CO-to-H2 conversion and spectral column density in molecular clouds: the variability of the XCO factor

We study the CO line luminosity ($L_{\rm CO}$), the shape of the CO Spectral Line Energy Distribution (SLED), and the value of the CO-to-$\rm H_2$ conversion factor in galaxies in the Epoch of Reionization (EoR). To this aim, we construct a model that simultaneously takes into account the radiative transfer and the clumpy structure of giant molecular clouds (GMCs) where the CO lines are excited. We then use it to post-process state-of-the-art zoomed, high resolution ($30\, \rm{pc}$), cosmological simulation of a main-sequence ($M_{*}\approx10^{10}\, \rm{M_{\odot}}$, $SFR\approx 100\,\rm{M_{\odot}\, yr^{-1}}$) galaxy, "Alth{\ae}a", at $z\approx6$. We find that the CO emission traces the inner molecular disk ($r\approx 0.5 \,\rm{kpc}$) of Alth{\ae}a with the peak of the CO surface brightness co-located with that of the [CII] 158$\rm \mu m$ emission. Its $L_{\rm CO(1-0)}=10^{4.85}\, \rm{L_{\odot}}$ is comparable to that observed in local galaxies with similar stellar mass. The high ($\Sigma_{gas} \approx 220\, \rm M_{\odot}\, pc^{-2}$) gas surface density in Alth{\ae}a, its large Mach number (\mach$\approx 30$), and the warm kinetic temperature ($T_{k}\approx 45 \, \rm K$) of GMCs yield a CO SLED peaked at the CO(7-6) transition, i.e. at relatively high-$J$, and a CO-to-$\rm H_2$ conversion factor $\alpha_{\rm CO}\approx 1.5 \, \rm M_{\odot} \rm (K\, km\, s^{-1}\, pc^2)^{-1} $ lower than that of the Milky Way. The ALMA observing time required to detect (resolve) at 5$\sigma$ the CO(7-6) line from galaxies similar to Alth{\ae}a is $\approx13$ h ($\approx 38$ h).

We observed a 10x20 pc region of the molecular cloud M17 in the 12CO and 13CO J=3-2 and J=2-1 transitions to determine their global behavior and to assess the reliability of using ratios of CO line intensities integrated over an entire cloud to determine the physical conditions within the cloud. Both the 12CO/13CO J=2-1 and J=3-2 line ratios correlate with the 13CO integrated intensity, with smaller line ratios observed at locations with large integrated intensities. This correlation is likely due to variations in the column density from one position to another within M17. The 12CO and 13CO (J=3-2/J=2-1) line ratios show no significant variation from place to place within M17, even on the peak of the photon-dominated region. A Large Velocity Gradient analysis of globally averaged line ratios gives results in reasonable agreement with the results obtained for individual lines-of-sight through the cloud, which suggests that the typical physical conditions in a molecular cloud can be determined using CO line ratios integrated over the entire cloud. There appears to be a clear trend of increasing 12CO/13CO J=2-1 and J=3-2 line ratios as one moves from Galactic molecular cloud cores to entire Galactic molecular clouds to normal galaxies. The most likely explanation of the high line ratios for normal galaxies is a significant contribution to the CO emission by low column density material, such as diffuse molecular clouds or the outer envelopes of giant molecular clouds.

view Abstract Citations (29) References (10) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS A Molecular Cloud in IC 1396 Loren, Robert B. ; Peters, William L. ; Vanden Bout, Paul A. Abstract Observations of the large cometary nebula in IC 1396 show it to be a strong source of molecular line emission. The "C'6O and `8C'6O (J = 1-0) line intensities have been mapped and are well correlated with the optical appearance of the cloud. Emission from SO, HCN, and CS has been detected at the position of peak CO line intensity. Analysis of the CO line intensity maps reveals differing distributions of CO excitation temperature and column density. A heating source is required for the cloud, and a search for an infrared source is suggested. Subject headings: interstellar matter - molecules, interstellar - nebulae Publication: The Astrophysical Journal Pub Date: January 1975 DOI: 10.1086/153305 Bibcode: 1975ApJ...195...75L full text sources ADS |

view Abstract Citations (31) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The relationship of submillimeter optical depth to 13CO column density in molecular clouds. Righini-Cohen, G. ; Simon, M. Abstract The relationship between dust and molecular gas within a molecular cloud is studied by investigating the correlation of 350-micron and 1-mm optical depths with (C-13)O column density in ten very dense molecular sources that are visibly opaque and probably characterized by an extinction factor well in excess of 20. The cited correlation is examined at a number of points within Sgr B2 and at the peak molecular positions in the other nine sources. A strong correlation is found in each case, and the overall correlations obtained are shown to be real, internally consistent, and not markedly influenced by the assumption that the dust temperature is twice the gas temperature. Contributions to the observed scatter in the correlations are assessed. Publication: The Astrophysical Journal Pub Date: April 1977 DOI: 10.1086/155168 Bibcode: 1977ApJ...213..390R Keywords: Abundance; Infrared Radiation; Interstellar Matter; Microwave Emission; Molecular Gases; Submillimeter Waves; Carbon Monoxide; Cosmic Dust; Gas Density; Interstellar Radiation; Nebulae; Optical Thickness; Astrophysics full text sources ADS |

We present 38'' resolution maps of the CO and {sup 13}CO J = 2-1 lines in the molecular clouds toward the H II region complex W51. The maps cover a 1.{sup 0}25 x 1{sup 0} section of the galactic plane and span +30 to +85 km s{sup -1} (LSR) in velocity. The spectral resolution is {approx}1.3 km s{sup -1}. The velocity range of the images includes all the gas in the Sagittarius spiral arm. Color figures display the peak line brightness temperature, the velocity-integrated intensity, and 2 km s{sup -1} channel-averaged maps for both isotopologs, and also the CO/{sup 13}CO J = 2-1 line intensity ratio as a function of velocity. The CO and {sup 13}CO line intensity image cubes are made available in standard FITS format as electronically readable tables. We compare our molecular line maps with the 1.1 mm continuum image from the BOLOCAM Galactic Plane Survey. From our {sup 13}CO image cube, we derive kinematic information for the 99 BGPS sources in the mapped field in the form of Gaussian component fits. The integrated {sup 13}CO line intensity and the 1.1 mm source flux density show only a modest degree of correlation for the 99 sources, likelymore » due to a range of dust and gas physical conditions within the sources. However, the 1.1 mm continuum surface brightness and the integrated {sup 13}CO line intensity for small regions containing single BGPS sources and molecular clouds show very good correlations in many cases. Differences in the shapes of these correlations from one spatial region to another probably result from different physical conditions or structure in the clouds.« less

We present SOFIA/GREAT [C ii] 2 P 3/2 → 2 P 1/2 (1.9005369 THz) observations of nearby clouds near the lines of sight towards the quasars B0355+508 and B0212+735. These clouds have previously been identified as warm non-LTE diffuse clouds with a temperature of T ≳ 30 K and sub-thermally excited CO lines. They are highly structured in CO with small-scale bright spots ( I (CO J = 1–0)~ 5–20 K km s -1 ), both spectrally and spatially. This small-scale structure has been interpreted as small-scale variations in the chemistry, not as density and column-density structure. We did not detect [C ii] 158 μ m emission within the rms noise of ~0.1–0.3 K. Our non-detection in [C ii] contradicts the above scenario. In diffuse clouds, the efficiency of photo-electric heating is highest. Under the assumption that [C ii] is the dominant coolant in diffuse clouds, we can calculate the predicted [C ii] emission arising from these clouds. Based on the derived hydrogen column densities for the diffuse clouds, a line width in [C ii] of similar order to that of CO, and when at least the minimum amount of heating in the clouds is due to cosmic-ray heating, [C ii] line intensities ≳1.5 to 5 K km s -1 are expected, which is a factor ~3 to 15 above the upper limits of the observations. The upper limits of the [C ii] and the observed CO line intensities are, however, consistent with the intensities predicted for photon-dominated region (PDR) surfaces on regular cold ( T ~ 15 K) low-density cloud fragments. Lower temperatures lead to less excited [C ii]. The assumption of lower densities, which would equally lower the [C ii] excitation, contradicts the observed cloud sizes and column densities. The CO(2–1)/CO(1–0) line ratios observed in these clouds are consistent with cloud temperatures of T ~ 15 K. The KOSMA- τ PDR-model of a cold moderate-density clump or an ensemble of such clumps with a canonical mass-size relation and mass spectrum, consistent with the total column densities derived for low density, shows that cold PDRs can reproduce the observed CO intensities, the observed CO(1–0) and CO(2–1) ratio, and the observed upper limits for [C ii].

Measuring the mass distribution of infrared dark clouds (IRDCs) over the wide dynamic range of their column densities is a fundamental obstacle in determining the initial conditions of high-mass star formation and star cluster formation. We present a new technique to derive high-dynamic-range, arcsecond-scale resolution column density data for IRDCs and demonstrate the potential of such data in measuring the density variance - sonic Mach number relation in molecular clouds. We combine near-infrared data from the UKIDSS/Galactic Plane Survey with mid-infrared data from the Spitzer/GLIMPSE survey to derive dust extinction maps for a sample of ten IRDCs. We then examine the linewidths of the IRDCs using 13CO line emission data from the FCRAO/Galactic Ring Survey and derive a column density - sonic Mach number relation for them. For comparison, we also examine the relation in a sample of nearby molecular clouds. The presented column density mapping technique provides a very capable, temperature independent tool for mapping IRDCs over the column density range equivalent to A_V=1-100 mag at a resolution of 2". Using the data provided by the technique, we present the first direct measurement of the relationship between the column density dispersion, \sigma_{N/<N>}, and sonic Mach number, M_s, in molecular clouds. We detect correlation between the variables with about 3-sigma confidence. We derive the relation \sigma_{N/<N>} = (0.047 \pm 0.016) Ms, which is suggestive of the correlation coefficient between the volume density and sonic Mach number, \sigma_{\rho/<\rho>} = (0.20^{+0.37}_{-0.22}) Ms, in which the quoted uncertainties indicate the 3-sigma range. When coupled with the results of recent numerical works, the existence of the correlation supports the picture of weak correlation between the magnetic field strength and density in molecular clouds (i.e., B ~ \rho^{0.5}).

view Abstract Citations (24) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nearby molecular clouds. I. Ophiuchus-Sagittarius, B > 10. Lebrun, F. ; Huang, Y. -L. Abstract Observations of a 370-sq-deg area at b = 10-24 deg in the Oph-Sag region at the 115-GHz 1-0 transition of CO, obtained with a 256-channel spectrometer on the 1.2-m mm-wave telescope at Columbia University during winter 1980-1981 are reported. Observing parameters include full beamwidth at half power 8 arcmin, resolution 1 or 0.5 deg, velocity resolution 0.65 km/s, and frequency-shifting-mode shift 5 MHz; the data-processing scheme is described in detail. The results are presented in a map and a diagram and discussed with regard to other observations. An extended complex of molecular clouds near the sun and probably connected with the Aquila Rift, the Rho Oph Cloud, and the Gould Belt is detected. A correlation is found between the CO line intensity and the H I deficiency observed in the region, suggesting H2 formation with H2 column densities up to 1 x 10 to the 21st/sq cm. Publication: The Astrophysical Journal Pub Date: June 1984 DOI: 10.1086/162138 Bibcode: 1984ApJ...281..634L Keywords: Galactic Structure; Milky Way Galaxy; Molecular Clouds; Carbon Monoxide; Interstellar Extinction; Astrophysics full text sources ADS | data products SIMBAD (1) Related Materials (1) Part 2: 1986ApJ...306...16L

We have used a numerical simulation of a turbulent cloud to synthesize maps of the thermal emission from dust at a variety of far-IR and submillimeter wavelengths. The average column density and external radiation field in the simulation is well matched to clouds such as Perseus and Ophiuchus. We use pairs of single-wavelength emission maps to derive the dust color temperature and column density, and we compare the derived column densities with the true column density. We demonstrate that longer wavelength emission maps yield less biased estimates of column density than maps made toward the peak of the dust emission spectrum. We compare the scatter in the derived column density with the observed scatter in Perseus and Ophiuchus. We find that while in Perseus all of the observed scatter in the emission-derived versus the extinction-derived column density can be attributed to the flawed assumption of isothermal dust along each line of sight, in Ophiuchus there is additional scatter above what can be explained by the isothermal assumption. Our results imply that variations in dust emission properties within a molecular cloud are not necessarily a major source of uncertainty in column density measurements.

After morphological classification of 18,190 12CO molecular clouds, we further investigate the properties of their internal molecular gas structures traced by the 13CO (J = 1−0) line emissions. Using three different methods to extract the 13CO gas structures within each 12CO cloud, we find that ∼15% of the 12CO clouds (2851) have 13CO gas structures and these 12CO clouds contribute about 93% of the total integrated flux of 12CO emission. In each of the 2851 12CO clouds with 13CO gas structures, the 13CO emission area generally does not exceed 70% of the 12CO emission area, and the 13CO integrated flux does not exceed 20% of the 12CO integrated flux. We reveal a strong correlation between the velocity-integrated intensities of 12CO lines and those of 13CO lines in both 12CO and 13CO emission regions. This indicates the H2 column densities of molecular clouds are crucial for the 13CO line emission. After linking the 13CO structure detection rates of the 18,190 12CO molecular clouds to their morphologies, i.e., nonfilaments and filaments, we find that the 13CO gas structures are primarily detected in 12CO clouds with filamentary morphologies. Moreover, these filaments tend to harbor more than one 13CO structure. That demonstrates filaments not only have larger spatial scales, but also have more molecular gas structures traced by 13CO lines, i.e., local gas density enhancements. Our results favor the turbulent compression scenario for filament formation, in which dynamical compression of turbulent flows induces local density enhancements. The nonfilaments tend to be in the low-pressure and quiescent turbulent environments of the diffuse interstellar medium.

The most common means of converting an observed CO line intensity into a molecular gas mass requires the use of a conversion factor (XCO). While in the Milky Way this quantity does not appear to vary significantly, there is good reason to believe that XCO will depend on the larger‐scale galactic environment. With sensitive instruments pushing detections to increasingly high redshift, characterizing XCO as a function of physical conditions is crucial to our understanding of galaxy evolution. Utilizing numerical models, we investigate how varying metallicities, gas temperatures and velocity dispersions in galaxies impacts the way CO line emission traces the underlying H2 gas mass, and under what circumstances XCO may differ from the Galactic mean value. We find that, due to the combined effects of increased gas temperature and velocity dispersion, XCO is depressed below the Galactic mean in high surface density environments such as ultraluminous infrared galaxies (ULIRGs). In contrast, in low‐metallicity environments, XCO tends to be higher than in the Milky Way, due to photodissociation of CO in metal‐poor clouds. At higher redshifts, gas‐rich discs may have gravitationally unstable clumps that are warm (due to increased star formation) and have elevated velocity dispersions. These discs tend to have XCO values ranging between present‐epoch gas‐rich mergers and quiescent discs at low z. This model shows that on average mergers do have lower XCO values than disc galaxies, though there is significant overlap. XCO varies smoothly with the local conditions within a galaxy, and is not a function of global galaxy morphology. We combine our results to provide a general fitting formula for XCO as a function of CO line intensity and metallicity. We show that replacing the traditional approach of using one constant XCO for starbursts and another for discs with our best‐fitting function produces star formation laws that are continuous rather than bimodal, and that have significantly reduced scatter.

The current understanding of the abundance of CO in interstellar clouds is reviewed from both observational and theoretical points of view. In special circumstances, the CO and H2 column densities can be measured directly by ultraviolet and infrared absorption line techniques. Indirect methods invoke mean relations between CO line intensities and extinction, diffuse far-infrared flux, and diffuse gamma ray flux, or assume that the clouds are in virial equilibrium. The problems associated with these indirect methods are considered, and the range of applicability of the empirical relations is investigated. A better understanding of the abundance of CO is necessary if it is to be used effectively as a quantitative tracer of molecular material in the Milky Way and other galaxies. Theoretical models of the structure and chemistry of interstellar clouds can be used to investigate the depth dependence of the abundance of CO, as well as the isotope fractionation. The models treat the photochemical zone in detail and incorporate the most recent laboratory data on poorly understood photodissociation processes. Such models can be tested by comparison with observations of CO in diffuse and translucent molecular clouds. Models of dense clouds must account for the observed fractions of CO in solid form in such clouds.

We use the COMPLETE Survey's observations of the Perseus star-forming region to assess and intercompare three methods for measuring column density in molecular clouds: extinction mapping (NIR); thermal emission mapping (FIR); and mapping the intensity of CO isotopologues. The structures shown by all three tracers are morphologically similar, but important differences exist. Dust-based measures give similar, log-normal, distributions for the full Perseus region, once careful calibration corrections are made. We also compare dust- and gas-based column density distributions for physically-meaningful sub-regions of Perseus, and we find significant variations in the distributions for those regions. Even though we have used 12CO data to estimate excitation temperatures, and we have corrected for opacity, the 13CO maps seem unable to give column distributions that consistently resemble those from dust measures. We have edited out the effects of the shell around the B-star HD 278942. In that shell's interior and in the parts where it overlaps the molecular cloud, there appears to be a dearth of 13CO, likely due either to 13CO not yet having had time to form in this young structure, and/or destruction of 13CO in the molecular cloud. We conclude that the use of either dust or gas measures of column density without extreme attention to calibration and artifacts is more perilous than even experts might normally admit. And, the use of 13CO to trace total column density in detail, even after proper calibration, is unavoidably limited in utility due to threshold, depletion, and opacity effects. If one's main aim is to map column density, then dust extinction seems the best probe. Linear fits amongst column density tracers are given, quantifying the inherent uncertainties in using one tracer (when compared with others). [abridged]

Does star formation proceed in the same way in large spirals such as the Milky Way and in smaller chemically younger galaxies? Earlier work suggests a more rapid transformation of H$_2$ into stars in these objects but (1) a doubt remains about the validity of the H$_2$ mass estimates and (2) there is currently no explanation for why star formation should be more efficient. M~33, a local group spiral with a mass $\sim 10$\% and a metallicity half that of the Galaxy, represents a first step towards the metal poor Dwarf Galaxies. We have searched for molecular clouds in the outer disk of M~33 and present here a set of detections of both $^{12}$CO and $^{13}$CO, including the only detections (for both lines) beyond the R$_{25}$ radius in a subsolar metallicity galaxy. The spatial resolution enables mass estimates for the clouds and thus a measure of the $N({\rm H}_2) / I_{\rm CO}$ ratio, which in turn enables a more reliable calculation of the H$_2$ mass. Our estimate for the outer disk of M~33 is $N({\rm H}_2) / I_{\rm CO(1-0)} \sim 5 \times 10^{20} \,{\rm cm^{-2}/(K{\rm \ km \ s^{-1}})}$ with an estimated uncertainty of a factor $\le 2$. While the $^{12/13}$CO line ratios do not provide a reliable measure of $N({\rm H}_2) / I_{\rm CO}$, the values we find are slightly greater than Galactic and corroborate a somewhat higher $N({\rm H}_2) / I_{\rm CO}$ value. Comparing the CO observations with other tracers of the interstellar medium, no reliable means of predicting where CO would be detected was identified. In particular, CO detections were often not directly on local HI or FIR or H$\alpha$ peaks, although generally in regions with FIR emission and high HI column density. The results presented here provide support for the quicker transformation of H$_2$ into stars in M~33 than in large local universe spirals.

We discuss the probability distribution function (PDF) of column density resulting from density fields with lognormal PDFs, applicable to isothermal gas (e.g., probably molecular clouds). For magnetic and nonmagnetic numerical simulations of compressible, isothermal turbulence forced at intermediate scales ( of the box size), we find that the autocorrelation function (ACF) of the density field decays over relatively short distances compared to the simulation size. We suggest that a "decorrelation length" can be defined as the distance over which the density ACF has decayed to, for example, 10% of its zero-lag value, so that the density "events" along a line of sight can be assumed to be independent over distances larger than this, and the central limit theorem should be applicable. However, using random realizations of lognormal fields, we show that the convergence to a Gaussian is extremely slow in the high-density tail. As a consequence, the column density PDF is not expected to exhibit a unique functional shape, but to transit instead from a lognormal to a Gaussian form as the ratio η of the column length to the decorrelation length (i.e., the number of independent events in the cloud) increases. Simultaneously, the variance of the PDF decreases. For intermediate values of η, the column density PDF assumes a nearly exponential decay. For cases with a density contrast of 104, as found in intermediate-resolution simulations, and expected from giant molecular clouds (GMCs) to dense molecular cores, the required value of η for convergence to a Gaussian is at least a few hundred, or, for 106, several thousand. We then discuss the density power spectrum and the expected value of η in actual molecular clouds, concluding that they are uncertain since they may depend on several physical parameters. Observationally, our results suggest that η may be inferred from the shape and width of the column density PDF in optically thin line or extinction studies. Our results should also hold for gas with finite-extent power-law underlying density PDFs, which should be characteristic of the diffuse, nonisothermal neutral medium (with temperatures ranging from a few hundred to a few thousand degrees). Finally, we note that for η ≳ 100, the dynamic range in column density is small (less than a factor of 10), but this is only an averaging effect, with no implication on the dynamic range of the underlying density distribution.