Adaptive Mesh Refinement Simulations Research Articles

LATE POP III STAR FORMATION DURING THE EPOCH OF REIONIZATION: RESULTS FROM THE RENAISSANCE SIMULATIONS

ABSTRACT We present results on the formation of Population III (Pop III) stars at redshift 7.6 from the Renaissance Simulations, a suite of extremely high-resolution and physics-rich radiation transport hydrodynamics cosmological adaptive-mesh refinement simulations of high-redshift galaxy formation performed on the Blue Waters supercomputer. In a survey volume of about 220 comoving Mpc3, we found 14 Pop III galaxies with recent star formation. The surprisingly late formation of Pop III stars is possible due to two factors: (i) the metal enrichment process is local and slow, leaving plenty of pristine gas to exist in the vast volume; and (ii) strong Lyman–Werner radiation from vigorous metal-enriched star formation in early galaxies suppresses Pop III formation in (“not so”) small primordial halos with mass less than ∼3 × 107 M ⊙. We quantify the properties of these Pop III galaxies and their Pop III star formation environments. We look for analogs to the recently discovered luminous Ly α emitter CR7, which has been interpreted as a Pop III star cluster within or near a metal-enriched star-forming galaxy. We find and discuss a system similar to this in some respects, however, the Pop III star cluster is far less massive and luminous than CR7 is inferred to be.

Level-by-level artificial viscosity and visualization for MHD simulation with adaptive mesh refinement

We propose a numerical method to determine the artificial viscosity in magnetohydrodynamics (MHD) simulations with adaptive mesh refinement (AMR) method, where the artificial viscosity is adaptively changed due to the resolution level of the AMR hierarchy. Although the suitable value of the artificial viscosity depends on the governing equations and the model of target problem, it can be determined by von Neumann stability analysis. By means of the new method, “level-by-level artificial viscosity method,” MHD simulations of Rayleigh–Taylor instability (RTI) are carried out with the AMR method. The validity of the level-by-level artificial viscosity method is confirmed by the comparison of the linear growth rates of RTI between the AMR simulations and the simple simulations with uniform grid and uniform artificial viscosity whose resolution is the same as that in the highest level of the AMR simulation. Moreover, in the nonlinear phase of RTI, the secondary instability is clearly observed where the hierarchical data structure of AMR calculation is visualized as high resolution region floats up like terraced fields. In the applications of the method to general fluid simulations, the growth of small structures can be sufficiently reproduced, while the divergence of numerical solutions can be suppressed.

A novel high-order, entropy stable, 3D AMR MHD solver with guaranteed positive pressure

We describe a high-order numerical magnetohydrodynamics (MHD) solver built upon a novel non-linear entropy stable numerical flux function that supports eight travelling wave solutions. By construction the solver conserves mass, momentum, and energy and is entropy stable. The method is designed to treat the divergence-free constraint on the magnetic field in a similar fashion to a hyperbolic divergence cleaning technique. The solver described herein is especially well-suited for flows involving strong discontinuities. Furthermore, we present a new formulation to guarantee positivity of the pressure. We present the underlying theory and implementation of the new solver into the multi-physics, multi-scale adaptive mesh refinement (AMR) simulation code $\texttt{FLASH}$ (http://flash.uchicago.edu). The accuracy, robustness and computational efficiency is demonstrated with a number of tests, including comparisons to available MHD implementations in $\texttt{FLASH}$.

Role of cosmic rays in the circumgalactic medium

We explore the impact of cosmic rays (CRs) on cosmological adaptive-mesh refinement simulations of a forming 10^12 Msolar halo, focusing on the circumgalactic medium (CGM), and its resulting low-redshift structure and composition. In contrast to a run with star formation and energetic feedback but no CRs, the CR-inclusive runs feature a CGM substantially enriched with CRs and with metals to roughly 0.1 Zsolar, thanks to robust, persistent outflows from the disk. The CR-inclusive CGMs also feature more diffuse gas at lower temperatures, down to 10^4 K, than the non-CR run, with diffuse material often receiving a majority of its pressure support from the CR proton fluid. We compare to recent observations of the CGM of L ~ L* galaxies at low redshift, including UV absorption lines within background quasar spectra. The combination of metal-enriched, CR-driven winds and large swaths of CR pressure-supported, cooler diffuse gas leads to a CGM that provides a better match to data from COS-Halos (for HI, SiIV, CIII and OVI) than the non-CR run. We also compare our models to recent, preliminary observations of diffuse gamma-ray emission in local group halos. For our lower CR-diffusion runs with kappa_CR in the range 0.3 to 1 x 10^28 cm^2/s, the CR enriched CGM produces an inconsistently high level of gamma emission. But the model with a relatively high kappa_CR = 3 x 10^28 cm^2/s provided a gamma-ray luminosity consistent with the extra-galactic gamma-ray background observed by FERMI and roughly consistent with preliminary measures of the emission from M31's CGM.

MASS TRANSPORT AND TURBULENCE IN GRAVITATIONALLY UNSTABLE DISK GALAXIES. I. THE CASE OF PURE SELF-GRAVITY

The role of gravitational instability-driven turbulence in determining the structure and evolution of disk galaxies, and the extent to which gravity rather than feedback can explain galaxy properties, remains an open question. To address it, we present high-resolution adaptive mesh refinement simulations of Milky Way-like isolated disk galaxies, including realistic heating and cooling rates and a physically motivated prescription for star formation, but no form of star formation feedback. After an initial transient, our galaxies reach a state of fully nonlinear gravitational instability. In this state, gravity drives turbulence and radial inflow. Despite the lack of feedback, the gas in our galaxy models shows substantial turbulent velocity dispersions, indicating that gravitational instability alone may be able to power the velocity dispersions observed in nearby disk galaxies on 100 pc scales. Moreover, the rate of mass transport produced by this turbulence approaches yr−1 for Milky Way-like conditions, sufficient to fully fuel star formation in the inner disks of galaxies. In a companion paper, we add feedback to our models, and use the comparison between the two cases to understand which galaxy properties depend sensitively on feedback and which can be understood as the product of gravity alone. All of the code, initial conditions, and simulation data for our model are publicly available.

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 dynamic 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 adaptive mesh refinement (AMR) simulations. Moreover, the notion of shear-improved models for in-homogeneous 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.

3D ADAPTIVE MESH REFINEMENT SIMULATIONS OF THE GAS CLOUD G2 BORN WITHIN THE DISKS OF YOUNG STARS IN THE GALACTIC CENTER

The dusty, ionized gas cloud G2 is currently passing the massive black hole in the Galactic Center at a distance of roughly 2400 Schwarzschild radii. We explore the possibility of a starting point of the cloud within the disks of young stars. We make use of the large amount of new observations in order to put constraints on G2's origin. Interpreting the observations as a diffuse cloud of gas, we employ three-dimensional hydrodynamical adaptive mesh refinement (AMR) simulations with the PLUTO code and do a detailed comparison with observational data. The simulations presented in this work update our previously obtained results in multiple ways: (1) high resolution three-dimensional hydrodynamical AMR simulations are used, (2) the cloud follows the updated orbit based on the Brackett-$\gamma$ data, (3) a detailed comparison to the observed high-quality position-velocity diagrams and the evolution of the total Brackett-$\gamma$ luminosity is done. We concentrate on two unsolved problems of the diffuse cloud scenario: the unphysical formation epoch only shortly before the first detection and the too steep Brackett-$\gamma$ light curve obtained in simulations, whereas the observations indicate a constant Brackett-$\gamma$ luminosity between 2004 and 2013. For a given atmosphere and cloud mass, we find a consistent model that can explain both, the observed Brackett-$\gamma$ light curve and the position-velocity diagrams of all epochs. Assuming initial pressure equilibrium with the atmosphere, this can be reached for a starting date earlier than roughly 1900, which is close to apo-center and well within the disks of young stars.

THE LAUNCHING OF COLD CLOUDS BY GALAXY OUTFLOWS. I. HYDRODYNAMIC INTERACTIONS WITH RADIATIVE COOLING

To better understand the nature of the multiphase material found in outflowing galaxies, we study the evolution of cold clouds embedded in flows of hot and fast material. Using a suite of adaptive-mesh refinement simulations that include radiative cooling, we investigate both cloud mass loss and cloud acceleration under the full range of conditions observed in galaxy outflows. The simulations are designed to track the cloud center of mass, enabling us to study the cloud evolution at long disruption times. For supersonic flows, a Mach cone forms around the cloud, which damps the Kelvin-Helmholtz instability but also establishes a streamwise pressure gradient that stretches the cloud apart. If time is expressed in units of the cloud crushing time, both the cloud lifetime and the cloud acceleration rate are independent of cloud radius, and we find simple scalings for these quantities as a function of the Mach number of the external medium. A resolution study suggests that our simulations have sufficient resolution to accurately describe the evolution of cold clouds in the absence of thermal conduction and magnetic fields, physical processes whose roles will be studied in forthcoming papers.

Supernova feedback in an inhomogeneous interstellar medium

Supernova (SN) feedback is one of the key processes shaping the interstellar medium (ISM) of galaxies. SNe contribute to (and in some cases may dominate) driving turbulence in the ISM and accelerating galactic winds. Modern cosmological simulations have sufficient resolution to capture the main structures in the ISM of galaxies, but are typically still not capable of explicitly resolving all of the small-scale stellar feedback processes, including the expansion of supernova remnants (SNRs). We perform a series of controlled three-dimensional hydrodynamic (adaptive mesh refinement) simulations of single SNRs expanding in an inhomogeneous density field with statistics motivated by those of the turbulent ISM. We use these to quantify the momentum and thermal energy injection from SNe as a function of spatial scale and the density, metallicity, and structure of the ambient medium. We develop a series of analytic formulae that we fit to the simulations. These formulae can be used as a basis for a more predictive sub-resolution model for SN feedback for galaxy formation simulations. We then use simulations of multiple, stochastically driven SNe that resolve the key phases of SNRs to test the sub-resolution model, and show that it accurately captures the turbulent kinetic energy and thermal energy in the ISM. By contrast, proposed SN feedback models in the literature based on `delayed cooling' significantly overpredict the late-time thermal energy and momentum in SNRs.

The effect of dark matter resolution on the collapse of baryons in high-redshift numerical simulations

We examine the impact of dark matter particle resolution on the formation of a baryonic core in high resolution adaptive mesh refinement simulations. We test the effect that both particle smoothing and particle splitting have on the hydrodynamic properties of a collapsing halo at high redshift (z > 20). Furthermore, we vary the background field intensity, with energy below the Lyman limit (< 13.6 eV), as may be relevant for the case of metal-free star formation and super-massive black hole seed formation. We find that using particle splitting methods greatly increases our particle resolution without introducing any numerical noise and allows us to achieve converged results over a wide range of external background fields. Additionally, we find that for lower values of the background field a lower dark matter particle mass is required. We define the radius of the core as the point at which the enclosed baryonic mass dominates over the enclosed dark matter mass. For our simulations this results in $\rm{R_{core} \sim 5\ pc}$. We find that in order to produce converged results which are not affected by dark matter particles requires that the relationship ${M_{\rm{core}} / M_{\rm{DM}}} > 100.0$ be satisfied, where ${M_{\rm{core}}}$ is the enclosed baryon mass within the core and $M_{\rm{DM}}$ is the minimum dark matter particle mass. This ratio should provide a very useful starting point for conducting convergence tests before any production run simulations. We find that dark matter particle smoothing is a useful adjunct to already highly resolved simulations.

Triggered star formation: Rotation, magnetic fields and outflows

Star formation can be triggered by compression from wind or supernova driven shock waves that sweep over molecular clouds. In a previous work we used Adaptive Mesh Refinement (AMR) simulation methods, including sink particles, to simulate the full collapse of a stable Bonnor–Ebert sphere subjected to a passing shock. We tracked the flow of cloud material after a star (a sink particle) had formed. For rotating clouds we observed the formation of disks which then interact with the post-shock flow. In this paper we take the next step forward in complexity, presenting first results of simulations that include a magnetized cloud. Our results show that after a disk is formed a collimated magneto-centrifugal outflow is launched. The outflow is bipolar but asymmetric, due to interactions with the shocked flow. We explore the influence of the outflows on the post-triggering collapse dynamics.

COSMOLOGICAL SIMULATIONS OF GALAXY FORMATION WITH COSMIC RAYS

We investigate the dynamical impact of cosmic rays in cosmological simulations of galaxy formation using adaptive-mesh refinement simulations of a $10^{12}$ solar mass halo. In agreement with previous work, a run with only our standard thermal energy feedback model results in a massive spheroid and unrealistically peaked rotation curves. However, the addition of a simple two-fluid model for cosmic rays drastically changes the morphology of the forming disk. We include an isotropic diffusive term and a source term tied to star formation due to (unresolved) supernova-driven shocks. Over a wide range of diffusion coefficients, the CRs generate thin, extended disks with a significantly more realistic (although still not flat) rotation curve. We find that the diffusion of CRs is key to this process, as they escape dense star forming clumps and drive outflows within the more diffuse ISM.

Massive black hole and gas dynamics in galaxy nuclei mergers – I. Numerical implementation

Numerical effects are known to plague adaptive mesh refinement (AMR) codes when treating massive particles, e.g. representing massive black holes (MBHs). In an evolving background, they can experience strong, spurious perturbations and then follow unphysical orbits. We study by means of numerical simulations the dynamical evolution of a pair MBHs in the rapidly and violently evolving gaseous and stellar background that follows a galaxy major merger. We confirm that spurious numerical effects alter the MBH orbits in AMR simulations, and show that numerical issues are ultimately due to a drop in the spatial resolution during the simulation, drastically reducing the accuracy in the gravitational force computation. We therefore propose a new refinement criterion suited for massive particles, able to solve in a fast and precise way for their orbits in highly dynamical backgrounds. The new refinement criterion we designed enforces the region around each massive particle to remain at the maximum resolution allowed, independently upon the local gas density. Such maximally-resolved regions then follow the MBHs along their orbits, and effectively avoids all spurious effects caused by resolution changes. Our suite of high resolution, adaptive mesh-refinement hydrodynamic simulations, including different prescriptions for the sub-grid gas physics, shows that the new refinement implementation has the advantage of not altering the physical evolution of the MBHs, accounting for all the non trivial physical processes taking place in violent dynamical scenarios, such as the final stages of a galaxy major merger.

Influence of adaptive mesh refinement and the hydro solver on shear-induced mass stripping in a minor-merger scenario

We compare two different codes for simulations of cosmological structure formation to investigate the sensitivity of hydrodynamical instabilities to numerics, in particular, the hydro solver and the application of adaptive mesh refinement (AMR). As a simple test problem, we consider an initially spherical gas cloud in a wind, which is an idealized model for the merger of a subcluster or galaxy with a big cluster. Based on an entropy criterion, we calculate the mass stripping from the subcluster as a function of time. Moreover, the turbulent velocity field is analyzed with a multi-scale filtering technique. We find remarkable differences between the commonly used PPM solver with directional splitting in the Enzo code and an unsplit variant of PPM in the Nyx code, which demonstrates that different codes can converge to systematically different solutions even when using uniform grids. For the test case of an unbound cloud, AMR simulations reproduce uniform-grid results for the mass stripping quite well, although the flow realizations can differ substantially. If the cloud is bound by a static gravitational potential, however, we find strong sensitivity to spurious fluctuations which are induced at the cutoff radius of the potential and amplified by the bow shock. This gives rise to substantial deviations between uniform-grid and AMR runs performed with Enzo, while the mass stripping in Nyx simulations of the subcluster is nearly independent of numerical resolution and AMR. Although many factors related to numerics are involved, our study indicates that unsplit solvers with advanced flux limiters help to reduce grid effects and to keep numerical noise under control, which is important for hydrodynamical instabilities and turbulent flows.

Effects of turbulence and rotation on protostar formation as a precursor of massive black holes

Context. The seeds of the first supermassive black holes may have resulted from the direct collapse of hot primordial gas in $\gtrsim 10^4$ K haloes, forming a supermassive or quasistar as an intermediate stage. Aims. We explore the formation of a protostar resulting from the collapse of primordial gas in the presence of a strong Lyman-Werner radiation background. Particularly, we investigate the impact of turbulence and rotation on the fragmentation behaviour of the gas cloud. We accomplish this goal by varying the initial turbulent and rotational velocities. Methods. We performed 3D adaptive mesh refinement simulations with a resolution of 64 cells per Jeans length using the ENZO code, simulating the formation of a protostar up to unprecedentedly high central densities of $10^{21}$ cm$^{-3}$, and spatial scales of a few solar radii. To achieve this goal, we employed the KROME package to improve modelling of the chemical and thermal processes. Results. We find that the physical properties of the simulated gas clouds become similar on small scales, irrespective of the initial amount of turbulence and rotation. After the highest level of refinement was reached, the simulations have been evolved for an additional ~5 freefall times. A single bound clump with a radius of $2 \times 10^{-2}$ AU and a mass of ~$7 \times 10^{-2}$ M$_{\odot}$ is formed at the end of each simulation, marking the onset of protostar formation. No strong fragmentation is observed by the end of the simulations, regardless of the initial amount of turbulence or rotation, and high accretion rates of a few solar masses per year are found. Conclusions. Given such high accretion rates, a quasistar of $10^5$ M$_{\odot}$ is expected to form within $10^5$ years.

The 2.35 year itch of Cygnus OB2 #9

X-ray and radio data recently acquired as part of a project to study Cyg OB2#9 are used to constrain physical models of the binary system, providing in-depth knowledge about the wind-wind collision and the thermal, and non-thermal, emission arising from the shocks. We use a three-dimensional, adaptive mesh refinement simulation (including wind acceleration, radiative cooling, and the orbital motion of the stars) to model the gas dynamics of the wind-wind collision. The simulation output is used as the basis for radiative transfer calculations considering the thermal X-ray emission and the thermal/non-thermal radio emission. To obtain good agreement with the X-ray observations, our initial mass-loss rate estimates require a down-shift by a factor of roughly 7.7 to $6.5\times10^{-7}$ and $7.5\times10^{-7}$ solar mass per year for the primary and secondary star, respectively. Furthermore, the low gas densities and high shock velocities in Cyg OB2#9 are suggestive of unequal electron and ion temperatures, and the X-ray analysis indicates that an (immediately post-shock) electron-ion temperature ratio of $\simeq 0.1$ is also required. The radio emission is dominated by (non-thermal) synchrotron emission. A parameter space exploration provides evidence against models assuming equipartition between magnetic and relativistic energy densities. However, fits of comparable quality can be attained with models having stark contrasts in the ratio of magnetic-to-relativistic energy densities. The radio models also reveal a subtle effect whereby inverse Compton cooling leads to an increase in emissivity as a result of the synchrotron characteristic frequency being significantly reduced. Finally, using the results of the radio analysis, we estimate the surface magnetic field strengths to be $\approx 0.3-52\;$G. (Abridged)

Chemodynamics of a simulated disc galaxy: initial mass functions and Type Ia supernova progenitors

We trace the formation and advection of several elements within a cosmological adaptive mesh refinement simulation of an L* galaxy. We use nine realisations of the same initial conditions with different stellar Initial Mass Functions (IMFs), mass limits for type-II and type-Ia supernovae (SNII, SNIa) and stellar lifetimes to constrain these sub-grid phenomena. Our code includes self-gravity, hydrodynamics, star formation, radiative cooling and feedback from multiple sources within a cosmological framework. Under our assumptions of nucleosynthesis we find that SNII with progenitor masses of up to 100 Msun are required to match low metallicity gas oxygen abundances. Tardy SNIa are necessary to reproduce the classical chemical evolution knee in [O/Fe]-[Fe/H]: more prompt SNIa delayed time distributions do not reproduce this feature. Within our framework of hydrodynamical mixing of metals and galaxy mergers we find that chemical evolution is sensitive to the shape of the IMF and that there exists a degeneracy with the mass range of SNII. We look at the abundance plane and present the properties of different regions of the plot, noting the distinct chemical properties of satellites and a series of nested discs that have greater velocity dispersions, are more alpha-rich and metal poor with age.

Triggered star formation and its consequences

Star formation can be triggered by compression from wind or supernova-driven shock waves that sweep over molecular clouds. Because these shocks will likely contain processed elements, triggered star formation has been proposed as an explanation for short-lived radioactive isotopes (SLRIs) in the Solar system. Previous studies have tracked the triggering event to the earliest phases of collapse and have focused on the shock properties required for both successful star formation and mixing of SLRIs. In this paper, we use adaptive mesh refinement simulation methods, including sink particles, to simulate the full collapse and subsequent evolution of a stable Bonnor– Ebert sphere subjected to a shock and post-shock wind. We track the flow of the cloud material after a star (a sink particle) has formed. For non-rotating clouds, we find robust triggered collapse and little bound circumstellar material remaining around the post-shock collapsed core. When we add initial cloud rotation, we observe the formation of discs around the collapsed core which then interact with the post-shock flow. Our results indicate that these circumstellar discs are massive enough to form planets and are long lived, in spite of the ablation driven by post-shock-flow ram pressure. As a function of the initial conditions, we also track the time evolution of the accretion rates and particle mixing between the ambient wind and cloud material. The latter is maximized for cases of highest Mach number.

ON THE ROLE OF AMBIENT ENVIRONMENTS IN THE COLLAPSE OF BONNOR-EBERT SPHERES

We consider the interaction between a marginally stable Bonnor-Ebert (BE) sphere and the surrounding ambient medium. In particular, we explore how the infall from an evolving ambient medium can trigger collapse of the sphere using 3-D adaptive mesh refinement simulations. We find the resulting collapse dynamics to vary considerably with ambient density. In the highest ambient density cases, infalling material drives a strong compression wave into the cloud. It is the propagation of this wave through the cloud interior that triggers the subsequent collapse. For lower ambient densities, we find the main trigger of collapse to be a quasistatic adjustment of the BE sphere to gravitational settling of the ambient gas. In all cases, we find that the classic "outside-in" collapse mode for super-critical BE spheres is recovered before a protostar (i.e. sink particle) forms. Our work supports scenarios in which BE dynamics naturally begins with either a compression-wave or infall dominated phase, and only later assumes the usual outside-in collapse behavior.

A STELLAR WIND ORIGIN FOR THE G2 CLOUD: THREE-DIMENSIONAL NUMERICAL SIMULATIONS

We present 3D, adaptive mesh refinement simulations of G2, a cloud of gas moving in a highly eccentric orbit towards the galactic center. We assume that G2 originates from a stellar wind interacting with the environment of the Sgr A* black hole. The stellar wind forms a cometary bubble which becomes increasingly elongated as the star approaches periastron. A few months after periastron passage, streams of material begin to accrete on the central black hole with accretion rates $\dot{M} \sim 10^{-8}$ M$_\odot$ yr$^{-1}$. Predicted Br$\gamma$ emission maps and position-velocity diagrams show an elongated emission resembling recent observations of G2. A large increase in luminosity is predicted by the emission coming from the shocked wind region during periastron passage. The observations, showing a constant Br$\gamma$ luminosity, remain puzzling, and are explained here assuming that the emission is dominated by the free-wind region. The observed Br$\gamma$ luminosity ($\sim 8 \times 10^{30}$ erg s$^{-1}$) is reproduced by a model with a $v_w=50$ km s$^{-1}$ wind velocity and a $10^{-7}$ M$_\odot$ yr$^{-1}$ mass loss rate if the emission comes from the shocked wind. A faster and less dense wind reproduces the Br$\gamma$ luminosity if the emission comes from the inner, free wind region. The extended cometary wind bubble, largely destroyed by the tidal interaction with the black hole, reforms a few years after periastron passage. As a result, the Br$\gamma$ emission is more compact after periastron passage.