ALBERT

Description: We perform a comparison between the smoothed particle magnetohydrodynamics (SPMHD) code, phantom , and the Eulerian grid-based code, flash , on the small-scale turbulent dynamo in driven, Mach 10 turbulence. We show, for the first time, that the exponential growth and saturation of an initially weak magnetic field via the small-scale dynamo can be successfully reproduced with SPMHD. The two codes agree on the behaviour of the magnetic energy spectra, the saturation level of magnetic energy, and the distribution of magnetic field strengths during the growth and saturation phases. The main difference is that the dynamo growth rate, and its dependence on resolution, differs between the codes, caused by differences in the numerical dissipation and shock capturing schemes leading to differences in the effective Prandtl number in phantom and flash .

Description: Star formation is inefficient. Only a few per cent 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 time-scale. 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 per cent. 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.

Description: The density variance–Mach number relation of the turbulent interstellar medium is relevant for theoretical models of the star formation rate, efficiency, and the initial mass function of stars. Here we use high-resolution hydrodynamical simulations with grid resolutions of up to 1024 3 cells to model compressible turbulence in a regime similar to the observed interstellar medium. We use fyris alpha , a shock-capturing code employing a high-order Godunov scheme to track large density variations induced by shocks. We investigate the robustness of the standard relation between the logarithmic density variance ( $\sigma _s^2$ ) and the sonic Mach number ( $\mathcal {M}$ ) of isothermal interstellar turbulence, in the non-isothermal regime. Specifically, we test ideal gases with diatomic molecular ( = 7/5) and monatomic ( = 5/3) adiabatic indices. A periodic cube of gas is stirred with purely solenoidal forcing at low wavenumbers, leading to a fully developed turbulent medium. We find that as the gas heats in adiabatic compressions, it evolves along the relationship in the density variance–Mach number plane, but deviates significantly from the standard expression for isothermal gases. Our main result is a new density variance–Mach number relation that takes the adiabatic index into account: $\sigma _s^2=\ln \left(1+b^2 \mathcal {M}^{(5\gamma +1)/3}\right)$ and provides good fits for $b\mathcal {M}\lesssim 1$ . A theoretical model based on the Rankine–Hugoniot shock jump conditions is derived, $\sigma _s^2 = \ln \lbrace 1 + (\gamma +1)b^2\mathcal {M}^2/[(\gamma -1)b^2\mathcal {M}^2+2]\rbrace$ , and provides good fits also for $b\mathcal {M} 〉 1$ . We conclude that this new relation for adiabatic turbulence may introduce important corrections to the standard relation, if the gas is not isothermal ( != 1).

Description: 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 3D 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 ( sonic ) of molecular cloud turbulence. Our derivation provides sonic as a function of the cloud diameter L , the velocity dispersion v , the gas sound speed c s , and the ratio of thermal to magnetic pressure, plasma β. For typical cloud conditions in the Milky Way spiral arms, we find 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,    r – p with the collision of two planar shocks forming a filament at their intersection.

Description: We use principal component analysis (PCA) to study the gas dynamics in numerical simulations of typical molecular clouds (MCs). Our simulations account for the non-isothermal nature of the gas and include a simplified treatment of the time-dependent gas chemistry. We model the CO line emission in a post-processing step using a 3D radiative transfer code. We consider mean number densities n 0  = 30, 100, 300 cm –3 that span the range of values typical for MCs in the solar neighbourhood and investigate the slope α PCA of the pseudo-structure function computed by PCA for several components: the total density, H 2 density, 12 CO density, 12 CO J = 1 -〉 0 intensity and 13 CO J = 1 -〉 0 intensity. We estimate power-law indices α PCA for different chemical species that range from 0.5 to 0.9, in good agreement with observations, and demonstrate that optical depth effects can influence the PCA. We show that when the PCA succeeds, the combination of chemical inhomogeneity and radiative transfer effects can influence the observed PCA slopes by as much as ±0.1. The method can fail if the CO distribution is very intermittent, e.g. in low-density clouds where CO is confined to small fragments.

Description: The interstellar medium of galaxies is governed by supersonic turbulence, which likely controls the star formation rate (SFR) and the initial mass function (IMF). Interstellar turbulence is non-universal, with a wide range of Mach numbers, magnetic fields strengths and driving mechanisms. Although some of these parameters were explored, most previous works assumed that the gas is isothermal. However, we know that cold molecular clouds form out of the warm atomic medium, with the gas passing through chemical and thermodynamic phases that are not isothermal. Here we determine the role of temperature variations by modelling non-isothermal turbulence with a polytropic equation of state (EOS), where pressure and temperature are functions of gas density, $P\sim \rho ^\Gamma$ , T  ~  – 1 . We use grid resolutions of 2048 3 cells and compare polytropic exponents  = 0.7 (soft EOS),  = 1 (isothermal EOS) and  = 5/3 (stiff EOS). We find a complex network of non-isothermal filaments with more small-scale fragmentation occurring for  〈 1, while  〉 1 smoothes out density contrasts. The density probability distribution function (PDF) is significantly affected by temperature variations, with a power-law tail developing at low densities for  〉 1. In contrast, the PDF becomes closer to a lognormal distribution for   1. We derive and test a new density variance–Mach number relation that takes into account. This new relation is relevant for theoretical models of the SFR and IMF, because it determines the dense gas mass fraction of a cloud, from which stars form. We derive the SFR as a function of and find that it decreases by a factor of ~5 from  = 0.7 to 5/3.

Description: We introduce a new method for observationally estimating the fraction of momentum density ( v ) power contained in solenoidal modes (for which · v = 0) in molecular clouds. The method is successfully tested with numerical simulations of supersonic turbulence that produce the full range of possible solenoidal/compressible fractions. At present, the method assumes statistical isotropy, and does not account for anisotropies caused by (e.g.) magnetic fields. We also introduce a framework for statistically describing density–velocity correlations in turbulent clouds.

Description: Observations of external galaxies and of local star-forming clouds in the Milky Way have suggested a variety of star formation laws, i.e. simple direct relations between the column density of star formation ( SFR : the amount of gas forming stars per unit area and time) and the column density of available gas ( gas ). Extending previous studies, we show that these different, sometimes contradictory relations for Milky Way clouds, nearby galaxies, and high-redshift discs and starbursts can be combined in one universal star formation law in which SFR is about 1 per cent of the local gas collapse rate, gas / t ff , but a significant scatter remains in this relation. Using computer simulations and theoretical models, we find that the observed scatter may be primarily controlled by physical variations in the Mach number of the turbulence and by differences in the star formation efficiency. Secondary variations can be induced by changes in the virial parameter, turbulent driving and magnetic field. The predictions of our models are testable with observations that constrain both the Mach number and the star formation efficiency in Milky Way clouds, external disc and starburst galaxies at low and high redshift. We also find that reduced telescope resolution does not strongly affect such measurements when SFR is plotted against gas / t ff .

Description: The formation of stars occurs in the dense molecular cloud phase of the interstellar medium. Observations and numerical simulations of molecular clouds have shown that supersonic magnetized turbulence plays a key role for the formation of stars. Simulations have also shown that a large fraction of the turbulent energy dissipates in shock waves. The three families of MHD shocks – fast, intermediate and slow – distinctly compress and heat up the molecular gas, and so provide an important probe of the physical conditions within a turbulent cloud. Here, we introduce the publicly available algorithm, shockfind , to extract and characterize the mixture of shock families in MHD turbulence. The algorithm is applied to a three-dimensional simulation of a magnetized turbulent molecular cloud, and we find that both fast and slow MHD shocks are present in the simulation. We give the first prediction of the mixture of turbulence-driven MHD shock families in this molecular cloud, and present their distinct distributions of sonic and Alfvénic Mach numbers. Using subgrid one-dimensional models of MHD shocks we estimate that ~0.03 per cent of the volume of a typical molecular cloud in the Milky Way will be shock heated above 50 K, at any time during the lifetime of the cloud. We discuss the impact of this shock heating on the dynamical evolution of molecular clouds.

Description: 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 probability distribution function (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 by fitting to a recent theoretical model for intermittent density PDFs. 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 number $\mathcal{M}=17$ . The spectrum of the density-weighted velocity 1/3 v , however, does not provide the previously suggested universal scaling for supersonic turbulence. We find that the power spectrum P ( 1/3 v ) scales with wavenumber as k –1.74 for solenoidal driving, close to incompressible Kolmogorov turbulence ( k –5/3 ), but is significantly steeper with k –2.10 for compressive driving. We show that this is consistent with a recent theoretical model for compressible turbulence that predicts P ( 1/3 v )  k –19/9 in the presence of a strong $\nabla \cdot {\boldsymbol {v}}$ component as is produced by compressive driving and remains remarkably constant throughout the supersonic turbulent cascade.