On the universality of supersonic turbulence
01 Dec 2013-Monthly Notices of the Royal Astronomical Society (Oxford University Press)-Vol. 436, Iss: 2, pp 1245-1257
TL;DR: In this article, the authors present and analyse the world's largest simulations of supersonic turbulence and compare hydrodynamical models with numerical resolutions of 256^3-4096^3 mesh points and with two distinct driving mechanisms, solenoidal (divergence-free) driving and compressive (curl free) driving.
Abstract: Compressible turbulence shapes the structure of the interstellar medium of our Galaxy and likely plays an important role also during structure formation in the early Universe The density PDF and the power spectrum of such compressible, supersonic turbulence are the key ingredients for theories of star formation However, both the PDF and the spectrum are still a matter of debate, because theoretical predictions are limited and simulations of supersonic turbulence require enormous resolutions to capture the inertial-range scaling To advance our limited knowledge of compressible turbulence, we here present and analyse the world's largest simulations of supersonic turbulence We compare hydrodynamic models with numerical resolutions of 256^3-4096^3 mesh points and with two distinct driving mechanisms, solenoidal (divergence-free) driving and compressive (curl-free) driving We find convergence of the density PDF, with compressive driving exhibiting a much wider and more intermittent density distribution than solenoidal driving Analysing the power spectrum of the turbulence, we find a pure velocity scaling close to Burgers turbulence with P(v) k^(-2) for both driving modes in our hydrodynamical simulations with Mach = 17 The spectrum of the density-weighted velocity rho^(1/3)v, however, does not provide the previously suggested universal scaling for supersonic turbulence We find that the power spectrum P(rho^(1/3)v) scales with wavenumber as k^(-174) for solenoidal driving, close to incompressible Kolmogorov turbulence, k^(-5/3), but is significantly steeper with k^(-210) for compressive driving We show that this is consistent with a recent theoretical model for compressible turbulence that predicts P(rho^(1/3)v) k^(-19/9) in the presence of a strong div(v) component as is produced by compressive driving and remains remarkably constant throughout the supersonic turbulent cascade
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01 Jan 1997
TL;DR: In this paper, a model for the origin of the stellar initial mass function (IMF) is developed, which contains a dependence on the average physical parameters (temperature, density, velocity dispersion) of the large scale site of star formation.
Abstract: We propose that the stellar initial mass function (IMF) is universal in the sense that its functional form arises as a consequence of the statistics of random supersonic flows.
A model is developed for the origin of the stellar IMF, that contains a dependence on the average physical parameters (temperature, density, velocity dispersion) of the large scale site of star formation. The model is based on recent numerical experiments of highly supersonic random flows that have a strong observational counterpart.
It is shown that a Miller-Scalo like IMF is naturally produced by the model for the typical physical conditions in molecular clouds. A more ``massive'' IMF in star bursts is also predicted.
322 citations
TL;DR: A review of the current state of the field of star formation can be found in this article, focusing on three central questions: What controls the rate at which gas in a galaxy converts to stars? What determines how those stars are clustered, and what fraction of the stellar population ends up in gravitationally-bound structures?
318 citations
Cites methods from "On the universality of supersonic t..."
...The core data set plotted was compiled by 11 Krumholz et al. (2012a), and then extended by Federrath (2013b)....
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TL;DR: In this article, the authors run high-resolution simulations including gravity, turbulence, magnetic fields, and jet/outflow feedback and conclude that only models with turbulence producing large virial parameters, and including magnetic fields and feedback can produce realistic star formation rate.
Abstract: Star formation is inefficient. Only a few percent of the available gas in molecular clouds forms stars, leading to the observed low star formation rate (SFR). The same holds when averaged over many molecular clouds, such that the SFR of whole galaxies is again surprisingly low. Indeed, considering the low temperatures, molecular clouds should be highly gravitationally unstable and collapse on their global mean freefall timescale. And yet, they are observed to live about 10-100 times longer, i.e., the SFR per freefall time (SFR_ff) is only a few percent. Thus, other physical mechanisms must counteract the quick global collapse. Turbulence, magnetic fields and stellar feedback have been proposed as regulating agents, but it is still unclear which of these processes is the most important and what their relative contributions are. Here we run high-resolution simulations including gravity, turbulence, magnetic fields, and jet/outflow feedback. We confirm that clouds collapse on a mean freefall time, if only gravity is considered, producing stars at an unrealistic rate. In contrast, if turbulence, magnetic fields, and feedback are included step-by-step, the SFR is reduced by a factor of 2-3 with each additional physical ingredient. When they all act in concert, we find a constant SFR_ff = 0.04, currently the closest match to observations, but still about a factor of 2-4 higher than the average. A detailed comparison with other simulations and with observations leads us to conclude that only models with turbulence producing large virial parameters, and including magnetic fields and feedback can produce realistic SFRs.
220 citations
Cites background from "On the universality of supersonic t..."
...The remaining scatter in this new relation is discussed and explained in Federrath (2013b), by variations in the turbulent properties—primarily in the turbulent Mach number—of the molecular clouds forming stars in the observations....
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...The extragalactic data of disc (D) and starburst (SB) galaxies at low and high redshift were compiled in Krumholz et al. (2012a, 2013), and summarized and extended by the Small Magellanic Cloud (SMC) in Federrath (2013b)....
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...…largest scales (Heyer et al. 2006; Brunt et al. 2009) and with a power spectrum, E(k) ∼ k−2, consistent with supersonic, compressible turbulence (Larson 1981; Heyer & Brunt 2004; Roman-Duval et al. 2011) and confirmed by simulations (Kritsuk et al. 2007; Federrath et al. 2010b; Federrath 2013a)....
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210 citations
Cites background or methods from "On the universality of supersonic t..."
...Simulations with solenoidal (or mixed) driving and large Mach number, Ms 1, yield values χ(k) ≈ 0.3 − 0.5 (Kritsuk et al. 2010; Federrath 2013), with only a slight decline towards large wave numbers....
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...…2008; Molina et al. 2012), the magnetic field amplification by turbulence (Federrath et al. 2011a), and the inertial-range velocity scaling (Schmidt et al. 2008, 2009; Federrath 2013), with possible consequences for models of star formation or for turbulence in galaxy clusters (Porter et al. 2015)....
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...At the opposite extreme, simulations with purely compressive driving find χ(k) ∼ 1 in the inertial range, and the same Burgers-like slopes for both modes, Ec(k) ∼ Es(k) ∝ k−2 (Federrath 2013)....
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TL;DR: In this paper, high-resolution magnetohydrodynamical simulations that follow the evolution of molecular clouds and the formation of filaments and stars were performed to find a remarkably universal filament width of 0.10 +/- 0.02 pc, independent of the star formation history of the clouds.
Abstract: Filaments are ubiquitous in the universe. Recent observations have revealed that stars and star clusters form preferentially along dense filaments. Understanding the formation and properties of filaments is therefore a crucial step in understanding star formation. Here we perform three-dimensional high-resolution magnetohydrodynamical simulations that follow the evolution of molecular clouds and the formation of filaments and stars. We apply a filament detection algorithm and compare simulations with different combinations of physical ingredients: gravity, turbulence, magnetic fields and jet/outflow feedback. We find that gravity-only simulations produce significantly narrower filament profiles than observed, while simulations that include turbulence produce realistic filament properties. For these turbulence simulations, we find a remarkably universal filament width of 0.10 +/- 0.02 pc, which is independent of the star formation history of the clouds. We derive a theoretical model that provides a physical explanation for this characteristic filament width, based on the sonic scale (lambda_sonic) of molecular cloud turbulence. Our derivation provides lambda_sonic as a function of the cloud diameter L, the velocity dispersion sigma_v, the gas sound speed c_s, and the ratio of thermal to magnetic pressure, plasma beta. For typical cloud conditions in the Milky Way spiral arms, we find lambda_sonic = 0.04-0.16 pc, in excellent agreement with the filament width of 0.05-0.15 pc from observations. Consistent with the theoretical model assumptions, we find that the velocity dispersion inside the filaments is subsonic and supersonic outside. We further explain the observed p=2 scaling of the filament density profile, rho ~ r^(-p) with the collision of two planar shocks forming a filament at their intersection.
179 citations
Cites background or methods from "On the universality of supersonic t..."
...This type of turbulence spectrum is consistent with simulations of supersonic turbulence (Kritsuk et al. 2007; Schmidt et al. 2009; Federrath et al. 2010b; Federrath 2013)....
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...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....
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...…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,…...
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References
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TL;DR: In this paper, the authors present a Gebrauch bestimmt ausschließlich für den persönlichen, nicht kommerziellen Gebrauchs, which is a rechtschutzbestimmter gebrauch, and gilt vorbehaltlich der folgenden Einschränkungen.
Abstract: ----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen, nicht kommerziellen Gebrauch bestimmt. Das Copyright bleibt bei den Herausgebern oder sonstigen Rechteinhabern. Als Nutzer sind Sie sind nicht dazu berechtigt, eine Lizenz zu übertragen, zu transferieren oder an Dritte weiter zu geben. Die Nutzung stellt keine Übertragung des Eigentumsrechts an diesem Dokument dar und gilt vorbehaltlich der folgenden Einschränkungen: Sie müssen auf sämtlichen Kopien dieses Dokuments alle Urheberrechtshinweise und sonstigen Hinweise auf gesetzlichen Schutz beibehalten; und Sie dürfen dieses Dokument nicht in irgend einer Weise abändern, noch dürfen Sie dieses Dokument für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, aufführen, vertreiben oder anderweitig nutzen; es sei denn, es liegt Ihnen eine schriftliche Genehmigung von DigiZeitschriften e.V. und vom Herausgeber oder sonstigen Rechteinhaber vor. Mit dem Gebrauch von DigiZeitschriften e.V. und der Verwendung dieses Dokuments erkennen Sie die Nutzungsbedingungen an.
3,675 citations
Book•
01 Nov 1995
TL;DR: In this article, the authors present a modern account of turbulence, one of the greatest challenges in physics, put into historical perspective five centuries after the first studies of Leonardo and half a century after the attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers.
Abstract: This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.
2,745 citations
2,529 citations
TL;DR: In this paper, an overall theoretical framework and the observations that motivate it are outlined, outlining the key dynamical processes involved in star formation, including turbulence, magnetic fields, and self-gravity.
Abstract: We review current understanding of star formation, outlining an overall theoretical framework and the observations that motivate it. A conception of star formation has emerged in which turbulence plays a dual role, both creating overdensities to initiate gravitational contraction or collapse, and countering the effects of gravity in these overdense regions. The key dynamical processes involved in star formation—turbulence, magnetic fields, and self-gravity— are highly nonlinear and multidimensional. Physical arguments are used to identify and explain the features and scalings involved in star formation, and results from numerical simulations are used to quantify these effects. We divide star formation into large-scale and small-scale regimes and review each in turn. Large scales range from galaxies to giant molecular clouds (GMCs) and their substructures. Important problems include how GMCs form and evolve, what determines the star formation rate (SFR), and what determines the initial mass function (IMF). Small scales range from dense cores to the protostellar systems they beget. We discuss formation of both low- and high-mass stars, including ongoing accretion. The development of winds and outflows is increasingly well understood, as are the mechanisms governing angular momentum transport in disks. Although outstanding questions remain, the framework is now in place to build a comprehensive theory of star formation that will be tested by the next generation of telescopes.
2,522 citations
"On the universality of supersonic t..." refers background in this paper
...This kind of turbulence is relevant for the highly compressible interstellar medium (Elmegreen & Scalo 2004; Mac Low & Klessen 2004; McKee & Ostriker 2007), because it controls the rate of star formation triggered by gas compression in shocks (Krumholz & McKee 2005; Hennebelle & Chabrier 2011;…...
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TL;DR: The first version of a new-generation simulation code, FLASH, solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement and contains state-of-the-art modules for the equations of state and thermonuclear reaction networks.
Abstract: We report on the completion of the first version of a new-generation simulation code, FLASH. The FLASH code solves the fully compressible, reactive hydrodynamic equations and allows for the use of adaptive mesh refinement. It also contains state-of-the-art modules for the equations of state and thermonuclear reaction networks. The FLASH code was developed to study the problems of nuclear flashes on the surfaces of neutron stars and white dwarfs, as well as in the interior of white dwarfs. We expect, however, that the FLASH code will be useful for solving a wide variety of other problems. This first version of the code has been subjected to a large variety of test cases and is currently being used for production simulations of X-ray bursts, Rayleigh-Taylor and Richtmyer-Meshkov instabilities, and thermonuclear flame fronts. The FLASH code is portable and already runs on a wide variety of massively parallel machines, including some of the largest machines now extant.
2,319 citations
"On the universality of supersonic t..." refers methods in this paper
...We use the FLASH code (Fryxell et al. 2000; Dubey et al. 2008) in its current version (v4) to solve the compressible gas-dynamical equations on three-dimensional, uniform, periodic grids of fixed side length L with resolutions of 2563, 5123, 10243, 20483 and 40963 grid points....
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