facilities, ngVLA will have a key role in understanding star-formation in the local universe while complementing future studies with the Square Kilometer Array.

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arXiv2018

X-ray, UV, and optical observations of the accretion disk and boundary layer in the symbiotic star RT Cru

Compared to mass transfer in cataclysmic variables, the nature of accretion in symbiotic binaries in which red giants transfer material to white dwarfs (WDs) has been difficult to uncover. The accretion flows in a symbiotic binary are most clearly observable, however, when there is no quasi-steady shell burning on the WD to hide them. RT Cru is the prototype of such non-burning symbiotics, with its hard (δ-type) X-ray emission providing a view of its innermost accretion structures. In the past 20 yr, RT Cru has experienced two similar optical brightening events, separated by 4000 days and with amplitudes of ΔV 1.5 mag. After Swift became operative, the Burst Alert Telescope (BAT) detector revealed a hard X-ray brightening event almost in coincidence with the second optical peak. Spectral and timing analyses of multi-wavelength observations that we describe here, from NuSTAR, Suzaku, Swift/X-Ray Telescope (XRT) + BAT + UltraViolet Optical Telescope (UVOT) (photometry) and optical photometry and spectroscopy, indicate that accretion proceeds through a disk that reaches down to the WD surface. The scenario in which a massive, magnetic WD accretes from a magnetically truncated accretion disk is not supported. For example, none of our data show the minute-time-scale periodic modulations (with tight upper limits from X-ray data) expected from a spinning, magnetic WD. Moreover, the similarity of the UV and X-ray fluxes, as well as the approximate constancy of the hardness ratio within the BAT band, indicate that the boundary layer of the accretion disk remained optically thin to its own radiation throughout the brightening event, during which the rate of accretion onto the WD increased to 6.7 $\times$ 10-9 Msun yr^{-1} (d/2 kpc)^2. (Abridged abstract version)

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arXiv2018

The [C II] emission as a molecular gas mass tracer in galaxies at low and high redshift

We present ALMA Band 9 observations of the [C II]158um emission for a sample of 10 main-sequence galaxies at redshift z ~ 2, with typical stellar masses (log M*/Msun ~ 10.0 - 10.9) and star formation rates (~ 35 - 115 Msun/yr). Given the strong and well understood evolution of the interstellar medium from the present to z = 2, we investigate the behaviour of the [C II] emission and empirically identify its primary driver. We detect [C II] from six galaxies (four secure, two tentative) and estimate ensemble averages including non detections. The [C II]-to-infrared luminosity ratio (L[C II]/LIR) of our sample is similar to that of local main-sequence galaxies (~ 2 x 10^-3), and ~ 10 times higher than that of starbursts. The [C II] emission has an average spatial extent of 4 - 7 kpc, consistent with the optical size. Complementing our sample with literature data, we find that the [C II] luminosity correlates with galaxies' molecular gas mass, with a mean absolute deviation of 0.2 dex and without evident systematics: the [C II]-to-H2 conversion factor (alpha_[C II] ~ 30 Msun/Lsun) is largely independent of galaxies' depletion time, metallicity, and redshift. [C II] seems therefore a convenient tracer to estimate galaxies' molecular gas content regardless of their starburst or main-sequence nature, and extending to metal-poor galaxies at low and high redshifts. The dearth of [C II] emission reported for z > 6 - 7 galaxies might suggest either a high star formation efficiency or a small fraction of UV light from star formation reprocessed by dust.

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arXiv2018

An 800-million-solar-mass black hole in a significantly neutral Universe at redshift 7.5

Quasars are the most luminous non-transient objects known and as a result they enable studies of the Universe at the earliest cosmic epochs. Despite extensive efforts, however, the quasar ULAS J1120+0641 at z=7.09 has remained the only one known at z>7 for more than half a decade. Here we report observations of the quasar ULAS J134208.10+092838.61 (hereafter J1342+0928) at redshift z=7.54. This quasar has a bolometric luminosity of 4e13 times the luminosity of the Sun and a black hole mass of 8e8 solar masses. The existence of this supermassive black hole when the Universe was only 690 million years old---just five percent of its current age---reinforces models of early black-hole growth that allow black holes with initial masses of more than about 1e4 solar masses or episodic hyper-Eddington accretion. We see strong evidence of absorption of the spectrum of the quasar redwards of the Lyman alpha emission line (the Gunn-Peterson damping wing), as would be expected if a significant amount (more than 10 per cent) of the hydrogen in the intergalactic medium surrounding J1342+0928 is neutral. We derive a significant fraction of neutral hydrogen, although the exact fraction depends on the modelling. However, even in our most conservative analysis we find a fraction of more than 0.33 (0.11) at 68 per cent (95 per cent) probability, indicating that we are probing well within the reionization epoch of the Universe.

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arXiv2018

Resolving the Powerful Radio-loud Quasar at z~6

We present high angular resolution imaging ($23.9 \times 11.3$ mas, $138.6 \times 65.5$ pc) of the radio-loud quasar PSO~J352.4034$-$15.3373 at $z=5.84$ with the Very Long Baseline Array (VLBA) at 1.54 GHz. This quasar has the highest radio-to-optical flux density ratio at such a redshift, making it the radio-loudest source known to date at $z \sim 6$. The VLBA observations presented here resolve this quasar into multiple components with an overall linear extent of 1.62 kpc ($0\rlap{.}{''}28$) and with a total flux density of $6.57 \pm 0.38$ mJy, which is about half of the emission measured at a much lower angular resolution. The morphology of the source is comparable with either a radio core with a one-sided jet, or a compact or a medium-size Symmetric Object (CSO/MSO). If the source is a CSO/MSO, and assuming an advance speed of $0.2c$, then the estimated kinematic age is $\sim 10^4$ yr.

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arXiv2018

Resolving the ISM at the peak of cosmic star formation with ALMA - The distribution of CO and dust continuum in z~2.5 sub-millimetre galaxies

We use ALMA observations of four sub-millimetre galaxies (SMGs) at $z\sim2-3$ to investigate the spatially resolved properties of the inter-stellar medium (ISM) at scales of 1--5 kpc (0.1--0.6$''$). The velocity fields of our sources, traced by the $^{12}$CO($J$=3-2) emission, are consistent with disk rotation to first order, implying average dynamical masses of $\sim$3$\times10^{11}$M$_{\odot}$ within two half-light radii. Through a Bayesian approach we investigate the uncertainties inherent to dynamically constraining total gas masses. We explore the covariance between the stellar mass-to-light ratio and CO-to-H$_{2}$ conversion factor, $α_{\rm CO}$, finding values of $α_{\rm CO}=1.1^{+0.8}_{-0.7}$ for dark matter fractions of 15 \%. We show that the resolved spatial distribution of the gas and dust continuum can be uncorrelated to the stellar emission, challenging energy balance assumptions in global SED fitting. Through a stacking analysis of the resolved radial profiles of the CO(3-2), stellar and dust continuum emission in SMG samples, we find that the cool molecular gas emission in these sources (radii $\sim$5--14 kpc) is clearly more extended than the rest-frame $\sim$250 $μ$m dust continuum by a factor $>2$. We propose that assuming a constant dust-to-gas ratio, this apparent difference in sizes can be explained by temperature and optical-depth gradients alone. Our results suggest that caution must be exercised when extrapolating morphological properties of dust continuum observations to conclusions about the molecular gas phase of the ISM.

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arXiv2018

The dust and [CII] morphologies of redshift ~4.5 sub-millimeter galaxies at ~200pc resolution: The absence of large clumps in the interstellar medium of high-redshift galaxies

We present deep high resolution (0.03", 200pc) ALMA Band 7 observations covering the dust continuum and [CII] $\lambda157.7μ$m emission in four $z\sim4.4-4.8$ sub-millimeter galaxies (SMGs) selected from the ALESS and AS2UDS surveys. The data show that the rest-frame 160$μ$m (observed 345 GHz) dust emission is consistent with smooth morphologies on kpc scales for three of the sources. One source, UDS47.0, displays apparent substructure but this is also consistent with a smooth morphology, as indicated by simulations showing that smooth exponential disks can appear clumpy when observed at high angular resolution (0.03") and depth of these observations ($σ_{345\text{GHz}} \sim27-47μ$Jy beam$^{-1}$). The four SMGs are bright [CII] emitters, and we extract [CII] spectra from the high resolution data, and recover $\sim20-100$% of the [CII] flux and $\sim40-80$% of the dust continuum emission, compared to the previous lower resolution observations. When tapered to 0.2" resolution our maps recover $\sim80-100$% of the continuum emission, indicating that $\sim60$% of the emission is resolved out on $\sim200$pc scales. We find that the [CII] emission in high-redshift galaxies is more spatially extended than the rest-frame 160$μ$m dust continuum by a factor of $1.6\pm0.4$. By considering the $L_{\text{[CII]}}$/$L_{\text{FIR}}$ ratio as a function of the star-formation rate surface density ($Σ_{\text{SFR}}$) we revisit the [CII] deficit, and suggest that the decline in the $L_{\text{[CII]}}$/$L_{\text{FIR}}$ ratio as a function of $Σ_{\text{SFR}}$ is consistent with local processes. We also explore the physical drivers that may be responsible for these trends and can give rise to the properties found in the densest regions of SMGs.

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arXiv2018

Chandra X-rays from the redshift 7.54 quasar ULAS J1342+0928

We present a 45 ks Chandra observation of the quasar ULAS J1342+0928 at z=7.54. We detect 14.0^{+4.8}_{-3.7} counts from the quasar in the observed-frame energy range 0.5-7.0 keV (6-sigma detection), representing the most distant non-transient astronomical source identified in X-rays to date. The present data are sufficient only to infer rough constraints on the spectral parameters. We find an X-ray hardness ratio of HR = -0.51^{+0.26}_{-0.28} between the 0.5-2.0 keV and 2.0-7.0 keV ranges and derive a power-law photon index of Gamma = 1.95^{+0.55}_{-0.53}. Assuming a typical value for high-redshift quasars of Gamma = 1.9, ULAS J1342+0928 has a 2-10 keV rest-frame X-ray luminosity of L_{2-10} = 11.6^{+4.3}_{-3.5} x 10^{44} erg/s. Its X-ray-to-optical power-law slope is alpha_{OX}=-1.67^{+0.16}_{-0.10}, consistent with the general trend indicating that the X-ray emission in the most bolometrically powerful quasars is weaker relative to their optical emission.

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arXiv2018

PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions

This paper provides an update of our previous scaling relations (Genzel et al.2015) between galaxy integrated molecular gas masses, stellar masses and star formation rates, in the framework of the star formation main-sequence (MS), with the main goal to test for possible systematic effects. For this purpose our new study combines three independent methods of determining molecular gas masses from CO line fluxes, far-infrared dust spectral energy distributions, and ~1mm dust photometry, in a large sample of 1444 star forming galaxies (SFGs) between z=0 and 4. The sample covers the stellar mass range log(M*/M_solar)=9.0-11.8, and star formation rates relative to that on the MS, delta_MS=SFR/SFR(MS), from 10^{-1.3} to 10^{2.2}. Our most important finding is that all data sets, despite the different techniques and analysis methods used, follow the same scaling trends, once method-to-method zero point offsets are minimized and uncertainties are properly taken into account. The molecular gas depletion time t_depl, defined as the ratio of molecular gas mass to star formation rate, scales as (1+z)^{-0.6}x(delta_MS)^{-0.44}, and is only weakly dependent on stellar mass. The ratio of molecular-to-stellar mass mu_gas depends on (1+z)^{2.5}x (delta_MS)^{0.52}x(M*)^{-0.36}, which tracks the evolution of the specific star formation rate. The redshift dependence of mu_gas requires a curvature term, as may the mass-dependences of t_depl and mu_gas. We find no or only weak correlations of t_depl and mu_gas with optical size R or surface density once one removes the above scalings, but we caution that optical sizes may not be appropriate for the high gas and dust columns at high-z.

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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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