Cosmological Code Research Articles

COSMOLOGICAL ADAPTIVE MESH REFINEMENT MAGNETOHYDRODYNAMICS WITH ENZO

In this work, we present MHDEnzo, the extension of the cosmological code Enzo to include the effects magnetic fields through the ideal MHD approximation. We use a higher order Godunov Riemann solver for the computation of interface fluxes. We use two constrained transport methods to compute the electric field from those interface fluxes, which simultaneously advances the induction equation and maintains the divergence of the magnetic field. A third order divergence free reconstruction technique is used to interpolate the magnetic fields in the block structured AMR framework already extant in Enzo. This reconstruction also preserves the divergence of the magnetic field to machine precision. We use operator splitting to include gravity and cosmological expansion. We then present a series of cosmological and non cosmological tests problems to demonstrate the quality of solution resulting from this combination of solvers.

ADAPTIVELY REFINED LARGE EDDY SIMULATIONS OF A GALAXY CLUSTER: TURBULENCE MODELING AND THE PHYSICS OF THE INTRACLUSTER MEDIUM

We present a numerical scheme for modelling unresolved turbulence in cosmological adaptive mesh refinement codes. As a first application, we study the evolution of turbulence in the intra-cluster medium and in the core of a galaxy cluster. Simulations with and without subgrid scale model are compared in detail. Since the flow in the ICM is subsonic, the global turbulent energy contribution at the unresolved length scales is smaller than 1% of the internal energy. We find that the production of turbulence is closely correlated with merger events occurring in the cluster environment, and its dissipation locally affects the cluster energy budget. Because of this additional source of dissipation, the core temperature is larger and the density is smaller in the presence of subgrid scale turbulence than in the standard adiabatic run, resulting in a higher entropy core value.

An MHD gadget for cosmological simulations

Various radio observations have showed that the hot atmospheres of galaxy clusters are magnetized. However, our understanding of the origin of these magnetic fields, their implications on structure formation and their interplay with the dynamics of the cluster atmosphere, especially in the centers of galaxy clusters is still very limited. In preparation to the upcoming new generation of radio telescopes (like EVLA, LWA, LOFAR and SKA), a huge effort is being made to learn more about cosmological magnetic fields from the observational perspective. Here we present the implementation of magneto hydrodynamics in the cosmological SPH code GADGET. We discuss the details of the implementation and various schemes to suppress numerical instabilities as well as regularization schemes, in the context of cosmological simulations. The performance of the SPH MHD code is demonstrated in various one and two dimensional test problems, which we performed if a fully, three dimensional setup to test the code under realistic circumstances. Comparing with solutions obtained with ATHENA, we find excellent agreement with our SPH MHD implementation. Finally we apply our SPH MHD implementation to forming galaxy clusters within a large, cosmological box. Performing a resolution study we demonstrate the robustness of the predicted shape of the magnetic field profiles in galaxy clusters, which is in good agreement with previous studies.

The Adaptive TreePM: an adaptive resolution code for cosmologicalN-body simulations

Cosmological N-Body simulations are used for a variety of applications. Indeed progress in the study of large scale structures and galaxy formation would have been very limited without this tool. For nearly twenty years the limitations imposed by computing power forced simulators to ignore some of the basic requirements for modeling gravitational instability. One of the limitations of most cosmological codes has been the use of a force softening length that is much smaller than the typical inter-particle separation. This leads to departures from collisionless evolution that is desired in these simulations. We propose a particle based method with an adaptive resolution where the force softening length is reduced in high density regions while ensuring that it remains well above the local inter-particle separation. The method, called the Adaptive TreePM, is based on the TreePM code. We present the mathematical model and an implementation of this code, and demonstrate that the results converge over a range of options for parameters introduced in generalizing the code from the TreePM code. We explicitly demonstrate collisionless evolution in collapse of an oblique plane wave. We compare the code with the fixed resolution TreePM code and also an implementation that mimics adaptive mesh refinement methods and comment on the agreement, and disagreements in the results. We find that in most respects the ATreePM code performs at least as well as the fixed resolution TreePM in highly over-dense regions, from clustering and number density of haloes, to internal dynamics of haloes. We also show that the adaptive code is faster than the corresponding high resolution TreePM code.

Hybrid petacomputing meets cosmology: The Roadrunner Universe project

The target of the Roadrunner Universe project at Los Alamos National Laboratory is a set of very large cosmological N-body simulation runs on the hybrid supercomputer Roadrunner, the world's first petaflop platform. Roadrunner's architecture presents opportunities and difficulties characteristic of next-generation supercomputing. We describe a new code designed to optimize performance and scalability by explicitly matching the underlying algorithms to the machine architecture, and by using the physics of the problem as an essential aid in this process. While applications will differ in specific exploits, we believe that such a design process will become increasingly important in the future. The Roadrunner Universe project code, MC3 (Mesh-based Cosmology Code on the Cell), uses grid and direct particle methods to balance the capabilities of Roadrunner's conventional (Opteron) and accelerator (Cell BE) layers. Mirrored particle caches and spectral techniques are used to overcome communication bandwidth limitations and possible difficulties with complicated particle-grid interaction templates.

An implementation of radiative transfer in the cosmological simulation code gadget

We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code {\small GADGET}. It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the `OTVET'-suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionisation and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump, and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying reionisation, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the reionisation process of the Universe.

RICO: A NEW APPROACH FOR FAST AND ACCURATE REPRESENTATION OF THE COSMOLOGICAL RECOMBINATION HISTORY

We present Rico, a code designed to compute the ionization fraction of the Universe during the epoch of hydrogen and helium recombination with an unprecedented combination of speed and accuracy. This is accomplished by training the machine learning code Pico on the calculations of a multi-level cosmological recombination code which self-consistently includes several physical processes that were neglected previously. After training, Rico is used to fit the free electron fraction as a function of the cosmological parameters. While, for example at low redshifts (z<~900), much of the net change in the ionization fraction can be captured by lowering the hydrogen fudge factor in Recfast by about 3%, Rico provides a means of effectively using the accurate ionization history of the full recombination code in the standard cosmological parameter estimation framework without the need to add new or refined fudge factors or functions to a simple recombination model. Within the new approach presented here it is easy to update Rico whenever a more accurate full recombination code becomes available. Once trained, Rico computes the cosmological ionization history with negligible fitting error in ~10 milliseconds, a speed-up of at least 10^6 over the full recombination code that was used here. Also Rico is able to reproduce the ionization history of the full code to a level well below 0.1%, thereby ensuring that the theoretical power spectra of CMB fluctuations can be computed to sufficient accuracy and speed for analysis from upcoming CMB experiments like Planck. Furthermore it will enable cross-checking different recombination codes across cosmological parameter space, a comparison that will be very important in order to assure the accurate interpretation of future cosmic microwave background data.

Crash2: coloured packets and other updates

In this paper, we report on the improvements implemented in the cosmological radiative transfer code crash. In particular, we present a new multi-frequency algorithm for spectra sampling which makes use of coloured photon packets: we discuss the need for the multi-frequency approach, describe its implementation and present the improved crash performance in reproducing the effects of ionizing radiation with an arbitrary spectrum. We further discuss minor changes in the code implementation which allow for more efficient performance and an increased precision.

Dark matter caustics

Caustics are a generic feature of the nonlinear growth of structure in the dark matter distribution. If the dark matter were absolutely cold, its mass density would diverge at caustics, and the integrated annihilation probability would also diverge for individual particles participating in them. For realistic dark matter candidates, this behaviour is regularised by small but non-zero initial thermal velocities. We present a mathematical treatment of evolution from Hot, Warm or Cold Dark Matter initial conditions which can be directly implemented in cosmological N-body codes. It allows the identification of caustics and the estimation of their annihilation radiation in fully general simulations of structure formation.

Cosmological structure formation under MOND: a new numerical solver for Poisson's equation

We present a novel solver for an analogue to Poisson's equation in the framework of modified Newtonian dynamics (MOND). This equation is highly non-linear and hence standard codes based upon tree structures and/or FFT's in general are not applicable; one needs to defer to multi-grid relaxation techniques. After a detailed description of the necessary modifications to the cosmological N-body code AMIGA (formerly known as MLAPM) we utilize the new code to revisit the issue of cosmic structure formation under MOND. We find that the proper (numerical) integration of a MONDian Poisson's equation has some noticable effects on the final results when compared against simulations of the same kind but based upon rather ad-hoc assumptions about the properties of the MONDian force field. Namely, we find that the large-scale structure evolution is faster in our revised MOND model leading to an even stronger clustering of galaxies, especially when compared to the standard LCDM paradigm.

Discreteness Effects in ΛCDM Simulations: A Wavelet‐Statistical View

The effects of particle discreteness in N-body LambdaCDM simulations are still an intensively debated issue. In this paper we explore such effects, taking into account the scatter caused by the randomness of the initial conditions and focusing on the statistical properties of the cosmological density field. For this purpose, we run large sets of LambdaCDM simulations and analyze them using a wide variety of diagnostics, including new and powerful wavelet statistics. Among other facts, we point out (1) that dynamical evolution does not propagate discreteness noise up from the small scales at which it is introduced and (2) that one should aim to satisfy the condition e~2d, where e is the force resolution and d is the interparticle distance. We clarify what such a condition means and how to implement it in modern cosmological codes.

Provenance in Comparative Analysis: A Study in Cosmology

Provenance - the logging of information about how data came into being and how it was processed - is an essential aspect of managing large-scale simulation and data-intensive projects. Using a cosmology code comparison project as an example, this article presents how a provenance system can play a key role in such applications.

How well do we understand cosmological recombination?

The major theoretical limitation for extracting cosmological parameters from the CMB sky lies in the precision with which we can calculate the cosmological recombination process. Uncertainty in the details of hydrogen and helium recombination could effectively increase the errors or bias the values of the cosmological parameters derived from the Planck satellite, for example. Here we modify the cosmological recombination code RECFAST by introducing one more parameter to reproduce the recent numerical results for the speed-up of the helium recombination. Together with the existing hydrogen fudge factor, we vary these two parameters to account for the remaining dominant uncertainties in cosmological recombination. By using the CosmoMC code with Planck forecast data, we find that we need to determine the parameters to better than ten per cent for He I and one per cent for H, in order to obtain negligible effects on the cosmological parameters. For helium recombination, if the existing studies have calculated the ionization fraction to the 0.1 per cent level by properly including the relevant physical processes, then we already have numerical calculations which are accurate enough for Planck. For hydrogen, setting the fudge factor to speed up low redshift recombination by 14 per cent appears to be sufficient for Planck. However, more work still needs to be done to carry out comprehensive numerical calculations of all the relevant effects for hydrogen, as well as to check for effects which couple hydrogen and helium recombinaton through the radiation field.

The fine-grained phase-space structure of cold dark matter haloes

We present a new and completely general technique for calculating the fine-grained phase-pace structure of dark matter (DM) throughout the Galactic halo. Our goal is to understand this structure on the scales relevant for direct and indirect detection experiments. Our method is based on evaluating the geodesic deviation equation along the trajectories of individual DM particles. It requires no assumptions about the symmetry or stationarity of the halo formation process. In this paper we study general static potentials which exhibit more complex behaviour than the separable potentials studied previously. For ellipsoidal logarithmic potentials with a core, phase mixing is sensitive to the resonance structure, as indicated by the number of independent orbital frequencies. Regions of chaotic mixing can be identified by the very rapid decrease in the real-space density of the associated DM streams. We also study the evolution of stream-density in ellipsoidal NFW haloes with radially varying isopotential shape, showing that if such a model is applied to the Galactic halo, at least 10(5) streams are expected near the Sun. The most novel aspect of our approach is that general non-static systems can be studied through implementation in a cosmological N-body code. Such an implementation allows a robust and accurate evaluation of the enhancements in annihilation radiation due to fine-scale structure such as caustics. We embed the scheme in the current state-of-the-art code GADGET-3 and present tests which demonstrate that N-body discreteness effects can be kept under control in realistic configurations.

CosmoMHD: A Cosmological Magnetohydrodynamics Code

In this era of precision cosmology, a detailed physical understanding on the evolution of cosmic baryons is required. Cosmic magnetic fields, though still poorly understood, may represent an important component in the global cosmic energy flow that affects the baryon dynamics. We have developed an Eulerian-based cosmological magnetohydrodynamics code (CosmoMHD) with modern shock capturing schemes to study the formation and evolution of cosmic structures in the presence of magnetic fields. The code solves the ideal MHD equations as well as the non-equilibrium rate equations for multiple species, the Vlasov equation for dynamics of collisionless particles, the Poisson's equation for the gravitational potential field and the equation for the evolution of the intergalactic ionizing radiation field. In addition, a detailed star formation prescription and feedback processes are implemented. Several methods for solving the MHD by high-resolution schemes with finite-volume and finite-difference methods are implemented. The divergence-free condition of the magnetic fields is preserved at a level of computer roundoff error via the constraint transport method. We have also implemented a high-resolution method via dual-equation formulations to track the thermal energy accurately in very high Mach number or high Alfven-Mach number regions. Several numerical tests have demonstrated the efficacy of the proposed schemes.

Relativistic Hydrodynamic Flows Using Spatial and Temporal Adaptive Structured Mesh Refinement

Astrophysical relativistic flow problems require high-resolution three-dimensional (3D) numerical simulations. In this paper, we describe a new parallel 3D code for simulations of special relativistic hydrodynamics (SRHD) using both spatially and temporally structured adaptive mesh refinement (AMR). We used the method of lines to discretize the SRHD equations spatially and a total variation diminishing (TVD) Runge-Kutta scheme for time integration. For spatial reconstruction, we have implemented piecewise linear method (PLM), piecewise parabolic method (PPM), third-order convex essentially nonoscillatory (CENO) and third- and fifth-order weighted essentially nonoscillatory (WENO) schemes. Flux is computed using either direct flux reconstruction or approximate Riemann solvers including HLL, modified Marquina flux, local Lax-Friedrichs flux formulas, and HLLC. The AMR part of the code is built on top of the cosmological Eulerian AMR code enzo. We discuss the coupling of the AMR framework with the relativistic solvers. Via various test problems, we emphasize the importance of resolution studies in relativistic flow simulations because extremely high resolution is required especially when shear flows are present in the problem. We also present the results of two 3D simulations of astrophysical jets: AGN jets and GRB jets. Resolution study of those two cases further highlights the need of high resolutions to calculate accurately relativistic flow problems.

Intrinsic galaxy alignments from the 2SLAQ and SDSS surveys: luminosity and redshift scalings and implications for weak lensing surveys

Correlations between intrinsic shear and the density field on large scales, a potentially important contaminant for cosmic shear surveys, have been robustly detected at low redshifts with bright galaxies in Sloan Digital Sky Survey (SDSS) data. Here we present a more detailed characterization of this effect, which can cause anticorrelations between gravitational lensing shear and intrinsic ellipticity (GI correlations). This measurement uses 36 278 luminous red galaxies (LRGs) from the SDSS spectroscopic sample with 0.15 3σ detections of the effect on large scales (up to 60 h−1 Mpc) for all galaxy subsamples within the SDSS LRG sample; for the 2SLAQ sample, we find a 2σ detection for a bright subsample, and no detection for a fainter subsample. Fitting formulae are provided for the scaling of the GI correlations with luminosity, transverse separation and redshift (for which the 2SLAQ sample, while small, provides crucial constraints due to its longer baseline in redshift). We estimate contamination in the measurement of σ8 for future cosmic shear surveys on the basis of the fitted dependence of GI correlations on galaxy properties. We find contamination to the power spectrum ranging from −1.5 per cent (optimistic) to −33 per cent (pessimistic) for a toy cosmic shear survey using all galaxies to a depth of R = 24 using scales l ≈ 500, though the central value of predicted contamination is −6.5 per cent. This corresponds to a bias in σ8 of Δσ8 = −0.004 (optimistic), −0.02 (central) or −0.10 (pessimistic). We provide a prescription for inclusion of this error in cosmological parameter estimation codes. The principal uncertainty is in the treatment of the L ≤ L blue galaxies, for which we have no detection of the GI signal, but which could dominate the GI contamination if their GI amplitude is near our upper limits. Characterization of the tidal alignments of these galaxies, especially at redshifts relevant for cosmic shear, should be a high priority for the cosmic shear community.

Are the nearby groups of galaxies gravitationally bound objects?

We have compared numerical simulations to observations for the nearby (< 40 Mpc) groups of galaxies (Huchra & Geller 1982 and Ramella et al. 2002). The group identi- fication is carried out using a group-finding algorithm developed by Huchra & Geller (1982). Using cosmological N-body simulation code with theCDM cosmology, we show that the dynamical properties of groups of galaxies identified from the simulation data are, in general, in a moderate, within 2σ, agreement with the observational cat- alogues of groups of galaxies. As simulations offer more dynamical information than observations, we used the N-body simulation data to calculate whether the nearby groups of galaxies are gravitationally bound objects by using their virial ratio. We show that in aCDM cosmology about 20 per cent of nearby groups of galaxies, identified by the same algorithm as in the case of observations, are not bound, but merely groups in a visual sense. This is quite significant, specifically because estima- tions of group masses in observations are often based on an assumption that groups of galaxies found by the friends-of-friends algorithm are gravitationally bound objects. Simulations with different resolutions show the same results. We also show how the fraction of gravitationally unbound groups varies when the apparent magnitude limit of the sample and the value of the cosmological constantis changed. In general, a larger value of thegenerates slightly more unbound groups.

TKira—A Hybrid N-Body Code

AbstractAccurately modeling the evolution of a star cluster in a strong tidal field poses unique computational challenges. We present a hybrid code that combines the strengths of two different approaches to computing gravitational forces. The internal, collisional, dynamics of the cluster is followed with a direct N-body integrator, Kira, while the galactic tidal field is modeled with a cosmological code, GADGET, that uses a Barnes-Hut tree to evaluate gravitational forces in O(N log N) time. The quadrupole moment at the center of mass of the cluster is used to compute the external potential and provides a mechanism for mass loss. This forms a robust, bidirectional interaction. The advantages of combining two highly-developed and well-established software packages at such high level are obvious and many; not the least of the these is the ability to include other physical processes, e.g., stellar evolution. One problem to which we applied this technique is the evolution of a dense star cluster near the Galactic Center. We are also using this code to explore the effects of the strong time variation in the tidal field of merging galaxies on the evolution of young star clusters forming during the merger.

The H ii Region of a Primordial Star

The concordance model of cosmology and structure formation predicts the formation of isolated very massive stars at high redshifts in dark matter dominated halos of 10{sup 5} to 10{sup 6} Msun. These stars photo-ionize their host primordial molecular clouds, expelling all the baryons from their halos. When the stars die, a relic H II region is formed within which large amounts of molecular hydrogen form which will allow the gas to cool efficiently when gravity assembles it into larger dark matter halos. The filaments surrounding the first star hosting halo are largely shielded and provide the pathway for gas to stream into the halo when the star has died. We present the first fully three dimensional cosmological radiation hydrodynamical simulations that follow all these effects. A novel adaptive ray casting technique incorporates the time dependent radiative transfer around point sources. This approach is fast enough so that radiation transport, kinetic rate equations, and hydrodynamics are solved self-consistently. It retains the time derivative of the transfer equation and is explicitly photon conserving. This method is integrated with the cosmological adaptive mesh refinement code enzo, and runs on distributed and shared memory parallel architectures. Where applicable the three dimensional calculation not onlymore » confirm expectations from earlier one dimensional results but also illustrate the multi-fold hydrodynamic complexities of H II regions. In the absence of stellar winds the circumstellar environments of the first supernovae and putative early gamma-ray bursts will be of low density {approx}1 cm{sup -3}. Albeit marginally resolved, ionization front instabilities lead to cometary and elephant trunk like small scale structures reminiscent of nearby star forming regions.« less