Comparing the statistics of interstellar turbulence in simulations and observations - Solenoidal versus compressive turbulence forcing

By Christoph Federrath, J. Roman-Duval, Ralf Klessen, Wolfram Schmidt, M. Mac Low. 2009

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Context. Molecular clouds (MCs) exhibit supersonic turbulent velocity and density fluctuations on virtually all scales observed by modern telescopes. The origin and structural characteristics of this turbulence are, however, still poorly understood. Aims. To shed light on this subject, we study two extreme cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing, and compressive (curl-free) forcing. We compare our results to observational data reported in the literature. Methods. We solve the equations of isothermal hydrodynamics on periodic uniform grids with up to 1024 3 grid points. We compare results obtained with five di! erent analysis techniques to observational data: density probability distribution functions (PDFs), centroid velocity increments, principal component analyses, Fourier spectra and " -variances. Results. Using Fourier spectra and " -variance analyses, we find that both compressive and solenoidal forcings yield velocity dispersion‐size relations consistent with observations and independent numerical simulations. Compressive forcing yields stronger compression and rarefaction at the same RMS Mach number, resulting in roughly three times larger dispersions of volumetric and column density PDFs. Comparing these results with the column density PDFs obtained in the Perseus MC indicates the presence of a mainly compressive forcing agent within the Shell region investigated by Goodman and coworkers. The PDFs of both volumetric and column densities are typically close to log-normal distributions, but they nevertheless exhibit non-Gaussian higher-order moments (skewness and kurtosis) caused by intermittent fluctuations. We compare intermittency statistics of centroid velocity increments with observational studies by Hily-Blant et al., showing that the turbulence statistics of solenoidal forcing agree well with the statistics measured in the Polaris Flare. Furthermore, we compare results of principal component analysis with observational studies by Heyer et al., showing that G216-2.5 and most of the Rosette MC is in very good agreement with the statistics obtained in solenoidal forcing. On the other hand, the interior of an ionising shell within the Rosette MC displays clear signatures of compressive turbulence forcing. Additionally, we find a weak correlation between density and Mach number, such that the local Mach number decreases with increasing density on average. We speculate that this may naturally explain the observed transonic velocity dispersions typically measured for prestellar cores, if these cores formed close to the sonic scale in a supersonic turbulent medium. Conclusions. We conclude that both solenoidal and compressive forcings are compatible with observations. Depending on the subregion, observational data exhibit statistical signatures obtained for both solenoidal and compressive turbulence forcings, with compressive forcing primarily occurring in swept-up shells.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/31131949ac9c70d0aae946fd9e063a22179fe0c9

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Citations in the corpus

RELATIVISTIC JET FEEDBACK IN EVOLVING GALAXIES (2010, background): “In numerical simulations of supersonic turbulence, Federrath et al. (2010) find σ2 ≈ 3.6 and 35 for solenoidal (divergence free) and compressive (curl free) forcing respectively, so that our adopted value of 5 is closer to their solenoidal result.”
On the fraction of star formation occurring in bound stellar clusters (2012, background): “…isothermal, supersonically turbulent clouds and larger structures of cold gas is well described by a lognormal function (Vazquez-Semadeni 1994; Padoan, Nordlund & Jones 1997; Padoan & Nordlund 2002; Federrath, Klessen & Schmidt 2008; Federrath et al. 2010; Padoan & Nordlund 2011; Hill et al. 2012).”
Modelling CO emission – I. CO as a column density tracer and the X factor in molecular clouds (2010, background): “5 relationship (Shetty et al. In preparation), as found in numerous similar turbulent cloud models (e.g. Klessen 2000; Ostriker et al. 2001; Federrath et al. 2010).”
Jet-induced star formation in gas-rich galaxies (2011, background): “…distribution function (PDF) caused by the onset of the jet activity is a robust and purely hydrodynamical result (cf. compressional forcing, Federrath et al. 2010) with the direct consequence of a larger expected star formation rate independent of the actual implementation; the time…”
Inefficient star formation through turbulence, magnetic fields and feedback (2015, methodology): “This avoids spurious formation of sink particles and guarantees that only bound and collapsing gas forms stars (Federrath et al. 2010a), which is important for accurately measuring the SFR.”
ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, methodology): “If all these criteria are fulfilled, the excess mass above the density threshold defined by Equation (1) is removed from the MHD system and added to the sink particle, such that mass, momentum and angular momentum are conserved by construction (see Federrath et al. 2010a, 2011a, for details).”
Dynamic star formation in the massive DR21 filament (2010, methodology): “…is assumed that clumps are produced by turbulent flows because in this case, the densest gas has been shocked and slowed down so that the largest velocity dispersions do not occur in the densest regions but in the outskirts (Klessen et al. 2005, Vazquez-Semadeni et al. 2008, Federrath et al. 2009).”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “…to resolve a modest Reynolds number of ∼ 100, then since the super-sonic cascade |v2(λ)|1/2 ∝ λ1/2 (where λ is a parameter reflecting spatial scale; see Federrath et al. 2010), we expect the smallest “resolved” eddies to be randomly advecting through the box with bulk motions set by the…”
Relativistic jet feedback in high-redshift galaxies – I. Dynamics (2016, background): “However, recent simulations have shown significant deviation from a lognormal behaviour in the tail of the distribution (Federrath et al. 2010; Konstandin et al. 2012; Federrath & Klessen 2013; Federrath & Banerjee 2015).”
On the universality of interstellar filaments: theory meets simulations and observations (2015, methodology): “Columns 2–5: whether gravity and star formation are included, the type of turbulence driving (Federrath et al. 2010b; Federrath 2013), the magnetic field strength, and whether jet/outflow feedback is included.”
The density variance–Mach number relation in supersonic turbulence – I. Isothermal, magnetized gas (2012, methodology): “…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 2s exp [ − (s − s0)…”
FORMATION OF MASSIVE MOLECULAR CLOUD CORES BY CLOUD–CLOUD COLLISION (2013, result): “This result is consistent with the Heitsch et al. (2001) and Federrath et al. (2010), which showed that tens of numerical cells are necessary to resolve turbulent eddies.”
THE GENERATION OF STRONG MAGNETIC FIELDS DURING THE FORMATION OF THE FIRST STARS (2010, result): “This is also consistent with the turbulence simulations by Federrath et al. (2010), who concluded that at least 30 grid cells are required to resolve turbulent vortices.”
How Stellar Feedback Simultaneously Regulates Star Formation and Drives Outflows (2015, background): “For supersonic isothermal turbulence, the probability distribution functions (PDFs) of both the volume and surface densities are approximately lognormal (e.g. Ostriker et al. 2001; Vázquez-Semadeni & García 2001; Federrath et al. 2010; Konstandin et al. 2012a,b, 2015).”
Scale decomposition in compressible turbulence (2010, methodology): “erical simulations of forced compressible turbulence stir the ow with a large-scale acceleration of the form F<K 0 (e.g. Kida and Orszag (1990); Schmidt et al. (2009); Petersen and Livescu (2010); Federrath et al. (2010); Kritsuk et al. (2007)), to the best of our knowledge, the rst study to 13 p”
A sub-parsec resolution simulation of the Milky Way: global structure of the interstellar medium and properties of molecular clouds (2013, background): “They can be connected to the width σPDF of the log-normal PDF through σ2PDF = ln ( 1 + b2M2 ) , with b describing the relative importance of solenoidal and compressible modes of turbulence (Federrath et al. 2008, 2010; Molina et al. 2012).”
WHAT DETERMINES THE DENSITY STRUCTURE OF MOLECULAR CLOUDS? A CASE STUDY OF ORION B WITH HERSCHEL (2013, methodology): “Moreover, it is probably also caused by 3S = 1 σ3 ∫ ∞ −∞ dη p(η)[η − 〈η〉]3 and K = 1 σ4 ∫ ∞ −∞ dη p(η)[η − 〈η〉]4 (see, e.g., Federrath et al. 2010) 4Compressive modes on large to small scales are generated by galactic spiral shocks, expanding supernova shells and H II regions, gravitational…”