Understanding the velocity field is very important for modern cosmology: it gives insights to structure formation in general, and also its properties are crucial ingredients in modelling redshift-space distortions and in interpreting measurements of
the kinetic Sunyaev-Zeldovich effect. Unfortunately, characterising the velocity field in cosmological N-body simulations is inherently complicated by two facts: i) The velocity field becomes manifestly multi-valued after shell-crossing and has discontinuities at caustics. This is due to the collisionless nature of dark matter. ii) N-body simulations sample the velocity field only at a set of discrete locations, with poor resolution in low-density regions. In this paper, we discuss how the associated problems can be circumvented by using a phase-space interpolation technique. This method provides extremely accurate estimates of the cosmic velocity fields and its derivatives, which can be properly defined without the need of the arbitrary coarse-graining procedure commonly used. We explore in detail the configuration-space properties of the cosmic velocity field on very large scales and in the highly nonlinear regime. In particular, we characterise the divergence and curl of the velocity field, present their one-point statistics, analyse the Fourier-space properties and provide fitting formulae for the velocity divergence bias relative to the non-linear matter power spectrum. We furthermore contrast some of the interesting differences in the velocity fields of warm and cold dark matter models. We anticipate that the high-precision measurements carried out here will help to understand in detail the dynamics of dark matter and the structures it forms.
We introduce the AGORA project, a comprehensive numerical study of well-resolved galaxies within the LCDM cosmology. Cosmological hydrodynamic simulations with force resolutions of ~100 proper pc or better will be run with a variety of code platforms
to follow the hierarchical growth, star formation history, morphological transformation, and the cycle of baryons in and out of 8 galaxies with halo masses M_vir ~= 1e10, 1e11, 1e12, and 1e13 Msun at z=0 and two different (violent and quiescent) assembly histories. The numerical techniques and implementations used in this project include the smoothed particle hydrodynamics codes GADGET and GASOLINE, and the adaptive mesh refinement codes ART, ENZO, and RAMSES. The codes will share common initial conditions and common astrophysics packages including UV background, metal-dependent radiative cooling, metal and energy yields of supernovae, and stellar initial mass function. These are described in detail in the present paper. Subgrid star formation and feedback prescriptions will be tuned to provide a realistic interstellar and circumgalactic medium using a non-cosmological disk galaxy simulation. Cosmological runs will be systematically compared with each other using a common analysis toolkit, and validated against observations to verify that the solutions are robust - i.e., that the astrophysical assumptions are responsible for any success, rather than artifacts of particular implementations. The goals of the AGORA project are, broadly speaking, to raise the realism and predictive power of galaxy simulations and the understanding of the feedback processes that regulate galaxy metabolism. The proof-of-concept dark matter-only test of the formation of a galactic halo with a z=0 mass of M_vir ~= 1.7e11 Msun by 9 differe
Recently, we have shown how current cosmological N-body codes already follow the fine grained phase-space information of the dark matter fluid. Using a tetrahedral tesselation of the three-dimensional manifold that describes perfectly cold fluids in
six-dimensional phase space, the phase-space distribution function can be followed throughout the simulation. This allows one to project the distribution function into configuration space to obtain highly accurate densities, velocities, and velocity dispersions. Here, we exploit this technique to show first steps on how to devise an improved particle-mesh technique. At its heart, the new method thus relies on a piecewise linear approximation of the phase space distribution function rather than the usual particle discretisation. We use pseudo-particles that approximate the masses of the tetrahedral cells up to quadrupolar order as the locations for cloud-in-cell (CIC) deposit instead of the particle locations themselves as in standard CIC deposit. We demonstrate that this modification already gives much improved stability and more accurate dynamics of the collisionless dark matter fluid at high force and low mass resolution. We demonstrate the validity and advantages of this method with various test problems as well as hot/warm-dark matter simulations which have been known to exhibit artificial fragmentation. This completely unphysical behaviour is much reduced in the new approach. The current limitations of our approach are discussed in detail and future improvements are outlined.
The primordial velocity dispersion of dark matter is small compared to the velocities attained during structure formation. The initial density distribution is close to uniform and it occupies an initial sheet in phase space that is single valued in v
elocity space. Because of gravitational forces this three dimensional manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points. N-body simulations already follow the motion of this sheet in phase space. This fact can be used to extract full fine-grained phase-space-structure information from existing cosmological N-body simulations. Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined. We show how to obtain the space density of the fluid, detect caustics, and count the number of streams as well as their individual contributions to any point in configuration-space. We calculate the bulk velocity, local velocity dispersions, and densities from the sheet - all without averaging over control volumes. This gives a wealth of new information about dark matter fluid flow which had previously been thought of as inaccessible to N-body simulations. We outline how this mapping may be used to create new accurate collisionless fluid simulation codes that may be able to overcome the sparse sampling and unphysical two-body effects that plague current N-body techniques.
The first stars form in dark matter halos of masses ~10^6 M_sun as suggested by an increasing number of numerical simulations. Radiation feedback from these stars expels most of the gas from their shallow potential well of their surrounding dark matt
er 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 10^8 solar mass 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 H_2 cooling create a complex, multi-phase 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 10^4 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.
(Abridged) Using ab initio cosmological Eulerian adaptive mesh refinement radiation hydrodynamical calculations, we discuss how very massive stars start the process of cosmological reionization. The models include non-equilibrium primordial gas chemi
stry and cooling processes and accurate radiation transport in the Case B approximation using adaptively ray traced photon packages, retaining the time derivative in the transport equation. Supernova feedback is modeled by thermal explosions triggered at parsec scales. All calculations resolve the local Jeans length by at least 16 grid cells at all times and as such cover a spatial dynamic range of ~10^6. These first sources of reionization are highly intermittent and anisotropic and first photoionize the small scales voids surrounding the halos they form in, rather than the dense filaments they are embedded in. As the merging objects form larger, dwarf sized galaxies, the escape fraction of UV radiation decreases and the HII regions only break out on some sides of the galaxies making them even more anisotropic. In three cases, SN blast waves induce star formation in overdense regions that were formed earlier from ionization front instabilities. These stars form tens of parsecs away from the center of their parent DM halo. Approximately 5 ionizing photons are needed per sustained ionization when star formation in 10^6 M_sun halos are dominant in the calculation. As the halos become larger than ~10^7 M_sun, the ionizing photon escape fraction decreases, which in turn increases the number of photons per ionization to 15-50, in calculations with stellar feedback only. Supernova feedback in these more massive halos creates a more diffuse medium, allowing the stellar radiation to escape more easily and maintaining the ratio of 5 ionizing photons per sustained ionization.
