Lacking the ability to follow individual galaxies on cosmological time-scales, our understanding of individual galaxy evolution is broadly inferred from population trends and behaviours. In its most prohibitive form, this approach assumes that galactic star formation properties exhibit ergodicity, so that individual galaxy evolution can be statistically inferred via ensemble behaviours. The validity of this assumption is tested through the use of observationally motivated simulations of isolated galaxies. The suite of simulated galaxies is statistically constructed to match observed galaxy properties by using kernel density estimation to create structural parameter distributions, augmented by theoretical relationships where necessary. We also test the impact of different physical processes, such as stellar winds or the presence of halo substructure on the star formation behaviour. We consider the subtleties involved in constraining ergodic properties, such as the distinction between stationarity imposed by stellar wind feedback and truly ergodic behaviour. However, without sufficient variability in star formation properties, individual galaxies are unable to explore the full parameter space. While, as expected, full ergodicity appears to be ruled out, we find reasonable evidence for partial ergodicity, where averaging over mass-selected subsets of galaxies more broadly resembles time averages, where the average largest deviation across physical scenarios is 0.20 dex. As far as we are aware, this the first time partial ergodicity has been considered in an astronomical context, and provides a promising statistical concept. Despite morphological changes introduced by close encounters with dark matter substructure, subhaloes are not found to significantly increase deviations from ergodic assumptions.

Maps of the Rees-Sciama (RS) effect are simulated using the parallel N-body code, HYDRA, and a run-time ray-tracing procedure. A method designed for the analysis of small, square cosmic microwave background (CMB) maps is applied to our RS maps. Each of these techniques has been tested and successfully applied in previous papers. Within a range of angular scales, our estimate of the RS angular power spectrum due to variations in the peculiar gravitational potential on scales smaller than 42/h megaparsecs is shown to be robust. An exhaustive study of the redshifts and spatial scales relevant for the production of RS anisotropy is developed for the first time. Results from this study demonstrate that (i) to estimate the full integrated RS effect, the initial redshift for the calculations (integration) must be greater than 25, (ii) the effect produced by strongly non-linear structures is very small and peaks at angular scales close to 4.3 arcmin, and (iii) the RS anisotropy cannot be detected either directly-in temperature CMB maps-or by looking for cross-correlations between these maps and tracers of the dark matter distribution. To estimate the RS effect produced by scales larger than 42/h megaparsecs, where the density contrast is not strongly non-linear, high accuracy N-body simulations appear unnecessary. Simulations based on approximations such as the Zel'dovich approximation and adhesion prescriptions, for example, may be adequate. These results can be used to guide the design of future RS simulations.

Building on the initial results of the nIFTy simulated galaxy cluster comparison, we compare and contrast the impact of baryonic physics with a single massive galaxy cluster, run with 11 state-of-the-art codes, spanning adaptive mesh, moving mesh, classic and modern smoothed particle hydrodynamics (SPH) approaches. For each code represented we have a dark-matter-only (DM) and non-radiative (NR) version of the cluster, as well as a full physics (FP) version for a subset of the codes. We compare both radial mass and kinematic profiles, as well as global measures of the cluster (e.g. concentration, spin, shape), in the NR and FP runs with that in the DM runs. Our analysis reveals good consistency ⪅20 per cent) between global properties of the cluster predicted by different codes when integrated quantities are measured within the virial radius R200. However, we see larger differences for quantities within R2500, especially in the FP runs. The radial profiles reveal a diversity, especially in the cluster centre, between the NR runs, which can be understood straightforwardly from the division of codes into classic SPH and non-classic SPH (including the modern SPH, adaptive and moving mesh codes); and between the FP runs, which can also be understood broadly from the division of codes into those that include active galactic nucleus feedback and those that do not. The variation with respect to the median is much larger in the FP runs with different baryonic physics prescriptions than in the NR runs with different hydrodynamics solvers.

In previous editions of Frontiers of Fundamental Physics Symposia, [1,2,3,4,5] we presented numerical computations of Cosmic Microwave Background (CMB) anisotropies at small angular scales (high 's).Our ray-tracing procedure was implemented in different N-body codes to calculate these anisotropies.A certain Particle-Mesh (PM) code and parallel Adaptative-Particle-Particle-Particle-Mesh (AP3M) Hydra codes have been used.This way we have been able to estimate weak lensing, Rees-Sciama (RS) and Sunyaev-Zel'dovich contributions to the CMB anisotropy.The use of a parallel AP3M code led to more accurate computations [6,7], but further research is necessary.Almost a decade ago, we computed the RS effect by using a PM N-body code [8].Here, some preliminary estimations of the RS effect, obtained with a parallel AP3M Hydra code, are presented.These results improve on those obtained with PM codes and, moreover, they are the starting point for a more detailed study of the RS anisotropy component.

We have simulated the formation of a galaxy cluster in a Lambda cold dark matter universe using 13 different codes modelling only gravity and non-radiative hydrodynamics (RAMSES, ART, AREPO, HYDRA and nine incarnations of GADGET). This range of codes includes particle-based, moving and fixed mesh codes as well as both Eulerian and Lagrangian fluid schemes. The various GADGET implementations span classic and modern smoothed particle hydrodynamics (SPH) schemes. The goal of this comparison is to assess the reliability of cosmological hydrodynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at z = 0, global properties such as mass and radial profiles of various dynamical and thermodynamical quantities. The underlying gravitational framework can be aligned very accurately for all the codes allowing a detailed investigation of the differences that develop due to the various gas physics implementations employed. As expected, the mesh-based codes RAMSES, ART and AREPO form extended entropy cores in the gas with rising central gas temperatures. Those codes employing classic SPH schemes show falling entropy profiles all the way into the very centre with correspondingly rising density profiles and central temperature inversions. We show that methods with modern SPH schemes that allow entropy mixing span the range between these two extremes and the latest SPH variants produce gas entropy profiles that are essentially indistinguishable from those obtained with grid-based methods.

An Adaptative-Particle-Particle-Particle-Mesh code (HYDRA) plus a ray-tracing procedure was used in [1] to perform an exhaustive analysis of the weak lensing anisotropy. Other nonlinear Cosmic Microwave Background anisotropies, such as the Rees-Sciama and the Sunyaev-Zel. dovich effects are also being studied by using the same tools. Here we present some advances in our study of these nonlinear anisotropies. The primary advance is due to the use of better simulations with greater particle densities and appropriate softening, although other parameters have also been adjusted to get better estimates. Thus, we improve on a previous paper [2] where the Rees-Sciama effect was studied with Particle-Mesh simulations. We focus particular attention on the resolution improvement and its consequences.

We investigate the high-redshift evolution of the rest-frame UV-luminosity function (LF) of galaxies via hydrodynamical cosmological simulations, coupled with an emulated observational astronomy pipeline that provides a direct comparison with observations. We do this by creating mock images and synthetic galaxy catalogs of approximate to 100 arcmin(-2) fields from the numerical model at redshifts approximate to 4.5 to 10.4. We include the effects of dust extinction and the point-spread function (PSF) for the Hubble WFC3 camera for comparison with space observations. We also include the expected zodiacal background to predict its effect on space observations, including future missions such as the James Webb Space Telescope (JWST). When our model catalogs are fitted to Schechter function parameters, we predict that the faint-end slope (alpha) of the LF evolves as alpha = -1.16-0.12z over the redshift range z approximate to 4.5-7.7, in excellent agreement with observations from, e.g., Hathi and coworkers. However, for redshifts z approximate to 6-10.4, alpha(z) appears to display a shallower evolution, alpha = -1.79-0.03z. Augmenting the simulations with more detailed physics-specifically stellar winds and supernovae (SN)-produces similar results. The model shows an overproduction of galaxies, especially at faint magnitudes, compared with the observations, although the discrepancy is reduced when dust extinction is taken into account.

From FFP6 to FFP11, we presented the advances in our Cosmic Microwave Background (CMB) anisotropy computations using N-body Hydra Codes. For such computations, codes without baryons were used: First sequential versions and afterwards parallel ones. With both of them we computed the weak lensing and the Rees-Sciama contributions to the CMB angular power spectrum. Using our numerical techniques, we reported a lensing effect higher than that estimated in previous papers (for very small angular scales). Our CMB computations require less interpolations and approximations than other approaches. This could explain part of our excess of power in lensing computations. Our higher time and angular resolutions could also contribute to this excess. Here, recent advances on previous computations are presented. Computations with baryons have been started. These calculations allow us to compute the Sunyaev-Zel’dovich contribution to the CMB angular power spectrum. We are also trying to compute the three effects—weak lensing, Rees-Sciama and Sunyaev-Zel’dovich—at the same time, with the essential aim of seeing how their power spectra couple among them.

We examine simulations of isolated galaxies to analyse the effects of localized feedback on the formation and evolution of molecular clouds. Feedback contributes to turbulence and the destruction of clouds, leading to a population of clouds that is younger, less massive, and with more retrograde rotation. We investigate the evolution of clouds as they interact with each other and the diffuse interstellar medium, and determine that the role of cloud interactions differs strongly with the presence of feedback: in models without feedback, scattering events dramatically increase the retrograde fraction, but in models with feedback, mergers between clouds may slightly increase the prograde fraction. We also produce an estimate of the viscous time-scale due to cloud-cloud collisions, which increases with increasing strength of feedback (t$_{ν}$ {} 20 Gyr versus t$_{ν}$ {} 10 Gyr), but is still much smaller than previous estimates (t$_{ν}$ {} 1000 Gyr); although collisions become more frequent with feedback, less energy is lost in each collision than in the models without feedback.

Several years ago, we designed a particular ray tracing method. Combined with a Hydra parallel code (without baryons), it may compute some CMB anisotropies: weak lensing (WL) and Rees–Sciama (RS) effects. Only dark matter is fully necessary to estimate these effects. For very small angular scales, we made an exhaustive study leading to a lensing contribution slightly—but significantly—greater than previous ones. Afterwards, the same ray tracing procedure was included in a parallel Hydra code with baryons. The resulting code was then tested. This code is being currently applied to the study of the thermal and kinetic Sunyaev–Zel’dovich (SZ) contributions to the CMB anisotropies. We present here our first results.

Observations have revealed cold gas with large velocity dispersions (~300 km/s) within the hot outflows of ultra-luminous infrared galaxies (ULIRGs). This gas may trace its origin to the Rayleigh-Taylor (RT) fragmentation of a super-bubble or may arise on smaller scales. We model a ULIRG outflow at two scales to recreate this gas in three-dimensional hydrodynamic simulations using FLASH. Although resolution is limited, these models successfully produce cold gas in outflows with large velocity dispersions. Our small-scale models produce this cold gas through RT fragmentation of the super-bubble wall, but the large-scale models produce the cold gas after hot bubbles fragment the disc's gas into cold clouds which are then accelerated by thermal pressure, and supplemented by cooling within the outflow. We produce simple mock spectra to compare these simulations to observed absorption spectra and find line-widths of ~250 km/s, agreeing with the lower end of observations.

We examine the correlation between the star formation rate (SFR) and black hole accretion rate (BHAR) across a suite of different active galactic nuclei (AGN) feedback models, using the time evolution of a merger simulation. By considering three different stages of evolution, and a distinction between the nuclear and outer regions of star formation, we consider 63 different cases. Despite many of the feedback models fitting the M-sigma relationship well, there are often distinct differences in the SFR-BHAR correlations, with close to linear trends only being present after the merger. Some of the models also show evolution in the SFR-BHAR parameter space that is at times directly across the long-term averaged SFR-BHAR correlation. This suggests that the observational SFR-BHAR correlation found for ensembles of galaxies is an approximate statistical trend, as suggested by Hickox et al. Decomposing the SFR into nuclear and outer components also highlights notable differences between models and there is only modest agreement with observational studies examining this in Seyfert galaxies. For the fraction of the black hole mass growth from the merger event relative to the final black hole mass, we find as much as a factor of 3 variation among models. This also translates into a similar variation in the post-starburst black hole mass growth. Overall, we find that while qualitative features are often similar amongst models, precise quantitative analysis shows there can be quite distinct differences.

A recent approach to simulating localized feedback from active galactic nuclei (AGN) by Power et al. uses an accretion disc particle to represent both the black hole and its accretion disc. We have extrapolated and adapted this approach to simulations of Milky Way sized galaxy mergers containing black holes and explored the impact of the various parameters in this model as well as its resolution dependence. The two key parameters in the model are an effective accretion radius, which determines the radius within which gas particles are added to the accretion disc, and a viscous time-scale which determines how long it takes for material in the accretion disc to accrete on to the black hole itself. We find that there is a limited range of permitted accretion radii and viscous time-scales, with unphysical results produced outside this range. For permitted model parameters, the nuclear regions of simulations with the same resolution follow similar evolutionary paths, producing final black hole masses that are consistent within a factor of 2. When comparing the resolution dependence of the model, there is a trend towards higher resolution producing slightly lower mass black holes, but values for the two resolutions studied again agree within a factor of 2. We also compare these results to two other AGN feedback algorithms found in the literature. While the evolution of the systems vary, most notably the intermediate total black hole mass, the final black hole masses differ by less than a factor of 5 among all of our models, and the remnants exhibit similar structural parameters. The implication of this accretion model is that, unlike most accretion algorithms, a decoupling of the accretion rate on to the black hole and the local gas properties is permitted and obtained; this allows for black hole growth even after feedback has prevented additional accretion events on to the disc.

In the early universe, substantial relative "stream" velocities between the gas and dark matter arise due to radiation pressure and persist after recombination. To assess the impact of these velocities on high-redshift structure formation, we carry out a suite of high-resolution adaptive mesh refinement (AMR) cosmological simulations, which use smoothed particle hydrodynamic data sets as initial conditions, converted using a new tool developed for this work. These simulations resolve structures with masses as small as a few 100 M-circle dot, and we focus on the 10(6) M-circle dot "mini-halos" in which the first stars formed. At z approximate to 17, the presence of stream velocities has only a minor effect on the number density of halos below 10(6) M-circle dot, but it greatly suppresses gas accretion onto all halos and the dark matter structures around them. Stream velocities lead to significantly lower halo gas fractions, especially for approximate to 10(5) M-circle dot objects, an effect that is likely to depend on the orientation of a halo's accretion lanes. This reduction in gas density leads to colder, more compact radial profiles, and it substantially delays the redshift of collapse of the largest halos, leading to delayed star formation and possibly delayed reionization. These many differences suggest that future simulations of early cosmological structure formation should include stream velocities to properly predict gas evolution, star formation, and the epoch of reionization.

Modelling active galactic nuclei (AGN) feedback in numerical simulations is both technically and theoretically challenging, with numerous approaches having been published in the literature. We present a study of five distinct approaches to modelling AGN feedback within gravitohydrodynamic simulations of major mergers of Milky Way-sized galaxies. To constrain differences to only be between AGN feedback models, all simulations start from the same initial conditions and use the same star formation algorithm. Most AGN feedback algorithms have five key aspects: the black hole accretion rate, energy feedback rate and method, particle accretion algorithm, black hole advection algorithm and black hole merger algorithm. All models follow different accretion histories, and in some cases, accretion rates differ by up to three orders of magnitude at any given time. We consider models with either thermal or kinetic feedback, with the associated energy deposited locally around the black hole. Each feedback algorithm modifies the region around the black hole to different extents, yielding gas densities and temperatures within r similar to 200 pc that differ by up to six orders of magnitude at any given time. The particle accretion algorithms usually maintain good agreement between the total mass accreted by. M dt and the total mass of gas particles removed from the simulation, although not all algorithms guarantee this to be true. The black hole advection algorithms dampen inappropriate dragging of the black holes by two-body interactions. Advecting the black hole a limited distance based upon local mass distributions has many desirably properties, such as avoiding large artificial jumps and allowing the possibility of the black hole remaining in a gas void. Lastly, two black holes instantly merge when given criteria are met, and we find a range of merger times for different criteria. This is important since the AGN feedback rate changes across the merger in a way that is dependent on the specific accretion algorithm used. Using the M-BH-sigma relation as a diagnostic of the remnants yields three models that lie within the one-sigma scatter of the observed relation and two that fall below the expected relation. The wide variation in accretion behaviours of the models reinforces the fact that there remains much to be learnt about the evolution of galactic nuclei.

We examine radial and vertical metallicity gradients using a suite of disk galaxy simulations, supplemented with two classic chemical evolution approaches. We determine the rate of change of gradient and reconcile differences between extant models and observations within the `inside-out' disk growth paradigm. A sample of 25 disks is used, consisting of 19 from our RaDES (Ramses Disk Environment Study) sample, realised with the adaptive mesh refinement code RAMSES. Four disks are selected from the MUGS (McMaster Unbiased Galaxy Simulations) sample, generated with the smoothed particle hydrodynamics (SPH) code GASOLINE, alongside disks from Rahimi et al. (GCD+) and Kobayashi & Nakasato (GRAPE-SPH). Two chemical evolution models of inside-out disk growth were employed to contrast the temporal evolution of their radial gradients with those of the simulations. We find that systematic differences exist between the predicted evolution of radial abundance gradients in the RaDES and chemical evolution models, compared with the MUGS sample; specifically, the MUGS simulations are systematically steeper at high-redshift, and present much more rapid evolution in their gradients. We find that the majority of the models predict radial gradients today which are consistent with those observed in late-type disks, but they evolve to this self-similarity in different fashions, despite each adhering to classical `inside-out' growth. We find that radial dependence of the efficiency with which stars form as a function of time drives the differences seen in the gradients; systematic differences in the sub-grid physics between the various codes are responsible for setting these gradients. Recent, albeit limited, data at redshift z=1.5 are consistent with the steeper gradients seen in our SPH sample, suggesting a modest revision of the classical chemical evolution models may be required.

Recent observations of the cosmic microwave background anisotropy indicate that, at very small angular scales, the power of the CMB angular spectrum is smaller than that suggested by previous observations. Moreover, new recent simulations of the lensing effect conducted by us -at the same scales- give powers larger than those obtained in previous numerical estimates. In order to study the compatibility between our numerical predictions (lensing effect) and current observations, the coupling among Sunyaev-Zel'dovich, lensing and Rees-Sciama effects should be simulated.

We examine radial and vertical metallicity gradients using a suite of disk galaxy simulations, supplemented with two classic chemical evolution approaches. We determine the rate of change of gradient and reconcile differences between extant models and observations within the `inside-out' disk growth paradigm. A sample of 25 disks is used, consisting of 19 from our RaDES (Ramses Disk Environment Study) sample, realised with the adaptive mesh refinement code RAMSES. Four disks are selected from the MUGS (McMaster Unbiased Galaxy Simulations) sample, generated with the smoothed particle hydrodynamics (SPH) code GASOLINE, alongside disks from Rahimi et al. (GCD+) and Kobayashi Nakasato (GRAPE-SPH). Two chemical evolution models of inside-out disk growth were employed to contrast the temporal evolution of their radial gradients with those of the simulations. We find that systematic differences exist between the predicted evolution of radial abundance gradients in the RaDES and chemical evolution models, compared with the MUGS sample; specifically, the MUGS simulations are systematically steeper at high-redshift, and present much more rapid evolution in their gradients. We find that the majority of the models predict radial gradients today which are consistent with those observed in late-type disks, but they evolve to this self-similarity in different fashions, despite each adhering to classical `inside-out' growth. We find that radial dependence of the efficiency with which stars form as a function of time drives the differences seen in the gradients; systematic differences in the sub-grid physics between the various codes are responsible for setting these gradients. Recent, albeit limited, data at redshift z=1.5 are consistent with the steeper gradients seen in our SPH sample, suggesting a modest revision of the classical chemical evolution models may be required.