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

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 threedimensional 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 b 2 β/(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.

The Self-gravitating Gas Fraction and the Critical Density for Star Formation

“…The PDF widths derived in(Kainulainen & Federrath 2017) are overestimated in the context of the model presented here since they fit a single lognormal PDF rather than a lognormal + powerlaw PDF.…”

“…When the dense self-gravitating gas is in the power-law the observed gas fraction is slightly anti-correlated with sonic Mach number. This is because s t moves towards Kainulainen et al (2014) and Kainulainen & Federrath (2017). Kainulainen et al (2014) reported values of the radial density distribution slope (κ), which can be related to the power law slope as α = 3/κ.…”

“…Kainulainen et al (2014) found similar values for clouds on the verge of forming stars. In addition to measuring the critical density, Kainulainen et al (2014) and Kainulainen & Federrath (2017) published values of the sonic Mach numbers, cloud mean densities, and PDF power law tail slopes. Using these values (e.g.…”

The Star Formation Rate in the Gravoturbulent Interstellar Medium

“…An important distinction between the analytic SFR model derived in this work and the works of Krumholz & McKee (2005), Padoan & Nordlund (2011) and Hennebelle & Chabrier (2011) is that they provide a constant SF R f f and/or f f for given turbulence parameters, such as the sonic Mach number and the forcing, which set the lognormal width. However, it is not likely that differences in f f observed in the data is due the properties of turbulence, as most of these clouds have similar sonic Mach numbers and similar line width size relations (Kainulainen & Federrath 2017). The LN+PL model SF R f f calculation presented here is inherently time varying as the slope of the power law varies with cloud evolution due to gravitational collapse and feedback.…”

Large-scale periodic velocity oscillation in the filamentary cloud G350.54+0.69

“…These values indicate that the filament G350.5 as a whole is supersonic with a mach number of M3D > 2 (see Fig. 4b), where the 3D Mach number is M3D = √ 3σNT,int/σ th given the 1D measurement σNT,int, and assuming isotropic turbulence in three dimensions (e.g., Kainulainen & Federrath 2017).…”