The reliability of observational measurements of column density probability distribution functions

¹ I. Physikalisches Institut, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
e-mail: ossk@ph1.uni-koeln.de
² Max-Planck Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
³ Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia
⁴ Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, 69120 Heidelberg, Germany

Received: 8 January 2016
Accepted: 8 March 2016

Abstract

Context. Probability distribution functions (PDFs) of column densities are an established tool to characterize the evolutionary state of interstellar clouds.

Aims. Using simulations, we show to what degree their determination is affected by noise, line-of-sight contamination, field selection, and the incomplete sampling in interferometric measurements.

Methods. We solve the integrals that describe the convolution of a cloud PDF with contaminating sources such as noise and line-of-sight emission, and study the impact of missing information on the measured column density PDF. In this way we can quantify the effect of the different processes and propose ways to correct for their impact to recover the intrinsic PDF of the observed cloud.

Results. The effect of observational noise can be easily estimated and corrected for if the root mean square (rms) of the noise is known. For σ_noise values below 40% of the typical cloud column density, N_peak, this involves almost no degradation in the accuracy of the PDF parameters. For higher noise levels and narrow cloud PDFs the width of the PDF becomes increasingly uncertain. A contamination by turbulent foreground or background clouds can be removed as a constant shield if the peak of the contamination PDF falls at a lower column or is narrower than that of the observed cloud. Uncertainties in cloud boundary definition mainly affect the low-column density part of the PDF and the mean density. As long as more than 50% of a cloud is covered, the impact on the PDF parameters is negligible. In contrast, the incomplete sampling of the uv-plane in interferometric observations leads to uncorrectable PDF distortions in the maps produced. An extension of the capabilities of the Atacama Large Millimeter Array (ALMA) would allow us to recover the high-column density tail of the PDF, but we found no way to measure the intermediate- and low-column density part of the underlying cloud PDF in interferometric observations.