Kolmogorov‐Burgers Model for Star‐forming Turbulence

Boldyrev, Stanislav

doi:10.1086/339403

Cited by 140 publications

(213 citation statements)

References 36 publications

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“…6). It rather means that CVI scaling is different from the absolute scaling exponents following from the intermittency models by She & Leveque (1994) and Boldyrev (2002). This is mainly because of two reasons: first, these models do not account for density fluctuations (see however Schmidt et al 2008), and second, CVIs are 2D projections of the 3D turbulence.…”

Section: The Structure Function Scaling Of Centroid Velocity Incrementsmentioning

confidence: 98%

“…This also means that direct tests of the theoretical models will be very difficult to achieve, unless a means of relating the CVI-based moments to the 3D moments is developed. Moreover, the fractal dimension of structures changes in a non-trivial way upon projection (Stutzki et al 1998;Sánchez et al 2005;Federrath et al 2009), which severely limits the comparison of CVI statistics with the 3D intermittency models by She & Leveque (1994), Boldyrev (2002) and Schmidt et al (2008).…”

Section: The Structure Function Scaling Of Centroid Velocity Incrementsmentioning

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: The Structure Function Scaling Of Centroid Velocity Incrementsmentioning

confidence: 98%

Section: The Structure Function Scaling Of Centroid Velocity Incrementsmentioning

confidence: 99%

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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“…(17) applies to a variety of turbulent flows at high Reynolds number, η(p) substantially deviates from linearity at higher orders p, a phenomenon often referred to as "intermittency." She & Leveque (1994) have proposed a model for incompressible turbulence based on intermittency, further extended by Boldyrev (2002) and tested with numerical simulations of supersonic turbulence .…”

Section: Cloud Structure Functionsmentioning

confidence: 99%

2MASS wide field extinction maps

Lombardi

Lada

Alves

2010

A&A

129

126

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We present a near-infrared extinction map of a large region in the sky (∼3500 deg 2 ) in the general directions of Taurus, Perseus, and Aries. The map has been obtained using robust and optimal methods to map dust column density at near-infrared wavelengths (Nicer, described in Lombardi & Alves 2001, A&A, 377, 1023 and Nicest, described in Lombardi 2009 toward ∼23 million stars from the Two Micron All Sky Survey (2MASS) point source catalog. We measure extinction as low as A K = 0.04 mag with a 1-σ significance, and a resolution of 2.5 arcmin in our map. A 250 deg 2 section of our map encompasses the Taurus, Perseus, and California molecular cloud complexes. We determine the distances of the clouds by comparing the observed density of foreground stars with the prediction of galactic models, and we obtain results that are in excellent agreement with recent VLBI parallax measurements. We characterize the large-scale structure of the map and find a ∼25 • × 15 • region close to the galactic plane (l ∼ 135 • , b ∼ −14 • ) with small extinction (A K < 0.04 mag); we name this region the Perseus-Andromeda hole. We find that over the region that encompasses the Taurus, Perseus, and California clouds the column density measurements below A K < 0.2 mag are perfectly described by a log-normal distribution, and that a significant deviation is observed at larger extinction values. If turbulence models are invoked to justify the log-normal distribution, the observed departure could be interpreted as the result of the effect of gravity that acts on the cores of the clouds. Finally, we investigate the cloud structure function, and show that significant deviations from the results predicted by turbulent models are observed in at least one cloud.

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“…However, despite a wide range of work on the subject, enabled in large part by the explosive growth in computational power (e.g., Kritsuk et al 2007;Lemaster & Stone 2008;Molina et al 2012;Federrath 2013;Pan et al 2016 and references therein), much less is known about the statistical properties of supersonic turbulence in comparison to its subsonic cousin (Federrath 2013;Pan et al 2016). For example, despite some promising results (e.g., Boldyrev 2002;Aluie 2011;Banerjee & Galtier 2013), we currently lack a well-accepted theory for the velocity power spectrum, similar to the standard Kolmogorov phenomenology for subsonic turbulence (Kolmogorov 1941). Further, an important aspect of supersonic turbulence theory, which is much less relevant in subsonic turbulence, is the density statistics.…”

Section: Introductionmentioning

confidence: 99%

The distribution of density in supersonic turbulence

Squire

Hopkins

2017

Monthly Notices of the Royal Astronomical Society

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We propose a model for the density statistics in supersonic turbulence, which play a crucial role in star-formation and the physics of the interstellar medium (ISM). Motivated by [Hopkins, MNRAS, 430, 1880(2013], the model considers the density to be arranged into a collection of strong shocks of width ∼ M −2 , where M is the turbulent Mach number. With two physically motivated parameters, the model predicts all density statistics for M > 1 turbulence: the density probability distribution and its intermittency (deviation from log-normality), the density variance-Mach number relation, power spectra, and structure functions. For the proposed model parameters, reasonable agreement is seen between model predictions and numerical simulations, albeit within the large uncertainties associated with current simulation results. More generally, the model could provide a useful framework for more detailed analysis of future simulations and observational data. Due to the simple physical motivations for the model in terms of shocks, it is straightforward to generalize to more complex physical processes, which will be helpful in future more detailed applications to the ISM. We see good qualitative agreement between such extensions and recent simulations of non-isothermal turbulence.

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Kolmogorov‐Burgers Model for Star‐forming Turbulence

Cited by 140 publications

References 36 publications

Comparing the statistics of interstellar turbulence in simulations and observations

Comparing the statistics of interstellar turbulence in simulations and observations

2MASS wide field extinction maps

The distribution of density in supersonic turbulence

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