Numerical simulations of compressively driven interstellar turbulence. I. Isothermal gas

By Wolfram Schmidt, Christoph Federrath, M. Hupp, Sebastian Kern, Jens C. Niemeyer. 2008

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Context. Supersonic turbulence is ubiquitous in the interstellar me dium and plays an important role in contemporary star formation. Aims. To perform a high-resolution numerical simulation of supersonic isothermal turbulence driven by compressive large-scale forcing and to analyse various statistical properties. Methods. The compressible Euler equations with an external stochastic force field dominated by rotation-free modes are solved wi th the piecewise parabolic method. Both a static grid and adaptive mesh refinement is used with an effective resolution N = 768 3 . Results. After a transient phase dominated by shocks, turbulence evolves into a steady state with root mean square Mach number ≈ 2.2... 2.5, in which cloud-like structures of over-dense gas are surr ounded by highly rarefied gas. The index of the turbulence ene rgy spectrum functionβ≈ 2.0 in the shock-dominated phase. As the flow approaches statis tical equilibrium, the spectrum flattens, with β≈ 1.9. For the scaling exponent of the root mean square velocity fl uctuation, we obtainγ≈ 0.43 from the velocity structure functions of second order. These results are well within the range of observed scaling properties for the velocity dispersion in molecular clouds. Calculating structure functions of order p = 1,..., 5, we find for all scaling exponents significant deviations from the Kolmogor ovBurgers model proposed by Boldyrev. Our results are very well described by a general log-Poisson model with a higher degree of intermittency, which implies an influence of the forcing on t he scaling properties. The spectral index of the quadratic l ogarithmic density fluctuation βδ≈ 1.8. Contrary to previous numerical results for isothermal turbulence, we obtain a skewed probability density function of the mass density fluctuations that is not consist ent with log-normal statistics and entails a substantially higher fraction of mass in the density peaks than implied by the Padoan-Nordlund relation between the variance of the density fluctuation s and the Mach number. Conclusions. Even putting aside further complexity due to magnetic fields , gravity or thermal processes, we question the notion that Larson-type relations are a consequence of universal supersonic turbulence scaling. For a genuine understanding, it seems necessary to account for the production mechanism of turbulence in the ISM.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/7114b756bb9708a78015720b3ee636abe03ab699

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Citations in the corpus

Modelling CO formation in the turbulent interstellar medium (2009, background): “However, the tails of the PDFs may significantly deviate from this log-normal distribution due to intermittent fluctuations (Kritsuk et al. 2007; Schmidt et al. 2009; Federrath et al. 2009).”
ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, methodology): “…on the largest scales of the system, T = L/(2Mcs), with the RMS sonic Mach number M and the constant sound speed cs = 0.2 km s −1, leading to a smoothly varying stochastic forcing in space and time (for details, see Schmidt et al. 2009; Federrath et al. 2010b; Konstandin et al. 2012a, Paper I).”
On the relationship between molecular hydrogen and carbon monoxide abundances in molecular clouds (2010, background): “Deviations from the lognormal form are apparent in the wings of the PDFs, where one would expect the effects of turbulent intermittency to be most pronounced (Kritsuk et al. 2007; Schmidt et al. 2009; Federrath et al. 2010).”
Relativistic jet feedback – III. Feedback on gas discs (2018, background): “Numerical simulations (Kritsuk et al. 2007; Schmidt et al. 2009) and measurements of velocity structure function in giant molecular clouds (Brunt 2003; Heyer & Brunt 2004) have shown that the exponent to vary is ζ ∼ 0.4 − 0.5.”
The density variance–Mach number relation in supersonic turbulence – I. Isothermal, magnetized gas (2012, background): “…& Padoan 1999; Klessen 2000; Ostriker et al. 2001; Li, Klessen & Mac Low 2003; Kritsuk et al. 2007; Federrath et al. 2008b; Lemaster & Stone 2008; Schmidt et al. 2009; Federrath et al. 2010; Glover et al. 2010; Collins et al. 2011; Padoan & Nordlund 2011; Price et al. 2011), psds = 1√ 2πσ…”
Comparing the statistics of interstellar turbulence in simulations and observations - Solenoidal versus compressive turbulence forcing (2009, methodology): “Following Schmidt et al. (2009), the corresponding sonic wavenumber ks in Fourier space is defined by solving the equation ∫ kc ks E(k) dk 3 1 2 c2s (32) implicitly for ks.”
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).”
On the universality of supersonic turbulence (2013, methodology): “Because of its complexity and three-dimensional nature, the properties of supersonic, compressible turbulence are primarily investigated through numerical simulations (e.g. Porter, Pouquet & Woodward 1992; Kritsuk et al. 2007; Schmidt et al. 2009; Federrath et al. 2010).”
Turbulent molecular clouds (2012, background): “Indeed various authors have computed the power spectrum of s, both in the isothermal and two–phase cases (Beresnyak et al. 2005, Schmidt et al. 2009, Audit & Hennebelle 2010) and they all find that the exponent of the power spectrum of s is always not too far from the Kolmogorov exponent although…”
THE FRACTAL DENSITY STRUCTURE IN SUPERSONIC ISOTHERMAL TURBULENCE: SOLENOIDAL VERSUS COMPRESSIVE ENERGY INJECTION (2007, methodology): “…forcings are significantly steeper (∼ 1.9) compared to the Kolmogorov slope (5/3), in agreement with previous studies (e.g., Kritsuk et al. 2007; Schmidt et al. 2009) and in agreement with velocity dispersion to size relations inferred from observations (e.g., Larson 1981; Falgarone et al.…”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “…turbulence, and find similar systematic differences between methods (with overall properties consistent with those well-known from previous studies; Schmidt et al. 2009; Federrath et al. 2010); stationary-grid methods there perform slightly poorer since larger c© 0000 RAS, MNRAS 000,…”
A NEW JEANS RESOLUTION CRITERION FOR (M)HD SIMULATIONS OF SELF-GRAVITATING GAS: APPLICATION TO MAGNETIC FIELD AMPLIFICATION BY GRAVITY-DRIVEN TURBULENCE (2011, background): “The measured PDFs in Figure 6, however, exhibit significant deviations from the log-normal function due to intermittency (Kritsuk et al. 2007; Schmidt et al. 2009; Federrath et al. 2010b) and the convolution with the radial density distribution inside the Jeans radius of the collapsing Bonnor-Ebert…”
Small-scale dynamo action during the formation of the first stars and galaxies - I. The ideal MHD limit (2010, background): “…consists of rotational and compressional components of comparable strength (Haugen et al. 2004c; Federrath et al. 2008, 2010), and dedicated studies by Kritsuk et al. (2007), Schmidt et al. (2009) and Federrath et al. (2010) typically find power-laws in between the Burgers and Kolmogorov case.”
On the universality of interstellar filaments: theory meets simulations and observations (2015, methodology): “In this regime, numerical simulations find a steeper powerlaw dependence, σv(`) ∝ `1/2 (Kritsuk et al. 2007; Schmidt et al. 2009; Federrath et al. 2010b; Federrath 2013) than in Kolmogorov turbulence. c© 0000 RAS, MNRAS 000, 000–000 This power-law scaling of the turbulence, σv(`) ∝ `α with α > 0,…”
Physical Processes in the Interstellar Medium (2014, background): “A natural mix of forcing modes results in b≈ 0.4 (see e.g. Federrath et al., 2008; Federrath et al., 2010; Schmidt et al., 2009; Seifried et al., 2011; Konstandin et al., 2012).”
MODELING COLLAPSE AND ACCRETION IN TURBULENT GAS CLOUDS: IMPLEMENTATION AND COMPARISON OF SINK PARTICLES IN AMR AND SPH (2010, background): “…∝ k−4, consistent with the observed velocity dispersionsize relation in molecular clouds (e.g., Larson 1981; Heyer & Brunt 2004), and consistent with the velocity spectra usually obtained for driven supersonic turbulence (e.g., Federrath et al. 2009a; Schmidt et al. 2009; Federrath et al. 2009b).”
Importance of the Initial Conditions for Star Formation - I. Cloud Evolution and Morphology (2010, background): “…distributions, with three times larger standard deviations of the density probability distribution function in the case of compressive compared to solenoidal driving (see also the follow-up studies by Schmidt et al. 2009, 2010; Price, Federrath & Brunt 2011; Seifried, Schmidt & Niemeyer 2011).”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, background): “…1994), intermittency introduces skewness and kurtosis in the distributions (Klessen 2000; Kritsuk et al. 2007; Burkhart et al. 2009), which becomes stronger for more compressive forcing (Schmidt et al. 2009; Federrath et al. 2010b) and for higher Mach numbers (Konstandin et al. 2012b).”