The Fractal Density Structure in Supersonic Isothermal Turbulence: Solenoidal versus Compressive Energy Injection

Abstract

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 Delta-variance analysis, which yields power-law exponents beta~3.4 for compressive forcing and beta~2.8 for solenoidal forcing. We obtain fractal dimension estimates from the density spectra and Delta-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 Delta-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 forcing obtained from velocity spectra follow a power law with exponents in the range 0.4-0.5, in good agreement with previous studies.

17 pages, 11 figures, ApJ in press, minor changes to language, simulation movies available at http://www.ita.uni-heidelberg.de/~chfeder/videos.shtml?lang=en

References in corpus (13)

• The Statistics of Supersonic Isothermal Turbulence
• The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
• Density Fluctuations in MHD Turbulence: Spectra, Intermittency and Topology
• Numerical simulations of compressively driven interstellar turbulence: I. Isothermal gas
• Velocity centroids as tracers of the turbulent velocity statistics
• Driven and Decaying Turbulence Simulations of Low-Mass Star Formation: From Clumps to Cores to Protostars
• The Power Spectrum of Supersonic Turbulence in Perseus
• Density Probability Distribution Functions in Supersonic Hydrodynamic and MHD Turbulence
• Inertial range scaling in numerical turbulence with hyperviscosity
• Structure analysis of interstellar clouds: I. Improving the Delta-variance method
• Core Mass Function: The Role of Gravity
• Dissipative structures of diffuse molecular gas III -- Small-scale intermittency of intense velocity-shears
• Interstellar cloud structure: The statistics of centroid velocities

Cited by in corpus (71)

• Modeling Collapse and Accretion in Turbulent Gas Clouds: Implementation and Comparison of Sink Particles in AMR and SPH
• On the Star Formation Efficiency of Turbulent Magnetized Clouds
• Physical properties of molecular clouds for the entire Milky Way disk
• The link between turbulence, magnetic fields, filaments, and star formation in the Central Molecular Zone cloud G0.253+0.016
• A robust numerical scheme for highly compressible magnetohydrodynamics: Nonlinear stability, implementation and tests
• Magnetic field amplification in turbulent astrophysical plasmas
• The sonic scale revealed by the world's largest supersonic turbulence simulation
• A cluster in the making: ALMA reveals the initial conditions for high-mass cluster formation
• A model of acceleration of Anomalous Cosmic Rays by Reconnection in the Heliosheath
• The density structure and star formation rate of non-isothermal polytropic turbulence
• Turbulence and star formation efficiency in molecular clouds: solenoidal versus compressive motions in Orion B
• Numerical Simulations of Turbulent, Molecular Clouds Regulated by Radiation Feedback Forces I: Star Formation Rate and Efficiency
• The Spatial Relation between Young Star Clusters and Molecular Clouds in M 51 with LEGUS
• A Census of Large-Scale ($\ge$ 10 pc), Velocity-Coherent, Dense Filaments in the Northern Galactic Plane: Automated Identification Using Minimum Spanning Tree
• The natural emergence of the correlation between H2 and star formation rate surface densities in galaxy simulations
• Larson's scaling laws, and the gravitational instability of clumpy discs at high redshift
• Magnetic field amplification by shocks in galaxy clusters: application to radio relics
• The fractal dimension of star-forming regions at different spatial scales in M33
• On the dynamics and survival of fractal clouds in galactic winds
• Velocity structure functions in multiphase turbulence: interpreting kinematics of H$\alpha$ filaments in cool core clusters
• The Fractal Distribution of HII Regions in Disk Galaxies
• The effect of ISM turbulence on the gravitational instability of galactic discs
• Magnetic field fluctuations in anisotropic, supersonic turbulence
• The Cosmological Simulation Code OpenGadget3 -- Implementation of Meshless Finite Mass
• Shock-multicloud interactions in galactic outflows -- I. Cloud layers with log-normal density distributions
• Analytical core mass function (CMF) from filaments: Under which circumstances can filament fragmentation reproduce the CMF?
• Compressible turbulence in the interstellar medium: New insights from a high-resolution supersonic turbulence simulation
• Filaments and striations: anisotropies in observed, supersonic, highly-magnetised turbulent clouds
• Turbulent diffusion of streaming cosmic rays in compressible, partially ionised plasma
• An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds
• Simulating the H2 content of high-redshift galaxies
• A scaling relation for the molecular cloud lifetime in Milky Way-like galaxies
• The VMC Survey XXII. Hierarchical Star Formation in the 30 Doradus-N158-N159-N160 Star-Forming Complex
• Molecular Clouds in the Second Quadrant of the Milky Way Mid-plane from l$=$104$.{}^{\circ }$75 to l=119$.{}^{\circ }$75 and b=$-$5$.{}^{\circ }$25 to b=5$.{}^{\circ }$25
• The relation between the turbulent Mach number and observed fractal dimensions of turbulent clouds
• The Velocity Statistics of Turbulent Clouds in the Presence of Gravity, Magnetic fields, Radiation, and Outflow Feedback
• The role of the turbulence driving mode for the Initial Mass Function
• Magnetic Field Orientation in Self-Gravitating Turbulent Molecular Clouds
• The SATIN project I: Turbulent multi-phase ISM in Milky Way simulations with SNe feedback from stellar clusters
• The relation between the true and observed fractal dimensions of turbulent clouds
• A new method for spatially resolving the turbulence driving mixture in the ISM with application to the Small Magellanic Cloud
• Messenger Monte-Carlo MAPPINGS V (M^3) -- A self-consistent three-dimensional photoionization code
• The Dependence of the Hierarchical Distribution of Star Clusters on Galactic Environment
• Prospects for future studies using deep imaging: Analysis of individual Galactic cirrus filaments
• The VMC Survey XXVII. Young Stellar Structures in the LMC${}^{\prime }$s Bar Star-Forming Complex
• Magnetic fields in elliptical galaxies: an observational probe of the fluctuation dynamo action
• Fractal dimension of optical cirrus in Stripe82
• Evidence of large scale energy cascade in the spiral galaxy NGC 5236
• Wide binary stars formed in the turbulent interstellar medium
• Probes of turbulent driving mechanisms in molecular clouds from fluctuations in synchrotron intensity
• The VMC survey -- XLVII. Turbulence-Controlled Hierarchical Star Formation in the Large Magellanic Cloud
• Unravelling cosmic velocity flows: a Helmholtz-Hodge decomposition algorithm for cosmological simulations
• Small-scale clustering of nano-dust grains in supersonic turbulence
• The Dependence of Prestellar Core Mass Distributions on the Structure of the Parental Cloud
• High-order Discontinuous Galerkin hydrodynamics with sub-cell shock capturing on GPUs
• Vortex-p: a Helmholtz-Hodge and Reynolds decomposition algorithm for particle-based simulations
• Topography of the Young Galactic Disk: Spatial and Kinematic Patterns of the Clustered Star Formation in the Solar Neighborhood
• Exploring the intermittency of magnetohydrodynamic turbulence by synchrotron polarization radiation
• Characterising lognormal fractional-Brownian-motion density fields with a Convolutional Neural Network
• Gibbs Point Process Model for Young Star Clusters in M33
• The complex multi-scale structure in simulated and observed emission maps of the proto-cluster cloud G0.253+0.016 (`the Brick')
• Supersonic turbulence simulations with GPU-based high-order Discontinuous Galerkin hydrodynamics
• Effects of Forcing on Shocks and Energy Dissipation in Interstellar and Intracluster Turbulences
• Fading in the Flow: Suppression of cold gas growth in expanding galactic outflows
• Shock waves in Interstellar Cloud-Cloud and Wind-Cloud Collisions
• Structure of iso-density sets in supersonic isothermal turbulence
• Supernova remnants in clumpy medium: A model of hydrodynamic and radio synchrotron evolution
• Formation of prestellar cores via non-isothermal gas fragmentation
• Impact of the shape of the prestellar density fluctuations on the core mass function
• Analysis of Galactic cirrus filaments in HSC-SSP high-resolution deep images using artificial neural networks
• From 2D to 3D: Recovering Turbulent Density Dispersions from Noisy Data