The Effect of Projection on Derived Mass-Size and Linewidth-Size Relationships

Power law mass-size and linewidth-size correlations, two of "Larson's laws," are often studied to assess the dynamical state of clumps within molecular clouds. Using the result of a hydrodynamic simulation of a molecular cloud, we investigate how geometric projection may affect the derived Larson relationships. We find that large scale structures in the column density map have similar masses and sizes to those in the 3D simulation (PPP). Smaller scale clumps in the column density map are measured to be more massive than the PPP clumps, due to the projection of all emitting gas along lines of sight. Further, due to projection effects, structures in a synthetic spectral observation (PPV) may not necessarily correlate with physical structures in the simulation. In considering the turbulent velocities only, the linewidth-size relationship in the PPV cube is appreciably different from that measured from the simulation. Including thermal pressure in the simulated linewidths imposes a minimum linewidth, which results in a better agreement in the slopes of the linewidth-size relationships, though there are still discrepancies in the offsets, as well as considerable scatter. Employing commonly used assumptions in a virial analysis, we find similarities in the computed virial parameters of the structures in the PPV and PPP cubes. However, due to the discrepancies in the linewidth- and mass- size relationships in the PPP and PPV cubes, we caution that applying a virial analysis to observed clouds may be misleading due to geometric projection effects. We speculate that consideration of physical processes beyond kinetic and gravitational pressure would be required for accurately assessing whether complex clouds, such as those with highly filamentary structure, are bound.Comment: 25 pages, including 7 Figures; Accepted for publication in Ap

TurbuStat: Turbulence Statistics in Python

We present TurbuStat (v1.0): a Python package for computing turbulence statistics in spectral-line data cubes. TurbuStat includes implementations of fourteen methods for recovering turbulent properties from observational data. Additional features of the software include: distance metrics for comparing two data sets; a segmented linear model for fitting lines with a break-point; a two-dimensional elliptical power-law model; multi-core fast-fourier-transform support; a suite for producing simulated observations of fractional Brownian Motion fields, including two-dimensional images and optically-thin HI data cubes; and functions for creating realistic world coordinate system information for synthetic observations. This paper summarizes the TurbuStat package and provides representative examples using several different methods. TurbuStat is an open-source package and we welcome community feedback and contributions.Comment: Accepted in AJ. 21 pages, 8 figure

Assessing the Impact of Astrochemistry on Molecular Cloud Turbulence Statistics

We analyze hydrodynamic simulations of turbulent, star-forming molecular clouds that are post-processed with the photo-dissociation region astrochemistry code 3D-PDR. We investigate the sensitivity of 15 commonly applied turbulence statistics to post-processing assumptions, namely variations in gas temperature, abundance and external radiation field. We produce synthetic $^{12}$CO(1-0) and CI($^{3}$P$_{1}$-$^{3}$P$_{0}$) observations and examine how the variations influence the resulting emission distributions. To characterize differences between the datasets, we perform statistical measurements, identify diagnostics sensitive to our chemistry parameters, and quantify the statistic responses by using a variety of distance metrics. We find that multiple turbulent statistics are sensitive not only to the chemical complexity but also to the strength of the background radiation field. The statistics with meaningful responses include principal component analysis, spatial power spectrum and bicoherence. A few of the statistics, such as the velocity coordinate spectrum, are primarily sensitive to the type of tracer being utilized, while others, like the delta-variance, strongly respond to the background radiation field. Collectively, these findings indicate that more realistic chemistry impacts the responses of turbulent statistics and is necessary for accurate statistical comparisons between models and observed molecular clouds.Comment: 27 pages, 21 figures, accepted to Ap

The Perils of Clumpfind: The Mass Spectrum of Sub-structures in Molecular Clouds

We study the mass spectrum of sub-structures in the Perseus Molecular Cloud Complex traced by 13CO (1-0), finding that $dN/dM\propto M^{-2.4}$ for the standard Clumpfind parameters. This result does not agree with the classical $dN/dM\propto M^{-1.6}$. To understand this discrepancy we study the robustness of the mass spectrum derived using the Clumpfind algorithm. Both 2D and 3D Clumpfind versions are tested, using 850 $\mu$m dust emission and 13CO spectral-line observations of Perseus, respectively. The effect of varying threshold is not important, but varying stepsize produces a different effect for 2D and 3D cases. In the 2D case, where emission is relatively isolated (associated with only the densest peaks in the cloud), the mass spectrum variability is negligible compared to the mass function fit uncertainties. In the 3D case, however, where the 13CO emission traces the bulk of the molecular cloud, the number of clumps and the derived mass spectrum are highly correlated with the stepsize used. The distinction between "2D" and "3D" here is more importantly also a distinction between "sparse" and "crowded" emission. In any "crowded" case, Clumpfind should not be used blindly to derive mass functions. Clumpfind's output in the "crowded" case can still offer a statistical description of emission useful in inter-comparisons, but the clump-list should not be treated as a robust region decomposition suitable to generate a physically-meaningful mass function. We conclude that the 13CO mass spectrum depends on the observations resolution, due to the hierarchical structure of MC.Comment: 5 pages, 3 figures. Accepted for publication in ApJ Letter

What is a GMC? Are observers and simulators discussing the same star-forming clouds?

As both simulations and observations reach the resolution of the star-forming molecular clouds, it becomes important to clarify if these two techniques are discussing the same objects in galaxies. We compare clouds formed in a high-resolution galaxy simulation identified as continuous structures within a contour, in the simulator's position-position-position (PPP) coordinate space and the observer's position-position-velocity space (PPV). Results indicate that the properties of the cloud populations are similar in both methods and up to 70 per cent of clouds have a single counterpart in the opposite data structure. Comparing individual clouds in a one-to-one match reveals a scatter in properties mostly within a factor of 2. However, the small variations in mass, radius and velocity dispersion produce significant differences in derived quantities such as the virial parameter. This makes it difficult to determine if a structure is truly gravitationally bound. The three cloud types originally found in the simulation in Fujimoto et al. are identified in both data sets, with around 80 per cent of the clouds retaining their type between identification methods. We also compared our results when using a peak decomposition method to identify clouds in both PPP and PPV space. The number of clouds increased with this technique, but the overall cloud properties remained similar. However, the more crowded environment lowered the ability to match clouds between techniques to 40 per cent. The three cloud types also became harder to separate, especially in the PPV data set. The method used for cloud identification therefore plays a critical role in determining cloud properties, but both PPP and PPV can potentially identify the same structure

The Bolocam Galactic Plane Survey. XIV. Physical Properties of Massive Starless and Star Forming Clumps

We sort $4683$ molecular clouds between $10^\circ< \ell <65^\circ$ from the Bolocam Galactic Plane Survey based on observational diagnostics of star formation activity: compact $70$ $\mu{\rm m}$ sources, mid-IR color-selected YSOs, ${\rm H_2O}$ and ${\rm CH_3OH}$ masers, and UCHII regions. We also present a combined ${\rm NH_3}$-derived gas kinetic temperature and ${\rm H_2O}$ maser catalog for $1788$ clumps from our own GBT 100m observations and from the literature. We identify a subsample of $2223$ ($47.5\%$) starless clump candidates, the largest and most robust sample identified from a blind survey to date. Distributions of flux density, flux concentration, solid angle, kinetic temperature, column density, radius, and mass show strong ($>1$ dex) progressions when sorted by star formation indicator. The median starless clump candidate is marginally sub-virial ($\alpha \sim 0.7$) with $>75\%$ of clumps with known distance being gravitationally bound ($\alpha < 2$). These samples show a statistically significant increase in the median clump mass of $\Delta M \sim 170-370$ M$_\odot$ from the starless candidates to clumps associated with protostars. This trend could be due to (i) mass growth of the clumps at $\dot{M}\sim200-440$ Msun Myr$^{-1}$ for an average free-fall $0.8$ Myr time-scale, (ii) a systematic factor of two increase in dust opacity from starless to protostellar phases, (iii) and/or a variation in the ratio of starless to protostellar clump lifetime that scales as $\sim M^{-0.4}$. By comparing to the observed number of ${\rm CH_3OH}$ maser containing clumps we estimate the phase-lifetime of massive ($M>10^3$ M$_\odot$) starless clumps to be $0.37 \pm 0.08 \ {\rm Myr} \ (M/10^3 \ {\rm M}_\odot)^{-1}$; the majority ($M<450$ M$_\odot$) have phase-lifetimes longer than their average free-fall time.Comment: Accepted for publication in ApJ; 33 pages; 22 figures; 7 table

The CO-to-H2 Conversion Factor From Infrared Dust Emission Across the Local Group

We estimate the conversion factor relating CO emission to H2 mass, alpha_CO, in five Local Group galaxies that span approximately an order of magnitude in metallicity - M31, M 33, the Large Magellanic Cloud (LMC), NGC 6822, and the Small Magellanic Cloud (SMC). We model the dust mass along the line of sight from infrared (IR) emission and then solve for the alpha_CO that best allows a single gas-to-dust ratio (delta_GDR) to describe each system. This approach remains sensitive to CO-dark envelopes of H2 surrounding molecular clouds. In M 31, M 33, and the LMC we find alpha_CO \approx 3-9 M_sun pc^-2 (K km s^-1)^-1, consistent with the Milky Way value within the uncertainties. The two lowest metallicity galaxies in our sample, NGC 6822 and the SMC (12 + log(O/H) \approx 8.2 and 8.0), exhibit a much higher alpha_CO. Our best estimates are \alpha_NGC6822 \approx 30 M_sun/pc^-2 (K km s^-1)^-1 and \alpha_SMC \approx 70 M_sun/pc^-2 (K km s-1)-1. These results are consistent with the conversion factor becoming CO a strong function of metallicity around 12 + log(O/H) \sim 8.4 - 8.2. We favor an interpretation where decreased dust-shielding leads to the dominance of CO-free envelopes around molecular clouds below this metallicity.Comment: Accepted for publication in the Astrophysical Journal, 15 pages, 7 figure