Adaptive Mesh Refinement Simulations Research Articles

Convergence of SPH and AMR simulations

AbstractWe present the first results of a large suite of convergence tests between Adaptive Mesh Refinement (AMR) Finite Difference Hydrodynamics and Smoothed Particle Hydrodynamics (SPH) simulations of the non-linear thin shell instability and the Kelvin-Helmholtz instability. We find that the two methods converge in the limit of high resolution and accuracy. AMR and SPH simulations of the non-linear thin shell instability converge with each other with standard algorithms and parameters. The Kelvin-Helmholtz instability in SPH requires both an artificial conductivity term and a kernel with larger compact support and more neighbours (e.g. the quintic kernel) in order converge with AMR. For purely hydrodynamical problems, SPH simulations take an order of magnitude longer than the grid code when converged.

Cosmological simulations of low-mass galaxies: some potential issues

AbstractCosmological Adaptive Mesh Refinement simulations are used to study the specific star formation rate (sSFR=SSF/Ms) history and the stellar mass fraction, fs=Ms/MT, of small galaxies, total masses MT between few × 1010 M⊙ to few ×1011 M⊙. Our results are compared with recent observational inferences that show the so-called “downsizing in sSFR” phenomenon: the less massive the galaxy, the higher on average is its sSFR, a trend seen at least since z ~ 1. The simulations are not able to reproduce this phenomenon, in particular the high inferred values of sSFR, as well as the low values of fs constrained from observations. The effects of resolution and sub-grid physics on the SFR and fs of galaxies are discussed.

Supermassive black hole formation by direct collapse: keeping protogalactic gas H2free in dark matter haloes with virial temperaturesTvir>rsim 104K

In the absence of H_2 molecules, the primordial gas in early dark matter halos with virial temperatures just above T_vir >~ 10^4 K cools by collisional excitation of atomic H. Although it cools efficiently, this gas remains relatively hot, at a temperature near T ~ 8000 K, and consequently might be able to avoid fragmentation and collapse directly into a supermassive black hole (SMBH). In order for H_2--formation and cooling to be strongly suppressed, the gas must be irradiated by a sufficiently intense ultraviolet (UV) flux. We performed a suite of three--dimensional hydrodynamical adaptive mesh refinement (AMR) simulations of gas collapse in three different protogalactic halos with T_vir >~ 10^4 K, irradiated by a UV flux with various intensities and spectra. We determined the critical specific intensity, Jcrit, required to suppress H_2 cooling in each of the three halos. For a hard spectrum representative of metal--free stars, we find (in units of 10^{-21} erg s^{-1} Hz^{-1} sr^{-1} cm^{-2}) 10^4<Jcrit<10^5, while for a softer spectrum, which is characteristic of a normal stellar population, and for which H^{-} --dissociation is important, we find 30<Jcrit<300. These values are a factor of 3--10 lower than previous estimates. We attribute the difference to the higher, more accurate H_2 collisional dissociation rate we adopted. The reduction in Jcrit exponentially increases the number of rare halos exposed to super--critical radiation. When H_2 cooling is suppressed, gas collapse starts with a delay, but it ultimately proceeds more rapidly. The infall velocity is near the increased sound speed, and an object as massive as M ~ 10^5 solar mass may form at the center of these halos, compared to the M ~ 10^2 solar mass stars forming when H_2--cooling is efficient.

Two-dimensional adaptive mesh refinement simulations of colliding flows

Colliding flows are a commonly used scenario for the formation of molecular clouds in numerical simulations. Due to the thermal instability of the warm neutral medium, turbulence is produced by cooling. We carry out a two-dimensional numerical study of such colliding flows in order to test whether statistical properties inferred from adaptive mesh refinement (AMR) simulations are robust with respect to the applied refinement criteria. We compare probability density functions of various quantities as well as the clump statistics and fractal dimension of the density fields in AMR simulations to a static-grid simulation. The static grid with 2048^2 cells matches the resolution of the most refined subgrids in the AMR simulations. The density statistics is reproduced fairly well by AMR. Refinement criteria based on the cooling time or the turbulence intensity appear to be superior to the standard technique of refinement by overdensity. Nevertheless, substantial differences in the flow structure become apparent. In general, it is difficult to separate numerical effects from genuine physical processes in AMR simulations.

Disc formation and the origin of clumpy galaxies at high redshift

Abstract Observations of high-redshift galaxies have revealed a multitude of large clumpy rapidly star-forming galaxies. Their formation scenario and their link to present-day spirals are still unknown. In this Letter, we perform adaptive mesh refinement simulations of disc formation in a cosmological context that are unrivalled in terms of mass and spatial resolution. We find that the so-called ‘chain-galaxies’ and ‘clump-clusters’ are a natural outcome of early epochs of enhanced gas accretion from cold dense streams as well as tidally and ram-pressured stripped material from minor mergers and satellites. Through interaction with the hot halo gas, this freshly accreted cold gas settles into a large disc-like system, not necessarily aligned to an older stellar component, that undergoes fragmentation and subsequent star formation, forming large clumps in the mass range 107–109 M⊙. Galaxy formation is a complex process at this important epoch when most of the central baryons are being acquired through a range of different mechanisms – we highlight that a rapid mass loading epoch is required to fuel the fragmentation taking place in the massive arms in the outskirts of extended discs, an accretion mode that occurs naturally in the hierarchical assembly process at early epochs.

THE DISTRIBUTION OF Li-LIKE IONS IN THE LOCAL BUBBLE

We study, by means of three-dimensional adaptive mesh refinement simulations, the spatial distribution of the Li-like ions C IV, N V, and O VI inside the Local Bubble (LB), powered by 19 missing stars of subgroup B1 of the Pleiades suggested as responsible for its origin. The ions C IV, N V, and O VI, and the distribution of their column density ratios (N(C IV)/N(O VI) and N(N V)/N(O VI)) in the simulations are monitored through lines of sight (with lengths as large as 150 pc) emanating from the Solar position. The main results are: (i) there is a weak distribution of C IV and N V in the regions where O VI is strong, (ii) there is a small amount of C IV and N V ions inside the bubble translating into upper limits of –1.0 of the ratios log[N(C IV)/N(O VI)] and log[N(N V)/N(O VI)], consistent with observations, and (iii) with the lack of heat conduction, turbulent mixing, due to the strong shear between the hotter and cooler regions inside the LB, is responsible for the generation and distribution of these ions.

MAGNETOHYDRODYNAMIC SIMULATIONS OF DISK GALAXY FORMATION: THE MAGNETIZATION OF THE COLD AND WARM MEDIUM

We modeled the formation and early evolution of disk galaxies with a magnetized interstellar medium using magnetohydrodynamic (MHD) adaptive mesh refinement simulations. For a 1010 M☉ halo with initial Navarro–Frenk–White dark matter and gas profiles, we impose a uniform 10−9 G magnetic field and follow its collapse, disk formation and evolution up to 1 Gyr. We find that the initial magnetic fields are quickly amplified by the differentially rotating turbulent disk with the amplification rate roughly one e-folding per orbit. After the initial rapid amplification lasting ∼500 Myr, subsequent field amplification appears self-regulated. The field strengths in the self-regulated regime have similar strength as the observed fields in the Milky Way galaxy both in the warm and the cold H i phases. Since supernova explosions, which we neglected in our current model, are likely to further amplify the magnetic field, our calculation suggests that Milky Way strength magnetic field might be common in high redshift disk galaxies. After saturation, highly magnetized material also begins to form above and below the disk, which may affect subsequent galaxy evolution, especially mergers, significantly. The global azimuthal magnetic fields reverse at different radii and the amplitude declines as a function of radius of the disk. We also find that magnetic force can provide further support in the cold gas and lead to a decline of the amount of cold gas at high density which may lead to a decline in the star formation rate.

GALAXY MERGERS WITH ADAPTIVE MESH REFINEMENT: STAR FORMATION AND HOT GAS OUTFLOW

In hierarchical structure formation, merging of galaxies is frequent and known to dramatically affect their properties. To comprehend these interactions high-resolution simulations are indispensable because of the nonlinear coupling between pc and Mpc scales. To this end, we present the first adaptive mesh refinement (AMR) simulation of two merging, low mass, initially gas-rich galaxies (1.8e10 Ms each), including star formation and feedback. With galaxies resolved by ~2e7 total computational elements, we achieve unprecedented resolution of the multiphase interstellar medium, finding a widespread starburst in the merging galaxies via shock-induced star formation. The high dynamic range of AMR also allows us to follow the interplay between the galaxies and their embedding medium depicting how galactic outflows and a hot metal-rich halo form. These results demonstrate that AMR provides a powerful tool in understanding interacting galaxies.

THE SHAPES OF MOLECULAR CLOUD CORES IN SIMULATIONS AND OBSERVATIONS

In this study, we investigate the shapes of starless and protostellar cores using hydrodynamic, self-gravitating adaptive mesh refinement simulations of turbulent molecular clouds. We simulate observations of these cores in dust emission, including realistic noise and telescope resolution, and compare to the observed core shapes measured in Orion by Nutter & Ward-Thompson (2007). The simulations and the observations have generally high statistical similarity, with particularly good agreement between simulations and Orion B. Although protostellar cores tend to have semi-major axis to semi-minor axis ratios closer to one, the distribution of axis ratios for starless and protostellar cores are not significantly different for either the actual observations of Orion or the simulated observations. Because of the high level of agreement between the non-magnetic hydrodynamic simulations and observation, contrary to a number of previous authors, one cannot infer the presence of magnetic fields from core shape distributions.

Cosmological Shocks in Adaptive Mesh Refinement Simulations and the Acceleration of Cosmic Rays

We present new results characterizing cosmological shocks within adaptive mesh refinement N-body/hydrodynamic simulations that are used to predict nonthermal components of large-scale structure. This represents the first study of shocks using adaptive mesh refinement. We propose a modified algorithm for finding shocks from those used on unigrid simulations that reduces the shock frequency of low Mach number shocks by a factor of ~3. We then apply our new technique to a large, (512 h−1 Mpc)3, cosmological volume and study the shock Mach number () distribution as a function of preshock temperature, density, and redshift. Because of the large volume of the simulation, we have superb statistics that result from having thousands of galaxy clusters. We find that the Mach number evolution can be interpreted as a method to visualize large-scale structure formation. Shocks with 20 generally follow accretion onto filaments and galaxy clusters, respectively. By applying results from nonlinear diffusive shock acceleration models using the first-order Fermi process, we calculate the amount of kinetic energy that is converted into cosmic-ray protons. The acceleration of cosmic-ray protons is large enough that in order to use galaxy clusters as cosmological probes, the dynamic response of the gas to the cosmic rays must be included in future numerical simulations.

Resolving the Formation of Protogalaxies. III. Feedback from the First Stars

The first stars form in dark matter halos of masses ~106 -->M? as suggested by an increasing number of numerical simulations. Radiation feedback from these stars expels most of the gas from the shallow potential well of their surrounding dark matter halos. We use cosmological adaptive mesh refinement simulations that include self-consistent Population III star formation and feedback to examine the properties of assembling early dwarf galaxies. Accurate radiative transport is modeled with adaptive ray tracing. We include supernova explosions and follow the metal enrichment of the intergalactic medium. The calculations focus on the formation of several dwarf galaxies and their progenitors. In these halos, baryon fractions in 108 -->M? halos decrease by a factor of 2 with stellar feedback and by a factor of 3 with supernova explosions. We find that radiation feedback and supernova explosions increase gaseous spin parameters up to a factor of 4 and vary with time. Stellar feedback, supernova explosions, and H2 cooling create a complex, multiphase interstellar medium whose densities and temperatures can span up to 6 orders of magnitude at a given radius. The pair-instability supernovae of Population III stars alone enrich the halos with virial temperatures of 104 K to approximately 10?3 of solar metallicity. We find that 40% of the heavy elements resides in the intergalactic medium (IGM) at the end of our calculations. The highest metallicity gas exists in supernova remnants and very dilute regions of the IGM.

The Impact of HD Cooling on the Formation of the First Stars

We use numerical simulations to investigate the importance of HD formation and cooling on the first generation of metal-free stars in a LCDM cosmology. We have implemented and tested non-equilibrium HD chemistry in an adaptive mesh refinement simulation code and applied it to two situations. (1) It is first applied to the formation of 10^5 - 10^6 Msun halos which form in the absence of any ionizing source. We show, in agreement with previous work, that HD cooling is of only marginal importance for most halos; however, we find that for the lowest mass halos, HD cooling can equal or surpass the H2 cooling rate. This leads to a population of stars formed in halos with effective HD cooling that are less massive by a factor of ~6 compared to halos dominated by H2 cooling. (2) In the second part of the paper, we ionize the halos in order to explore the impact of HD cooling in the presence of an ample population of free electrons. This leads to cooler temperatures (due to the electron- catalyzed production of H2) and somewhat lower resulting proto-stellar mass. Adding HD chemistry lowers the temperature further, to the level of the CMB. We find that HD cooling dominates over H2 cooling in the density range 10^2 cm^-3 to 10^6 cm^-3, but above this density, the temperature rises and H2 cooling dominates again. Because of this, the accretion rate on to the protostar is almost the same as in the H2 case (at least for accreted masses below 50-100 Msun), therefore we argue that HD cooling in ionized halos will probably not result in a population of significantly lower mass stars.

Resolving the Formation of Protogalaxies. II. Central Gravitational Collapse

Numerous cosmological hydrodynamic studies have addressed the formation of galaxies. Here we choose to study the first stages of galaxy formation, including nonequilibrium atomic primordial gas cooling, gravity, and hydrodynamics. Using initial conditions appropriate for the concordance cosmological model of structure formation, we perform two adaptive mesh refinement simulations of ~108 M☉ galaxies at high redshift. The calculations resolve the Jeans length at all times with more than 16 cells and capture over 14 orders of magnitude in length scales. In both cases, the dense, 105 solar mass, one parsec central regions are found to contract rapidly and have turbulent Mach numbers up to 4. Despite the ever decreasing Jeans length of the isothermal gas, we only find one site of fragmentation during the collapse. However, rotational secular bar instabilities transport angular momentum outward in the central parsec as the gas continues to collapse and lead to multiple nested unstable fragments with decreasing masses down to sub-Jupiter mass scales. Although these numerical experiments neglect star formation and feedback, they clearly highlight the physics of turbulence in gravitationally collapsing gas. The angular momentum segregation seen in our calculations plays an important role in theories that form supermassive black holes from gaseous collapse.

Hydrodynamical adaptive mesh refinement simulations of turbulent flows - I. Substructure in a wind

The problem of the resolution of turbulent flows in adaptive mesh refinement (AMR) simulations is investigated by means of 3D hydrodynamical simulations in an idealised setup, representing a moving subcluster during a merger event. AMR simulations performed with the usual refinement criteria based on local gradients of selected variables do not properly resolve the production of turbulence downstream of the cluster. Therefore we apply novel AMR criteria which are optimised to follow the evolution of a turbulent flow. We demonstrate that these criteria provide a better resolution of the flow past the subcluster, allowing us to follow the onset of the shear instability, the evolution of the turbulent wake and the subsequent back-reaction on the subcluster core morphology. We discuss some implications for the modelling of cluster cold fronts.

THE KINEMATICS OF MOLECULAR CLOUD CORES IN THE PRESENCE OF DRIVEN AND DECAYING TURBULENCE: COMPARISONS WITH OBSERVATIONS

In this study we investigate the formation and properties of prestellar and protostellar cores using hydrodynamic, self-gravitating Adaptive Mesh Refinement simulations, comparing the cases where turbulence is continually driven and where it is allowed to decay. We model observations of these cores in the C$^{18}$O$(2\to 1)$, NH$_3(1,1)$, and N$_2$H$^+(1\to 0)$ lines, and from the simulated observations we measure the linewidths of individual cores, the linewidths of the surrounding gas, and the motions of the cores relative to one another. Some of these distributions are significantly different in the driven and decaying runs, making them potential diagnostics for determining whether the turbulence in observed star-forming clouds is driven or decaying. Comparing our simulations with observed cores in the Perseus and $\rho$ Ophiuchus clouds shows reasonably good agreement between the observed and simulated core-to-core velocity dispersions for both the driven and decaying cases. However, we find that the linewidths through protostellar cores in both simulations are too large compared to the observations. The disagreement is noticably worse for the decaying simulation, in which cores show highly supersonic infall signatures in their centers that decrease toward their edges, a pattern not seen in the observed regions. This result gives some support to the use of driven turbulence for modeling regions of star formation, but reaching a firm conclusion on the relative merits of driven or decaying turbulence will require more complete data on a larger sample of clouds as well as simulations that include magnetic fields, outflows, and thermal feedback from the protostars.

A Comparison of Two Shallow-Water Models with Nonconforming Adaptive Grids

Abstract In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models, an interpolation-based spectral element shallow-water model on a cubed-sphere grid is compared to a block-structured finite-volume method in latitude–longitude geometry. Both models utilize a nonconforming adaptation approach that doubles the resolution at fine–coarse mesh interfaces. The underlying AMR libraries are quad-tree based and ensure that neighboring regions can only differ by one refinement level. The models are compared via selected test cases from a standard test suite for the shallow-water equations, and via a barotropic instability test. These tests comprise the passive advection of a cosine bell and slotted cylinder, a steady-state geostrophic flow, a flow over an idealized mountain, a Rossby–Haurwitz wave, and the evolution of a growing barotropic wave. Both static and dynamics adaptations are evaluated, which reveal the strengths and weaknesses of the AMR techniques. Overall, the AMR simulations show that both models successfully place static and dynamic adaptations in local regions without requiring a fine grid in the global domain. The adaptive grids reliably track features of interests without visible distortions or noise at mesh interfaces. Simple threshold adaptation criteria for the geopotential height and the relative vorticity are assessed.

Interface reconstruction in two- and three-dimensional arbitrary Lagrangian-Eulerian adaptive mesh refinement simulations

Modeling of high power laser and ignition facilities requires new techniques because of the higher energies and higher operational costs. We report on the development and application of a new interface reconstruction algorithm for chamber modeling code that combines ALE (Arbitrary Lagrangian Eulerian) techniques with AMR (Adaptive Mesh Refinement). The code is used for the simulation of complex target elements in the National Ignition Facility (NIF) and other similar facilities. The interface reconstruction scheme is required to adequately describe the debris/shrapnel (including fragments or droplets) resulting from energized materials that could affect optics or diagnostic sensors. Traditional ICF modeling codes that choose to implement ALE + AMR techniques will also benefit from this new scheme. The ALE formulation requires material interfaces (including those of generated particles or droplets) to be tracked. We present the interface reconstruction scheme developed for NIF's ALE-AMR and discuss how it is affected by adaptive mesh refinement and the ALE mesh. Results of the code are shown for NIF and OMEGA target configurations.

Why Do Only Some Galaxy Clusters Have Cool Cores?

Flux-limited X-ray samples indicate that about half of rich galaxy clusters have cool cores. Why do only some clusters have cool cores while others do not? In this paper, cosmological N-body + Eulerian hydrodynamic simulations, including radiative cooling and heating, are used to address this question as we examine the formation and evolution of cool core (CC) and noncool core (NCC) clusters. These adaptive mesh refinement simulations produce both CC and NCC clusters in the same volume. They have a peak resolution of 15.6 h−1 kpc within a (256 h−1 Mpc)3 box. Our simulations suggest that there are important evolutionary differences between CC clusters and their NCC counterparts. Many of the numerical CC clusters accreted mass more slowly over time and grew enhanced CCs via hierarchical mergers; when late major mergers occurred, the CCs survived the collisions. By contrast, NCC clusters experienced major mergers early in their evolution that destroyed embryonic CCs and produced conditions that prevented CC reformation. As a result, our simulations predict observationally testable distinctions in the properties of CC and NCC beyond the core regions in clusters. In particular, we find differences between CC versus NCC clusters in the shapes of X-ray surface brightness profiles, between the temperatures and hardness ratios beyond the cores, between the distribution of masses, and between their supercluster environs. It also appears that CC clusters are no closer to hydrostatic equilibrium than NCC clusters, an issue important for precision cosmology measurements.

Suppression of H2Cooling in the Ultraviolet Background

The first luminous objects in the concordance cosmology form by molecular hydrogen cooling in dark matter dominated halos of masses ~106 M☉. We use Eulerian adaptive mesh refinement simulations to demonstrate that in the presence of a large soft ultraviolet radiation background, molecular hydrogen is the dominant coolant. Even for very large radiation backgrounds, the halo masses that cool and collapse are up to 2 orders of magnitude smaller than the halos that cool via atomic hydrogen line cooling. The abundance of cooling halos and the cosmic mass fraction contained within them depends exponentially on this critical mass scale. Consequently, the majority of current models of cosmological reionization, chemical evolution, supermassive black hole formation, and galaxy formation underestimate the number of star-forming progenitors of a given system by orders of magnitude. At the highest redshifts, this disagreement is largest. We also show that even in the absence of residual electrons, collisional ionization in central shocks create a sufficient amount of electrons to form molecular hydrogen and cool the gas in halos of virial temperatures far below the atomic cooling limit.

Resolving the Formation of Protogalaxies. I. Virialization

Galaxies form in hierarchically assembling dark matter halos. With cosmological three dimensional adaptive mesh refinement simulations, we explore in detail the virialization of baryons in the concordance cosmology, including optically thin primordial gas cooling. We focus on early protogalaxies with virial temperatures of 10 4 K and their progenitors. Without cooling, virial heating occurs in shocks close to the virial radius for material falling in from voids. Material in dense filaments penetrates deeper to about half that radius. With cooling the virial shock position shrinks and also the filaments reach scales as small as a third the virial radius. The temperatures in protogalaxies found in adiabatic simulations decrease by a factor of two from the center and show flat entropy cores. In cooling halos the gas reaches virial equilibrium with the dark matter potential through its turbulent velocities. We observe turbulent Mach numbers ranging from one to three in the cooling cases. This turbulence is driven by the large scale merging and interestingly remains supersonic in the centers of these early galaxies even in the absence of any feedback processes. The virial theorem is shown to approximately hold over 3 orders of magnitude in length scale with the turbulent pressure prevailing over the thermal energy. The turbulent velocity distributions are Maxwellian and by far dominate the small rotation velocities associated with the total angular momentum of the galaxies. Decomposing the velocity field using the Cauchy-Stokes theorem, we show that ample amounts of vorticity are present around shocks even at the very centers of these objects. In the cold flow regime of galaxy formation for halo masses below 10 12 M⊙, this dominant role of virialization driven turbulence should play an important role in for star formation as well as the build up of early magnetic fields. Subject headings: Cosmology: high-redshift—galaxy formation—star formation