Scaling Relations of Supersonic Turbulence in Star‐forming Molecular Clouds

Boldyrev, Stanislav; Nordlund, Åke; Padoan, Paolo

doi:10.1086/340758

Cited by 121 publications

(153 citation statements)

References 41 publications

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“…14 (top panels). Both solenoidal and compressive forcing yield slopes consistent with size-linewidth relations inferred from observations (e.g., Larson 1981;Myers 1983;Perault et al 1986;Solomon et al 1987;Falgarone et al 1992;Miesch & Bally 1994;Ossenkopf & Mac Low 2002;Padoan et al 2003;Heyer & Brunt 2004;Padoan et al 2006;Ossenkopf et al 2008b;Heyer et al 2009), and with the results of independent numerical simulations (e.g., Klessen et al 2000;Boldyrev et al 2002;Padoan et al 2004;Kritsuk et al 2007;Schmidt et al 2009). Note that size-linewidth relations of the form σ v ∝ l γ with scaling exponents γ = 0.4−0.5 correspond to Fourier spectra E(k) ∝ k −β with scaling exponents in the range β = 1.8−2.0, because γ = (β − 1)/2.…”

Section: Velocity Fourier Spectrasupporting

confidence: 84%

“…The flat part of the data in Fig. 8 for ζ > 0.5 explains why in previous studies with a natural forcing mixture (e.g., Mac Low et al 1998;Klessen et al 2000;Li et al 2003;Kritsuk et al 2007;Glover et al 2010), the turbulence statistics were close to the purely solenoidal forcing case (e.g., Padoan et al 1997;Stone et al 1998;Boldyrev et al 2002;Kowal et al 2007;Lemaster & Stone 2008;Burkhart et al 2009). In contrast, b increases much more strongly for ζ < ∼ 0.5, until it reaches b ≈ 1 for purely compressive forcing (e.g., Federrath et al 2008b;Schmidt et al 2009).…”

Section: The Forcing Dependence Of the Density Dispersion-mach Numbermentioning

confidence: 54%

“…Equations (2) and (3) have been solved before in the context of molecular cloud dynamics, studying compressible turbulence with either solenoidal (divergence-free) forcing or with a 2:1 mixture of solenoidal to compressive modes in the turbulence forcing (e.g., Padoan et al 1997;Stone et al 1998;Mac Low et al 1998;Mac Low 1999;Klessen et al 2000;Heitsch et al 2001;Klessen 2001;Boldyrev et al 2002;Li et al 2003;Padoan et al 2004;Jappsen et al 2005;Ballesteros-Paredes et al 2006;Kritsuk et al 2007;Dib et al 2008;Kissmann et al 2008;Offner et al 2008;Schmidt et al 2009). The case of a 2:1 mixture of solenoidal to compressive modes is the natural result obtained for 3D forcing, if no Helmholtz decomposition (see below) is performed.…”

Section: Forcing Modulementioning

confidence: 99%

“…In numerical experiments of driven supersonic isothermal turbulence with solenoidal and/or weakly compressive forcing (e.g., Vázquez-Semadeni 1994;Padoan et al 1997;Stone et al 1998;Mac Low 1999;Boldyrev et al 2002;Li et al 2003;Padoan et al 2004;Kritsuk et al 2007;Beetz et al 2008), but also in decaying turbulence (e.g., Ostriker et al 1999;Klessen 2000;Ostriker et al 2001;Glover & Mac Low 2007b) it was shown that the density PDF p s is close to a log-normal distribution,…”

Section: The Density Pdf For Solenoidal Forcingmentioning

confidence: 99%

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Comparing the statistics of interstellar turbulence in simulations and observations

Federrath

Duval

Klessen³

et al. 2010

A&A

823

101

1,286

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Context. Density and velocity fluctuations on virtually all scales observed with modern telescopes show that molecular clouds (MCs) are turbulent. The forcing and structural characteristics of this turbulence are, however, still poorly understood. Aims. To shed light on this subject, we study two limiting cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing and compressive (curl-free) forcing, and compare our results to observations. Methods. We solve the equations of hydrodynamics on grids with up to 1024 3 cells for purely solenoidal and purely compressive forcing. Eleven lower-resolution models with different forcing mixtures are also analysed. Results. Using Fourier spectra and Δ-variance, we find velocity dispersion-size relations consistent with observations and independent numerical simulations, irrespective of the type of forcing. However, compressive forcing yields stronger compression at the same rms Mach number than solenoidal forcing, resulting in a three times larger standard deviation of volumetric and column density probability distributions (PDFs). We compare our results to different characterisations of several observed regions, and find evidence of different forcing functions. Column density PDFs in the Perseus MC suggest the presence of a mainly compressive forcing agent within a shell, driven by a massive star. Although the PDFs are close to log-normal, they have non-Gaussian skewness and kurtosis caused by intermittency. Centroid velocity increments measured in the Polaris Flare on intermediate scales agree with solenoidal forcing on that scale. However, Δ-variance analysis of the column density in the Polaris Flare suggests that turbulence is driven on large scales, with a significant compressive component on the forcing scale. This indicates that, although likely driven with mostly compressive modes on large scales, turbulence can behave like solenoidal turbulence on smaller scales. Principal component analysis of G216-2.5 and most of the Rosette MC agree with solenoidal forcing, but the interior of an ionised shell within the Rosette MC displays clear signatures of compressive forcing. Conclusions. The strong dependence of the density PDF on the type of forcing must be taken into account in any theory using the PDF to predict properties of star formation. We supply a quantitative description of this dependence. We find that different observed regions show evidence of different mixtures of compressive and solenoidal forcing, with more compressive forcing occurring primarily in swept-up shells. Finally, we emphasise the role of the sonic scale for protostellar core formation, because core formation close to the sonic scale would naturally explain the observed subsonic velocity dispersions of protostellar cores.

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Section: Velocity Fourier Spectrasupporting

confidence: 84%

Section: The Forcing Dependence Of the Density Dispersion-mach Numbermentioning

confidence: 54%

Section: Forcing Modulementioning

confidence: 99%

Section: The Density Pdf For Solenoidal Forcingmentioning

confidence: 99%

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Comparing the statistics of interstellar turbulence in simulations and observations

Federrath

Duval

Klessen³

et al. 2010

A&A

823

101

1,286

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“…Time evolution of the mean s 0 and standard deviation σ s of the logarithmic density s = ln (ρ/ρ 0 ) for all codes/runs. Boldyrev et al 2002a;Li et al 2003;Padoan et al 2004;Glover & Mac Low 2007;Kritsuk et al 2007;Beetz et al 2008;Federrath et al 2008b;Lemaster & Stone 2008;Schmidt et al 2009;Federrath et al 2009a;Glover et al 2009). …”

Section: Time Evolution Of the Sonic Scalementioning

confidence: 99%

Algorithmic comparisons of decaying, isothermal, supersonic turbulence

Kitsionas¹,

Federrath

Klessen

et al. 2009

A&A

100

120

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Context. Simulations of astrophysical turbulence have reached such a level of sophistication that quantitative results are now starting to emerge. However, contradicting results have been reported in the literature with respect to the performance of the numerical techniques employed for its study and their relevance to the physical systems modelled. Aims. We aim at characterising the performance of a variety of hydrodynamics codes including different particle-based and grid-based techniques on the modelling of decaying supersonic turbulence. This is the first such large-scale comparison ever conducted. Methods. We modelled driven, compressible, supersonic, isothermal turbulence with an rms Mach number of M rms ∼ 4, and then let it decay in the absence of gravity, using runs performed with four different grid codes (ENZO, FLASH, TVD, ZEUS) and three different SPH codes (GADGET, PHANTOM, VINE). We additionally analysed two calculations denoted as PHANTOM A and PHANTOM B using two different implementations of artificial viscosity in PHANTOM. We analysed the results of our numerical experiments using volumeaveraged quantities like the rms Mach number, volume-and density-weighted velocity Fourier spectrum functions, and probability distribution functions of density, velocity, and velocity derivatives. Results. Our analysis indicates that grid codes tend to be less dissipative than SPH codes, though details of the techniques used can make large differences in both cases. For example, the Morris & Monaghan viscosity implementation for SPH results in less dissipation (PHANTOM B and VINE versus GADGET and PHANTOM A). For grid codes, using a smaller diffusion parameter leads to less dissipation, but results in a larger bottleneck effect (our ENZO versus FLASH runs). As a general result, we find that by using a similar number of resolution elements N for each spatial direction means that all codes (both grid-based and particle-based) show encouraging similarity of all statistical quantities for isotropic supersonic turbulence on spatial scales k N/32 (all scales resolved by more than 32 grid cells), while scales smaller than that are significantly affected by the specific implementation of the algorithm for solving the equations of hydrodynamics. At comparable numerical resolution (N particles ≈ N cells ), the SPH runs were on average about ten times more computationally intensive than the grid runs, although with variations of up to a factor of ten between the different SPH runs and between the different grid runs. Conclusions. At the resolutions employed here, the ability to model supersonic to transonic flows is comparable across the various codes used in this study.

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The turbulent ISM and the stellar IMF

Clark

Klessen

2008

Astron Nachr

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In this contribution, we focus on the role that turbulence can play in setting the initial mass function (IMF) of stars. Two theories are contrasted. In the first, the so-called 'turbulent' fragmentation theory, the turbulence is directly responsible for breaking up the cloud into 'cores' which go on to form either a single star or a small N system. In such a picture, the IMF is primordial, since the mass reservoir form the young protostellar system is assumed to be set by the mass of the natal core. In the alternative picture, 'competitive accretion', the final mass of a protostar is determined by its position in the potential well of the cluster. As such the IMF is determined through gravitational dynamics rather than turbulence. We discuss the observation motivation for each of these cases.

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Scaling Relations of Supersonic Turbulence in Star‐forming Molecular Clouds

Cited by 121 publications

References 41 publications

Comparing the statistics of interstellar turbulence in simulations and observations

Comparing the statistics of interstellar turbulence in simulations and observations

Algorithmic comparisons of decaying, isothermal, supersonic turbulence

The turbulent ISM and the stellar IMF

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