Turbulence and its effect on protostellar disk formation

We analyse simulations of turbulent, magnetised molecular cloud cores focussing on the formation of Class 0 stage protostellar discs and the physical conditions in their surroundings. We show that for a wide range of initial conditions Keplerian discs are formed in the Class 0 stage already. Furthermore, we show that the accretion of mass and angular momentum in the surroundings of protostellar discs occurs in a highly anisotropic manner, by means of a few narrow accretion channels. The magnetic field structure in the vicinity of the discs is highly disordered, revealing field reversals up to distances of 1000 AU. These findings demonstrate that as soon as even mild turbulent motions are included, the classical disc formation scenario of a coherently rotating environment and a well-ordered magnetic field breaks down.Comment: Invited contribution to the NIC proceedings 2016 for the John von Neumann-Institut f\"ur Computing (NIC) Symposium 201

The structure of self-gravitating clouds

To study the interaction of star-formation and turbulent molecular cloud structuring, we analyse numerical models and observations of self-gravitating clouds using the Delta-variance as statistical measure for structural characteristics. In the models we resolve the transition from purely hydrodynamic turbulence to gravitational collapse associated with the formation and mass growth of protostellar cores. We compare models of driven and freely decaying turbulence with and without magnetic fields. Self-gravitating supersonic turbulence always produces a density structure that contains most power on the smallest scales provided by collapsed cores as soon as local collapse sets in. This is in contrast to non-self-gravitating hydrodynamic turbulence where the Delta-variance is dominated by large scale structures. To detect this effect in star-forming regions observations have to resolve the high density contrast of protostellar cores with respect to their ambient molecular cloud. Using the 3mm continuum map of a star-forming cluster in Serpens we show that the dust emission traces the full density evolution. On the contrary, the density range accessible by molecular line observations is insufficient for this analysis. Only dust emission and dust extinction observations are able to to determine the structural parameters of star-forming clouds following the density evolution during the gravitational collapse.Comment: 12 pages, 9 figures, A&A in pres

Gravoturbulent Star Formation: Effects of the Equation of State on Stellar Masses

Stars form by gravoturbulent fragmentation of interstellar gas clouds. The supersonic turbulence ubiquitously observed in Galactic molecular gas generates strong density fluctuations with gravity taking over in the densest and most massive regions. Collapse sets in to build up stars and star clusters. Turbulence plays a dual role. On global scales it provides support, while at the same time it can promote local collapse. Stellar birth is thus intimately linked to the dynamic behavior of parental gas clouds, which governs when and where protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud material to build up stars. The equation of state plays a pivotal role in the fragmentation process. Under typical cloud conditions, massive stars form as part of dense clusters following the "normal" mass function observed, e.g. in the solar neighborhood. However, for gas with an effective polytropic index greater than unity star formation becomes biased towards isolated massive stars. This is relevant for understanding the properties of zero-metallicity stars (Population III) or stars that form under extreme environmental conditions like in the Galactic center or in luminous starbursts.Comment: 9 pages, 4 figure, to be published in the Proceedings of the IAU Colloquium No. 227, 2005, "Massive Star Birth: A Crossroads of Astrophysics

Accretion and magnetic field morphology around Class 0 stage protostellar discs

We analyse simulations of turbulent, magnetised molecular cloud cores focussing on the formation of Class 0 stage protostellar discs and the physical conditions in their surroundings. We show that for a wide range of initial conditions Keplerian discs are formed in the Class 0 stage already. In particular, we show that even subsonic turbulent motions reduce the magnetic braking efficiency sufficiently in order to allow rotationally supported discs to form. We therefore suggest that already during the Class 0 stage the fraction of Keplerian discs is significantly higher than 50%, consistent with recent observational trends but significantly higher than predictions based on simulations with misaligned magnetic fields, demonstrating the importance of turbulent motions for the formation of Keplerian discs. We show that the accretion of mass and angular momentum in the surroundings of protostellar discs occurs in a highly anisotropic manner, by means of a few narrow accretion channels. The magnetic field structure in the vicinity of the discs is highly disordered, revealing field reversals up to distances of 1000 AU. These findings demonstrate that as soon as even mild turbulent motions are included, the classical disc formation scenario of a coherently rotating environment and a well-ordered magnetic field breaks down. Hence, it is highly questionable to assess the magnetic braking efficiency based on non-turbulent collapse simulation. We strongly suggest that, in addition to the global magnetic field properties, the small-scale accretion flow and detailed magnetic field structure have to be considered in order to assess the likelihood of Keplerian discs to be present.Comment: 14 pages, 6 figures, accepted for publication in MNRAS, updated to final versio

The relation between the true and observed fractal dimensions of turbulent clouds

Observations of interstellar gas clouds are typically limited to two-dimensional (2D) projections of the intrinsically three-dimensional (3D) structure of the clouds. In this study, we present a novel method for relating the 2D projected fractal dimension ($\mathcal{D}_{\text{p}}$) to the 3D fractal dimension ($\mathcal{D}_{\text{3D}}$) of turbulent clouds. We do this by computing the fractal dimension of clouds over two orders of magnitude in turbulent Mach number $(\mathcal{M} = 1-100)$, corresponding to seven orders of magnitude in spatial scales within the clouds. This provides us with the data to create a new empirical relation between $\mathcal{D}_{\text{p}}$ and $\mathcal{D}_{\text{3D}}$. The proposed relation is $\mathcal{D}_{\text{3D}}(\mathcal{D}_{\text{p}}) = \Omega_1 erfc ( \xi_1 erfc^{-1}[ (\mathcal{D}_{\text{p}} - \mathcal{D}_{\text{p,min}})/\Omega_2 ] + \xi_2 ) + \mathcal{D}_{\text{3D,min}}$, where the minimum 3D fractal dimension, $\mathcal{D}_{\text{3D,min}} = 2.06 \pm 0.35$, the minimum projected fractal dimension, $\mathcal{D}_{\text{p,min}} = 1.55 \pm 0.13$, $\Omega_1 = 0.47 \pm 0.18$, $\Omega_2 = 0.22 \pm 0.07$, $\xi_1 = 0.80 \pm 0.18$ and $\xi_2 = 0.26 \pm 0.19$. The minimum 3D fractal dimension, $\mathcal{D}_{\text{3D,min}} = 2.06 \pm 0.35$, indicates that in the high $\mathcal{M}$ limit the 3D clouds are dominated by planar shocks. The relation between $\mathcal{D}_{\text{p}}$ and $\mathcal{D}_{\text{3D}}$ of molecular clouds may be a useful tool for those who are seeking to understand the 3D structures of molecular clouds, purely based upon 2D projected data and shows promise for relating the physics of the turbulent clouds to the fractal dimension.Comment: 14 pages, 7 figures. Accepted 2019 May 1