Envelopes Of Molecular Clouds Research Articles

Characterizing the 3D Structure of Molecular Cloud Envelopes in the Cloud Factory Simulations

We leverage recent numerical simulations of highly resolved star-forming regions in a Milky Way–like galaxy to explore the nature of extended gaseous envelopes around molecular clouds. We extract a sample of two dozen star-forming clouds from the feedback-dominated suite of Cloud Factory simulations. With the goal of exploring the 3D thermal and chemical structure of the gas, we measure and fit the clouds’ radial profiles with multiple tracers, including nHI , nH2 , nHtot , n CO, and gas temperature. We find that while solar neighborhood clouds recently detected via 3D dust mapping have radially symmetric, low-density envelopes that extend ∼10–15 pc, the simulated cloud envelopes are primarily radially asymmetric with low-density envelopes that extend only ∼2–3 pc. One potential explanation for the absence of extended envelopes in the simulated clouds may be the lack of magnetic fields, while a stronger local feedback prescription compared to solar neighborhood conditions may drive the radially asymmetric cloud morphologies. We make the pipeline used to extract and characterize the radial profiles of the clouds publicly available, which can be used in complementary and future simulations to shed additional light on the key physics shaping the formation and evolution of star-forming structures in the Milky Way.

Absorption and Self-absorption of [C ii] and [O i] Far Infrared Lines toward a Bright Bubble in the Nessie Infrared Dark Cloud

Using the upGREAT instrument on board the Stratospheric Observatory for Infrared Astronomy, we imaged [C ii] 157.74 and [O i] 63.18 μm line emission from a bright photodissociation region (PDR) associated with an ionized bubble located in the Nessie Nebula, a filamentary infrared dark cloud. A comparison with Australia Telescope Compact Array data reveals a classic photodissociation region (PDR) structure, with a uniform progression from ionized gas, to photodissociated gas, and to molecular gas from the bubble’s interior to its exterior. [O i] line emission from the bubble’s PDR reveals self-absorption features. Toward a far-IR bright protostar, both [O i] and [C ii] show an absorption feature at a velocity of −18 km s−1, the same velocity as an unrelated foreground molecular cloud. Since the gas density in typical molecular clouds is well below the [O i] and [C ii] critical densities, the excitation temperatures for both lines are low (∼20 K). The Meudon models demonstrate that the surface of a molecular cloud, externally illuminated by a standard G 0 = 1 interstellar radiation field, can produce absorption features in both transitions. Thus, the commonly observed [O i] and [C ii] self-absorption and absorption features plausibly arise from the subthermally excited, externally illuminated photodissociated envelopes of molecular clouds. The luminous young stellar object AGAL337.916-00.477, located precisely where the expanding bubble strikes the Nessie filament, is associated with two shock tracers: NH3 (3,3) maser emission and SiO 2−1 emission, indicating an interaction between the bubble and the filament. The interaction of the expanding bubble with its parental dense filament has triggered star formation.

A Revised Description of the Cosmic Ray Induced Desorption of Interstellar Ices

Abstract Nonthermal desorption of ices on interstellar grains is required to explain observations of molecules that are not synthesized efficiently in the gas phase in cold dense clouds. Perhaps the most important nonthermal desorption mechanism is one induced by cosmic rays (CRs), which, when passing through a grain, heat it transiently to a high temperature—the grain cools back to its original equilibrium temperature via the (partial) sublimation of the ice. Current cosmic ray induced desorption (CRD) models assume a fixed grain cooling time. In this work, we present a revised description of CRD in which the desorption efficiency depends dynamically on the ice content. We apply the revised desorption scheme to two-phase and three-phase chemical models in physical conditions corresponding to starless and prestellar cores, and to molecular cloud envelopes. We find that, inside starless and prestellar cores, introducing dynamic CRD can decrease gas-phase abundances by up to an order of magnitude in two-phase chemical models. In three-phase chemical models, our model produces results very similar to those of the static cooling scheme—when only one monolayer of ice is considered active. Ice abundances are generally insensitive to variations in the grain cooling time. Further improved CRD models need to take into account additional effects in the transient heating of the grains—introduced, for example, by the adoption of a spectrum of CR energies.

Formation of Dust Filaments in the Diffuse Envelopes of Molecular Clouds

Abstract The path to understanding star formation processes begins with the study of the formation of molecular clouds. The outskirts of these clouds are characterized by low column densities that allow the penetration of ultraviolet radiation, resulting in a nonnegligible ionization fraction and the charging of the small dust grains that are mixed with the gas; this diffuse phase is then coupled to the ambient magnetic field. Despite the general assumption that dust and gas are tightly correlated, several observational and theoretical studies have reported variations in the dust-to-gas ratio toward diffuse and cold clouds. In this work, we present the implementation of a new charged particles module for analyzing the dust dynamics in molecular cloud envelopes. We study the evolution of a single population of small charged grains (0.05 μm) in the turbulent, magnetized molecular cloud envelope using this module. We show that variations in the dust-to-gas ratio arise due to the coupling of the grains with the magnetic field, forming elongated dust structures decoupled from the gas. This emphasizes the importance of considering the dynamics of charged dust when simulating the different phases of the interstellar medium, especially for star formation studies.

Exclusion of Cosmic Rays from Molecular Clouds by Self-generated Electric Fields

Abstract It was recently discovered that in some regions of the Galaxy, the cosmic-ray (CR) abundance is several orders of magnitude higher than previously thought. Additionally, there is evidence that in molecular cloud envelopes, the CR ionization may be dominated by electrons. We show that for regions with high, electron-dominated ionization, the penetration of CR electrons into molecular clouds is modulated by the electric field that develops as a result of the charge they deposit. We evaluate the significance of this novel mechanism of self-modulation and show that the CR penetration can be reduced by a factor of a few to a few hundred in high-ionization environments, such as those found near the Galactic center.

A Survey of Magnetic Field Strengths in the Envelopes of Molecular Clouds via the 18 cm OH Zeeman Effect

We present the results of an extensive Arecibo observational survey of magnetic field strengths in the inter-core regions of molecular clouds to determine their role in the evolution and collapse of molecular clouds as a whole. Sensitive 18 cm OH Zeeman observations of absorption lines from Galactic molecular gas in the direction of extragalactic continuum sources yielded 38 independent measurements of magnetic field strengths. Zeeman detections were achieved at the three sigma level toward 9 clouds, while the others revealed sensitive upper limits to the magnetic field strength. Our results suggest that total field strengths in the inter-core regions of GMCs are about 15 microgauss.

A Galaxy-scale Fountain of Cold Molecular Gas Pumped by a Black Hole

Abstract We present Atacama Large Millimeter/submillimeter Array and Multi-Unit Spectroscopic Explorer observations of the brightest cluster galaxy in Abell 2597, a nearby (z = 0.0821) cool core cluster of galaxies. The data map the kinematics of a three billion solar mass filamentary nebula that spans the innermost 30 kpc of the galaxy’s core. Its warm ionized and cold molecular components are both cospatial and comoving, consistent with the hypothesis that the optical nebula traces the warm envelopes of many cold molecular clouds that drift in the velocity field of the hot X-ray atmosphere. The clouds are not in dynamical equilibrium, and instead show evidence for inflow toward the central supermassive black hole, outflow along the jets it launches, and uplift by the buoyant hot bubbles those jets inflate. The entire scenario is therefore consistent with a galaxy-spanning “fountain,” wherein cold gas clouds drain into the black hole accretion reservoir, powering jets and bubbles that uplift a cooling plume of low-entropy multiphase gas, which may stimulate additional cooling and accretion as part of a self-regulating feedback loop. All velocities are below the escape speed from the galaxy, and so these clouds should rain back toward the galaxy center from which they came, keeping the fountain long lived. The data are consistent with major predictions of chaotic cold accretion, precipitation, and stimulated feedback models, and may trace processes fundamental to galaxy evolution at effectively all mass scales.

Can the removal of molecular cloud envelopes by external feedback affect the efficiency of star formation?

We investigate how star formation efficiency can be significantly decreased by the removal of a molecular cloud's envelope by feedback from an external source. Feedback from star formation has difficulties halting the process in dense gas but can easily remove the less dense and warmer envelopes where star formation does not occur. However, the envelopes can play an important role keeping their host clouds bound by deepening the gravitational potential and providing a constraining pressure boundary. We use numerical simulations to show that removal of the cloud envelopes results in all cases in a fall in the star formation efficiency (SFE). At 1.38 free-fall times our 4 pc cloud simulation experienced a drop in the SFE from 16 to six percent, while our 5 pc cloud fell from 27 to 16 per cent. At the same time, our 3 pc cloud (the least bound) fell from an SFE of 5.67 per cent to zero when the envelope was lost. The star formation efficiency per free-fall time varied from zero to $\approx$ 0.25 according to $\alpha$, defined to be the ratio of the kinetic plus thermal to gravitational energy, and irrespective of the absolute star forming mass available. Furthermore the fall in SFE associated with the loss of the envelope is found to even occur at later times. We conclude that the SFE will always fall should a star forming cloud lose its envelope due to stellar feedback, with less bound clouds suffering the greatest decrease.

OH 18 cm TRANSITION AS A THERMOMETER FOR MOLECULAR CLOUDS

We have observed the four hyperfine components of the 18 cm OH transition toward the translucent cloud eastward of Heiles Cloud 2 (HCL2E), the cold dark cloud L134N, and the photodissociation region of the $\rho$-Ophiuchi molecular cloud with the Effelsberg 100 m telescope. We have found intensity anomalies amongst the hyperfine components in all three regions. In particular, an absorption feature of the 1612 MHz satellite line against the cosmic microwave background has been detected toward HCL2E and two positions of the $\rho$-Ophiuchi molecular cloud. On the basis of statistical equilibrium calculations, we find that the hyperfine anomalies originate from the non-LTE population of the hyperfine levels, and can be used to determine the kinetic temperature of the gas over a wide range of H$_2$ density (10$^2$ - 10$^7$ cm$^{-3}$). Toward the center of HCL2E, the gas kinetic temperature is determined to be 53$\pm$1 K, and it increases toward the cloud peripheries ($\sim$ 60 K). The ortho-to-para ratio of H$_2$ is determined to be 3.5 $\pm$ 0.9 from the averaged spectrum for the 8 positions. In L134N, a similar increase of the temperature is also seen toward the periphery. In the $\rho$-Ophiuchi molecular cloud, the gas kinetic temperature decreases as a function of the distance from the exciting star HD147889. These results demonstrate a new aspect of the OH 18 cm line as a good thermometer of molecular cloud envelopes. The OH 18 cm line can be used to trace a new class of warm molecular gas surrounding a molecular cloud, which is not well traced by emission of CO and its isotopologues.

DUST AND GAS IN THE MAGELLANIC CLOUDS FROM THE HERITAGE HERSCHEL KEY PROJECT. II. GAS-TO-DUST RATIO VARIATIONS ACROSS INTERSTELLAR MEDIUM PHASES

The spatial variations of the gas-to-dust ratio (GDR) provide constraints on the chemical evolution and lifecycle of dust in galaxies. We examine the relation between dust and gas at 10-50 pc resolution in the Large and Small Magellanic Clouds (LMC and SMC) based on Herschel far-infrared (FIR), H I 21 cm, CO, and Halpha observations. In the diffuse atomic ISM, we derive the gas-to-dust ratio as the slope of the dust-gas relation and find gas-to-dust ratios of 380+250-130 in the LMC, and 1200+1600-420 in the SMC, not including helium. The atomic-to-molecular transition is located at dust surface densities of 0.05 Mo pc-2 in the LMC and 0.03 Mo pc-2 in the SMC, corresponding to AV ~ 0.4 and 0.2, respectively. We investigate the range of CO-to-H2 conversion factor to best account for all the molecular gas in the beam of the observations, and find upper limits on XCO to be 6x1020 cm-2 K-1 km-1 s in the LMC (Z=0.5Zo) at 15 pc resolution, and 4x 1021 cm-2 K-1 km-1 s in the SMC (Z=0.2Zo) at 45 pc resolution. In the LMC, the slope of the dust-gas relation in the dense ISM is lower than in the diffuse ISM by a factor ~2, even after accounting for the effects of CO-dark H2 in the translucent envelopes of molecular clouds. Coagulation of dust grains and the subsequent dust emissivity increase in molecular clouds, and/or accretion of gas-phase metals onto dust grains, and the subsequent dust abundance (dust-to-gas ratio) increase in molecular clouds could explain the observations. In the SMC, variations in the dust-gas slope caused by coagulation or accretion are degenerate with the effects of CO-dark H2. Within the expected 5--20 times Galactic XCO range, the dust-gas slope can be either constant or decrease by a factor of several across ISM phases. Further modeling and observations are required to break the degeneracy between dust grain coagulation, accretion, and CO-dark H2.

HYDROXYL AS A TRACER OF H2IN THE ENVELOPE OF MBM40

We observed 51 positions in the OH 1667 MHz main line transitions in the translucent, high latitude cloud MBM40. We detected OH emission in 8 out of 8 positions in the molecular core of the cloud and 24 out of 43 in the surrounding, lower extinction envelope and periphery of the cloud. Using a linear relationship between the integrated OH line intensity and E(B-V), we estimate the mass in the core, the envelope, and the periphery of the cloud to be 4, 8, and 5 solar masses. As much as a third of the total cloud mass may be found in the in the periphery (E(B-V) $<$ 0.12 mag) and about a half in the envelope (0.12 $\le$ E(B-V) $\le$ 0.17 mag). If these results are applicable to other translucent clouds the OH 1667 MHz line is an excellent tracer of gas in very low extinction regions and high-sensitivity mapping of the envelopes of molecular clouds may reveal the presence of significant quantities of molecular mass.

INTERSTELLAR CN AND CH+IN DIFFUSE MOLECULAR CLOUDS:12C/13C RATIOS AND CN EXCITATION

We present very high signal-to-noise ratio absorption-line observations of CN and CH+ along 13 lines of sight through diffuse molecular clouds. The data are examined to extract precise isotopologic ratios of 12CN/13CN and 12CH+/13CH+ in order to assess predictions of diffuse cloud chemistry. Our results on 12CH+/13CH+ confirm that this ratio does not deviate from the ambient 12C/13C ratio in local interstellar clouds, as expected if the formation of CH+ involves nonthermal processes. We find that 12CN/13CN, however, can be significantly fractionated away from the ambient value. The dispersion in our sample of 12CN/13CN ratios is similar to that found in recent surveys of 12CO/13CO. For sight lines where both ratios have been determined, the 12CN/13CN ratios are generally fractionated in the opposite sense compared to 12CO/13CO. Chemical fractionation in CO results from competition between selective photodissociation and isotopic charge exchange. An inverse relationship between 12CN/13CN and 12CO/13CO follows from the coexistence of CN and CO in diffuse cloud cores. However, an isotopic charge exchange reaction with CN may mitigate the enhancements in 12CN/13CN for lines of sight with low 12CO/13CO ratios. For two sight lines with high values of 12CO/13CO, our results indicate that about 50 percent of the carbon is locked up in CO, which is consistent with the notion that these sight lines probe molecular cloud envelopes where the transition from C+ to CO is expected to occur. An analysis of CN rotational excitation yields a weighted mean value for T_01(12CN) of 2.754 +/- 0.002 K, which implies an excess over the temperature of the cosmic microwave background of only 29 +/- 3 mK. This modest excess eliminates the need for a local excitation mechanism beyond electron and neutral collisions. The rotational excitation temperatures in 13CN show no excess over the temperature of the CMB.

Self-consistent analysis of OH-Zeeman observations: too much noise about noise

We had recently re-analyzed in a self-consistent way OH-Zeeman observations in four molecular-cloud envelopes and we had shown that, contrary to claims by Crutcher et al., there is no evidence that the mass-to-flux ratio decreases from the envelopes to the cores of these clouds. The key difference between our data analysis and the earlier one by Crutcher et al. is the relaxation of the overly restrictive assumption made by Crutcher et al, that the magnetic field strength is independent of position in each of the four envelopes. In a more recent paper, Crutcher et al. (1) claim that our analysis is not self-consistent, in that it misses a cosine factor, and (2) present new arguments to support their contention that the magnetic-field strength is indeed independent of position in each of the four envelopes. We show that the claim of the missing cosine factor is false, that the new arguments contain even more serious problems than the Crutcher et al. original data analysis, and we present new observational evidence, independent of the OH-Zeeman data, that suggests significant variations in the magnetic-field strength in the four cloud envelopes.

LONG-LIVED MAGNETIC-TENSION-DRIVEN MODES IN A MOLECULAR CLOUD

We calculate and analyze the longevity of magnetohydrodynamic (MHD) wave modes that occur in the plane of a magnetic thin sheet. Initial turbulent conditions applied to a magnetically subcritical cloud are shown to lead to relatively rapid energy decay if ambipolar diffusion is introduced at a level corresponding to partial ionization primarily by cosmic rays. However, in the flux-freezing limit, as may be applicable to photoionized molecular cloud envelopes, the turbulence persists at "nonlinear" levels in comparison with the isothermal sound speed $\cs$, with one-dimensional rms material motions in the range of $\approx 2\,\cs -5\,\cs$ for cloud sizes in the range of $\approx 2\,\pc - 16\,\pc$. These fluctuations persist indefinitely, maintaining a significant portion of the initial turbulent kinetic energy. We find the analytic explanation for these persistent fluctuations. They are magnetic-tension-driven modes associated with the interaction of the sheet with the external magnetic field. The phase speed of such modes is quite large, allowing residual motions to persist without dissipation in the flux-freezing limit, even as they are nonlinear with respect to the sound speed. We speculate that long-lived large-scale MHD modes such as these may provide the key to understanding observed supersonic motions in molecular clouds.

Magnetic Diffusion in Star Formation

AbstractMagnetic diffusion plays a vital role in star formation. We trace its influence from interstellar cloud scales down to star-disk scales. On both scales, we find that magnetic diffusion can be significantly enhanced by the buildup of strong gradients in magnetic field structure. Large scale nonlinear flows can create compressed cloud layers within which ambipolar diffusion occurs rapidly. However, in the flux-freezing limit that may be applicable to photoionized molecular cloud envelopes, supersonic motions can persist for long times if driven by an externally generated magnetic field that corresponds to a subcritical mass-to-flux ratio. In the case of protostellar accretion, rapid magnetic diffusion (through Ohmic dissipation with additional support from ambipolar diffusion) near the protostar causes dramatic magnetic flux loss. By doing so, it also allows the formation of a centrifugal disk, thereby avoiding the magnetic braking catastrophe.

THE GALACTIC POSITRON ANNIHILATION RADIATION AND THE PROPAGATION OF POSITRONS IN THE INTERSTELLAR MEDIUM

The ratio of the luminosity of diffuse 511 keV annihilation radiation, measured by INTEGRAL in its four years, from a Galactic positron ( 3.5 kpc), the cascade of the magnetic turbulence, which scatters the positrons, is damped by ion-neutral friction, allowing positrons to stream along magnetic flux tubes. We find that nearly 1/2 of the positrons produced in the disk escape from it into the halo. On the other hand, we show that within the extended, or interstellar, bulge (<3.5 kpc), essentially all of the positrons are born in the hot plasmas which fill that volume. We find that the diffusion mean free path is long enough that only a negligible fraction annihilate there and ~80% of them escape down into the H II and H I envelopes of molecular clouds that lie within 1.5 kpc before they slow down and annihilate, while the remaining ~20% escape out into the halo and the disk beyond. This propagation accounts for the low observed annihilation radiation luminosity of the disk compared to the bulge. In addition, we show that the primary annihilation sites of the propagating positrons in both the bulge and the disk are in the warm ionized phases of the interstellar medium. Such annihilation can also account for those two basic properties of the emission, the fraction (~93% ± 7%) of annihilation via positronium and the ratio (~0.5) of broad (~5.4 keV) to narrow (~1.3 keV) components of the bulge 511 keV line emission. Moreover, we expect that the bulk of this broad line emission comes from the tilted disk region (0.5 < R < 1.5 kpc) with a very large broad/narrow flux ratio of ~6, while much of the narrow line emission comes from the inner bulge (R < 0.5 kpc) with a negligible broad/narrow flux ratio. Separate spectral analyses of the 511 keV line emission from these two regions should be able to test this prediction, and further probe the structure of the interstellar medium. Lastly, we show that the asymmetry in the inner disk annihilation line flux, which has been suggested as added evidence for new sources, can also be fully understood from propagation and the asymmetry in the inner spiral arms as viewed from our solar perspective without any additional sources.

CH, CO, andE(B−V) as Molecular Gas Tracers in a Translucent Cloud

The effectiveness of three molecular hydrogen gas tracers—the CH 2Π1/2, J = 1/2, F = 1-1 transition, the CO(1-0) transition, and the color excess, E(B-V)—is evaluated for the translucent molecular cloud MBM 16. The CH emission line and E(B-V) are well correlated with each other but not with the CO(1-0) emission line. It is likely that in translucent molecular clouds CO is not a linear tracer of the molecular hydrogen column density because, in these objects, the CO/H2 ratio is undergoing rapid fluctuations as a function of the molecular hydrogen column density. For translucent and diffuse molecular clouds, and possibly for the translucent envelopes of giant molecular clouds, CH observations should be used to calibrate the CO to H2 conversion factor.

Ultra-high-resolution observations of CH in Southern Molecular Cloud envelopes

We present a mini-survey of ultrahigh-resolution spectroscopy (UHRS) of CH towards three southern molecular cloud envelopes. The sightlines are selected to probe physically similar gas in different Galactic environments. With a velocity resolution of ∼0.5 km s−1(R=575 000) these observations resolve most kinematic components of the absorption lines. We do, however, detect one line component in the Lupus region, which is not resolved and for which an upper limit of b<0.3 km s-1 is found. We find a correlation between distance of the absorbing gas from the Galactic mid-plane and the fractional abundance of CH. We show that this correlation can be explained as being a result of a fall-off in the ultraviolet radiation field intensity and propose that CH observations in carefully selected sightlines might allow a mapping of the variations in the interstellar radiation field.

Product Branching Ratios of the C(3P) + C2H3(2A‘) and CH(2Π) + C2H2(1Σg+) Reactions and Photodissociation of H2CC⋮CH(2B1) at 193 and 242 nm: an ab Initio/RRKM Study

The C(3P) + C2H3(2A‘) and CH(2Π) + C2H2 reactions have been studied using ab initio/RRKM calculations to investigate possible formations of C3H2 and C3H isomers in extraterrestrial environments such as circumstellar envelopes of carbon stars and cold molecular clouds, combustion processes, and CVD. Microcanonical rate constants and product branching ratios have been calculated. Product branching ratios for the C(3P) + C2H3(2A‘) are obtained as 78.3−81.8% for the HCCCH(3B) +H products, 6.1−7.3% for c-C3H2(1A1) + H, 4.4−8.1% for H2CCC(1A1) + H, 5.5% for HCCC(2A‘) + H2, and 1.0−2.0% for the CH(2Π) + C2H2 products, depending on the initial concentrations of intermediates c-H2CCCH and H2CC(H)C, both of which can be produced at the initial reaction step without entrance barrier. Thus, the C(3P) + C2H3(2A‘) reaction can be expected to mainly produce C3H2 isomers in extraterrestrial environments. Product branching ratios for the CH(2Π) + C2H2 reaction slightly vary with the initial concentrations of two initial complexes c-C3H3 and CHCHCH, which can be formed from the reactants without barriers and are calculated as 84.5−87.0% for HCCCH(3B) + H, 10.2−12.8% for c-C3H2(1A1) + H, 1.8−1.9% for HCCC(2A‘) + H2, and 0.9% for H2CCC(1A1) + H. The photodissociation of propargyl radical has been also investigated at photon energies of 193 and 242 nm, assuming internal conversion into the ground electronic state before dissociation. Product branching ratios calculated at 193 nm are 86.5% for the HCCCH(3B) + H channel, 3.6% for c-C3H2(1A1) + H, 5.5% for HCCC(2A‘) + H2, 3.5% for H2CCC(1A1) + H, and 0.9% for CH(2Π) + C2H2. These results are in line with experimental measurements (ref 24), which gave 96% and 4% branching ratios for the C3H2 + H and C3H + H2 channels, respectively. Product branching ratios obtained at 242 nm are 90.2% for the HCCCH(3B) + H channel, 5.1% for c-C3H2(1A1) + H, 3.0% for HCCC(2A‘) + H2, 1.6% for H2CCC(1A1) + H, and 0.1% for CH(2Π) + C2H2. Thus, HCCCH(3B) and H are predicted to be the major products, while c-C3H2 and H are expected to play only a minor role.

The Large‐ScaleJ = 3 → 2 andJ = 2 → 1 CO Emission from M17 and Its Implications for Extragalactic CO Observations

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.