Florian Bürzle

Protostellar collapse and fragmentation using an MHD gadget

Although the influence of magnetic fields is regarded as vital in the star formation process, only a few magnetohydrodynamics (MHD) simulations have been performed on this subject within the smoothed particle hydrodynamics method. This is largely due to the unsatisfactory treatment of non-vanishing divergence of the magnetic field. Recently smoothed particle magnetohydrodynamics (SPMHD) simulations based on Euler potentials have proven to be successful in treating MHD collapse and fragmentation problems, however these methods are known to have some intrinsic difficulties. We have performed SPMHD simulations based on a traditional approach evolving the magnetic field itself using the induction equation. To account for the numerical divergence, we have chosen an approach that subtracts the effects of numerical divergence from the force equation, and additionally we employ artificial magnetic dissipation as a regularization scheme. We apply this realization of SPMHD to a widely known setup, a variation of the ‘Boss and Bodenheimer standard isothermal test case’, to study the impact of the magnetic fields on collapse and fragmentation. In our simulations, we concentrate on setups, where the initial magnetic field is parallel to the rotation axis. We examine different field strengths and compare our results to other findings reported in the literature. We are able to confirm specific results found elsewhere, namely the delayed onset of star formation for strong fields, accompanied by the tendency to form only single stars. We also find that the ‘magnetic cushioning effect’, where the magnetic field is wound up to form a ‘cushion’ between the binary, aids binary fragmentation in a case where previously only formation of a single protostar was expected.

Magnetic field amplification and X-ray emission in galaxy minor mergers

We investigate the magnetic field evolution in a series of galaxy minor mergers using the N-body/smoothed particle hydrodynamics (SPH) code gadget. The simulations include the effects of radiative cooling, star formation and supernova feedback. Magnetohydrodynamics is implemented using the SPH method. We present 32 simulations of binary mergers of disc galaxies with mass ratios of 2:1 up to 100:1, whereby we have additionally varied the initial magnetic field strengths, disc orientations and resolutions. We investigate the amplification of a given initial magnetic field within the galaxies and an ambient intergalactic medium (IGM) during the interaction. We find that the magnetic field strengths of merger remnants with mass ratios up to 10:1 saturate at a common value of several μG. For higher mass ratios, the field strength saturates at lower values. The saturation values correspond to the equipartition value of magnetic and turbulent energy density. The initial magnetization, disc orientation and numerical resolution show only minor effects on the saturation value of the magnetic field. We demonstrate that a higher impact energy of the progenitor galaxies leads to a more efficient magnetic field amplification. The magnetic and turbulent energy densities are higher for larger companion galaxies, consistent with the higher impact energy supplied to the system. We present a detailed study of the evolution of the temperature and the bolometric X-ray luminosity within the merging systems. Thereby we find that magnetic fields cause a more efficient increase of the IGM temperature and the corresponding IGM X-ray luminosity after the first encounter. However, the presence of magnetic fields does not enhance the total X-ray luminosity. Generally, the final value of the X-ray luminosity is even clearly lower for higher initial magnetic fields.

Synthetic X-ray and radio maps for two different models of Stephan's Quintet

We present simulations of the compact galaxy group Stephans Quintet (SQ) including magnetic fields, performed with the N-body/smoothed particle hydrodynamics (SPH) code gadget. The simulations include radiative cooling, star formation and supernova feedback. Magnetohydrodynamics (MHD) is implemented using the standard smoothed particle MHD method. We adapt two different initial models for SQ based on Renaud et al. and Hwang et al., both including four galaxies (NGC 7319, NGC 7320c, NGC 7318a and NGC 7318b). Additionally, the galaxies are embedded in a magnetized, low-density intergalactic medium (IGM). The ambient IGM has an initial magnetic field of 10−9 G and the four progenitor discs have initial magnetic fields of 10−9 to 10−7 G. We investigate the morphology, regions of star formation, temperature, X-ray emission, magnetic field structure and radio emission within the two different SQ models. In general, the enhancement and propagation of the studied gaseous properties (temperature, X-ray emission, magnetic field strength and synchrotron intensity) are more efficient for the SQ model based on Renaud et al., whose galaxies are more massive, whereas the less massive SQ model based on Hwang et al. shows generally similar effects but with smaller efficiency. We show that the large shock found in observations of SQ is most likely the result of a collision of the galaxy NGC 7318b with the IGM. This large group-wide shock is clearly visible in the X-ray emission and synchrotron intensity within the simulations of both SQ models. The order of magnitude of the observed synchrotron emission within the shock front is slightly better reproduced by the SQ model based on Renaud et al., whereas the distribution and structure of the synchrotron emission are better reproduced by the SQ model based on Hwang et al.

Protostellar outflows with Smoothed Particle Magnetohydrodynamics (SPMHD)

The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D adaptive mesh refinement/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the smoothed particle hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly resolved. In this work, we use an approach where we evolve the magnetic field via the induction equation, augmented with stability correction and divergence cleaning schemes. We consider the collapse of a rotating core of one solar mass, threaded by a weak magnetic field initially parallel to the rotation axis so that the core is magnetically supercritical. We show that smoothed particle magnetohydrodynamics is able to handle the magnetorotational processes connected with outflow phenomena, and to produce meaningful results which are in good agreement with findings reported in the literature. Especially, our numerical scheme allows for a quantitative analysis of the evolution of the ratio of the toroidal to the poloidal magnetic field, which we performed in this work.

Phase transitions in two-dimensional model colloids in a one-dimensional external potential.

Two-dimensional melting transitions for model colloids in the presence of a one-dimensional external periodic potential are investigated using Monte Carlo simulation and finite size scaling techniques. Here we explore a hard disk system with commensurability ratio p=sqrt[3]as/(2d)=2, where as is the mean distance between the disks and d the period of the external potential. Three phases, the modulate liquid, the locked smectic, and the locked floating solid are observed, in agreement with other experimental and analytical studies. Various statistical quantities like order parameters, their cumulants, and response functions, are used to obtain a phase diagram for the transitions between these three phases.

Protostellar outflows with smoothed particle magnetohydrodynamics

The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D adaptive mesh refinement/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the smoothed particle hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly resolved. In this work, we use an approach where we evolve the magnetic field via the induction equation, augmented with stability correction and divergence cleaning schemes. We consider the collapse of a rotating core of one solar mass, threaded by a weak magnetic field initially parallel to the rotation axis so that the core is magnetically supercritical. We show that smoothed particle magnetohydrodynamics is able to handle the magnetorotational processes connected with outflow phenomena, and to produce meaningful results which are in good agreement with findings reported in the literature. Especially, our numerical scheme allows for a quantitative analysis of the evolution of the ratio of the toroidal to the poloidal magnetic field, which we performed in this work.

Computer Simulations of Complex Many-Body Systems

The static and dynamic properties of model magnetic systems have been studied by the Landau-Lifshitz-Gilbert equation. Soft matter systems have been investigated by Monte Carlo and Brownian Dynamics simulations. In particular the behaviour of two dimensional binary hard disk mixtures in external periodic potentials has been studied as well as the transport of colloids in micro-channels and the features of lipid bilayers under tension. Certain aspects of star cluster formation processes have been computed using smoothed particle hydrodynamics. The conductance of ferromagnetic atomic-sized contacts has been analyzed by Molecular Dynamics simulations with respect to their conductance and structural properties under stretching. In the next sections we give an overview on our recent results.

Protostellar outflows with smoothed particle magnetohydrodynamics: Protostellar jets and outflows with SPMHD

The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D adaptive mesh refinement/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the smoothed particle hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly resolved. In this work, we use an approach where we evolve the magnetic field via the induction equation, augmented with stability correction and divergence cleaning schemes. We consider the collapse of a rotating core of one solar mass, threaded by a weak magnetic field initially parallel to the rotation axis so that the core is magnetically supercritical. We show that smoothed particle magnetohydrodynamics is able to handle the magnetorotational processes connected with outflow phenomena, and to produce meaningful results which are in good agreement with findings reported in the literature. Especially, our numerical scheme allows for a quantitative analysis of the evolution of the ratio of the toroidal to the poloidal magnetic field, which we performed in this work.

Computer Simulations of Soft Matter- and Nano-Systems

Soft matter systems have been investigated by Monte Carlo and Brownian Dynamics simulations. In particular the behaviour of two dimensional binary hard disk mixtures in external periodic potentials has been studied as well as the transport of colloids in micro-channels and the features of proteins in lipid bilayers. Ni nanocontacts have been analyzed by Molecular Dynamics simulations with respect to their conductance and structural properties under stretching, and the effect of temperature, composition and system size on the structural properties of Ni x Fe1 −x alloys has been studied. The properties of Si clusters in external fields have been computed by density functional methods, and the static and dynamic properties of model magnetic systems by the Landau-Lifshitz-Gilbert equation. In the next sections we give an overview on our recent results.

Nano-Systems in External Fields and Reduced Geometry : Numerical Investigations

Properties of magnetic domain walls have been studied as well as flow properties and phase transitions of model colloids in external potentials and structural and electronic properties of nano-wires and Si clusters. In the following sections an overview is given on the results of our recent computations on quantum effects, structures and phase transitions in such systems.