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P. Gratier

Publications and source records attributed to P. Gratier.

At least 55 records · Page 3Linked to original sources

Variation in the dust emissivity index across M33 with Herschel and Spitzer (HerM33es)

We study the wavelength dependence of the dust emission as a function of position and environment across the disk of M33 at a linear resolution of 160 pc using Spitzer and Herschel photometric data. Expressing the emissivity of the dust as a power law, the power-law exponent (beta) is estimated from two independent approaches designed to properly treat the degeneracy between beta and the dust temperature. Both beta and the dust temperature are higher in the inner disk than in the outer disk, contrary to reported beta-T anti-correlations found in other sources. In the cold + warm dust model, the warm component and the ionized gas (Halpha) have a very similar distribution across the galaxy, demonstrating that the model separates the components in an appropriate fashion. The flocculent spiral arms and the dust lanes are evident in the map of the cold component. Both cold and warm dust column densities are high in star forming regions and reach their maxima toward the giant star forming complexes NGC604 and NGC595. beta declines from close to 2 in the center to about 1.3 in the outer disk. beta is positively correlated with star formation and with molecular gas column, as traced by Halpha and CO emission. The lower dust emissivity index in the outer parts of M33 is likely related to the reduced metallicity (different grain composition) and possibly different size distribution. It is not due to the decrease in stellar radiation field or temperature in a simple way because the FIR-bright regions in the outer disk also have a low beta. Like most spirals, M33 has a (decreasing) radial gradient in star formation and molecular-to-atomic gas ratio such that the regions bright in Halpha or CO tend to trace the inner disk, making it difficult to distinguish between their effects on the dust.

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Reactions forming C(0,+)n=2,10, Cn=2,4H(0,+) and C3H(0,+) in the gas phase: semi empirical branching ratios

The aim of this paper is to provide a new set of branching ratios for interstellar and planetary chemical networks based on a semi empirical model. We applied, instead of zero order theory (i.e. only the most exoergic decaying channel is considered), a statistical microcanonical model based on the construction of breakdown curves and using experimental high velocity collision branching ratios for their parametriza- tion. We applied the model to ion-molecule, neutral-neutral, and ion-pair reactions implemented in the few popular databases for astrochemistry such as KIDA, OSU and UMIST. We studied the reactions of carbon and hydrocarbon species with electrons, He+, H+, CH+, CH, C, and C+ leading to intermediate complexes of the type Cn=2,10, Cn=2,4 H, C3 H2, C+n=2,10, Cn=2,4 H+, or C3 H+2 . Comparison of predictions with measurements supports the validity of the model. Huge deviations with respect to database values are often obtained. Effects of the new branching ratios in time dependant chemistry for dark clouds and for photodissociation region chemistry with conditions similar to those found in the Horsehead Nebula are discussed.

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The IRAM-30m line survey of the Horsehead PDR: III. High abundance of complex (iso-)nitrile molecules in UV-illuminated gas

Complex (iso-)nitrile molecules, such as CH3CN and HC3N, are relatively easily detected in our Galaxy and in other galaxies. We constrain their chemistry through observations of two positions in the Horsehead edge: the photo-dissociation region (PDR) and the dense, cold, and UV-shielded core just behind it. We systematically searched for lines of CH3CN, HC3N, C3N, and some of their isomers in our sensitive unbiased line survey at 3, 2, and 1mm. We derived column densities and abundances through Bayesian analysis using a large velocity gradient radiative transfer model. We report the first clear detection of CH3NC at millimeter wavelength. We detected 17 lines of CH3CN at the PDR and 6 at the dense core position, and we resolved its hyperfine structure for 3 lines. We detected 4 lines of HC3N, and C3N is clearly detected at the PDR position. We computed new electron collisional rate coefficients for CH3CN, and we found that including electron excitation reduces the derived column density by 40% at the PDR position. While CH3CN is 30 times more abundant in the PDR than in the dense core, HC3N has similar abundance at both positions. The isomeric ratio CH3NC/CH3CN is 0.15+-0.02. In the case of CH3CN, pure gas phase chemistry cannot reproduce the amount of CH3CN observed in the UV-illuminated gas. We propose that CH3CN gas phase abundance is enhanced when ice mantles of grains are destroyed through photo-desorption or thermal-evaporation in PDRs, and through sputtering in shocks. (abridged)

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Gas and dust cooling along the major axis of M33 (HerM33es): ISO/LWS CII observations

We aim to better understand the heating of the gas by observing the prominent gas cooling line [CII] at 158um in the low-metallicity environment of the Local Group spiral galaxy M33 at scales of 280pc. In particular, we aim at describing the variation of the photoelectric heating efficiency with galactic environment. In this unbiased study, we used ISO/LWS [CII] observations along the major axis of M33, in combination with Herschel PACS and SPIRE continuum maps, IRAM 30m CO 2-1 and VLA HI data to study the variation of velocity integrated intensities. The ratio of [CII] emission over the far-infrared continuum is used as a proxy for the heating efficiency, and models of photon-dominated regions are used to study the local physical densities, FUV radiation fields, and average column densities of the molecular clouds. The heating efficiency stays constant at 0.8% in the inner 4.5kpc radius of the galaxy where it starts to increase to reach values of ~3% in the outskirts at about 6kpc radial distance. The rise of efficiency is explained in the framework of PDR models by lowered volume densities and FUV fields, for optical extinctions of only a few magnitudes at constant metallicity. In view of the significant fraction of HI emission stemming from PDRs, and for typical pressures found in the Galactic cold neutral medium (CNM) traced by HI emission, the CNM contributes ~15% to the observed [CII] emission in the inner 2kpc radius of M33. The CNM contribution remains largely undetermined in the south, while positions between 2 and 7.3kpc radial distance in the north of M33 show a contribution of ~40%+-20%.

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Dense Gas in M33 (HerM33es)

We aim to better understand the emission of molecular tracers of the diffuse and dense gas in giant molecular clouds and the influence that metallicity, optical extinction, density, far-UV field, and star formation rate have on these tracers. Using the IRAM 30m telescope, we detected HCN, HCO+, 12CO, and 13CO in six GMCs along the major axis of M33 at a resolution of ~ 114pc and out to a radial distance of 3.4kpc. Optical, far-infrared, and submillimeter data from Herschel and other observatories complement these observations. To interpret the observed molecular line emission, we created two grids of models of photon-dominated regions, one for solar and one for M33-type subsolar metallicity. The observed HCO+/HCN line ratios range between 1.1 and 2.5. Similarly high ratios have been observed in the Large Magellanic Cloud. The HCN/CO ratio varies between 0.4% and 2.9% in the disk of M33. The 12CO/13CO line ratio varies between 9 and 15 similar to variations found in the diffuse gas and the centers of GMCs of the Milky Way. Stacking of all spectra allowed HNC and C2H to be detected. The resulting HCO+/HNC and HCN/HNC ratios of ~ 8 and 6, respectively, lie at the high end of ratios observed in a large set of (ultra-)luminous infrared galaxies. HCN abundances are lower in the subsolar metallicity PDR models, while HCO+ abundances are enhanced. For HCN this effect is more pronounced at low optical extinctions. The observed HCO+/HCN and HCN/CO line ratios are naturally explained by subsolar PDR models of low optical extinctions between 4 and 10 mag and of moderate densities of n = 3x10^3 - 3x10^4 cm^-3, while the FUV field strength only has a small effect on the modeled line ratios. The line ratios are almost equally well reproduced by the solar-metallicity models, indicating that variations in metallicity only play a minor role in influencing these line ratios.

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Spectral Energy Distributions of HII regions in M33 (HerM33es)

Within the framework of the Herschel M 33 extended survey HerM33es we study the Spectral Energy Distribution (SED) of a set of HII regions in M 33 as a function of the morphology. We present a catalogue of 119 HII regions morphologically classified: 9 filled, 47 mixed, 36 shell, and 27 clear shell HII regions. For each object we extract the photometry at twelve available wavelength bands (from FUV-1516A to IR-250mi) and obtain the SED. We also obtain emission line profiles across the regions to study the location of the stellar, ionised gas, and dust components. We find trends for the SEDs related to the morphology, showing that the star and gas-dust configuration affects the ratios of the emission in different bands. The mixed and filled regions show higher emission at 24mi than the shells and clear shells, which could be due to the proximity of the dust to the stellar clusters in the case of mixed and filled regions. The FIR peak for shells and clear shells seems to be located towards longer wavelengths, indicating that the dust is colder for this type of objects.The logarithmic 100/70mi ratio for filled and mixed regions remains constant over one order of magnitude in Halpha and FUV surface brightness, while the shells and clear shells exhibit a wider range of values of almost two orders of magnitude. We derive dust masses and temperatures fitting the individual SEDs with dust models proposed in the literature. The derived dust mass range is between 10^2-10^4 Msun and the cold dust temperature spans T(cold)~12-27 K. The spherical geometrical model proposed for the Halpha clear shells is confirmed by the emission profile obtained from the observations and is used to infer the electron density within the envelope: the typical electron density is 0.7+-0.3 cm^-3, while filled regions can reach values two to five times higher.

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The hyperfine structure in the rotational spectrum of CF+

Context. CF+ has recently been detected in the Horsehead and Orion Bar photo-dissociation regions. The J=1-0 line in the Horsehead is double-peaked in contrast to other millimeter lines. The origin of this double-peak profile may be kinematic or spectroscopic. Aims. We investigate the effect of hyperfine interactions due to the fluorine nucleus in CF+ on the rotational transitions. Methods. We compute the fluorine spin rotation constant of CF+ using high-level quantum chemical methods and determine the relative positions and intensities of each hyperfine component. This information is used to fit the theoretical hyperfine components to the observed CF+ line profiles, thereby employing the hyperfine fitting method in GILDAS. Results. The fluorine spin rotation constant of CF+ is 229.2 kHz. This way, the double-peaked CF+ line profiles are well fitted by the hyperfine components predicted by the calculations. The unusually large hyperfine splitting of the CF+ line therefore explains the shape of the lines detected in the Horsehead nebula, without invoking intricate kinematics in the UV-illuminated gas.

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The IRAM-30m line survey of the Horsehead PDR: II. First detection of the l-C3H+ hydrocarbon cation

We present the first detection of the l-C3H+ hydrocarbon in the interstellar medium. The Horsehead WHISPER project, a millimeter unbiased line survey at two positions, namely the photo-dissociation region (PDR) and the nearby shielded core, revealed a consistent set of eight unidentified lines toward the PDR position. Six of them are detected with a signal-to-noise ratio from 6 to 19, while the two last ones are tentatively detected. Mostly noise appears at the same frequency toward the dense core, located less than 40" away. We simultaneously fit 1) the rotational and centrifugal distortion constants of a linear rotor, and 2) the Gaussian line shapes located at the eight predicted frequencies. The observed lines can be accurately fitted with a linear rotor model, implying a 1Sigma ground electronic state. The deduced rotational constant value is Be= 11244.9512 +/- 0.0015 MHz, close to that of l-C3H. We thus associate the lines to the l-C3H+ hydrocarbon cation, which enables us to constrain the chemistry of small hydrocarbons. A rotational diagram is then used to infer the excitation temperature and the column density. We finally compare the abundance to the results of the Meudon PDR photochemical model.

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A detailed view of a Molecular Cloud in the far outer disk of M33

The amount of H$_2$ present in spiral galaxies remains uncertain, particularly in the dim outer regions and in low-metallicity environments. We present high-resolution CO(1--0) observations with the Plateau de Bure interferometer of the most distant molecular cloud in the local group galaxy M 33. The cloud is a single entity rather than a set of smaller clouds within the broad beam of the original single-dish observations. The interferometer and single-dish fluxes are very similar and the line widths are indistinguishable, despite the difference in beamsize. At a spatial resolution of 10 pc, beyond the optical radius of the M 33, the CO brightness temperature reaches 2.4 Kelvins. A virial mass estimate for the cloud yields a mass of $4.3 \times 10^4$ \msun and a ratio $\ratio \simeq 3.5 \times 10^{20} \Xunit$. While no velocity gradient is seen where the emission is strong, the velocity is redshifted to the extreme SW and blue-shifted to the far NE. If the orientation of the cloud is along the plane of the disk (i.e. not perpendicular), then these velocities correspond to slow infall or accretion. The rather modest infall rate would be about $2 \times 10^{-4}$\moyr.

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Spectrally resolved CII emission in M~33 ({\tt HerM33es}): Physical conditions and kinematics around BCLMP 691

This work presents high spectral resolution observations of the \CII\ line at 158 \micron, one of the major cooling lines of the interstellar medium, taken with the HIFI heterodyne spectrometer on the Herschel satellite. In BCLMP 691, an \HII\ region far north (3.3 kpc) in the disk of M 33, the \CII\ and CO line profiles show similar velocities within $0.5 \kms$, while the \HI\ line velocities are systematically shifted towards lower rotation velocities by $\sim 5\kms$. Observed at the same $12"$ angular resolution, the \CII\ lines are broader than those of CO by about 50% but narrower than the \HI\ lines. The \CII\ line to far-infrared continuum ratio suggests a photoelectric heating efficiency of 1.1%. The data, together with published models indicate a UV field $G_0 \sim 100$ in units of the solar neighborhood value, a gas density $n_H \sim 1000 \cc$, and a gas temperature $T\sim 200$ K. Adopting these values, we estimate the C$^+$ column density to be $N_{C^+} \approx 1.3 \times 10^{17} \cmt$. The \CII\ emission comes predominantly from the warm neutral region between the \HII\ region and the cool molecular cloud behind it. From published abundances, the inferred C$^+$ column corresponds to a hydrogen column density of $N_H \sim 2 \times 10^{21} \cmt$. The CO observations suggest that $N_H = 2 N_{H_2} \sim 3.2 \times 10^{21} \cmt$ and 21cm measurements, also at $12"$ resolution, yield $N_\HI \approx 1.2 \times 10^{21} \cmt$ within the \CII\ velocity range. Thus, some H$_2$ not detected in CO must be present, in agreement with earlier findings based on the SPIRE 250 -- 500 $μ$m emission.

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The IRAM-30m line survey of the Horsehead PDR: I. CF+ as a tracer of C+ and a measure of the Fluorine abundance

C+ is a key species in the interstellar medium but its 158 μm fine structure line cannot be observed from ground-based telescopes. Current models of fluorine chemistry predict that CF+ is the second most important fluorine reservoir, in regions where C+ is abundant. We detected the J = 1-0 and J = 2-1 rotational lines of CF+ with high signal-to-noise ratio towards the PDR and dense core positions in the Horsehead. Using a rotational diagram analysis, we derive a column density of N(CF+) = (1.5 - 2.0) \times 10^12 cm^-2. Because of the simple fluorine chemistry, the CF+ column density is proportional to the fluorine abundance. We thus infer the fluorine gas-phase abundance to be F/H = (0.6 - 1.5) \times 10^-8. Photochemical models indicate that CF+ is found in the layers where C+ is abundant. The emission arises in the UV illuminated skin of the nebula, tracing the outermost cloud layers. Indeed, CF+ and C+ are the only species observed to date in the Horsehead with a double peaked line profile caused by kinematics. We therefore propose that CF+, which is detectable from the ground, can be used as a proxy of the C+ layers.

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Cool and warm dust emission from M33 (HerM33es)

We study the far-infrared emission from the nearby spiral galaxy M33 in order to investigate the dust physical properties such as the temperature and the luminosity density across the galaxy. Taking advantage of the unique wavelength coverage (100, 160, 250, 350 and 500 micron) of the Herschel Space Observatory and complementing our dataset with Spitzer-IRAC 5.8 and 8 micron and Spitzer-MIPS 24 and 70 micron data, we construct temperature and luminosity density maps by fitting two modified blackbodies of a fixed emissivity index of 1.5. We find that the 'cool' dust grains are heated at temperatures between 11 and 28 K with the lowest temperatures found in the outskirts of the galaxy and the highest ones in the center and in the bright HII regions. The infrared/submillimeter total luminosity (5 - 1000 micron) is estimated to be 1.9x10^9 Lsun. 59% of the total luminosity of the galaxy is produced by the 'cool' dust grains (~15 K) while the rest 41% is produced by 'warm' dust grains (~55 K). The ratio of the cool-to-warm dust luminosity is close to unity (within the computed uncertainties), throughout the galaxy, with the luminosity of the cool dust being slightly enhanced in the center of the galaxy. Decomposing the emission of the dust into two components (one emitted by the diffuse disk of the galaxy and one emitted by the spiral arms) we find that the fraction of the emission in the disk in the mid-infrared (24 micron) is 21%, while it gradually rises up to 57% in the submillimeter (500 micron). We find that the bulk of the luminosity comes from the spiral arm network that produces 70% of the total luminosity of the galaxy with the rest coming from the diffuse dust disk. The 'cool' dust inside the disk is heated at a narrow range of temperatures between 18 and 15 K (going from the center to the outer parts of the galaxy).

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Dust and gas power-spectrum in M33 (HERM33ES)

Power spectra of de-projected images of late-type galaxies in gas and/or dust emission are very useful diagnostics of the dynamics and stability of their interstellar medium. Previous studies have shown that the power spectra can be approximated as two power-laws, a shallow one at large scales (larger than 500 pc) and a steeper one at small scales, with the break between the two corresponding to the line-of-sight thickness of the galaxy disk. We present a thorough analysis of the power spectra of the dust and gas emission at several wavelengths in the nearby galaxy M33. In particular, we use the recently obtained images at five wavelengths by PACS and SPIRE onboard Herschel. The large dynamical range (2-3 dex in scale) of most images allow us to determine clearly the change in slopes from -1.5 to -4, with some variations with wavelength. The break scale is increasing with wavelength, from 100 pc at 24 and 100micron to 350 pc at 500micron, suggesting that the cool dust lies in a thicker disk than the warm dust, may be due to star formation more confined to the plane. The slope at small scale tends to be steeper at longer wavelength, meaning that the warmer dust is more concentrated in clumps. Numerical simulations of an isolated late-type galaxy, rich in gas and with no bulge, like M33, are carried out, in order to better interpret these observed results. Varying the star formation and feedback parameters, it is possible to obtain a range of power-spectra, with two power-law slopes and breaks, which nicely bracket the data. The small-scale power-law is indeed reflecting the 3D behaviour of the gas layer, steepening strongly while the feedback smoothes the structures, by increasing the gas turbulence. M33 appears to correspond to a fiducial model with an SFR of $\sim$ 0.7 Mo/yr, with 10% supernovae energy coupled to the gas kinematics.

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Giant Molecular Clouds in the Local Group Galaxy M33

We present an analysis of the systematic CO(2-1) survey at 12" resolution covering most of the local group spiral M 33 which, at a distance of 840 kpc, is close enough that individual giant molecular clouds (GMCs) can be identified. The goal of this work is to study the properties of the GMCs in this subsolar metallicity galaxy. The CPROPS (Cloud Properties) algorithm (Rosolowsky & Leroy 2006) was used to identify 337 GMCs in M 33, the largest sample to date in an external galaxy. The sample is used to study the GMC luminosity function, or mass spectrum under the assumption of a constant N(H2)/ICO ratio. We find that n(L)dL = K*L^(-2.0\pm0.1) for the entire sample. However, when the sample is divided into inner and outer disk samples, the exponent changes from 1.6 \pm 0.2 for the centre 2 kpc to 2.3 \pm 0.2 for galactocentric distances larger than 2 kpc. Based on the emission in the FUV, Halpha, 8mu, and 24mu bands, each cloud was classified in terms of its star forming activity - no star formation, embedded, or exposed star formation (visible in FUV and Halpha). At least one sixth of the clouds had no (massive) star formation, suggesting that the average time required for star formation to start is about one sixth of the total time for which the object is identifiable as a GMC. The clouds without star formation have significantly lower CO luminosities than those with star formation, whether embedded or exposed, presumably related to the lack of heating sources. Taking the cloud sample as a whole, the main non-trivial correlation was the decrease in cloud CO brightness (or luminosity) with galactocentric radius. The complete cloud catalog, including CO and HI spectra and the CO contours on the FUV, Halpha, 8mu, and 24mu images is presented in the appendix.

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The Herschel M33 extended survey (HerM33es): PACS spectroscopy of the star forming region BCLMP 302

Context: The emission line of [CII] at 158 micron is one of the strongest cooling lines of the interstellar medium (ISM) in galaxies. Aims: Disentangling the relative contributions of the different ISM phases to [CII] emission, is a major topic of the HerM33es program, a Herschel key project to study the ISM in the nearby spiral galaxy M33. Methods: Using PACS, we have mapped the emission of [CII] 158 micron, [OI] 63 micron, and other FIR lines in a 2'x2' region of the northern spiral arm of M33, centered on the HII region BCLMP302. At the peak of H-alpha emission, we have observed in addition a velocity resolved [CII] spectrum using HIFI. We use scatterplots to compare these data with PACS 160 micron continuum maps, and with maps of CO and HI data, at a common resolution of 12 arcsec or 50 pc. Maps of H-alpha and 24 micron emission observed with Spitzer are used to estimate the SFR. We have created maps of the [CII] and [OI] 63 micron emission and detected [NII] 122 micron and NIII 57 micron at individual positions. Results: The [CII] line observed with HIFI is significantly broader than that of CO, and slightly blue-shifted. In addition, there is little spatial correlation between [CII] observed with PACS and CO over the mapped region. There is even less spatial correlation between [CII] and the atomic gas traced by HI. Detailed comparison of the observed intensities towards the HII region with models of photo ionization and photon dominated regions, confirms that a significant fraction, 20--30%, of the observed [CII] emission stems from the ionized gas and not from the molecular cloud. The gas heating efficiency, using the ratio between [CII] and the TIR as a proxy, varies between 0.07 and 1.5%, with the largest variations found outside the HII region.

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Star formation in M33 (HerM33es)

Within the key project "Herschel M33 extended survey" (HerM33es), we are studying the physical and chemical processes driving star formation and galactic evolution in the nearby galaxy M33, combining the study of local conditions affecting individual star formation with properties only becoming apparent on global scales. Here, we present recent results obtained by the HerM33es team. Combining Spitzer and Herschel data ranging from 3.6um to 500um, along with HI, Halpha, and GALEX UV data, we have studied the dust at high spatial resolutions of 150pc, providing estimators of the total infrared (TIR) brightness and of the star formation rate. While the temperature of the warm dust at high brightness is driven by young massive stars, evolved stellar populations appear to drive the temperature of the cold dust. Plane-parallel models of photon dominated regions (PDRs) fail to reproduce fully the [CII], [OI], and CO maps obtained in a first spectroscopic study of one 2'x2' subregion of M33, located on the inner, northern spiral arm and encompassing the HII region BCLMP302.

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Molecular and Atomic Gas in the Local Group Galaxy M33

We present high resolution large scale observations of the molecular and atomic gas in the Local Group Galaxy M33. The observations were carried out using the HERA at the 30m IRAM telescope in the CO(2-1) line achieving a resolution of 12"x2.6 km/s, enabling individual GMCs to be resolved. The observed region mainly along the major axis out to a radius of 8.5 kpc, and covers the strip observed with HIFI/PACS Spectrometers as part of the HERM33ES Herschel key program. The achieved sensitivity in main beam temperature is 20-50 mK at 2.6 km/s velocity resolution. The CO(2-1) luminosity of the observed region is 1.7\pm0.1x10^7 Kkm/s pc^2, corresponding to H2 masses of 1.9x10^8 Msun (including He), calculated with a NH2/ICO twice the Galactic value due to the half-solar metallicity of M33. HI 21 cm VLA archive observations were reduced and the mosaic was imaged and cleaned using the multi-scale task in CASA, yielding a series of datacubes with resolutions ranging from 5" to 25". The HI mass within a radius of 8.5 kpc is estimated to be 1.4x10^9 Msun. The azimuthally averaged CO surface brightness decreases exponentially with a scale length of 1.9\pm0.1 kpc whereas the atomic gas surface density is constant at Sigma_HI=6\pm2 Msun/pc^2 deprojected to face-on. The central kiloparsec H_2 surface density is Sigma_H2=8.5\pm0.2 Msun/pc^2. The star formation rate per unit molecular gas (SF Efficiency, the rate of transformation of molecular gas into stars), as traced by the ratio of CO to Halpha and FIR brightness, is constant with radius. The SFE appears 2-4 times greater than of large spiral galaxies. A morphological comparison of molecular and atomic gas with tracers of star formation shows good agreement between these maps both in terms of peaks and holes. A few exceptions are noted. Several spectra, including those of a molecular cloud situated more than 8 kpc from the galaxy center, are presented.

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Cool gas and dust in M33: Results from the Herschel M33 extended survey (HERM33ES)

We present an analysis of the first space-based far-IR-submm observations of M 33, which measure the emission from the cool dust and resolve the giant molecular cloud complexes. With roughly half-solar abundances, M33 is a first step towards young low-metallicity galaxies where the submm may be able to provide an alternative to CO mapping to measure their H$_2$ content. In this Letter, we measure the dust emission cross-section $σ$ using SPIRE and recent CO and \HI\ observations; a variation in $σ$ is present from a near-solar neighborhood cross-section to about half-solar with the maximum being south of the nucleus. Calculating the total H column density from the measured dust temperature and cross-section, and then subtracting the \HI\ column, yields a morphology similar to that observed in CO. The H$_2$/\HI\ mass ratio decreases from about unity to well below 10% and is about 15% averaged over the optical disk. The single most important observation to reduce the potentially large systematic errors is to complete the CO mapping of M 33.

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