Statistical properties of supersonic turbulence in the Lagrangian and Eulerian frameworks

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show a significantly larger density contrast, a more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. We show that the absolute values of Lagrangian and Eulerian structure functions of all orders in the integral range are only a function of the root mean square Mach number, but independent of the forcing. With the assumption of a Gaussian distribution for the probability density function of the velocity increments on large scales, we derive a model that describes this behaviour.Comment: 24 pages, 13 figures, Journal of Fluid Mechanics in pres

Understanding the statistical properties of supersonic turbulence in hydrodynamical simulations

Turbulence is a dominant feature operating in gaseous flows in a variety of systems, from aerodynamics to highly compressible media common in astrophysical environments. We present a systematic analysis of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We study a series of high-resolution, hydrodynamical grid simulations and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing as well as varying root mean square Mach numbers on the parameters describing the statistical state of the system. The probability density functions of the gas density, velocity, and the velocity increments are measured. Structure functions and power spectra are investigated to quantify the two-point correlation properties of compressible turbulence. We find that the mode of the forcing mechanism has an influence on the all measurements mentioned above. Compressively driven simulations show a more intermittent behaviour, a larger fractal dimension of the most dissipative structures (Chapter 4), a significantly larger density contrast with more pronounced wings of the density PDF (Chapter 5), and steeper power spectra with a decreased influence of the bottleneck effect (Chapter 6), at the same root mean square Mach number

On the evolution of the density pdf in strongly self-gravitating systems

The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple appoximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form $\mathrm{P}_v(\rho)\propto\rho^{-1.54}$ for the (volume-weighted) PDF and $\mathrm{P}_m(\rho)\propto\rho^{-0.54}$ for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates. Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured star formation rates are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.Comment: accepted for publication, 13 page

Indications of a sub-linear and non-universal Kennicutt-Schmidt relationship

We estimate the parameters of the Kennicutt-Schmidt (KS) relationship, linking the star formation rate (Sigma_SFR) to the molecular gas surface density (Sigma_mol), in the STING sample of nearby disk galaxies using a hierarchical Bayesian method. This method rigorously treats measurement uncertainties, and provides accurate parameter estimates for both individual galaxies and the entire population. Assuming standard conversion factors to estimate Sigma_SFR and Sigma_mol from the observations, we find that the KS parameters vary between galaxies, indicating that no universal relationship holds for all galaxies. The KS slope of the whole population is 0.76, with the 2sigma range extending from 0.58 to 0.94. These results imply that the molecular gas depletion time is not constant, but varies from galaxy to galaxy, and increases with the molecular gas surface density. Therefore, other galactic properties besides just Sigma_mol affect Sigma_SFR, such as the gas fraction or stellar mass. The non-universality of the KS relationship indicates that a comprehensive theory of star formation must take into account additional physical processes that may vary from galaxy to galaxy.Comment: 7 pages, 2 figures, 1 table. Updated to match MNRAS accepted versio

Centroid Velocity Statistics of Molecular Clouds

We compute structure functions and Fourier spectra of 2D centroid velocity (CV) maps in order to study the gas dynamics of typical molecular clouds (MCs) in numerical simulations. We account for a simplified treatment of time-dependent chemistry and the non-isothermal nature of the gas and use a 3D radiative transfer tool to model the CO line emission in a post-processing step. We perform simulations using three different initial mean number densities of n_0 = 30, 100 and 300 cm^{-3} to span a range of typical values for dense gas clouds in the solar neighbourhood. We compute slopes of the centroid velocity increment structure functions (CVISF) and of Fourier spectra for different chemical components: the total density, H2 number density, 12CO number density as well as the integrated intensity of 12CO (J=1-0) and 13CO (J=1-0). We show that optical depth effects can significantly affect the slopes derived for the CVISF, which also leads to different scaling properties for the Fourier spectra. The slopes of CVISF and Fourier spectra for H2 are significantly steeper than those for the different CO tracers, independent of the density and the numerical resolution. This is due to the larger space-filling factor of H2 as it is better able to self-shield in diffuse regions, leading to a larger fractal co-dimension compared to CO.Comment: 12 pages, 6 figures, submitted to MNRA