The Fractal Dimension of Projected Clouds

Sánchez, Néstor; Alfaro, E. J.; Pérez, E.

doi:10.1086/429553

Cited by 103 publications

(141 citation statements)

References 34 publications

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“…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%

Comparing the statistics of interstellar turbulence in simulations and observations

Federrath

Duval

Klessen³

et al. 2010

A&A

834

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: 99%

Comparing the statistics of interstellar turbulence in simulations and observations

Federrath

Duval

Klessen³

et al. 2010

A&A

834

101

1,286

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“…This is a very interesting result, because this value is considerably smaller than the average value estimated for Galactic molecular clouds in recent studies, which is D f 2.6 − 2.7 (Sánchez et al 2005(Sánchez et al , 2007b. Young, newly born stars will probably reflect the conditions of the interstellar medium from which they formed.…”

Section: Discussionmentioning

confidence: 51%

The spatial distribution of stars in open clusters

Sánchez¹,

Alfaro²

2009

Proc. IAU

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Abstract. We study the internal spatial structure of 16 open clusters in the Milky Way spanning a wide range of ages. For this, we use the minimum-spanning-tree method (the Q parameter, which enables one to classify the stellar distribution as either radially or fractally clustered), King-profile fitting, and the correlation dimension (Dc ) for those clusters with fractal patterns. On average, clusters with fractal-like structure are younger than those exhibiting radial stellardensity profiles. There is a significant correlation between Q and the cluster age measured in crossing-time units. For fractal clusters, there is a significant correlation between fractal dimension and age. These results support the idea that stars in newly born clusters likely follow the fractal patterns of their parent molecular clouds, and eventually evolve towards more centrally concentrated structures. However, stellar clusters as old as ∼ 100 Myr can exist that have not totally destroyed their fractal structure. Finally, we have found the intriguing result that the lowest fractal dimensions obtained for the open clusters seem to be considerably smaller than the average value measured in Galactic molecular cloud complexes.

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“…As stressed before, these results are preliminary in that they do not take into account radiative transfer, density effects, or projection effects. That such factors matter is well established in the literature (Stutzki et al 1998;Brunt & Mac Low 2004;Sánchez et al 2005;Ossenkopf et al 2006;Esquivel et al 2007;Brunt et al 2009;Federrath et al 2010). Further analysis of our data in this direction is envisaged but beyond the scope of the present paper.…”

Section: Viewing Angle Effects?mentioning

confidence: 59%

Supersonic turbulence in 3D isothermal flow collision

Folini

Walder

Favre

2014

A&A

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Large scale supersonic bulk flows are present in a wide range of astrophysical objects, from O-star winds to molecular clouds, galactic sheets, accretion, or γ-ray bursts. Associated flow collisions shape observable properties and internal physics alike. Our goal is to shed light on the interplay between large scale aspects of such collision zones and the characteristics of the compressible turbulence they harbor. Our model setup is as simple as can be: 3D hydrodynamical simulations of two head-on colliding, isothermal, and homogeneous flows with identical upstream (subscript u) flow parameters and Mach numbers 2 < M u < 43. The turbulence in the collision zone is driven by the upstream flows, whose kinetic energy is partly dissipated and spatially modulated by the shocks confining the zone. Numerical results are in line with expectations from self-similarity arguments. The spatial scale of modulation grows with the collision zone. The fraction of energy dissipated at the confining shocks decreases with increasing M u . The mean density is ρ m ≈ 20ρ u , independent of M u . The root mean square Mach number is M rms ≈ 0.25M u . Deviations toward weaker turbulence are found as the collision zone thickens and for small M u . The density probability function is not log-normal. The turbulence is inhomogeneous, weaker in the center of the zone than close to the confining shocks. It is also anisotropic: transverse to the upstream flows M rms is always subsonic. We argue that uniform, head-on colliding flows generally disfavor turbulence that is at the same time isothermal, supersonic, and isotropic. The anisotropy carries over to other quantities like the density variance -Mach number relation. Line-of-sight effects thus exist. Structure functions differ depending on whether they are computed along a line-of-sight perpendicular or parallel to the upstream flow. Turbulence characteristics generally deviate markedly from those found for uniformly driven, supersonic, isothermal turbulence in 3D periodic box simulations. We suggest that this should be kept in mind when interpreting turbulence characteristics derived from observations. Our simulations show that even a simple model setup results in a richly structured interaction zone. The robustness of our findings toward more realistic setups remains to be tested.

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The Fractal Dimension of Projected Clouds

Cited by 103 publications

References 34 publications

Comparing the statistics of interstellar turbulence in simulations and observations

Comparing the statistics of interstellar turbulence in simulations and observations

The spatial distribution of stars in open clusters

Supersonic turbulence in 3D isothermal flow collision

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