Robert J. Thacker

Simulations of the formation, evolution and clustering of galaxies and quasars

The cold dark matter model has become the leading theoretical picture for the formation of structure in the Universe. This model, together with the theory of cosmic inflation, makes a clear prediction for the initial conditions for structure formation and predicts that structures grow hierarchically through gravitational instability. Testing this model requires that the precise measurements delivered by galaxy surveys can be compared to robust and equally precise theoretical calculations. Here we present a simulation of the growth of dark matter structure using 2,1603 particles, following them from redshift z = 127 to the present in a cube-shaped region 2.230 billion lightyears on a side. In postprocessing, we also follow the formation and evolution of the galaxies and quasars. We show that baryon-induced features in the initial conditions of the Universe are reflected in distorted form in the low-redshift galaxy distribution, an effect that can be used to constrain the nature of dark energy with future generations of observational surveys of galaxies.Numerical simulations are a primary theoretical tool to study the nonlinear gravitational growth of structure in the Universe, and to link the initial conditions of cold dark matter (CDM) cosmogonies to observations of galaxies at the present day. Without direct numerical simulation, the hierarchical build-up of structure with its threedimensional dynamics would be largely inaccessible. Since the dominant mass component, the dark matter, is assumed to consist of weakly interacting elementary particles that interact only gravitationally, such simulations use a set of discrete point particles to represent the collisionless dark matter fluid. This representation as an N-body system is obviously only a coarse approximation, and im-

Implementing Feedback in Simulations of Galaxy Formation: A Survey of Methods

We present a detailed description, and examine the performance of, a number of different approaches to modeling feedback in simulations of galaxy formation. Gasdynamic forces are evaluated using smoothed particle hydrodynamics (SPH). Star formation and supernova feedback are included using a three-parameter model which determines the star formation rate (SFR) normalization, feedback energy, and lifetime of feedback regions. The star formation rate is calculated for all gas particles which fall within prescribed temperature, density, and convergent flow criteria, and for cosmological simulations we also include a self-gravity criterion for gas particles to prevent star formation at high redshifts. A Lagrangian Schmidt law is used to calculate the star formation rate from the SPH density. Conversion of gas to stars is performed when the star mass for a gas particle exceeds a certain limit, typically half that of the gas particle. Feedback is incorporated by returning a precalculated amount of energy to the ISM as thermal heating. We compare the effects of distributing this energy over the smoothing scale or depositing it on a single particle. Radiative losses are prevented from heated particles by adjusting the density used in radiative cooling so that the decay of energy occurs over a set half-life, or by turning off cooling completely and allowing feedback regions a brief period of adiabatic expansion. We test the models on the formation of galaxies from cosmological initial conditions and also on isolated disk galaxies. For isolated prototypes of the Milky Way and the dwarf galaxy NGC 6503 we find feedback has a significant effect, with some algorithms being capable of unbinding gas from the dark matter halo (blow-away). As expected feedback has a stronger effect on the dwarf galaxy, producing significant disk evaporation and also larger feedback bubbles for the same parameters. In the critical-density CDM cosmological simulations, evolved to a redshift z = 1, we find that, barring extreme models, feedback has little effect. Further, feedback only manages to produce a disk with a specific angular momentum value approximately twice that of the run with no feedback, the disk thus has an specific angular momentum value that is characteristic of observed elliptical galaxies. We argue that this is a result of the extreme central concentration of the dark halos in the standard CDM model and the pervasiveness of the core-halo angular momentum transport mechanism (even in light of feedback). A simulation with extremely violent feedback, relative to our fiducial models, leads to a disk that resembles the other simulations at z = 1 and has a specific angular momentum value that is more typical of observed disk galaxies. At later times, z = 0.5, a large amount of halo gas which does not suffer an angular momentum deficit is present; however, the cooling time is too long to accrete on to the disk. We further point out that the disks formed in hierarchical simulations are partially a numerical artifact produced by the minimum mass scale of the simulation acting as a highly efficient support mechanism. Disk formation is strongly affected by the treatment of dense regions in the SPH method. The problems inherent in the treatment of high-density regions in SPH, in concert with the difficulty of representing the hierarchical formation process, means that realistic simulations of galaxy formation require far higher particle resolution than currently used.

Star Formation, Supernova Feedback, and the Angular Momentum Problem in Numerical Cold Dark Matter Cosmogony: Halfway There?

We present a smoothed particle hydrodynamic simulation that reproduces a galaxy that is a moderate facsimile of those observed. The primary failing point of previous simulations of disk formation, namely, excessive transport of angular momentum from gas to dark matter, is ameliorated by the inclusion of a supernova feedback algorithm that allows energy to persist in the model interstellar medium for a period corresponding to the lifetime of stellar associations. The inclusion of feedback leads to a disk at a redshift z = 0.52, with a specific angular momentum content within 10% of the value required to fit observations. An exponential fit to the disk baryon surface density gives a scale length within 17% of the theoretical value. Runs without feedback, with or without star formation, exhibit the drastic angular momentum transport observed elsewhere.

Metallicity gradients in disks - Do galaxies form inside-out?

Aims. We examine radial and vertical metallicity gradients using a suite of disk galaxy hydrodynamical simulations, supplemented with two classic chemical evolution approaches. We determine the rate of change of gradient slope and reconcile the differences existing between extant models and observations within the canonical “inside-out” disk growth paradigm. Methods. A suite of 25 cosmological disks is used to examine the evolution of metallicity gradients; this consists of 19 galaxies selected from the RaDES (Ramses Disk Environment Study) sample, realised with the adaptive mesh refinement code ramses ,i ncluding eight drawn from the “field” and six from “loose group” environments. Four disks are selected from the MUGS (McMaster Unbiased Galaxy Simulations) sample, generated with the smoothed particle hydrodynamics (SPH) code gasoline. 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. Results. We first show that generically flatter gradients are observed at redshift zero when comparing older stars with those forming today, consistent with expectations of kinematically hot simulations, but counter to that observed in the Milky Way. The vertical abundance gradients at ∼1−3 disk scalelengths are comparable to those observed in the thick disk of the Milky Way, but significantly shallower than those seen in the thin disk. Most importantly, 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. Conclusions. 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.

Quasars: What Turns Them Off?

While the high-redshift quasar luminosity function closely parallels the hierarchical growth of dark matter halos, at lower redshifts quasars exhibit an antihierarchical turnoff, which moves from the most luminous objects to the faintest. We explore the idea that this may arise from self-regulating feedback, caused by quasar outflows. Using a hybrid approach that combines a detailed hydrodynamic simulation with observationally derived relationships, we calculate the luminosity function of quasars down to a redshift of z = 1 in a large, cosmologically representative volume. Outflows are included explicitly by tracking halo mergers and driving shocks into the surrounding intergalactic medium, with an energy output equal to a fixed 5% fraction of the bolometric luminosity. Our results are in excellent agreement with measurements of the spatial distribution of quasars on both small and large scales, and we detect an intriguing excess of galaxy-quasar pairs at very short separations. Our results also reproduce an antihierarchical turnoff in the quasar luminosity function; however, this falls short of that observed, as well as that predicted by analogous semianalytic models. The difference can be traced to the treatment of gas heating within galaxies and the presence of in-shock cooling. The simulated galaxy cluster LX-T relationship is close to that observed for z ? 1 clusters, but the simulated galaxy groups at z = 1 are significantly perturbed by quasar outflows. Measurements of anomalously high X-ray emission in high-redshift groups, along with detections of 1000 km s-1 winds in poststarburst ellipticals, would provide definitive evidence for the AGN-heating hypothesis.

Toward an Improved Analytical Description of Lagrangian Bias

We carry out a detailed numerical investigation of the spatial correlation function of the initial positions of cosmological dark matter halos. In this Lagrangian coordinate system, which is especially useful for analytic studies of cosmological feedback, we are able to construct cross-correlation functions of objects with varying masses and formation redshifts and compare them with a variety of analytical approaches. For the case in which both formation redshifts are equal, we find good agreement between our numerical results and the bivariate model of Scannapieco & Barkana at all masses, redshifts, and separations, while the model of Porciani and coworkers does well for all parameters except for objects with different masses at small separations. We find that the standard mapping between Lagrangian and Eulerian bias performs well for rare objects at all separations, but fails if the objects are highly nonlinear (low-sigma) peaks. In the Lagrangian case, in which the formation redshifts differ, the model of Scannapieco & Barkana does well for all separations and combinations of masses, apart from a discrepancy at small separations in situations in which the smaller object is formed earlier, and the difference between redshifts or masses is large. As this same limitation arises in the standard approach to the single-point progenitor distribution developed by Lacey & Cole, we conclude that a more complete understanding of the progenitor distribution is the most important outstanding issue in the analytic modeling of Lagrangian bias.

Re-engineering the eastern Lake Erie littoral food web: The trophic function of non-indigenous Ponto-Caspian species

ABSTRACT The trophic roles of key Ponto-Caspian invaders (quagga mussels Dreissena bugensis, amphipods Echinogammarus ischnus and round goby Apollonia melanostomus) within the littoral food web of eastern Lake Erie were quantified using stable isotopes (&dgr;13C, &dgr;15N). A dual stable isotope parameter search with a mass balance component was used to assess the isotopic importance of quagga mussels and amphipods as dietary items to two size classes of round goby. The utility of the mass balance simulation was also evaluated as a tool to approximate isotopic contributions of feasible prey and identify gaps incurred by “missing” prey items not included in the sampling. The mass balance dietary simulation, confirmed by stomach content data, indicated that isotopically important prey to small round goby (<11.2 cm) were chironomids and Ponto-Caspian amphipods, while large round goby (≥11.2 cm) showed strong preference for quagga mussels. The dietary mass balance simulation output also supported the isotopic importance of round goby to the somatic growth of smallmouth bass, rock bass and freshwater drum. The isotopic mass balance output for yellow perch was more ambiguous, which may be in line with their known broadly omnivorous diet. The white bass output was in line with published data indicating increasing consumption of round goby for this species, while the brown trout output strongly favoured alewife isotopic contributions. However for white perch and walleye, the mass balance simulations were not in line with their known published diets in Lake Erie, probably due to a lack of key prey items in the sample set (e.g. zooplankton for white perch and shiner species for walleye). As expected, the Ponto-Caspian species have integrated themselves into the littoral food webs, and the “quagga mussel-round goby-smallmouth bass” food chain forms one of the key components within the trophodynamics of Lake Erie.

An N-body/SPH study of isolated galaxy mass density profiles

We investigate the evolution of mass density profiles in secular disk galaxy models, paying special attention to the development of a two-component profile from a single initial exponential disk free of cosmological evolution (i.e., no accretion or interactions). As the source of density profile variations, we examine the parameter space of the spin parameter, halo concentration, virial mass, disk mass and bulge mass, for a total of 162 simulations in the context of a plausible model of star formation and feedback. The isolated galaxy models are based on the method of Springel & White (1999) and were evolved using the N-body/SPH code GADGET-2. The initially pure exponential disks have a minimum of 1.4 million particles and most models were evolved over a period of 10 Gyr. We find that the slope of the outer density profile is in close agreement with that of the initial profile and remains stable over time, whereas the inner density profile slope evolves considerably as a result of angular momentum redistribution. The evolution of the galaxy mass density profile, including the development of a two-component profile with an inner and outer segment, is controlled by the ratio of the disk mass fraction, md, to the halo spin parameter, λ. The location of the break between the two components and speed at which it develops is directly proportional to md/λ; the amplitude of the transition between the inner and outer regions is however controlled by the ratio of halo concentration to virial velocity. The location of the divide between the inner and outer profile does not change with time. The condition for a two-component profile is roughly md/λ > 1. While the development of a two-component density profile is coupled to bar formation, not all barred galaxies develop a two-component profile. A galaxy model showing a clear minimum Toomre Q, normally linked to a double exponential in the stellar profile, may never exhibit any two-component feature thus yielding a fully evolved pure exponential disk.

A comparative study of AGN feedback algorithms

Modelling 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: 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, with accretion rates that 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 gas properties near the black hole to different extents. The particle accretion algorithms usually (but not always) maintain good agreement between the mass accreted by \dot{M} dt and the mass of gas particles removed from the simulation. 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. The black holes merge when given criteria are met, and we find a range of merger times for different criteria. 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 it. 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. (abridged)

A parallel adaptive P3M code with hierarchical particle reordering

Abstract We discuss the design and implementation of HYDRA_OMP a parallel implementation of the Smoothed Particle Hydrodynamics–Adaptive P 3 M (SPH-AP 3 M) code HYDRA. The code is designed primarily for conducting cosmological hydrodynamic simulations and is written in Fortran77+OpenMP. A number of optimizations for RISC processors and SMP-NUMA architectures have been implemented, the most important optimization being hierarchical reordering of particles within chaining cells, which greatly improves data locality thereby removing the cache misses typically associated with linked lists. Parallel scaling is good, with a minimum parallel scaling of 73% achieved on 32 nodes for a variety of modern SMP architectures. We give performance data in terms of the number of particle updates per second, which is a more useful performance metric than raw MFlops. A basic version of the code will be made available to the community in the near future.