Christoph Federrath - Monash Centre for Astrophysics, School of Mathematical Sciences, Monash University

Christoph Federrath
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Christoph Federrath
Monash Centre for Astrophysics, School of Mathematical Sciences, Monash University

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Astrophysics of Galaxies (34)
Solar and Stellar Astrophysics (31)
Physics - Fluid Dynamics (16)
Instrumentation and Methods for Astrophysics (13)
Cosmology and Nongalactic Astrophysics (12)
Physics - Computational Physics (10)
Physics - Plasma Physics (7)
Physics - Data Analysis; Statistics and Probability (3)
Computer Science - Distributed; Parallel; and Cluster Computing (2)
Nonlinear Sciences - Chaotic Dynamics (1)
Earth and Planetary Astrophysics (1)
High Energy Astrophysical Phenomena (1)

Publications Authored By Christoph Federrath

We carry out magnetohydrodynamical simulations with FLASH of the formation of a single, a tight binary ($a\sim$2.5 AU) and a wide binary star ($a\sim$45 AU). We study the outflows and jets from these systems to understand the contributions the circumstellar and circumbinary discs have on the efficiency and morphology of the outflow. Read More

Star formation in galaxies relies on the availability of cold, dense gas, which, in turn, relies on factors internal and external to the galaxies. In order to provide a simple model for how star formation is regulated by various physical processes in galaxies, we analyse data at redshift $z=0$ from a hydrodynamical cosmological simulation that includes prescriptions for star formation and stellar evolution, active galactic nuclei (AGN), and their associated feedback processes. This model can determine the star formation rate (SFR) as a function of galaxy stellar mass, gas mass, black hole mass, and environment. Read More

The outskirts of galaxy clusters are characterised by the interplay of gas accretion and dynamical evolution involving turbulence, shocks, magnetic fields and diffuse radio emission. The density and velocity structure of the gas in the outskirts provide an effective pressure support and affect all processes listed above. Therefore it is important to resolve and properly model the turbulent flow in these mildly overdense and relatively large cluster regions; this is a challenging task for hydrodynamical codes. Read More

We determine the physical properties and turbulence driving mode of molecular clouds formed in numerical simulations of a Milky Way-type disc galaxy with parsec-scale resolution. The clouds form through gravitational fragmentation of the gas, leading to average values for mass, radii and velocity dispersion in good agreement with observations of Milky Way clouds. The driving parameter (b) for the turbulence within each cloud is characterised by the ratio of the density contrast (sigma_rho) to the average Mach number (Mach) within the cloud, b = sigma_rho/Mach. Read More

Stars form in cold molecular clouds. However, molecular gas is difficult to observe because the most abundant molecule (H2) lacks a permanent dipole moment. Rotational transitions of CO are often used as a tracer of H2, but CO is much less abundant and the conversion from CO intensity to H2 mass is often highly uncertain. Read More

Molecular clouds are to a great extent influenced by turbulent motions in the gas. Numerical and observational studies indicate that the star formation rate and efficiency crucially depend on the mixture of solenoidal and compressive modes in the turbulent acceleration field, which can be quantified by the turbulent driving parameter b. For purely solenoidal (divergence-free) driving previous studies showed that b=1/3 and for entirely compressive (curl-free) driving b=1. Read More

Many scientific data sets contain temporal dimensions. These are the data storing information at the same spatial location but different time stamps. Some of the biggest temporal datasets are produced by parallel computing applications such as simulations of climate change and fluid dynamics. Read More

We present Phantom, a fast, parallel, modular and low-memory smoothed particle hydrodynamics and magnetohydrodynamics code developed over the last decade for astrophysical applications in three dimensions. The code has been developed with a focus on stellar, galactic, planetary and high energy astrophysics and has already been used widely for studies of accretion discs and turbulence, from the birth of planets to how black holes accrete. Here we describe and test the core algorithms as well as modules for magnetohydrodynamics, self-gravity, sink particles, H_2 chemistry, dust-gas mixtures, physical viscosity, external forces including numerous galactic potentials as well as implementations of Lense-Thirring precession, Poynting-Robertson drag and stochastic turbulent driving. Read More

Magnetic fields play an important role in astrophysical accretion discs, and in the interstellar and intergalactic medium. They drive jets, suppress fragmentation in star-forming clouds and can have a significant impact on the accretion rate of stars. However, the exact amplification mechanisms of cosmic magnetic fields remain relatively poorly understood. Read More

In spring 2015, the Leibniz Supercomputing Centre (Leibniz-Rechenzentrum, LRZ), installed their new Peta-Scale System SuperMUC Phase2. Selected users were invited for a 28 day extreme scale-out block operation during which they were allowed to use the full system for their applications. The following projects participated in the extreme scale-out workshop: BQCD (Quantum Physics), SeisSol (Geophysics, Seismics), GPI-2/GASPI (Toolkit for HPC), Seven-League Hydro (Astrophysics), ILBDC (Lattice Boltzmann CFD), Iphigenie (Molecular Dynamic), FLASH (Astrophysics), GADGET (Cosmological Dynamics), PSC (Plasma Physics), waLBerla (Lattice Boltzmann CFD), Musubi (Lattice Boltzmann CFD), Vertex3D (Stellar Astrophysics), CIAO (Combustion CFD), and LS1-Mardyn (Material Science). Read More

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 magnetised 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. Read More

Understanding turbulence is critical for a wide range of terrestrial and astrophysical applications. Here we present first results of the world's highest-resolution simulation of turbulence ever done. The current simulation has a grid resolution of 10048^3 points and was performed on 65536 compute cores on SuperMUC at the Leibniz Supercomputing Centre (LRZ). Read More

Star formation is inefficient. Only a few percent 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. Read More

Supersonic turbulence is believed to be at the heart of star formation. We have performed smoothed particle magnetohydrodynamics (SPMHD) simulations of the small-scale dynamo amplification of magnetic fields in supersonic turbulence. The calculations use isothermal gas driven at rms velocity of Mach 10 so that conditions are representative of star-forming molecular clouds in the Milky Way. Read More

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. Read More

Probability distribution functions (PDFs) of column densities are an established tool to characterize the evolutionary state of interstellar clouds. Using simulations, we show to what degree their determination is affected by noise, line-of-sight contamination, field selection, and the incomplete sampling in interferometric measurements. We solve the integrals that describe the convolution of a cloud PDF with contaminating sources and study the impact of missing information on the measured column density PDF. Read More

Filamentary structures are ubiquitous in the interstellar medium, yet their formation, internal structure, and longevity have not been studied in detail. We report the results from a comprehensive numerical study that investigates the characteristics, formation, and evolution of filaments arising from magnetohydrodynamic interactions between supersonic winds and dense clouds. Here we improve on previous simulations by utilising sharper density contrasts and higher numerical resolutions. Read More

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. Read More

The origin of strong magnetic fields in the Universe can be explained by amplifying weak seed fields via turbulent motions on small spatial scales and subsequently transporting the magnetic energy to larger scales. This process is known as the turbulent dynamo and depends on the properties of turbulence, i.e. Read More

Whilst the star formation rate (SFR) of molecular clouds and galaxies is key in understanding galaxy evolution, the physical processes which determine the SFR remain unclear. This uncertainty about the underlying physics has resulted in various different star formation laws, all having substantial intrinsic scatter. Extending upon previous works that define the column density of star formation (Sigma_SFR) by the gas column density (Sigma_gas), we develop a new universal star formation (SF) law based on the multi-freefall prescription of gas. Read More

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. Read More

Star formation is inefficient. Only a few percent 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. Read More

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. Read More

The turbulent dynamo may explain the origin of cosmic magnetism. While the exponential amplification of magnetic fields has been studied for incompressible gases, little is known about dynamo action in highly-compressible, supersonic plasmas, such as the interstellar medium of galaxies and the early Universe. Here we perform the first quantitative comparison of theoretical models of the dynamo growth rate and saturation level with three-dimensional magnetohydrodynamical simulations of supersonic turbulence with grid resolutions of up to 1024^3 cells. Read More

Powerful jets and outflows are launched from the protostellar disks around newborn stars. These outflows carry enough mass and momentum to transform the structure of their parent molecular cloud and to potentially control star formation itself. Despite their importance, we have not been able to fully quantify the impact of jets and outflows during the formation of a star cluster. Read More

The formation of high-mass stars is usually accompanied by powerful protostellar outflows. Such high-mass outflows are not simply scaled-up versions of their lower-mass counterparts, since observations suggest that the collimation degree degrades with stellar mass. Theoretically, the origins of massive outflows remain open to question because radiative feedback and fragmentation of the accretion flow around the most massive stars, with M > 15 M_Sun, may impede the driving of magnetic disk winds. Read More

Affiliations: 1Max-Planck-Institute for Astronomy, Heidelberg, 2Monash Centre for Astrophysics, School of Mathematical Sciences, Monash University, 3Max-Planck-Institute for Astronomy, Heidelberg

The formation of stars shapes the structure and evolution of entire galaxies. The rate and efficiency of this process are affected substantially by the density structure of the individual molecular clouds in which stars form. The most fundamental measure of this structure is the probability density function of volume densities (rho-PDF), which determines the star formation rates predicted with analytical models. Read More

We use Principal Component Analysis (PCA) to study the gas dynamics in numerical simulations of typical 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. Read More

We review recent advances in the analytical and numerical modeling of the star formation rate in molecular clouds and discuss the available observational constraints. We focus on molecular clouds as the fundamental star formation sites, rather than on the larger-scale processes that form the clouds and set their properties. Molecular clouds are shaped into a complex filamentary structure by supersonic turbulence, with only a small fraction of the cloud mass channeled into collapsing protostars over a free-fall time of the system. Read More

We presents results from Smoothed Particle Magnetohydrodynamics simulations of collapsing molecular cloud cores, and dynamo amplification of the magnetic field in the presence of Mach 10 magnetised turbulence. Our star formation simulations have produced, for the first time ever, highly collimated magnetised protostellar jets from the first hydrostatic core phase. Up to 40% of the initial core mass may be ejected through this outflow. Read More

Molecular clouds are supersonically turbulent. This turbulence governs the initial mass function and the star formation rate. In order to understand the details of star formation, it is therefore essential to understand the properties of turbulence, in particular the probability distribution of density in turbulent clouds. Read More

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 (Sigma_SFR: the amount of gas forming stars per unit area and time) and the column density of available gas (Sigma_gas). Read More

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 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. Read More

We examine the physical parameters that affect the accumulation of gas in molecular clouds to high column densities where the formation of stars takes place. In particular, we analyze the dense gas mass fraction (DGMF) in a set of self-gravitating, isothermal, magnetohydrodynamic turbulence simulations including sink particles to model star formation. We find that the simulations predict close to exponential DGMFs over the column density range N(H2) = 3-25 x 10^{21} cm^{-2} that can be easily probed via, e. Read More

(Abridged) The small-scale dynamo may play a substantial role in magnetizing the Universe under a large range of conditions, including subsonic turbulence at low Mach numbers, highly supersonic turbulence at high Mach numbers and a large range of magnetic Prandtl numbers Pm, i.e. the ratio of kinetic viscosity to magnetic resistivity. Read More

We study the star formation efficiency (SFE) in simulations and observations of turbulent, magnetized, molecular clouds. We find that the probability density functions (PDFs) of the density and the column density in our simulations with solenoidal, mixed, and compressive forcing of the turbulence, sonic Mach numbers of 3-50, and magnetic fields in the super- to the trans-Alfvenic regime, all develop power-law tails of flattening slope with increasing SFE. The high-density tails of the PDFs are consistent with equivalent radial density profiles, rho ~ r^(-kappa) with kappa ~ 1. Read More

We explore the amplification of magnetic fields in the high-redshift Universe. For this purpose, we perform high-resolution cosmological simulations following the formation of primordial halos with \sim10^7 M_solar, revealing the presence of turbulent structures and complex morphologies at resolutions of at least 32 cells per Jeans length. Employing a turbulence subgrid-scale model, we quantify the amount of unresolved turbulence and show that the resulting turbulent viscosity has a significant impact on the gas morphology, suppressing the formation of low-mass clumps. Read More

The first galaxies form due to gravitational collapse of primordial halos. During this collapse, weak magnetic seed fields get amplified exponentially by the small-scale dynamo - a process converting kinetic energy from turbulence into magnetic energy. We use the Kazantsev theory, which describes the small-scale dynamo analytically, to study magnetic field amplification for different turbulent velocity correlation functions. Read More

Stars form by the gravitational collapse of interstellar gas. The thermodynamic response of the gas can be characterized by an effective equation of state. It determines how gas heats up or cools as it gets compressed, and hence plays a key role in regulating the process of stellar birth on virtually all scales, ranging from individual star clusters up to the galaxy as a whole. Read More

We derive and compare six theoretical models for the star formation rate (SFR) - the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle & Chabrier (HC) models, and three multi-freefall versions of these, suggested by HC - all based on integrals over the log-normal distribution of turbulent gas. We extend all theories to include magnetic fields, and show that the SFR depends on four basic parameters: (1) virial parameter alpha_vir; (2) sonic Mach number M; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma beta=2(M_A/M)^2 with the Alfven Mach number M_A. We compare all six theories with MHD simulations, covering cloud masses of 300 to 4x10^6 solar masses and Mach numbers M = 3 to 50 and M_A = 1 to infinity, with solenoidal (b=1/3), mixed (b=0. Read More

The probability density function (PDF) of the gas density in subsonic and supersonic, isothermal, driven turbulence is analyzed with a systematic set of hydrodynamical grid simulations with resolutions up to 1024^3 cells. We performed a series of numerical experiments with root mean square (r.m. Read More

We investigate the process of metal-free star formation in the first galaxies with a high-resolution cosmological simulation. We consider the cosmologically motivated scenario in which a strong molecule-destroying Lyman-Werner (LW) background inhibits effective cooling in low-mass haloes, delaying star formation until the collapse or more massive haloes. Only when molecular hydrogen (H2) can self-shield from LW radiation, which requires a halo capable of cooling by atomic line emission, will star formation be possible. Read More

We study the amplification of magnetic fields during the formation of primordial halos. The turbulence generated by gravitational infall motions during the formation of the first stars and galaxies can amplify magnetic fields very efficiently and on short timescales up to dynamically significant values. Using the Kazantsev theory, which describes the so-called small-scale dynamo - a magnetohydrodynamical process converting kinetic energy from turbulence into magnetic energy - we can then calculate the growth rate of the small-scale magnetic field. Read More

Here we summarize our recent results of high-resolution computer simulations on the turbulent amplification of weak magnetic seed fields showing that such fields will be exponentially amplified also during the gravitational collapse reminiscent to the situation during primordial star formation. The exponential magnetic field amplification is driven by the turbulent small-scale dynamo that can be only observed in computer simulations if the turbulent motions in the central core are sufficiently resolved. We find that the Jeans length, which determines the central core region, has to be resolved by at least 30 grid cells to capture the dynamo activity. Read More

We study the influence of initial conditions on the magnetic field amplification during the collapse of a magnetised gas cloud. We focus on the dependence of the growth and saturation level of the dynamo generated field on the turbulent properties of the collapsing cloud. In particular, we explore the effect of varying the initial strength and injection scale of turbulence and the initial uniform rotation of the collapsing magnetised cloud. Read More

We investigate the formation of protostellar clusters during the collapse of dense molecular cloud cores with a focus on the evolution of potential and kinetic energy, the degree of substructure, and the early phase of mass segregation. Our study is based on a series of hydrodynamic simulations of dense cores, where we vary the initial density profile and the initial turbulent velocity. In the three-dimensional adaptive mesh refinement simulations, we follow the dynamical formation of filaments and protostars until a star formation efficiency of 20%. Read More

We study the mass-to-flux ratio (M/\Phi) of clumps and cores in simulations of supersonic, magnetohydrodynamical turbulence for different initial magnetic field strengths. We investigate whether the (M/\Phi)-ratio of core and envelope, R = (M/\Phi)_{core}/(M/\Phi)_{envelope} can be used to distinguish between theories of ambipolar diffusion and turbulence-regulated star formation. We analyse R for different Lines-of-Sight (LoS) in various sub-cubes of our simulation box. Read More

We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution, hydrodynamical grid simulations with Lagrangian tracer particles and examine the effects of solenoidal (divergence-free) and compressive (curl-free) forcing on structure functions, their scaling exponents, and the probability density functions of the gas density and velocity increments. Compressively driven simulations show a significantly larger density contrast, a more intermittent behaviour, and larger fractal dimension of the most dissipative structures at the same root mean square Mach number. Read More

We present new 3D magnetohydrodynamic (MHD) simulations of a supernova-driven, stratified interstellar medium. These simulations were run using the Waagan (2009) positivity preserving scheme for ideal MHD implemented in the Flash code. The scheme is stable even for the Mach numbers approaching 100 found in this problem. Read More