We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the ‘tree’ method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different time-steps. Individual and adaptive short-range time-steps may also be employed. The domain decomposition used in the parallelization algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10 10 dark matter particles, reaching a homogeneous spatial dynamic range of 10 5 per dimension in a three-dimensional box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community. Ke yw ords: methods: numerical ‐ galaxies: interactions ‐ dark matter.

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The Cosmological simulation code GADGET-2

We review in detail a number of approaches that have been adopted to try and explain the remarkable observation of our accelerating universe. In particular we discuss the arguments for and recent progress made towards understanding the nature of dark energy. We review the observational evidence for the current accelerated expansion of the universe and present a number of dark energy models in addition to the conventional cosmological constant, paying particular attention to scalar field models such as quintessence, K-essence, tachyon, phantom and dilatonic models. The importance of cosmological scaling solutions is emphasized when studying the dynamical system of scalar fields including coupled dark energy. We study the evolution of cosmological perturbations allowing us to confront them with the observation of the Cosmic Microwave Background and Large Scale Structure and demonstrate how it is possible in principle to reconstruct the equation of state of dark energy by also using Supernovae Ia observational data. We also discuss in detail the nature of tracking solutions in cosmology, particle physics and braneworld models of dark energy, the nature of possible future singularities, the effect of higher order curvature terms to avoid a Big Rip singularity, and approaches to modifying gravity which leads to a late-time accelerated expansion without recourse to a new form of dark energy.

Dynamics of dark energy

In this review the theory and application of Smoothed particle hydrodynamics (SPH) since its inception in 1977 are discussed. Emphasis is placed on the strengths and weaknesses, the analogy with particle dynamics and the numerous areas where SPH has been successfully applied.

https://iopscience.iop.org/article/10.1088/0034-4885/68/8/R01/pdf

Smoothed particle hydrodynamics

https://www.physics.rutgers.edu/grad/690/Padmanabhan-2003.pdf

Cosmological constant—the weight of the vacuum

Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Λ-term (cosmological constant). In this paper we review both observational and theoretical aspects of a small cosmological Λ-term. We discuss the current observational situation focusing on cosmological tests of Λ including the age of the universe, high redshift supernovae, gravitational lensing, galaxy clustering and the cosmic microwave background. We also review the theoretical debate surrounding Λ: the generation of Λ in models with spontaneous symmetry breaking and through quantum vacuum polarization effects — mechanisms which are known to give rise to a large value of Λ hence leading to the "cosmological constant problem." More recent attempts to generate a small cosmological constant at the present epoch using either field theoretic techniques, or by modelling a dynamical Λ-term by scalar fields are also extensively discussed. Anthropic arguments favouring a small Λ-term are briefly reviewed. A comprehensive bibliography of recent work on Λ is provided.

http://cds.cern.ch/record/385991/files/9904398.pdf

The Case for a Positive Cosmological Λ-Term

The detailed structure of the interaction of a strong stellar wind with the interstellar medium is presented. First, an adiabatic similarity solution is given which is applicable at early times. Second, a similarity solution is derived which includes the effects of thermal conduction between the hot (about 1 million K) interior and the cold shell of swept-up interstellar matter. This solution is then modified to include the effects of radiative energy losses. The evolution of an interstellar bubble is calculated, including the radiative losses. The quantitative results for the outer-shell radius and velocity and the column density of highly ionized species such as O VI are within a factor 2 of the approximate results of Castor, McCray, and Weaver (1975). The effect of stellar motion on the structure of a bubble, the hydrodynamic stability of the outer shell, and the observable properties of the hot region and the outer shell are discussed.

Interstellar bubbles. II - Structure and evolution

The suggestion that the observed 0.25 keV X-ray background and 0 vi absorption lines are produced by a new, hot (Tapprox.10/sup 6/ K), diffuse component of the interstellar medium is examined in the context of both a steady-state and a time-dependent model. It is concluded that such a component can explain the two observations only if the pressure of the cooler interstellar medium is approx.10 times higher than the previously estimated p/kapprox. =2000 cm/sup -3/ K; a mechanism such as the proposed convective-radiative ''galactic fountain'' exists to cool the hot gas; and another component is responsible for the presence of 0 ii at temperatures below 10/sup 6/ K. (AIP)

Consequences of a New Hot Component of the Interstellar Medium

Detailed results for the hydrodynamical, thermal, ionization, and molecular formation history of postshock cooling flows behind steady state shocks in a primordial gas at redshifts z = 5, 10, and 20 are presented and analyzed for a wide range of shock velocities from 50 to 400 km/s. The nonequilibrium results indicate that, for a significant range of shock velocities, if the shock-heated gas can cool to 10,000 K within the age of the universe, then it quite commonly forms an H2 fraction in excess of 0.001 and cools at nearly constant pressure to less than 100 K. The presence of an external flux of ionizing and dissociating radiation can, for a range of fluxes similar to that expected from a background of quasars, actually increase the peak H2 concentration to values of order 10 to the -1.5 or higher; it also increases the cooling time to 100 K. 78 references.

Hydrogen molecules and the radiative cooling of pregalactic shocks

We present the first large-scale radiative transfer simulat ions of cosmic reionization, in a simulation volume of (100 h 1 Mpc) 3 . This is more than a 2 orders of magnitude improvement over previous simulations. We achieve this by combining the results from extremely large, cosmological, N-body simulations with a new, fast and effici ent code for 3D radiative transfer, C 2 -Ray, which we have recently developed. These simulations allow us to do the first numerical studies of the large-scale structure of reionization w hich at the same time, and crucially, properly take account of the dwarf galaxy ionizing sources which are primarily responsible for reionization. In our realization, reionization starts around z � 21, and final overlap occurs by z � 11. The resulting electron-scattering optical depth is in goo d agreement with the firstyear WMAP polarization data. We show that reionization clearly proceeded in an inside-out fashion, with the high-density regions being ionized earli er, on average, than the voids. Ionization histories of smaller-size (5 to 10 comoving Mpc) subregions exabit a large scatter about the mean and do not describe the global reionization history well. This is true even when these subregions are at the mean density of the universe, which shows that small-box simulations of reionization have little predictive power for the evolut ion of the mean ionized fraction. The minimum reliable volume size for such predictions is � 30 Mpc. We derive the power-spectra of the neutral, ionized and total gas density fields and show t hat there is a significant boost of the density fluctuations in both the neutral and the ionized c omponents relative to the total at arcminute and larger scales. We find two populations of H II re gions according to their size, numerous, mid-sized (� 10 Mpc) regions and a few, rare, very large regions tens of Mpc in size. Thus, local overlap on fairly large scales of tens of Mp c is reached by z � 13, when our volume is only about 50% ionized, and well before the global overlap. We derive the statistical distributions of the ionized fraction and ionized gas densi ty at various scales and for the first time show that both distributions are clearly non-Gaussian. All these quantities are critical for predicting and interpreting the observational signals from reionization from a variety of observations like 21-cm emission, Ly-α emitter statistics, Gunn-Peterson optical depth and small-scale CMB secondary anisotropies due to patchy reionization.

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Simulating Cosmic Reionization at Large Scales I: the Geometry of Reionization

Energy released by a small fraction of the baryons in the Universe, which condensed out while the intergalactic medium (IGM) was cold, dark and neutral, reheated and reionized it by redshift 6, exposing other baryons already condensed into dwarf-galaxy minihaloes to the glare of ionizing radiation. We present the first gas dynamical simulations of the photoevaporation of cosmological minihaloes overtaken by the ionization fronts which swept through the IGM during the reionization epoch in the currently favoured A cold dark matter (ACDM) universe, including the effects of radiative transfer. These simulations demonstrate the phenomenon of I-front trapping inside minihaloes, in which the weak, R-type fronts which travelled supersonically across the IGM decelerated when they encountered the dense, neutral gas inside minihaloes, and were thereby transformed into D-type I-fronts, preceded by shock waves. For a minihalo with virial temperature below 10 4 K, the I-front gradually burned its way through the minihalo which trapped it, removing all of its baryonic gas by causing a supersonic, evaporative wind to blow backwards into the IGM, away from the exposed layers of minihalo gas just behind the advancing I-front. We describe this process in detail, along with some of its observable consequences, for the illustrative case of a minihalo of total mass 10 7 M ○. , exposed to a distant source of ionizing radiation with either a stellar or quasar-like spectrum, after it was overtaken at redshift z = 9 by the weak, R-type I-front which ionized the IGM surrounding the source. For a source at z = 9 which emits 10 56 ionizing photons per second at 1 Mpc (or, equivalently, 10 52 ionizing photons per second at 10 kpc), the photoevaporation of this minihalo takes about 100-150 Myr, depending on the source spectrum, ending at about z = 7.5. Such hitherto neglected feedback effects were widespread during the reionization epoch. N-body simulations and analytical estimates of halo formation in the ACDM model suggest that sub-kpc minihaloes such as these, with virial temperatures below 10 4 K, were so common as to cover the sky around larger-mass source haloes and possibly dominate the absorption of ionizing photons during reionization. This means that previous estimates of the number of ionizing photons per hydrogen atom required to complete reionization which neglected this effect may be too low. Regardless of their effect on the progress of reionization, however, the minihaloes were so abundant that random lines of sight through the high-z Universe should encounter many of them, which suggests that it may be possible to observe the processes described here in the absorption spectra of distant sources.

/pdf/photoevaporation-of-cosmological-minihaloes-during-3pxvc8w9lv.pdf

Paul R. Shapiro

Papers

Interstellar bubbles. II - Structure and evolution

Consequences of a New Hot Component of the Interstellar Medium

Hydrogen molecules and the radiative cooling of pregalactic shocks

Simulating Cosmic Reionization at Large Scales I: the Geometry of Reionization

Photoevaporation of cosmological minihaloes during reionization