arXiv subjects

Wolfram Schmidt

Publications and source records attributed to Wolfram Schmidt.

At least 19 recordsLinked to original sources

arXiv2024

Magnetic field and kinetic helicity evolution in simulations of interacting disk galaxies

We carried out a parameter study of interacting disk galaxies with impact parameters ranging from central collisions to weakly interacting scenarios. The orientations of the disks were also varied. In particular, we investigated how magnetic field amplification depends on these parameters. We used magnetohydrodynamics for gas disks in combination with live dark-matter halos in adaptive mesh refinement simulations. The disks were initialized using a setup for isolated disks in hydrostatic equilibrium. Small-scale filtering of the velocity and magnetic field allowed us to estimate the turbulent electromotive force (EMF) and kinetic helicity. Time series of the average magnetic field in central and outer disk regions show pronounced peaks during close encounters and mergers. This agrees with observed magnetic fields at different interaction stages. The central field strength exceeds 10 microgauss (corresponding to an amplification factor of 2 to 3) for small impact parameters. As the disks are increasingly disrupted and turbulence is produced by tidal forces, the small-scale EMF reaches a significant fraction of the total EMF. The small-scale kinetic helicity is initially antisymmetric across the disk plane. Though its evolution is sensitive to both the impact parameter and inclinations of the rotation axes with respect to the relative motion of the disks, antisymmetry is generally broken through interactions and the merger remnant loses most of the initial helicity. The EMF and the magnetic field also decay rapidly after coalescence. The strong amplification during close encounters of the interacting galaxies is mostly driven by helical flows and a mean-field dynamo. The small-scale dynamo contributes significantly in post-interaction phases. However, the amplification of the magnetic field cannot be sustained.

astro-ph.GA↗

arXiv2023

Inflationary and phase-transitional primordial magnetic fields in galaxy clusters

Primordial magnetic fields (PMFs) are possible candidates for explaining the observed magnetic fields in galaxy clusters. Two competing scenarios of primordial magnetogenesis have been discussed in the literature: inflationary and phase-transitional. We study the amplification of both large- and small-scale correlated magnetic fields, corresponding to inflation- and phase transition-generated PMFs, in a massive galaxy cluster. We employ high-resolution magnetohydrodynamic cosmological zoom-in simulations to resolve the turbulent motions in the intracluster medium. We find that the turbulent amplification is more efficient for the large-scale inflationary models, while the phase transition-generated seed fields show moderate growth. The differences between the models are imprinted on the spectral characteristics of the field (such as the amplitude and the shape of the magnetic power spectrum) and therefore on the final correlation length. We find a one order of magnitude difference between the final strengths of the inflation- and phase transition-generated magnetic fields, and a factor of 1.5 difference between their final coherence scales. Thus, the final configuration of the magnetic field retains information about the PMF generation scenarios. Our findings have implications for future extragalactic Faraday rotation surveys with the possibility of distinguishing between different magnetogenesis scenarios.

astro-ph.CO↗

arXiv2022

Evolution of primordial magnetic fields during large-scale structure formation

Primordial magnetic fields could explain the large-scale magnetic fields present in the Universe. Inflation and phase transitions in the early Universe could give rise to such fields with unique characteristics. We investigate the magneto-hydrodynamic evolution of these magnetogenesis scenarios with cosmological simulations. We evolve inflation-generated magnetic fields either as (i) uniform (homogeneous) or as (ii) scale-invariant stochastic fields, and phase transition-generated ones either as (iii) helical or as (iv) non-helical fields from the radiation-dominated epoch. We find that the final distribution of magnetic fields in the simulated cosmic web shows a dependence on the initial strength and the topology of the seed field. Thus, the observed field configuration retains information on the initial conditions at the moment of the field generation. If detected, primordial magnetic field observations would open a new window for indirect probes of the early universe. The differences between the competing models are revealed on the scale of galaxy clusters, bridges, as well as filaments and voids. The distinctive spectral evolution of different seed fields produces imprints on the correlation length today. We discuss how the differences between rotation measures from highly ionized regions can potentially be probed with forthcoming surveys.

astro-ph.CO↗

arXiv2022

Proceedings of the International Astronomical Union: Studying Magnetic Field Amplification in Interacting Galaxies Using Numerical Simulations

There are indications that the magnetic field evolution in galaxies might be massively shaped by tidal interactions and mergers between galaxies. The details of the connection between the evolution of magnetic fields and that of their host galaxies is still a field of research. We use a combined approach of magnetohydrodynamics for the baryons and an N-body scheme for the dark matter to investigate magnetic field amplification and evolution in interacting galaxies. We find that, for two colliding equal-mass galaxies and for varying initial relative spatial orientations, magnetic fields are amplified during interactions, yet cannot be sustained. Furthermore, we find clues for an active mean-field dynamo.

astro-ph.GA↗

arXiv2019

Kinetic and internal energy transfer in implicit large eddy simulations of forced compressible turbulence

We revisit the problem of how energy transfer through the turbulent cascade operates in compressible hydrodynamic turbulence. In general, there is no conservative compressible cascade since the kinetic and internal energy reservoirs can exchange energy through pressure dilatation. Moreover, statistically stationary turbulence at high Mach number can only be maintained in nearly isothermal gas, i.e., if excess heat produced by shock compression and kinetic energy dissipation is continuously removed from the system. We mimic this process by a linear cooling term in numerical simulations of turbulence driven by stochastic forcing. This allows us to investigate turbulence statistics for a broad range of Mach numbers. We compute the rate of change of kinetic and internal energy in wavenumber shells caused by advective, compressive, and pressure dilatation effects and constrain power-law fits to compressible turbulence energy spectra to a range of wavenumbers in which the total energy transfer is close to zero. The resulting scaling exponents are significantly affected by the forcing. Depending on the root mean square Mach number, we find a nearly constant advective component of the cross-scale flux of kinetic energy at intermediate wavenumbers for particular mixtures of solenoidal and compressive modes in the forcing. This suggests the existence of a natural, Mach number dependent mixture of forcing modes. Our findings also support an advection-dominated regime at high Mach numbers with specific scaling exponents (Burgers scaling for the pure velocity fluctuation $u$ and Kolmogorov scaling for the mass-weighted variable $v=ρ^{1/3}u$).

physics.flu-dyn↗

arXiv2019

Global dynamics of the interstellar medium in magnetised disc galaxies

Magnetic fields are an elemental part of the interstellar medium in galaxies. However, their impact on gas dynamics and star formation in galaxies remains controversial. We use a suite of global magnetohydrodynamical simulations of isolated disc galaxies to study the influence of magnetic fields on the diffuse and dense gas in the discs. We find that the magnetic field acts in multiple ways. Stronger magnetised discs fragment earlier due to the shorter growth time of the Parker instability. Due to the Parker instability in the magnetised discs we also find cold ($T<50\,\mathrm{K}$) and dense ($n\sim10^3-10^4\,\mathrm{cm}^{-3}$) gas several hundred pc above/below the midplane without any form of stellar feedback. In addition, magnetic fields change the fragmentation pattern. While in the hydrodynamical case, the disc breaks up into ring-like structures, magnetised discs show the formation of filamentary entities that extent both in the azimuthal and radial direction. These kpc scale filaments become magnetically (super-)critical very quickly and allow for the rapid formation of massive giant molecular clouds. Our simulations suggest that major differences in the behaviour of star formation - due to a varying magnetisation - in galaxies could arise.

astro-ph.GA↗

arXiv2019

Intermittent fragmentation and statistical variations during gas collapse in magnetised atomic cooling haloes

Observations reveal the presence of supermassive black holes (SMBH) as early as ~700 million years after the Big Bang. Their formation path is still subject to current debate. We explore the influence of magnetic fields, which are strongly amplified via the turbulent small-scale dynamo, on the formation of SMBH seeds within the direct collapse scenario. In this study, we perform for the first time cosmological magnetohydrodynamic large eddy simulations that employ a model for unresolved, compressible MHD turbulence. In total we perform 36 simulations for 9 haloes each with two different initial magnetic field strengths, and with and without employing the unresolved turbulence model. We make use of the adaptive mesh refinement approach to achieve an effective spatial resolution of less than one proper astronomical unit. We consider a regime where cooling is regulated by atomic hydrogen and the molecular hydrogen gets dissociated by a strong radiation field. Our main finding is that the majority of the gas properties in the haloes at the final output are predominantly determined by the run-away gravitational collapse. Turbulence is supersonic and super-Alfvénic in all cases, and magnetic fields are amplified to an approximately dynamically relevant regime. Finally, fragmentation during the collapse is intermittent and mass accretion rates range from 0.2-3 Msun/yr. This suggests that the presence of strongly amplified magnetic fields and turbulence provides additional pressure support on small scales and make the direct collapse a viable scenario for the formation of massive objects under the required ambient conditions.

astro-ph.GA↗

arXiv2018

The Origin of Filamentary Star Forming Clouds in Magnetised Galaxies

Observations show that galaxies and their interstellar media are pervaded by strong magnetic fields with energies in the diffuse component being at least comparable to the thermal and even as large or larger than the turbulent energy. Such strong magnetic fields prevent the formation of stars because patches of the interstellar medium are magnetically subcritical. Here we present the results from global numerical simulations of strongly magnetised and self-gravitating galactic discs, which show that the buoyancy of the magnetic field due to the Parker instability leads at first to the formation of giant filamentary regions. These filamentary structures become gravitationally unstable and fragment into $\sim10^5 M_{\odot}$ clouds that attract kpc long, coherent filamentary flows that build them into GMCs. Our results thus provide a solution to the long-standing problem of how the transition from sub- to supercritical regions in the interstellar medium proceeds.

astro-ph.GA↗

arXiv2017

Energy transfer in compressible magnetohydrodynamic turbulence

Magnetic fields, compressibility and turbulence are important factors in many terrestrial and astrophysical processes. While energy dynamics, i.e. how energy is transferred within and between kinetic and magnetic reservoirs, has been previously studied in the context of incompressible magnetohydrodynamic (MHD) turbulence, we extend shell-to-shell energy transfer analysis to the compressible regime. We derive four new transfer functions specifically capturing compressibility effects in the kinetic and magnetic cascade, and capturing energy exchange via magnetic pressure. To illustrate their viability, we perform and analyze four simulations of driven isothermal MHD turbulence in the sub- and supersonic regime with two different codes. On the one hand, our analysis reveals robust characteristics across regime and numerical method. For example, energy transfer between individual scales is local and forward for both cascades with the magnetic cascade being stronger than the kinetic one. Magnetic tension and magnetic pressure related transfers are less local and weaker than the cascades. We find no evidence for significant nonlocal transfer. On the other hand, we show that certain functions, e.g., the compressive component of the magnetic energy cascade, exhibit a more complex behavior that varies both with regime and numerical method. Having established a basis for the analysis in the compressible regime, the method can now be applied to study a broader parameter space.

physics.plasm-ph↗

arXiv2017

Comparative statistics of selected subgrid-scale models in large eddy simulations of decaying, supersonic MHD turbulence

Large eddy simulations (LES) are a powerful tool in understanding processes that are inaccessible by direct simulations due to their complexity, for example, in the highly turbulent regime. However, their accuracy and success depends on a proper subgrid-scale (SGS) model that accounts for the unresolved scales in the simulation. We evaluate the applicability of two traditional SGS models, namely the eddy-viscosity (EV) and the scale-similarity (SS) model, and one recently proposed nonlinear (NL) SGS model in the realm of compressible MHD turbulence. Using 209 simulations of decaying, supersonic (initial sonic Mach number of ~3) MHD turbulence with a shock-capturing scheme and varying resolution, SGS model and filter, we analyze the ensemble statistics of kinetic and magnetic energy spectra and structure functions. Furthermore, we compare the temporal evolution of lower and higher order statistical moments of the spatial distributions of kinetic and magnetic energy, vorticity, current density, and dilatation magnitudes. We find no statistical influence on the evolution of the flow by any model if grid-scale quantities are used to calculate SGS contributions. In addition, the SS models, which employ an explicit filter, have no impact in general. On the contrary, both EV and NL models change the statistics if an explicit filter is used. For example, they slightly increase the dissipation on the smallest scales. We demonstrate that the nonlinear model improves higher order statistics already with a small explicit filter, i.e. a three-point stencil. The results of e.g. the structure functions or the skewness and kurtosis of the current density distribution are closer to the ones obtained from simulations at higher resolution. We conclude that the nonlinear model with a small explicit filter is suitable for application in more complex scenarios when higher order statistics are important.

physics.flu-dyn↗

arXiv2016

A nonlinear structural subgrid-scale closure for compressible MHD Part I: derivation and energy dissipation properties

Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LES), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale (SGS) dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator (W.K. Yeo CUP 1993, ed. Galperin & Orszag) and require no assumptions about the nature of the flow or magnetic field. Thus the scope of their applicability ranges from the sub- to the hyper-sonic and -Alfvenic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular the anisotropy, of the flow. Their properties are $\textit{a priori}$ validated in an accompanying article (Grete et al. Phys. Plasmas, 2016) against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.

physics.flu-dyn↗

arXiv2016

Hot and Turbulent Gas in Clusters

The gas in galaxy clusters is heated by shock compression through accretion (outer shocks) and mergers (inner shocks). These processes additionally produce turbulence. To analyse the relation between the thermal and turbulent energies of the gas under the influence of non-adiabatic processes, we performed numerical simulations of cosmic structure formation in a box of 152 Mpc comoving size with radiative cooling, UV background, and a subgrid scale model for numerically unresolved turbulence. By smoothing the gas velocities with an adaptive Kalman filter, we are able to estimate bulk flows toward cluster cores. This enables us to infer the velocity dispersion associated with the turbulent fluctuation relative to the bulk flow. For halos with masses above $10^{13}\,M_\odot$, we find that the turbulent velocity dispersions averaged over the warm-hot intergalactic medium (WHIM) and the intracluster medium (ICM) are approximately given by powers of the mean gas temperatures with exponents around 0.5, corresponding to a roughly linear relation between turbulent and thermal energies and transonic Mach numbers. However, turbulence is only weakly correlated with the halo mass. Since the power-law relation is stiffer for the WHIM, the turbulent Mach number tends to increase with the mean temperature of the WHIM. This can be attributed to enhanced turbulence production relative to dissipation in particularly hot and turbulent clusters.

astro-ph.CO↗

arXiv2015

The small and the beautiful: How the star formation law affects galactic disk structure

We investigate the influence of different analytical parameterizations and fit functions for the local star formation rate in AMR simulations of an isolated disk galaxy with the Nyx code. Such parameterizations express the star formation efficiency as function of the local turbulent Mach number and virial parameter. By employing the method of adaptively refined large eddy simulations, we are able to evaluate these physical parameters from the numerically unresolved turbulent energy associated with the grid scale. We consider both single and multi free-fall variants of star formation laws proposed by Padoan & Nordlund, Hennebelle & Chabrier, and Krumholz & McKee, summarised and tested recently with numerical simulations by Federrath & Klessen. We find that the global star formation rate and the relation between the local star formation rate and the gas column density is reproduced in agreement with observational constraints by all multi free-fall models of star formation. Some models with obsolete calibration or a single free-fall time scale, however, result in an overly clumpy disk that does not resemble the structure of observed spirals.

astro-ph.GA↗

arXiv2015

Mach number study of supersonic turbulence: The properties of the density field

We model driven, compressible, isothermal, turbulence with Mach numbers ranging from the subsonic ($\mathcal{M} \approx 0.65$) to the highly supersonic regime ($\mathcal{M}\approx 16 $). The forcing scheme consists both solenoidal (transverse) and compressive (longitudinal) modes in equal parts. We find a relation $σ_{s}^2 = \mathrm{b}\log{(1+\mathrm{b}^2\mathcal{M}^2)}$ between the Mach number and the standard deviation of the logarithmic density with $\mathrm{b} = 0.457 \pm 0.007$. The density spectra follow $\mathcal{D}(k,\,\mathcal{M}) \propto k^{ζ(\mathcal{M})}$ with scaling exponents depending on the Mach number. We find $ζ(\mathcal{M}) = α\mathcal{M}^β$ with a coefficient $α$ that varies slightly with resolution, whereas $β$ changes systematically. We extrapolate to the limit of infinite resolution and find $α= -1.91 \pm 0.01,\, β=-0.30\pm 0.03$. The dependence of the scaling exponent on the Mach number implies a fractal dimension $D=2+0.96 \mathcal{M}^{-0.30}$. We determine how the scaling parameters depend on the wavenumber and find that the density spectra are slightly curved. This curvature gets more pronounced with increasing Mach number. We propose a physically motivated fitting formula $\mathcal{D}(k) = \mathcal{D}_0 k^{ζk^η}$ by using simple scaling arguments. The fit reproduces the spectral behaviour down to scales $k\approx 80$. The density spectrum follows a single power-law $η= -0.005 \pm 0.01$ in the low Mach number regime and the strongest curvature $η= -0.04 \pm 0.02$ for the highest Mach number. These values of $η$ represent a lower limit, as the curvature increases with resolution.

astro-ph.SR↗

arXiv2015

Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment -- magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures -- models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The subgrid-scale energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ($β_\mathrm{p} = 0.25, 1, 2.5, 5, 25$) and sonic Mach numbers ($M_s = 2, 2.5, 4$). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and $α-β-γ$ closures. We find only mediocre performance of the kinetic eddy-viscosity and $α-β-γ$ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlation and constant coefficient values over time and and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.

physics.flu-dyn↗

arXiv2014

Large-eddy simulations of isolated disc galaxies with thermal and turbulent feedback

We present a subgrid-scale model for the Multi-phase Interstellar medium, Star formation, and Turbulence (MIST) and explore its behaviour in high-resolution large-eddy simulations of isolated disc galaxies. MIST follows the evolution of a clumpy cold and a diffuse warm component of the gas within a volume element which exchange mass and energy via various cooling, heating and mixing processes. The star formation rate is dynamically computed from the state of the gas in the cold phase. An important feature of MIST is the treatment of unresolved turbulence in the two phases and its interaction with star formation and feedback by supernovae. This makes MIST a particularly suitable model for the interstellar medium in galaxy simulations. We carried out a suite of simulations varying fundamental parameters of our feedback implementation. Several observational properties of galactic star formation are reproduced in our simulations, such as an average star formation efficiency ~1%, a typical velocity dispersion around ~10 km/s in star-forming regions, and an almost linear relationship between the column densities of star formation and dense molecular gas.

astro-ph.GA↗

arXiv2014

Low-metallicity star formation: Relative impact of metals and magnetic fields

Low-metallicity star formation poses a central problem of cosmology, as it determines the characteristic mass scale and distribution for the first and second generations of stars forming in our Universe. Here, we present a comprehensive investigation assessing the relative impact of metals and magnetic fields, which may both be present during low-metallicity star formation. We show that the presence of magnetic fields generated via the small-scale dynamo stabilises the protostellar disc and provides some degree of support against fragmentation. In the absence of magnetic fields, the fragmentation timescale in our model decreases by a factor of ~10 at the transition from Z=0 to Z>0, with subsequently only a weak dependence on metallicity. Similarly, the accretion timescale of the cluster is set by the large-scale dynamics rather than the local thermodynamics. In the presence of magnetic fields, the primordial disc can become completely stable, therefore forming only one central fragment. At Z>0, the number of fragments is somewhat reduced in the presence of magnetic fields, though the shape of the mass spectrum is not strongly affected in the limits of the statistical uncertainties. The fragmentation timescale, however, increases by roughly a factor of 3 in the presence of magnetic fields. Indeed, our results indicate comparable fragmentation timescales in primordial runs without magnetic fields and Z>0 runs with magnetic fields.

astro-ph.GA↗

arXiv2014

Large Eddy Simulations in Astrophysics

In this review, the methodology of large eddy simulations (LES) is introduced and applications in astrophysics are discussed. As theoretical framework, the scale decomposition of the dynamical equations for neutral fluids by means of spatial filtering is explained. For cosmological applications, the filtered equations in comoving coordinates are also presented. To obtain a closed set of equations that can be evolved in LES, several subgrid scale models for the interactions between numerically resolved and unresolved scales are discussed, in particular the subgrid scale turbulence energy equation model. It is then shown how model coefficients can be calculated, either by dynamical procedures or, a priori, from high-resolution data. For astrophysical applications, adaptive mesh refinement is often indispensable. It is shown that the subgrid scale turbulence energy model allows for a particularly elegant and physically well motivated way of preserving momentum and energy conservation in AMR simulations. Moreover, the notion of shear-improved models for inhomogeneous and non-stationary turbulence is introduced. Finally, applications of LES to turbulent combustion in thermonuclear supernovae, star formation and feedback in galaxies, and cosmological structure formation are reviewed.

astro-ph.CO↗