One-Point Probability Distribution Functions of Supersonic Turbulent Flows in Self-gravitating Media

By Ralf Klessen. 2000

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Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability distribution functions (PDFs) of dynamical variables have been suggested as appropriate statistical measures and applied to several observed molecular clouds. However, the interpretation of these data requires comparison with numerical simulations. To address this issue, smoothed particle hydrodynamics (SPH) simulations of driven and decaying, supersonic, turbulent flows with and without self-gravity are presented. In addition, random Gaussian velocity fields are analyzed to estimate the influence of variance effects. To characterize the flow properties, the PDFs of the density, of the line-of-sight velocity centroids, and of the line centroid increments are studied. This is supplemented by a discussion of the dispersion and the kurtosis of the increment PDFs, as well as the spatial distribution of velocity increments for small spatial lags. From the comparison between different models of interstellar turbulence, it follows that the inclusion of self-gravity leads to better agreement with the observed PDFs in molecular clouds. The increment PDFs for small spatial lags become exponential for all considered velocities. However, all the processes considered here lead to non-Gaussian signatures, differences are only gradual, and the analyzed PDFs are in addition projection dependent. It appears therefore very difficult to distinguish between different physical processes on the basis of PDFs only, which limits their applicability for adequately characterizing interstellar turbulence.

Subfields: Astronomy and Astrophysics, Computational Mechanics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/c773f138b6bb31655ba02195254427e163aad673

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Citations in the corpus

ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, methodology): “This was seen first in smoothed particle hydrodynamics (SPH) simulations by Klessen (2000) and later confirmed in grid simulations with tracer particles (Federrath et al. 2008a) and in pure grid simulations (Dib & Burkert 2005; Vázquez-Semadeni et al. 2008; Cho & Kim 2011; Kritsuk et al. 2011a;…”
Accretion-driven turbulence as universal process: galaxies, molecular clouds, and protostellar disks (2009, background): “In this case, the density PDF is approximately log-normal (Vazquez-Semadeni 1994; Padoan et al. 1997; Klessen 2000; Kritsuk et al. 2007), however, with higher-order corrections that become significant for highly compressive forcing (Federrath et al. 2008, 2009), P(ρ) = 1√ 2πσ2 exp [ − (δ − δ̄)…”
What controls star formation in the central 500 pc of the Galaxy (2013, background): “However, the high-density tail can also (at least local y) be approximated by a power law, i.e.dp/dn ∝ n−β (e.g. Klessen 2000; Kritsuk, Norman & Wagner 2011; Elmegreen 2011; Hill et al. 2012).”
The Formation of Stellar Clusters in Turbulent Molecular Clouds: Effects of the Equation of State (2002, methodology): “This is a sign of better sampling – more modes contribute to the overall velocity field, thus the central limit theorem is more appropriately applied to the k = 7− 8 than to the k = 1− 2 case (Klessen 2000).”
Modelling CO formation in the turbulent interstellar medium (2009, background): “…turbulence in isothermal gas find that it has a log-normal form (e.g. Padoan et al. 1997; Passot & Vázquez-Semadeni 1998; Nordlund & Padoan 1999; Klessen 2000; Ostriker, Stone & Gammie 2001; Li et al. 2004; Lemaster & Stone 2008; Federrath, Klessen & Schmidt 2008): ps ds = 1√ 2πσ2s exp [ − (s…”
A comparison between grid and particle methods on the statistics of driven, supersonic, isothermal turbulence (2010, methodology): “11 in Kitsionas et al. 2009) and by previous authors (e.g. Vázquez-Semadeni et al. 2003; Klessen2000; Mac Low et al. 1998), whereby the SPH results were first interpolated to a grid and a PDF constructed as above for the grid-based results.”
Control of star formation by supersonic turbulence (2000, methodology): “More recent three-dimensional, high-resolution computations by Klessen et al. (1998, 2000) Klessen (2000), Klessen & Burkert (2000, 2001), and Heitsch et al. (2001) have now confirmed both of these results.”
2MASS wide field extinction maps. I. The Pipe nebula (2006, background): “…argument has been investigated in more detail using various simulations by a number of authors (e.g. Padoan et al. 1997c,b,a; Passot & Vázquez-Semadeni 1998; Klessen 2000), and in all cases the lognormal distribution was found to be a good approximation of the (projected) cloud density.”
Is molecular gas necessary for star formation (2011, result): “Similar features have been found in previous simulations of self-gravitating supersonic turbulence (e.g. Klessen 2000; Federrath et al. 2008; Kritsuk, Norman & Wagner 2011), in which run-away gravitational collapse has occurred.”
Star Formation Properties of a Large Sample of Irregular Galaxies (2004, background): “…and pressure variations, as in an HII region, the gas density should have a pdf that is approximately log-normal (Ostriker, Gammie & Stone 1999; Klessen 2000; Ostriker et al. 2001; Li et al. 2003) and the column density should have a pdf that is log-normal too, although somewhat diluted by the…”
Interstellar Turbulence I: Observations and Processes (2004, methodology): “If true, then hyper-Gaussian pdfs need not be a signature of intermittency (Klessen 2000).”
Probing the evolution of molecular cloud structure: From quiescence to birth (2009, background): “While supersonic turbulence is expected to develop a density PDF close to a log-normal distribution, prominent deviations from that shape are predicted in strongly self-gravitatingsystems (e.g. Klessen 2000; Federrath et al. 2008).”
THE FRACTAL DENSITY STRUCTURE IN SUPERSONIC ISOTHERMAL TURBULENCE: SOLENOIDAL VERSUS COMPRESSIVE ENERGY INJECTION (2007, background): “…turbulence (e.g., Porter et al. 1992; Vázquez-Semadeni 1994; Padoan et al. 1997; Passot & Vázquez-Semadeni 1998; Stone et al. 1998; Mac Low 1999; Klessen 2000; Ostriker et al. 2001; Boldyrev et al. 2002; Li et al. 2003; Padoan et al. 2004b; Jappsen et al. 2005; Ballesteros-Paredes et al.…”
Gravity or turbulence? II. Evolving column density PDFs in molecular clouds (2011, background): “Several groups have shown that the ρ-PDFs in those simulations develop power-law tails at late stages (Klessen 2000; Dib & Burkert 2005; Vázquez-Semadeni et al. 2008).”
Star Formation from Galaxies to Globules (2001, background): “The pdf of density alone, which is equal to the probability that a certain volume has a density , has been discussed extensively for turbulent and self-gravitating fluids (Vázquez-Semadeni 1994; Nordlund & Padoan 1999; Klessen 2000;Wada &Norman 2001).”
Comparing the statistics of interstellar turbulence in simulations and observations - Solenoidal versus compressive turbulence forcing (2009, background): “…et al. 2002; Li et al. 2003; Padoan et al. 2004; Kritsuk et al. 2007; Beetz et al. 2008), but also in decaying turbulence (e.g., Ostriker et al. 1999; Klessen 2000; Ostriker et al. 2001; Glover & Mac Low 2007b) it was shown that the density PDF ps is close to a log-normal distribution ps = 1 √…”
Turbulent molecular clouds (2012, background): “…collapse it is clear that it must have a strong impact on the density PDF. Numerical simulations indeed have revealed that as gravity takes over, a high density tail develops precisely because some gas is collapsing (e.g. Klessen 2000, Slyz et al. 2005, Hennebelle et al. 2008, Kritsuk et al. 2011).”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, background): “The strongest deviations from log-normal PDF arise, when the gas starts to collapse due to self-gravity, producing power-law tails at high densities (Klessen 2000; Dib & Burkert 2005; Federrath et al. 2008a; VázquezSemadeni et al. 2008; Cho & Kim 2011; Kritsuk et al. 2011a; Ballesteros-Paredes et…”