Relationship between turbulence energy and density variance in the solar neighbourhood molecular clouds

¹ Dept. of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden
e-mail: jouni.kainulainen@chalmers.se
² Max-Planck-Institute for Astronomy, Königstuhl 17, 69117 Heidelberg, Germany
³ Research School of Astronomy and Astrophysics, Australian National University, Canberra, ACT 2611, Australia

Received: 24 April 2017
Accepted: 4 November 2017

Abstract

The relationship between turbulence energy and gas density variance is a fundamental prediction for turbulence-dominated media and is commonly used in analytic models of star formation. We determine this relationship for 15 molecular clouds in the solar neighbourhood. We use the line widths of the CO molecule as the probe of the turbulence energy (sonic Mach number, ℳ_s) and three-dimensional models to reconstruct the density probability distribution function (ρ-PDF) of the clouds, derived using near-infrared extinction and Herschel dust emission data, as the probe of the density variance (σ_s). We find no significant correlation between ℳ_s and σ_s among the studied clouds, but we cannot rule out a weak correlation either. In the context of turbulence-dominated gas, the range of the ℳ_s and σ_s values corresponds to the model predictions. The data cannot constrain whether the turbulence-driving parameter, b, and/or thermal-to-magnetic pressure ratio, β, vary among the sample clouds. Most clouds are not in agreement with field strengths stronger than given by β ≲ 0.05. A model with b²β/ (β + 1) = 0.30 ± 0.06 provides an adequate fit to the cloud sample as a whole. Based on the average behaviour of the sample, we can rule out three regimes: (i) strong compression combined with a weak magnetic field (b ≳ 0.7 and β ≳ 3); (ii) weak compression (b ≲ 0.35); and (iii) a strong magnetic field (β ≲ 0.1). When we include independent magnetic field strength estimates in the analysis, the data rule out solenoidal driving (b < 0.4) for the majority of the solar neighbourhood clouds. However, most clouds have b parameters larger than unity, which indicates a discrepancy with the turbulence-dominated picture; we discuss the possible reasons for this.