The shapes of column density PDFs

Abstract

The probability distribution function of column density (PDF) has become the tool of choice for cloud structure analysis and star formation studies. Its simplicity is attractive, and the PDF could offer access to cloud physical parameters otherwise difficult to measure, but there has been some confusion in the literature on the definition of its completeness limit and shape at the low column density end. In this letter we use the natural definition of the completeness limit of a column density PDF, the last closed column density contour inside a surveyed region, and apply it to a set of large-scale maps of nearby molecular clouds. We conclude that there is no observational evidence for log-normal PDFs in these objects. We find that all studied molecular clouds have PDFs well described by power laws, including the diffuse cloud Polaris. Our results call for a new physical interpretation of the shape of the column density PDFs. We find that the slope of a cloud PDF is invariant to distance but not to the spatial arrangement of cloud material, and as such it is still a useful tool for investigating cloud structure.

The effect of magnetic fields and ambipolar diffusion on the column density probability distribution function in molecular clouds

“…Our models explore a larger dynamic range of magnetic field strength and instead demonstrate a clear trend where subcritical models (strong magnetic field) with linear perturbations show minimum star formation and have a steep power-law tail with index α ≈ 4. This broadly agrees with recent observational results from Herschel and Planck (Lombardi et al 2015;Alves et al 2017), which show that quiescent clouds with reduced star formation have similar power-law features.…”

“…Könyves et al (2015) also find a power-law PDF for the Aquila star-forming cloud using Herschel data, with index α ≈ 2. Alves et al (2017) extend the idea that PDFs of molecular clouds are only a power law, with slope varying from α ≈ 4 for diffuse clouds to α ≈ 2 for clouds with active star formation. This is consistent with the fact that steeper slopes mean a lack of high density material and thereby less star formation.…”

“…These PDFs should not be classified as lognormal just because they have a peak. Indeed observations often show a pure power-law PDF for both star forming and diffuse clouds (Lombardi et al , 2015Alves et al 2017). One possible explanation (Ward et al 2014) is that as the cloud evolves, the underlying lognormal shape may be lost.…”

“…However, the recent work by Tassis et al (2010) points out that lognormal column density PDFs may be a more generic feature of molecular clouds and should not be interpreted as a result of supersonic turbulence alone. Observationally there is also the claim by Alves et al (2017) that the lognormal peak may be an artifact arising due data incompleteness, and thereby not a result of supersonic turbulence. Tassis et al (2010) also show that gravitationallydriven ambipolar diffusion plays a significant role in shaping the PDFs.…”

Effect of Feedback of Massive Stars in the Fragmentation, Distribution, and Kinematics of the Gas in Two Star-forming Regions in the Carina Nebula

“…In a recent paper, Alves et al (2017) studied the effect of the boundary of a surveyed area of a given molecular cloud on the shape of the observed column density distribution. In their study, they considered molecular clouds in different evolutionary stages from diffuse to star forming ones.…”