THE FRACTAL DENSITY STRUCTURE IN SUPERSONIC ISOTHERMAL TURBULENCE: SOLENOIDAL VERSUS COMPRESSIVE ENERGY INJECTION

By Christoph Federrath, Ralf Klessen, Wolfram Schmidt. 2007

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In a systematic study, we compare the density statistics in high-resolution numerical experiments of supersonic isothermal turbulence, driven by the usually adopted solenoidal (divergence-free) forcing and by compressive (curl-free) forcing. We find that for the same rms Mach number, compressive forcing produces much stronger density enhancements and larger voids compared to solenoidal forcing. Consequently, the Fourier spectra of density fluctuations are significantly steeper. This result is confirmed using the Δ-variance analysis, which yields power-law exponents β ∼ 3.4 for compressive forcing and β ∼ 2.8 for solenoidal forcing. We obtain fractal dimension estimates from the density spectra and Δ-variance scaling, and by using the box counting, mass size, and perimeter area methods applied to the volumetric data, projections, and slices of our turbulent density fields. Our results suggest that compressive forcing yields fractal dimensions significantly smaller compared to solenoidal forcing. However, the actual values depend sensitively on the adopted method, with the most reliable estimates based on the Δ-variance, or equivalently, on Fourier spectra. Using these methods, we obtain D ∼ 2.3 for compressive and D ∼ 2.6 for solenoidal forcing, which is within the range of fractal dimension estimates inferred from observations (D ∼ 2.0–2.7). The velocity dispersion to size relations for both solenoidal and compressive forcings obtained from velocity spectra follow a power law with exponents in the range 0.4–0.5, in good agreement with previous studies.

Subfields: Astronomy and Astrophysics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/c68c5e3b83137112a46647c2e0e65c45903b889b

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Citations in the corpus

ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, background): “This has been noticed previously by Federrath et al. (2009), but only for M∼ 5–6 simulations in the purely turbulent regime, and is related to the different fractal dimensions Df obtained for solenoidal forcing (Df ∼ 2.6) and compressive forcing (Df ∼ 2.3).”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, background): “…we evolve the MHD equations for two turbulent crossing times, 2T = L/(Mcs) without self-gravity, in order to establish fully developed, compressible turbulence (e.g., Klessen et al. 2000; Klessen 2001; Heitsch et al. 2001; Federrath et al. 2009, 2010b; Price & Federrath 2010; Micic et al. 2012).”
Dispersal of molecular clouds by ionizing radiation (2012, unknown): “P (k) ∝ k−n) has box-coverage fractal dimension D = 4 − n 2 (1) (see also Federrath et al. 2009).”
Turbulent molecular clouds (2012, methodology): “The so-called mass size method has been applied by Kritsuk et al. (2007) and Federrath et al. (2009).”
Shocking results without shocks: Subsonic turbulence in smoothed particle hydrodynamics and moving-mesh simulations (2011, methodology): “Our method for calculating the acceleration field follows closely the procedure used in Schmidt et al. (2006); Federrath et al. (2008, 2009); Federrath et al. (2010) and Price & Federrath (2010).”
Importance of the Initial Conditions for Star Formation - I. Cloud Evolution and Morphology (2010, methodology): “A systematic study of different modes of the turbulence was done by Federrath et al. (2008, 2009, 2010b) and Seifried et al. (2011), but in a periodic box with driven turbulence and without gravity.”
PHYSICAL PROPERTIES AND GALACTIC DISTRIBUTION OF MOLECULAR CLOUDS IDENTIFIED IN THE GALACTIC RING SURVEY (2010, result): “The fractal dimension of molecular clouds has so far been investigated via the perimeter-area relation (Beech 1987; Wakker 1990; Bazell & Desert 1988; Scalo 1990; Federrath et al. 2009), which relates the perimeter of a molecular cloud to its projected area on the sky.”
A comparison between grid and particle methods on the statistics of driven, supersonic, isothermal turbulence (2010, methodology): “For driving turbulence we use the same driving routine used inSchmidt et al. (2006); Federrath et al. (2008, 2010, 2009)and Schmidt et al. (2009).”
Modelling CO formation in the turbulent interstellar medium (2009, methodology): “Since the PDF of CO number density significantly departs from a log-normal distribution, we make use of the expression for the linear density dispersion (Padoan et al. 1997; Passot & Vázquez-Semadeni 1998; Federrath et al. 2009), σρ = bM .”
PHYSICAL PROPERTIES OF MOLECULAR CLOUDS FOR THE ENTIRE MILKY WAY DISK (2016, background): “The mass–size relation has been investigated in numerical simulations of isothermal flows without gravity (Kritsuk et al. 2007; Federrath et al. 2009; Audit & Hennebelle 2010).”
MODELING COLLAPSE AND ACCRETION IN TURBULENT GAS CLOUDS: IMPLEMENTATION AND COMPARISON OF SINK PARTICLES IN AMR AND SPH (2010, background): “…multiple regions at the same time in parallel, reflecting the hierarchical and fractal nature of the gas density probability distribution (e.g., Scalo 1990; Vázquez-Semadeni 1994; Elmegreen & Falgarone 1996; Klessen et al. 2000; Federrath et al. 2008; Goodman et al. 2009; Federrath et al. 2009a).”
Comparing the statistics of interstellar turbulence in simulations and observations - Solenoidal versus compressive turbulence forcing (2009, methodology): “In Federrath et al. (2009), we investigated the fractal density distribution of our two models with solenoidal and compressive turbulence forcing, which showed that compressive forcing yields a significantly smaller fractal dimension (Df ≈ 2.3) compared to solenoidal forcing (Df ≈ 2.6).”
On the universality of supersonic turbulence (2013, background): “Solenoidal driving produces more space-filling structures with a fractal dimension Df ≈ 2.6, while Df ≈ 2.3 and thus closer to sheets for purely compressive driving (Federrath et al. 2009).”