Understanding star formation in molecular clouds

Abstract

Column-density maps of molecular clouds are one of the most important observables in the context of molecular cloud-and starformation (SF) studies. With the Herschel satellite it is now possible to precisely determine the column density from dust emission, which is the best tracer of the bulk of material in molecular clouds. However, line-of-sight (LOS) contamination from fore-or background clouds can lead to overestimating the dust emission of molecular clouds, in particular for distant clouds. This implies values that are too high for column density and mass, which can potentially lead to an incorrect physical interpretation of the column density probability distribution function (PDF). In this paper, we use observations and simulations to demonstrate how LOS contamination affects the PDF. We apply a first-order approximation (removing a constant level) to the molecular clouds of Auriga and Maddalena (low-mass star-forming), and Carina and NGC 3603 (both high-mass SF regions). In perfect agreement with the simulations, we find that the PDFs become broader, the peak shifts to lower column densities, and the power-law tail of the PDF for higher column densities flattens after correction. All corrected PDFs have a lognormal part for low column densities with a peak at A v ∼ 2 mag, a deviation point (DP) from the lognormal at A v (DP) ∼ 4−5 mag, and a power-law tail for higher column densities. Assuming an equivalent spherical density distribution ρ ∝ r −α , the slopes of the power-law tails correspond to α PDF = 1.8, 1.75, and 2.5 for Auriga, Carina, and NGC 3603. These numbers agree within the uncertainties with the values of α ≈ 1.5, 1.8, and 2.5 determined from the slope γ (with α = 1 − γ) obtained from the radial column density profiles (N ∝ r γ ). While α ∼ 1.5−2 is consistent with a structure dominated by collapse (local free-fall collapse of individual cores and clumps and global collapse), the higher value of α > 2 for NGC 3603 requires a physical process that leads to additional compression (e.g., expanding ionization fronts). From the small sample of our study, we find that clouds forming only low-mass stars and those also forming high-mass stars have slightly different values for their average column density (1.8 × 10 21 cm −2 vs. 3.0 × 10 21 cm −2 ), and they display differences in the overall column density structure. Massive clouds assemble more gas in smaller cloud volumes than low-mass SF ones. However, for both cloud types, the transition of the PDF from lognormal shape into power-law tail is found at the same column density (at A v ∼ 4−5 mag). Low-mass and high-mass SF clouds then have the same low column density distribution, most likely dominated by supersonic turbulence. At higher column densities, collapse and external pressure can form the power-law tail. The relative importance of the two processes can vary between clouds and thus lead to the observed differences in PDF and column density structure.

The Link Between Turbulence, Magnetic Fields, Filaments, and Star Formation in the Central Molecular Zone Cloud G0.253+0.016

“…We do not have direct access to the 3D (volume) density from observations-only to the 2D (column) density distribution (Berkhuijsen & Fletcher 2008;Kainulainen et al 2009;Lombardi et al 2011;Schneider et al 2012Schneider et al , 2013Hughes et al 2013;Kainulainen & Tan 2013;Berkhuijsen & Fletcher 2015;Schneider et al 2015). However, one can estimate the 3D density dispersion and the 3D density PDF by extrapolating the 2D density information given in the plane of the sky to the third dimension (along the line of sight), assuming isotropy of the clouds (Brunt et al 2010a(Brunt et al , 2010bKainulainen et al 2014).…”

A census of dense cores in the Taurus L1495 cloud from theHerschelGould Belt Survey

“…Those PDFs have been characterised by a lognormal at low column densities which becomes dominated by a power law tail at the high end (Kainulainen et al 2009;Schneider et al 2013Schneider et al , 2015Benedettini et al 2015). The presence of the lognormal component has, however, been questioned by Lombardi et al (2015) who argue that column density PDFs of molecular clouds can be accounted for entirely by truncated power laws.…”

Understanding star formation in molecular clouds

“…All Herschel maps have an absolute flux calibration, using Planckcorrections from the zeropointcorrection task in HIPE10 for SPIRE and IRAS maps for PACS. For the SED fit, we fix the specific dust opacity per unit mass (dust+gas) approximated by the power law κ ν = 0.1 (ν/1000 GHz) β cm 2 /g and β = 2, and leave the dust temperature and column density as free parameters (see Schneider et al 2015, for further details). We estimate the final uncertainties in the column density maps to be around ∼30−50%, mainly arising from the uncertainty in the assumed form of the opacity law and possible temperature gradients along the line-of-sight (Russeil et al 2013;Roy et al 2013).…”

“…5 Note that the DR21 ridge itself is an IRDC (Marston et al 2004), and that the IRDC G035.39-0.33 in W48 was already qualified as a ridge (Nguyen-Luong et al 2011) with the same physical properties. 6 We define η ≡ ln(N/ N ) as the natural logarithm of the column density N, divided by the mean column density N , and the quantity p η (η) then corresponds to the PDF of η with the normalisation Schneider et al 2015, for details).…”

“…Federrath & Klessen 2013, and references therein). Observational studies, based on near-IR extinction or Herschel dust column density maps, showed that the PDF of star-forming clouds has a log-normal distribution for low column densities and a power-law tail for higher column densities, where the power-law tail is either interpreted as due to external pressure (Kainulainen et al 2011b), self-gravity (Froebrich & Rowles 2010;Schneider et al 2013Schneider et al , 2015, or a combination of both (Tremblin et al 2014). Numerical simulations (e.g.…”