The density variance–Mach number relation in supersonic turbulence – I. Isothermal, magnetized gas

By F. Molina, S. Glover, Christoph Federrath, R. Lyon, Centre de Recherche Astrophysique, F. M. F. Astrophysics, School of Physical Sciences, Australia.. 2012

174 citations recorded by the source corpus.

It is widely accepted that supersonic, magnetized turbulence plays a fundamental role for star formation in molecular clouds. It produces the initial dense gas seeds out of which new stars can form. However, the exact relation between gas compression, turbulent Mach number and magnetic field strength is still poorly understood. Here, we introduce and test an analytical prediction for the relation between the density variance and the rms Mach number in supersonic, isothermal, magnetized turbulent flows. We approximate the density and velocity structure of the interstellar medium as a superposition of shock waves. We obtain the density contrast considering the momentum equation for a single magnetized shock and extrapolate this result to the entire cloud. Depending on the field geometry, we then make three different assumptions based on observational and theoretical constraints: B independent of ρ, B∝ρ1/2 and B∝ρ. We test the analytically derived density variance–Mach number relation with numerical simulations, and find that for B∝ρ1/2, the variance in the logarithmic density contrast, , fits very well to simulated data with turbulent forcing parameter b= 0.4, when the gas is super-Alfvenic. However, this result breaks down when the turbulence becomes trans-Alfvenic or sub-Alfvenic, because in this regime the turbulence becomes highly anisotropic. Our density variance–Mach number relations simplify to the purely hydrodynamic relation as the ratio of thermal to magnetic pressure β0∞.

Subfields: Astronomy and Astrophysics, Fluid Flow and Transfer Processes

View Paper: https://www.semanticscholar.org/paper/18534a132599e0a76a97402d6e136f419058967d

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Citations in the corpus

What controls star formation in the central 500 pc of the Galaxy (2013, methodology): “If we modify the density PDF accordingly (cf. Padoan & Nordlund 2011; Molina et al. 2012, adoptingB ∝ n1/2 as in Padoan & Nordlund 1999), the threshold density required by the observed SFR becomesnth ∼ 5 × 108 cm−3.”
Physical Processes in the Interstellar Medium (2014, background): “This is the log-normal form of the IMF first introduced by Miller & Scalo (1979). It fits very well the mass distribution of multiple stellar systems in the solar vicinity with masses less than few solar masses (e.”
On the fraction of star formation occurring in bound stellar clusters (2012, background): “A possible, first-order modification of the theory to allow for strong magnetic fields would be to add a factor β0/(β0 + 1) to the second term of equation (4), where β0 ≡ Pth/Pmag is the ratio of the thermal pressure to the magnetic pressure (Padoan & Nordlund 2011; Molina et al. 2012).”
WHAT DETERMINES THE DENSITY STRUCTURE OF MOLECULAR CLOUDS? A CASE STUDY OF ORION B WITH HERSCHEL (2013, background): “The gas can be condidered as isothermal, so that here magnetic fields may play a role (the strength is not known), leading to a narrow PDF (e.g., Molina et al. (2012)), or statistical density fluctuations and intermittency due to locally compressive turbulence.”
ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, background): “Molina et al. (2012) provide a rigorous derivation of the variance of the PDF, σ2s = ln ( 1 + b2M2 β β + 1 ) , (5) with the forcing parameter b, the sonic RMS Mach number M, and the ratio of thermal to magnetic pressure, which can be expressed as the ratio of sound to Alfvén speed or as the ratio…”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, methodology): “Molina et al. (2012) provide a rigorous derivation of σs for different correlations of the magnetic field with density.”
Turbulent molecular clouds (2012, background): “The influence of the magnetic field on the density PDF has also been investigated by various authors both in the isothermal case (Ostriker et al. 2001, Lemaster & Stone 2008, Molina et al. 2012) and in the two–phase case (e.g. Hennebelle et al. 2008) generally concluding that it has a weak impact.”
A sub-parsec resolution simulation of the Milky Way: global structure of the interstellar medium and properties of molecular clouds (2013, background): “They can be connected to the width σPDF of the log-normal PDF through σ2PDF = ln ( 1 + b2M2 ) , with b describing the relative importance of solenoidal and compressible modes of turbulence (Federrath et al. 2008, 2010; Molina et al. 2012).”