A nonlinear structural subgrid-scale closure for compressible MHD. I. Derivation and energy dissipation properties

This is the final version. Available from AIP Publishing via the DOI in this recordCompressible 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 (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale 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)] 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 -Alfvénic 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 a priori validated in Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.University of GöttingenDeutsche Forschungsgemeinschaft (DFG)Max Planck Institute for Dynamics and Self-OrganizationConicyt Fondecyt: Fondo Nacional de Desarrollo Científico y TecnológicoNorth-German Supercomputing Allianc

A nonlinear structural subgrid-scale closure for compressible MHD. II. A priori comparison on turbulence simulation data

This is the final version. Available from AIP Publishing via the DOI in this recordEven though compressible plasma turbulence is encountered in many astrophysical phenomena, its effect is often not well understood. Furthermore, direct numerical simulations are typically not able to reach the extreme parameters of these processes. For this reason, large-eddy simulations (LES), which only simulate large and intermediate scales directly, are employed. The smallest, unresolved scales and the interactions between small and large scales are introduced by means of a subgrid-scale (SGS) model. We propose and verify a new set of nonlinear SGS closures for future application as an SGS model in LES of compressible magnetohydrodynamics. We use 15 simulations (without explicit SGS model) of forced, isotropic, homogeneous turbulence with varying sonic Mach number Ms=0.2-20 as reference data for the most extensive a priori tests performed so far in literature. In these tests, we explicitly filter the reference data and compare the performance of the new closures against the most widely tested closures. These include eddy-viscosity and scale-similarity type closures with different normalizations. Performance indicators are correlations with the turbulent energy and cross-helicity flux, the average SGS dissipation, the topological structure and the ability to reproduce the correct magnitude and the direction of the SGS vectors. We find that only the new nonlinear closures exhibit consistently high correlations (median value > 0.8) with the data over the entire parameter space and outperform the other closures in all tests. Moreover, we show that these results are independent of resolution and chosen filter scale. Additionally, the new closures are effectively coefficient-free with a deviation of less than 20%.University of GöttingenDeutsche Forschungsgemeinschaft (DFG)Max Planck Institute for Dynamics and Self-OrganizationConicyt Fondecyt: Fondo Nacional de Desarrollo Científico y Tecnológic

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

This is the final version. Available from the American Physical Society via the DOI in this recordLarge-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) models, and one recently proposed nonlinear (NL) SGS model in the realm of compressible magnetohydrodynamic (MHD) turbulence. Using 209 simulations of decaying, supersonic (initial sonic Mach number Ms≈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 the 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. In addition, no additional regularization to stabilize the model is required. 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.University of GottingenMax-Planck-Institut MPI für Dynamik und SelbstorganisationConicyt Fondecyt: Fondo Nacional de Desarrollo Científico y TecnológicoCentro de Astrofísica y Tecnologías Afines CAT

Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

This is the final version. Available on open access from IOP Publishing via the DOI in this recordTurbulence 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 SGS 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 () and sonic Mach numbers (). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and closures. We find only mediocre performance of the kinetic eddy-viscosity and 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 correlations and constant coefficient values over time 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.University of GottingenDeutsche Forschungsgemeinschaft (DFG)Australian Research Council (ARC

The Formation of the First Massive Black Holes

Supermassive black holes (SMBHs) are common in local galactic nuclei, and SMBHs as massive as several billion solar masses already exist at redshift z=6. These earliest SMBHs may grow by the combination of radiation-pressure-limited accretion and mergers of stellar-mass seed BHs, left behind by the first generation of metal-free stars, or may be formed by more rapid direct collapse of gas in rare special environments where dense gas can accumulate without first fragmenting into stars. This chapter offers a review of these two competing scenarios, as well as some more exotic alternative ideas. It also briefly discusses how the different models may be distinguished in the future by observations with JWST, (e)LISA and other instruments.Comment: 47 pages with 306 references; this review is a chapter in "The First Galaxies - Theoretical Predictions and Observational Clues", Springer Astrophysics and Space Science Library, Eds. T. Wiklind, V. Bromm & B. Mobasher, in pres

Atypical Mg-poor Milky Way Field Stars with Globular Cluster Second-generation-like Chemical Patterns

We report the peculiar chemical abundance patterns of 11 atypical Milky Way (MW) field red giant stars observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE). These atypical giants exhibit strong Al and N enhancements accompanied by C and Mg depletions, strikingly similar to those observed in the so-called second-generation (SG) stars of globular clusters (GCs). Remarkably, we find low Mg abundances ([Mg/Fe] < 0.0) together with strong Al and N overabundances in the majority (5/7) of the metal-rich ([Fe/H] gsim −1.0) sample stars, which is at odds with actual observations of SG stars in Galactic GCs of similar metallicities. This chemical pattern is unique and unprecedented among MW stars, posing urgent questions about its origin. These atypical stars could be former SG stars of dissolved GCs formed with intrinsically lower abundances of Mg and enriched Al (subsequently self-polluted by massive AGB stars) or the result of exotic binary systems. We speculate that the stars Mg-deficiency as well as the orbital properties suggest that they could have an extragalactic origin. This discovery should guide future dedicated spectroscopic searches of atypical stellar chemical patterns in our Galaxy, a fundamental step forward to understanding the Galactic formation and evolution

The First Stars

The first stars to form in the Universe -- the so-called Population III stars -- bring an end to the cosmological Dark Ages, and exert an important influence on the formation of subsequent generations of stars and on the assembly of the first galaxies. Developing an understanding of how and when the first Population III stars formed and what their properties were is an important goal of modern astrophysical research. In this review, I discuss our current understanding of the physical processes involved in the formation of Population III stars. I show how we can identify the mass scale of the first dark matter halos to host Population III star formation, and discuss how gas undergoes gravitational collapse within these halos, eventually reaching protostellar densities. I highlight some of the most important physical processes occurring during this collapse, and indicate the areas where our current understanding remains incomplete. Finally, I discuss in some detail the behaviour of the gas after the formation of the first Population III protostar. I discuss both the conventional picture, where the gas does not undergo further fragmentation and the final stellar mass is set by the interplay between protostellar accretion and protostellar feedback, and also the recently advanced picture in which the gas does fragment and where dynamical interactions between fragments have an important influence on the final distribution of stellar masses.Comment: 72 pages, 4 figures. Book chapter to appear in "The First Galaxies - Theoretical Predictions and Observational Clues", 2012 by Springer, eds. V. Bromm, B. Mobasher, T. Wiklin

Formation of supermassive black hole seeds in nuclear star clusters via gas accretion and runaway collisions

More than 200 supermassive black holes (SMBHs) of masses ≳109M⊙≳109M⊙ have been discovered at z ≳ 6. One promising pathway for the formation of SMBHs is through the collapse of supermassive stars (SMSs) with masses ∼103−105M⊙∼103−105M⊙ into seed black holes which could grow upto few times 109M⊙109M⊙ SMBHs observed at z ∼ 7. In this paper, we explore how SMSs with masses ∼103−105M⊙∼103−105M⊙ could be formed via gas accretion and runaway stellar collisions in high-redshift, metal-poor nuclear star clusters (NSCs) using idealized N-body simulations. We explore physically motivated accretion scenarios, e.g. Bondi–Hoyle–Lyttleton accretion and Eddington accretion, as well as simplified scenarios such as constant accretions. While gas is present, the accretion time-scale remains considerably shorter than the time-scale for collisions with the most massive object (MMO). However, overall the time-scale for collisions between any two stars in the cluster can become comparable or shorter than the accretion time-scale, hence collisions still play a crucial role in determining the final mass of the SMSs. We find that the problem is highly sensitive to the initial conditions and our assumed recipe for the accretion, due to the highly chaotic nature of the problem. The key variables that determine the mass growth mechanism are the mass of the MMO and the gas reservoir that is available for the accretion. Depending on different conditions, SMSs of masses ∼103−105M⊙∼103−105M⊙ can form for all three accretion scenarios considered in this work

Formation of SMBH seeds in Population III star clusters through collisions: the importance of mass loss

Runaway collisions in dense clusters may lead to the formation of supermassive black hole (SMBH) seeds, and this process can be further enhanced by accretion, as recent models of SMBH seed formation in Population III star clusters have shown. This may explain the presence of SMBHs already at high redshift, z > 6. However, in this context, mass loss during collisions was not considered and could play an important role for the formation of the SMBH seed. Here, we study the effect of mass loss, due to collisions of protostars, in the formation and evolution of a massive object in a dense primordial cluster. We consider both constant mass-loss fractions as well as analytic models based on the stellar structure of the collision components. Our calculations indicate that mass loss can significantly affect the final mass of the possible SMBH seed. Considering a constant mass loss of 5 per cent for every collision, we can lose between 60–80 per cent of the total mass that is obtained if mass loss were not considered. Using instead analytical prescriptions for mass loss, the mass of the final object is reduced by 15–40 per cent, depending on the accretion model for the cluster we study. Altogether, we obtain masses of the order of 104M⊙104M⊙⁠, which are still massive enough to be SMBH seeds