Taming rotationally supported disks using state of the art numerical methods

Während des gravitativen Kollapses eines Objekts bleibt der Drehimpuls erhalten. Im Fall eines endlichen Drehimpulses im System kann sich eine rotierende Scheibe bilden, die durch die Rotation stabilisiert wird. Aufgrund der Einfachheit dieses Mechanismus sind Scheiben allgegenwärtig in der Astrophysik, beispielsweise als protoplanetare Scheiben, Akkretionsscheiben um Schwarze Löcher oder Spiralgalaxien. Insbesondere kalte Gasscheiben sind allerdings schwierig numerisch zu simulieren, da die Rotationsgeschwindigkeit deutlich über der Schallgeschwindigkeit liegt und bereits geringe Ungenauigkeiten in der verwendeten numerischen Methode zu einem unphysikalischem Wachstum von Fluidinstabilitäten führen können. Dies ist besonders dann problematisch, wenn man echte, physikalische Instabilitäten in diesen Systemen analysieren möchte. Eine Methode, die im Prinzip besonders geeignet für die Analyse von Scheibensystemen sein sollte, ist die Berechnung der magnetohydrodynamischen Gleichungen auf einem mitbewegten Gitter, wie sie in dem kosmologischen Code AREPO realisiert ist. Hierdurch kann die Überschallströmung des Gases aufgrund der Rotationsgeschwindigkeit in die Bewegung des Gitters aufgenommen und dadurch eliminiert werden. Die Bewegung und permanente Verzerrung der Gitterzellen aufgrund differentieller Rotation führt jedoch in der ursprünglichen Version von AREPO zu numerischem Rauschen, was die Nützlichkeit des Codes für kalte Scheiben deutlich reduziert hat. Das Ziel dieser Arbeit war es zunächst, die Ursache des Rauschens zu ermitteln und zu beheben. Anschließend sollte evaluiert werden, wie gut die verbesserte Methode kalte Scheiben beschreiben kann, insbesondere in Situationen, in denen Turbulenz durch Magnetfelder oder durch die Wechselwirkung von Strahlungskühlung und Gravitation erzeugt wird. Im Rahmen dieser Arbeit habe ich zuerst die sogenannte "Shearing-Box" Näherung in AREPO entwickelt, die es ermöglicht, einen kleinen Teil einer rotierenden Scheibe mit sehr hoher Auflösung zu simulieren. Im Gegensatz zu Implementierungen in anderen Codes bietet meine Lösung eine adaptive Gitterauflösung sowie vollständige Translationinvarianz. Daneben konnte ich durch eine präzisere numerische Integration der Flussfunktion über die Grenzflächen aneinanderstoßender Zellen das Rauschen auf Zellebene beheben und damit die Genauigkeit des Codes für Scherströmungen stark erhöhen. Auf Basis dieser Verbesserungen habe ich anschließend die magnetische Rotationsinstabilität (MRI) in der Shearing-Box und die dabei auftretenden magnetischen Dynamo-Effekte analysiert. Sowohl im linearen als auch im nichtlinearen Bereich habe ich gute Übereinstimmung mit früheren Ergebnissen in der Literatur gefunden, die mit statischen Gittercodes erzielt wurden. In einer weiteren Studie habe ich eine Codeerweiterung entwickelt, welche die Gravitationskräfte zwischen Massenelementen innerhalb der Simulationsregion unter Einbeziehung der speziellen Randbedingungen der Shearing-Box und ohne Auflösungsbeschränkungen berechnen kann. Mit Hilfe des sogenannten beta-Kühlens konnte ich zeigen, dass bei schwachem Strahlungskühlen unter Eigengravitation und Scherung ein gravitoturbulenter Zustand entsteht, während sich bei effizienterem Kühlen Fragmente aus kollabierenden Gaswolken herausbilden können. Schließlich habe ich die sogenannte Rossby-Wellen-Instabilität in globalen, zweidimensionalen Scheibensimulationen analysiert. Hierbei konnte ich sowohl im linearen als auch im nichtlinearen Bereich gute Übereinstimmung mit der Literatur erzielen. Die Entwicklung der Shearing-Box-Näherung und die Beseitigung des Rauschens auf Gitterebene in dem Verfahren mit einem bewegten Gitter ermöglicht vielfältige Forschungsanwendungen in der Zukunft. Einerseits kann die Wechselwirkung verschiedener Instabilitäten in Scheiben mit Hilfe der Shearing-Box präzise analysiert werden, andererseits sind nun auch globale Simulationen von ganzen Scheiben mit der Methode des bewegten Gitters möglich. Dieses Verfahren ermöglicht wesentlich größere Zeitschritte und geringere Advektionsfehler als herkömmliche Methoden mit stationären Gittern. Auch können Teile einer galaktischen Scheibe mit meiner Shearing-Box Methode in einem "Zoom" Modus simuliert werden, wobei insbesondere die geometrisch flexible, adaptive Auflösung der Methode von Vorteil ist.During the gravitational collapse of an object, the angular momentum is conserved. In the case of a finite angular momentum in the system, a rotating disk can form, stabilized by the rotation. Due to the simplicity of this mechanism, disks are ubiquitous in astrophysics, with prominent examples being protoplanetary disks, accretion disks around black holes, or spiral galaxies. However, cold gas disks in particular are difficult to be simulated numerically because the rotational velocity is much larger than the speed of sound and even small inaccuracies in the used numerical method can lead to the unphysical growth of fluid instabilities. This is particularly problematic when one tries to analyze real, physical instabilities in these systems. A method that in principle should be particularly suitable for the analysis of disk systems is the solution of the magnetohydrodynamic equations on a moving mesh, as realized in the cosmological code AREPO. This allows the supersonic flow of the gas due to the rotational velocity to be included in the mesh motion and thereby to be eliminated. However, the motion and constant distortion of the grid cells due to differential rotation introduce numerical noise in the original version of AREPO, which has significantly reduced the usefulness of the code for cold disks. The goal of this work was first to identify and remove the origin of this "grid noise'', and second to evaluate how well the improved method can describe cold disks, especially in situations where turbulence is generated by magnetic fields or by the interaction of radiative cooling and gravity. As part of this thesis, I first implemented the so-called "shearing-box'' approximation in AREPO, which allows a small portion of a rotating disk to be simulated at very high resolution. Unlike implementations in other codes, my solution provides an adaptive spatial resolution as well as full translation invariance. Additionally, by integrating the flux function more precisely over the interfaces of neighbouring cells, I was able to remove the grid noise, greatly increasing the accuracy of the code for shear flows. Based on these improvements, I analyzed the magnetorotational instability (MRI) in the shearing box and the magnetic dynamo effects that one can observe. In both the linear and nonlinear regimes, I found good agreement with previous results in the literature obtained with static grid codes. In a further line of work, I have developed a code extension that can compute gravitational forces between mass elements within the simulation box, including the special boundary conditions of the shearing box and without resolution constraints. Using the so-called beta-cooling, I was able to show that weak radiative cooling in combination with self-gravity and shear can produce a gravito-turbulent state, while more efficient cooling can produce fragments in the form of collapsing gas clouds. Finally, I analyzed the so-called Rossby wave instability in global, two-dimensional disk simulations. Here I was able to obtain good agreement with the literature in both the linear and nonlinear regimes. The development of the shearing-box approximation and the elimination of the grid noise in the moving mesh method allows a variety of research applications in the future. On the one hand, the interaction of different fluid instabilities in disks can be precisely analyzed using the shearing box, and on the other hand, global simulations of entire disks are now possible using the moving mesh method. This approach allows much larger time steps and smaller advection errors than conventional methods with stationary grids. Also, parts of a galactic disk can be simulated with my shearing box method in a ``zoom'' mode, where the geometrically flexible, adaptive resolution of the method is a particular advantage

Simulating the magnetorotational instability on a moving-mesh with the shearing box approximation

The magnetorotational instability (MRI) is an important process in sufficiently ionized accretion disks, as it can create turbulence that acts as an effective viscosity, mediating angular momentum transport. Due to its local nature, it is often analyzed in the shearing box approximation with Eulerian methods, which otherwise would suffer from large advection errors in global disk simulations. In this work, we report on an extensive study that applies the quasi-Lagrangian, moving-mesh code ${\rm \small AREPO}$, combined with the Dedner cleaning scheme to control deviations from $\nabla \cdot B = 0$, to the problem of magnetized flows in shearing boxes. We find that we can resolve the analytical linear growth rate of the MRI with mean background magnetic field well. In the zero net flux case, there is a threshold value for the strength of the divergence cleaning above which the turbulence eventually dies out, and in contrast to previous Eulerian simulations, the strength of the MRI does not decrease with increasing resolution. If we increase the vertical aspect ratio of our box we find the mean-field dynamo described in Shi et al. (2016), as well as an active shear current effect that can sustain MRI turbulence for at least 200 orbits. In stratified simulations, we obtain an active $\alpha \omega$ dynamo and the characteristic butterfly diagram, again for at least 200 orbits. Our results compare well with previous results obtained with static grid codes such as ${\rm\small ATHENA}$. We thus conclude that ${\rm \small AREPO}$ represents a particularly attractive alternative for global disk simulations, where the method benefits from its quasi-Lagrangian nature, as well as for shearing box simulations with large density variations, where ${\rm \small AREPO}$'s continuously adaptive resolution is advantageous.Comment: 20 pages, 22 figures, submitted to MNRA

On the interaction of a Bonnor-Ebert sphere with a stellar wind

The structure of protostellar cores can often be approximated by isothermal Bonnor-Ebert spheres (BES) which are stabilized by an external pressure. For the typical pressure of $10^4k_B\,\mathrm{K\,cm^{-3}}$ to $10^5k_B\,\mathrm{K\,cm^{-3}}$ found in molecular clouds, cores with masses below $1.5\,{\rm M_\odot}$ are stable against gravitational collapse. In this paper, we analyze the efficiency of triggering a gravitational collapse by a nearby stellar wind, which represents an interesting scenario for triggered low-mass star formation. We derive analytically a new stability criterion for a BES compressed by a stellar wind, which depends on its initial nondimensional radius $\xi_{max}$. If the stability limit is violated the wind triggers a core collapse. Otherwise, the core is destroyed by the wind. We estimate its validity range to $2.5<\xi_{max}<4.2$ and confirm this in simulations with the SPH Code GADGET-3. The efficiency to trigger a gravitational collapse strongly decreases for $\xi_{max}<2.5$ since in this case destruction and acceleration of the whole sphere begin to dominate. We were unable to trigger a collapse for $\xi_{max}<2$, which leads to the conclusion that a stellar wind can move the smallest unstable stellar mass to $0.5\,\mathrm{M_\odot}$ and destabilizing even smaller cores would require an external pressure larger than $10^5k_B\,\mathrm{K\,cm^{-3}}$. For $\xi_{max}>4.2$ the expected wind strength according to our criterion is small enough so that the compression is slower than the sound speed of the BES and sound waves can be triggered. In this case our criterion underestimates somewhat the onset of collapse and detailed numerical analyses are required.Comment: 13 pages, 10 Figures, accepted for publication in Ap

Non-ideal magnetohydrodynamics on a moving mesh I: Ohmic and ambipolar diffusion

Especially in cold and high-density regions, the assumptions of ideal magnetohydrodynamics (MHD) can break down, making first order non-ideal terms such as Ohmic and ambipolar diffusion as well as the Hall effect important. In this study we present a new numerical scheme for the first two resistive terms, which we implement in the moving-mesh code AREPO using the single-fluid approximation combined with a new gradient estimation technique based on a least-squares fit per interface. Through various test calculations including the diffusion of a magnetic peak, the structure of a magnetic C-shock, and the damping of an Alfv\'en wave, we show that we can achieve an accuracy comparable to the state-of-the-art code ATHENA++. We apply the scheme to the linear growth of the magnetorotational instability and find good agreement with the analytical growth rates. By simulating the collapse of a magnetised cloud with constant magnetic diffusion, we show that the new scheme is stable even for large density contrasts. Thanks to the Lagrangian nature of the moving mesh method the new scheme is thus well suited for intended future applications where a high resolution in the dense cores of collapsing protostellar clouds needs to be achieved. In a forthcoming work we will extend the scheme to the Hall effect.Comment: 17 pages, 18 figure

Simulating cosmic structure formation with the GADGET-4 code

Numerical methods have become a powerful tool for research in astrophysics, but their utility depends critically on the availability of suitable simulation codes. This calls for continuous efforts in code development, which is necessitated also by the rapidly evolving technology underlying today's computing hardware. Here we discuss recent methodological progress in the GADGET code, which has been widely applied in cosmic structure formation over the past two decades. The new version offers improvements in force accuracy, in time-stepping, in adaptivity to a large dynamic range in timescales, in computational efficiency, and in parallel scalability through a special MPI/shared-memory parallelization and communication strategy, and a more-sophisticated domain decomposition algorithm. A manifestly momentum conserving fast multipole method (FMM) can be employed as an alternative to the one-sided TreePM gravity solver introduced in earlier versions. Two different flavours of smoothed particle hydrodynamics, a classic entropy-conserving formulation and a pressure-based approach, are supported for dealing with gaseous flows. The code is able to cope with very large problem sizes, thus allowing accurate predictions for cosmic structure formation in support of future precision tests of cosmology, and at the same time is well adapted to high dynamic range zoom-calculations with extreme variability of the particle number density in the simulated volume. The GADGET-4 code is publicly released to the community and contains infrastructure for on-the-fly group and substructure finding and tracking, as well as merger tree building, a simple model for radiative cooling and star formation, a high dynamic range power spectrum estimator, and an initial conditions generator based on second-order Lagrangian perturbation theory.Comment: 82 pages, 65 figures, accepted by MNRAS, for the code see https://wwwmpa.mpa-garching.mpg.de/gadget

Unusual oxidation behavior of light metal hydride by tetrahydrofuran solvent molecules confined in ordered mesoporous carbon

Confining light metal hydrides in micro- or mesoporous scaffolds is considered to be a promising way to overcome the existing challenges for these materials, e.g. their application in hydrogen storage. Different techniques exist which allow us to homogeneously fill pores of a host matrix with the respective hydride, thus yielding well defined composite materials. For this report, the ordered mesoporous carbon CMK-3 was taken as a support for LiAlH4 realized by a solution impregnation method to improve the hydrogen desorption behavior of LiAlH4 by nanoconfinement effects. It is shown that upon heating, LiAlH4 is unusually oxidized by coordinated tetrahydrofuran solvent molecules. The important result of the herein described work is the finding of a final composite containing nanoscale aluminum oxide inside the pores of the CMK-3 carbon host instead of a metal or alloy. This newly observed unusual oxidation behavior has major implications when applying these compounds for the targeted synthesis of homogeneous metal–carbon composite materials

Unusual oxidation behavior of light metal hydride by tetrahydrofuran solvent molecules confined in ordered mesoporous carbon

Confining light metal hydrides in micro- or mesoporous scaffolds is considered to be a promising way to overcome the existing challenges for these materials, e.g. their application in hydrogen storage. Different techniques exist which allow us to homogeneously fill pores of a host matrix with the respective hydride, thus yielding well defined composite materials. For this report, the ordered mesoporous carbon CMK-3 was taken as a support for LiAlH₄ realized by a solution impregnation method to improve the hydrogen desorption behavior of LiAlH₄ by nanoconfinement effects. It is shown that upon heating, LiAlH₄ is unusually oxidized by coordinated tetrahydrofuran solvent molecules. The important result of the herein described work is the finding of a final composite containing nanoscale aluminum oxide inside the pores of the CMK-3 carbon host instead of a metal or alloy. This newly observed unusual oxidation behavior has major implications when applying these compounds for the targeted synthesis of homogeneous metal–carbon composite materials