The “True” Column Density Distribution in Star-Forming Molecular Clouds

Abstract

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: near-infrared extinction mapping; thermal emission mapping in the far-IR; and mapping the intensity of CO isotopologues. Overall, the structures shown by all three tracers are morphologically similar, but important differences exist amongst the tracers. We find that the dust-based measures (near-IR extinction and thermal emission) give similar, log-normal, distributions for the full (∼ 20 pc-scale) 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 (smaller, ∼few pc-scale) regions. Even though we have used 12 CO data to estimate excitation temperatures, and we have corrected for opacity, the 13 CO 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 from the column-density distribution comparisons. In that shell's interior and in the parts where it overlaps the molecular cloud, there appears to be a dearth of 13 CO, which is likely due either to 13 CO not yet having had time to form in this young structure, and/or destruction of 13 CO in the molecular cloud by the HD 278942's wind and/or radiation. We conclude that the use of either dust or gas measures of column density without extreme attention to calibration (e.g. of thermal emission zero-levels) and artifacts (e.g. the shell) is more perilous than even experts might normally admit. And, the use of 13 CO data 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 (rather than temperature or kinematics), then dust extinction seems the best probe, up to a limiting extinction caused by a dearth of sufficient background sources. Linear fits amongst all three tracers' estimates of column density are given, allowing us to quantify the inherent uncertainties in using one tracer, in comparison with the others.

Comparing the statistics of interstellar turbulence in simulations and observations

“…The ratio between solenoidal and compressive modes of the turbulence forcing may vary strongly across different regions of the ISM. This provides an explanation for the apparent lack of correlation between turbulent density and velocity dispersions found in observations (e.g., Goodman et al 2009;Pineda et al 2008). We conclude that solenoidal forcing is more likely to be realised in quiescent regions with low star formation activity as in the Polaris Flare and in Maddalena's Cloud.…”

“…Goodman et al (2009) measured column density PDFs using dust extinction and emission, as well as molecular lines of gas in the Perseus MC. Using dust extinction maps, Lombardi et al (2006) obtained the column density PDF for the Pipe nebula.…”

“…This is interesting to consider, because observations can only measure column density distributions at one single time. Improving the statistical significance would only be possible by studying multiple fields and averaging in space rather than in time invoking the ergodic theorem as suggested by Goodman et al (2009). However, even by studying one turbulent realisation only, the difference between solenoidal and compressive forcing is recovered from the dispersions of the distributions.…”

“…We therefore expect that using observations of column density PDFs, one can distinguish purely solenoidal from purely compressive forcing by measuring the dispersion of the column density PDF. Goodman et al (2009) provided measurements of the column density PDFs in the Perseus MC obtained with three different methods: dust extinction, dust emission, and 13 CO gas emission. Although systematic differences were found between the three methods, they conclude that in general, the measured column density PDFs are close to, but not perfect log-normal distributions, which is consistent with our results.…”

“…In Federrath et al (2008b), we found that supersonic turbulence driven by a purely compressive (curl-free) force field yields a density PDF with roughly three times larger standard deviation compared to solenoidal (divergence-free) turbulence forcing, which strongly affects the results obtained in these analytical models. Here, we want to compare our results for the density PDF to observations of column density PDFs (e.g., Goodman et al 2009). …”