TY - JOUR
T1 - The reliability of observational measurements of column density probability distribution functions
AU - Ossenkopf-Okada, V.
AU - Csengeri, T.
AU - Schneider, N.
AU - Federrath, C.
AU - Klessen, R. S.
N1 - Publisher Copyright:
© ESO, 2016.
PY - 2016
Y1 - 2016
N2 - 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 σnoise values below 40% of the typical cloud column density, Npeak, 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.
AB - 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 σnoise values below 40% of the typical cloud column density, Npeak, 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.
KW - Dust, extinction
KW - ISM: clouds
KW - ISM: structure
KW - Instrumentation: interferometers
KW - Methods: data analysis
KW - Methods: statistical
UR - http://www.scopus.com/inward/record.url?scp=84971461291&partnerID=8YFLogxK
U2 - 10.1051/0004-6361/201628095
DO - 10.1051/0004-6361/201628095
M3 - Article
SN - 0004-6361
VL - 590
JO - Astronomy and Astrophysics
JF - Astronomy and Astrophysics
M1 - A104
ER -