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Cosmological N-body simulations have been a major tool of theorists for decades, yet many of the numerical issues that these simulations face are still unexplored. This paper measures numerical biases in these large, dark matter-only simulations that affect the properties of their dark matter haloes. We compare many simulation suites in order to provide several tools for simulators and analysts which help mitigate these biases. We summarise our comparisons with practical `convergence limits that can be applied to a wide range of halo properties, including halo properties which are traditionally overlooked by the testing literature. We also find that the halo properties predicted by different simulations can diverge from one another at unexpectedly high resolutions. We demonstrate that many halo properties depend strongly on force softening scale and that this dependence leads to much of the measured divergence between simulations. We offer an empirical model to estimate the impact of such effects on the rotation curves of a halo population. This model can serve as a template for future empirical models of the biases in other halo properties.
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Cosmological simulations of galaxy formation often rely on prescriptions for star formation and feedback that depend on halo properties such as halo mass, central over-density, and virial temperature. In this paper we address the convergence of individual halo properties, based on their number of particles N, focusing in particular on the mass of halos near the resolution limit of a simulation. While it has been established that the halo mass function is sampled on average down to N~30 particles, we show that individual halo properties exhibit significant scatter, and some systematic biases, as one approaches the resolution limit. We carry out a series of cosmological simulations using the Gadget2 and Enzo codes with N_p=64^3 to N_p=1024^3 total particles, keeping the same large-scale structure in the simulation box. We consider boxes from l_{box} = 8 Mpc/h to l_{box} = 512 Mpc/h to probe different halo masses and formation redshifts. We cross-identify dark matter halos in boxes at different resolutions and measure the scatter in their properties. The uncertainty in the mass of single halos depends on the number of particles (scaling approximately as N^{-1/3}), but the rarer the density peak, the more robust its identification. The virial radius of halos is very stable and can be measured without bias for halos with N>30. In contrast, the average density within a sphere containing 25% of the total halo mass is severely underestimated (by more than a factor 2) and the halo spin is moderately overestimated for N<100. If sub-grid physics is implemented upon a cosmological simulation, we recommend that rare halos (~3sigma peaks) be resolved with N>100 particles and common halos (~1sigma peaks) with N>400 particles to avoid excessive numerical noise and possible systematic biases in the results.
NGC 5128 (Centaurus A) is, at the distance of just 3.8 Mpc, the nearest easily observable giant elliptical galaxy. Therefore it is the best target to investigate the early star formation history of an elliptical galaxy. Our aims are to establish when the oldest stars formed in NGC 5128, and whether this galaxy formed stars over a long period. We compare simulated colour-magnitude diagrams with the deep ACS/HST photometry. We find that that the observed colour-magnitude diagram can be reproduced satisfactorily only by simulations that have the bulk of the stars with ages in excess of ~10 Gyr, and that the alpha-enhanced models fit the data much better than the solar scaled ones. Data are not consistent with extended star formation over more than 3-4 Gyr. Two burst models, with 70-80% of the stars formed 12+/-1 Gyr ago and with 20-30% younger contribution with 2-4 Gyr old stars provide the best agreement with the data. The old component spans the whole metallicity range of the models (Z=0.0001-0.04), while for the young component the best fitting models indicate higher minimum metallicity (~1/10 - 1/4 Z_sun). The bulk of the halo stars in NGC5128 must have formed at redshift z>=2 and the chemical enrichment was very fast, reaching solar or even twice-solar metallicity already for the ~11-12 Gyr old population. The minor young component, adding ~20-30% of the stars to the halo, and contributing less than 10% of the mass, may have resulted from a later star formation event ~2-4 Gyr ago. (abridged)
We perform a suite of multimass cosmological zoom simulations of individual dark matter halos and explore how to best select Lagrangian regions for resimulation without contaminating the halo of interest with low-resolution particles. Such contamination can lead to significant errors in the gas distribution of hydrodynamical simulations, as we show. For a fixed Lagrange volume, we find that the chance of contamination increases systematically with the level of zoom. In order to avoid contamination, the Lagrangian volume selected for resimulation must increase monotonically with the resolution difference between parent box and the zoom region. We provide a simple formula for selecting Lagrangian regions (in units of the halo virial volume) as a function of the level of zoom required. We also explore the degree to which a halos Lagrangian volume correlates with other halo properties (concentration, spin, formation time, shape, etc.) and find no significant correlation. There is a mild correlation between Lagrange volume and environment, such that halos living in the most clustered regions have larger Lagrangian volumes. Nevertheless, selecting halos to be isolated is not the best way to ensure inexpensive zoom simulations. We explain how one can safely choose halos with the smallest Lagrangian volumes, which are the least expensive to resimulate, without biasing ones sample.
We study the nature of long gamma ray burst (LGRB) progenitors using cosmological simulations of structure formation and galactic evolution. LGRBs are potentially excellent tracers of stellar evolution in the early universe. We developed a Monte Carlo numerical code which generates LGRBs coupled to cosmological simulations. The simulations allows us to follow the ormation of galaxies self-consistently. We model the detectability of LGRBs and their host galaxies in order to compare results with observational data obtained by high-energy satellites. Our code also includes stochastic effects in the observed rate of LGRBs.
We study the properties of two bars formed in fully cosmological hydrodynamical simulations of the formation of Milky Way-mass galaxies. In one case, the bar formed in a system with disc, bulge and halo components and is relatively strong and long, as could be expected for a system where the spheroid strongly influences the evolution. The second bar is less strong, shorter, and formed in a galaxy with no significant bulge component. We study the strength and length of the bars, the stellar density profiles along and across the bars and the velocity fields in the bar region. We compare them with the results of dynamical (idealised) simulations and with observations, and find, in general, a good agreement, although we detect some important differences as well. Our results show that more or less realistic bars can form naturally in a $Lambda$CDM cosmology, and open up the possibility to study the bar formation process in a more consistent way than previously done, since the host galaxies grow, accrete matter and significantly evolve during the formation and evolution of the bar.
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