Magnetic fields in circumstellar disks: The potential of Zeeman observations

Context. Recent high angular resolution polarimetric continuum observations of circumstellar disks provide new insights into their magnetic field. However, direct constraints are limited to the plane of sky component of the magnetic field. Observations of Zeeman split spectral lines are a potential approach to enhance these insights by providing complementary information. Aims. We investigate which constraints for magnetic fields in circumstellar disks can be obtained from Zeeman observations of the $113~\mathrm{GHz}$ CN lines. Furthermore, we analyze the requirements to perform these observations and their dependence on selected quantities. Methods. We simulate the Zeeman splitting with the radiative transfer (RT) code POLARIS (Reissl et al. 2016) extended by our Zeeman splitting RT extension ZRAD (Brauer et al. 2017), which is based on the line RT code Mol3D (Ober et al. 2015). Results. We find that Zeeman observations of the $113~\mathrm{GHz}$ CN lines provide significant insights into the magnetic field of circumstellar disks. However, with the capabilities of recent and upcoming instrument/observatories, even spatially unresolved observations would be challenging. Nevertheless, these observations are feasible for the most massive disks with a strong magnetic field and high abundance of CN/H. The most restrictive quantity is the magnetic field strength, which should be at least in the order of $\sim1~\mathrm{mG}$. In addition, the inclination of the disk should be around $60\deg$ to preserve the ability to derive the line-of-sight (LOS) magnetic field strength and to obtain a sufficiently high circularly polarized flux.Comment: 15 pages, 14 figure

Magnetic fields in molecular clouds: Limitations of the analysis of Zeeman observations

Context. Observations of Zeeman split spectral lines represent an important approach to derive the structure and strength of magnetic fields in molecular clouds. In contrast to the uncertainty of the spectral line observation itself, the uncertainty of the analysis method to derive the magnetic field strength from these observations is not been well characterized so far. Aims. We investigate the impact of several physical quantities on the uncertainty of the analysis method, which is used to derive the line-of-sight (LOS) magnetic field strength from Zeeman split spectral lines. Methods. We simulate the Zeeman splitting of the 1665 MHz OH line with the 3D radiative transfer (RT) extension ZRAD. This extension is based on the line RT code Mol3D (Ober et al. 2015) and has been developed for the POLArized RadIation Simulator POLARIS (Reissl et al. 2016). Results. Observations of the OH Zeeman effect in typical molecular clouds are not significantly affected by the uncertainty of the analysis method. We derived an approximation to quantify the range of parameters in which the analysis method works sufficiently accurate and provide factors to convert our results to other spectral lines and species as well. We applied these conversion factors to CN and found that observations of the CN Zeeman effect in typical molecular clouds are neither significantly affected by the uncertainty of the analysis method. In addition, we found that the density has almost no impact on the uncertainty of the analysis method, unless it reaches values higher than those typically found in molecular clouds. Furthermore, the uncertainty of the analysis method increases, if both the gas velocity and the magnetic field show significant variations along the line-of-sight. However, this increase should be small in Zeeman observations of most molecular clouds considering typical velocities of ~1 km/s.Comment: 9 pages, 6 figure

Observability of characteristic binary-induced structures in circumbinary disks

Context: A substantial fraction of protoplanetary disks forms around stellar binaries. The binary system generates a time-dependent non-axisymmetric gravitational potential, inducing strong tidal forces on the circumbinary disk. This leads to a change in basic physical properties of the circumbinary disk, which should in turn result in unique structures that are potentially observable with the current generation of instruments. Aims: The goal of this study is to identify these characteristic structures, to constrain the physical conditions that cause them, and to evaluate the feasibility to observe them in circumbinary disks. Methods: To achieve this, at first two-dimensional hydrodynamic simulations are performed. The resulting density distributions are post-processed with a 3D radiative transfer code to generate re-emission and scattered light maps. Based on these, we study the influence of various parameters, such as the mass of the stellar components, the mass of the disk and the binary separation on observable features in circumbinary disks. Results: We find that the Atacama Large (sub-)Millimetre Array (ALMA) as well as the European Extremely Large Telescope (E-ELT) are capable of tracing asymmetries in the inner region of circumbinary disks which are affected most by the binary-disk interaction. Observations at submillimetre/millimetre wavelengths will allow the detection of the density waves at the inner rim of the disk and the inner cavity. With the E-ELT one can partially resolve the innermost parts of the disk in the infrared wavelength range, including the disk's rim, accretion arms and potentially the expected circumstellar disks around each of the binary components

Duality in matrix lattice Boltzmann models

The notion of duality between the hydrodynamic and kinetic (ghost) variables of lattice kinetic formulations of the Boltzmann equation is introduced. It is suggested that this notion can serve as a guideline in the design of matrix versions of the lattice Boltzmann equation in a physically transparent and computationally efficient way.Comment: 12 pages, 3 figure

Coupling between static friction force and torque for a tripod

If a body is resting on a flat surface, the maximal static friction force before motion sets in is reduced if an external torque is also applied. The coupling between the static friction force and static friction torque is nontrivial as our studies for a tripod lying on horizontal flat surface show. In this article we report on a series of experiments we performed on a tripod and compare these with analytical and numerical solutions. It turns out that the coupling between force and torque reveals information about the microscopic properties at the onset to sliding.Comment: 7 pages, 4 figures, revte

Coupling between static friction force and torque

We show that the static friction force which must be overcome to render a sticking contact sliding is reduced if an external torque is also exerted. As a test system we study a planar disk lying on horizontal flat surface. We perform experiments and compare with analytical results to find that the coupling between static friction force and torque is nontrivial: It is not determined by the Coulomb friction laws alone, instead it depends on the microscopic details of friction. Hence, we conclude that the macroscopic experiment presented here reveals details about the microscopic processes lying behind friction.Comment: 6 pages, 4 figures, revte

Quantum Weakly Nondeterministic Communication Complexity

We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this model of quantum nondeterministic communication complexity for a total function. This separation is quadratic.Comment: 12 pages. v3: minor correction