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The stellar stripping of satellites in cluster haloes is understood to play an important role in the production of intracluster light. Increasingly, cosmological simulations have been utilised to investigate its origin and assembly. However, such simulations typically model individual galaxies at relatively coarse resolutions, raising concerns about their accuracy. Although there is a growing literature on the importance of numerical resolution for the accurate recovery of the mass loss rates of dark matter (DM) haloes, there has been no comparable investigation into the numerical resolution required to accurately recover stellar mass loss rates in galaxy clusters. Using N-body simulations of satellite galaxies orbiting in a cluster halo represented by a static external potential, we conduct a set of convergence tests in order to explore the role of numerical resolution and force softening length on stellar stripping efficiency. We consider a number of orbital configurations, satellite masses and satellite morphologies. We find that stellar mass resolution is of minor importance relative to DM resolution. Resolving the central regions of satellite DM halos is critical to accurately recover stellar mass loss rates. Poorly resolved DM haloes develop cored inner profiles and, if this core is of comparable size to the stellar component of the satellite galaxy, this leads to significant over-stripping. To prevent this, relatively high DM mass resolutions of around $m_{\rm DM}\sim10^{6}$ M$_{\odot}$, better than those achieved by many contemporary cosmological simulations, are necessary., Comment: Accepted for publication in MNRAS. 19 pages, 13 figures

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance., Comment: Accepted for publication in the A&A special issue`Euclid on Sky'

Galaxy cluster outskirts mark the transition region from the mildly non-linear cosmic web to the highly non-linear, virialised, cluster interior. It is in this transition region that the intra-cluster medium (ICM) begins to influence the properties of accreting galaxies and groups, as ram pressure impacts a galaxy's cold gas content and subsequent star formation rate. Conversely, the thermodynamical properties of the ICM in this transition region should also feel the influence of accreting substructure (i.e. galaxies and groups), whose passage can drive shocks. In this paper, we use a suite of cosmological hydrodynamical zoom simulations of a single galaxy cluster, drawn from the nIFTy comparison project, to study how the dynamics of substructure accreted from the cosmic web influences the thermodynamical properties of the ICM in the cluster's outskirts. We demonstrate how features evident in radial profiles of the ICM (e.g. gas density and temperature) can be linked to strong shocks, transient and short-lived in nature, driven by the passage of substructure. The range of astrophysical codes and galaxy formation models in our comparison are broadly consistent in their predictions (e.g. agreeing when and where shocks occur, but differing in how strong shocks will be); this is as we would expect of a process driven by large-scale gravitational dynamics and strong, inefficiently radiating, shocks. This suggests that mapping such shock structures in the ICM in a cluster's outskirts (via e.g. radio synchrotron emission) could provide a complementary measure of its recent merger and accretion history., Comment: 15 pages, 13 figures, version accepted for publication in MNRAS

The primary difficulty in measuring dynamical masses of galaxy clusters from galaxy data lies in the separation between true cluster members from interloping galaxies along the line of sight. We study the impact of membership contamination and incompleteness on cluster mass estimates obtained with 25 commonly used techniques applied to nearly 1000 mock clusters. We show that all methods overestimate or underestimate cluster masses when applied to contaminated or incomplete galaxy samples respectively. This appears to be the main source of the intrinsic scatter in the mass scaling relation. Applying corrections based on a prior knowledge of contamination and incompleteness can reduce the scatter to the level of shot noise expected for poorly sampled clusters. We establish an empirical model quantifying the effect of imperfect membership on cluster mass estimation and discuss its universal and method-dependent features. We find that both imperfect membership and the response of the mass estimators depend on cluster mass, effectively causing a flattening of the estimated - true mass relation. Imperfect membership thus alters cluster counts determined from spectroscopic surveys, hence the cosmological parameters that depend on such counts., Comment: 18 pages, 11 figures, 3tables; accepted for publication in MNRAS

With the advent of wide-field cosmological surveys, we are approaching samples of hundreds of thousands of galaxy clusters. While such large numbers will help reduce statistical uncertainties, the control of systematics in cluster masses becomes ever more crucial. Here we examine the effects of an important source of systematic uncertainty in galaxy-based cluster mass estimation techniques: the presence of significant dynamical substructure. Dynamical substructure manifests as dynamically distinct subgroups in phase-space, indicating an 'unrelaxed' state. This issue affects around a quarter of clusters in a generally selected sample. We employ a set of mock clusters whose masses have been measured homogeneously with commonly-used galaxy-based mass estimation techniques (kinematic, richness, caustic, radial methods). We use these to study how the relation between observationally estimated and true cluster mass depends on the presence of substructure, as identified by various popular diagnostics. We find that the scatter for an ensemble of clusters does not increase dramatically for clusters with dynamical substructure. However, we find a systematic bias for all methods, such that clusters with significant substructure have higher measured masses than their relaxed counterparts. This bias depends on cluster mass: the most massive clusters are largely unaffected by the presence of significant substructure, but masses are significantly overestimated for lower mass clusters, by $\sim10\%$ at $10^{14}$ and $\geq20\%$ for $\leq10^{13.5}$. The use of cluster samples with different levels of substructure can, therefore, bias certain cosmological parameters up to a level comparable to the typical uncertainties in current cosmological studies., Comment: 14 pages, 8 figures, 3 tables. Submitted to MNRAS

This article is the second in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilise the positions, velocities and colours of galaxies. Our aim is to quantify the scatter, systematic bias and completeness of cluster masses derived from a diverse set of 25 galaxy-based methods using two contrasting mock galaxy catalogues based on a sophisticated halo occupation model and a semi-analytic model. Analysing 968 clusters, we find a wide range in the RMS errors in log M200c delivered by the different methods (0.18 to 1.08 dex, i.e., a factor of ~1.5 to 12), with abundance matching and richness methods providing the best results, irrespective of the input model assumptions. In addition, certain methods produce a significant number of catastrophic cases where the mass is under- or over-estimated by a factor greater than 10. Given the steeply falling high-mass end of the cluster mass function, we recommend that richness or abundance matching-based methods are used in conjunction with these methods as a sanity check for studies selecting high mass clusters. We see a stronger correlation of the recovered to input number of galaxies for both catalogues in comparison with the group/cluster mass, however, this does not guarantee that the correct member galaxies are being selected. We do not observe significantly higher scatter for either mock galaxy catalogues. Our results have implications for cosmological analyses that utilise the masses, richnesses, or abundances of clusters, which have different uncertainties when different methods are used., Comment: 25 pages, 19 figures, 7 tables. Accepted for publication in MNRAS

This paper is the first in a series in which we perform an extensive comparison of various galaxy-based cluster mass estimation techniques that utilise the positions, velocities and colours of galaxies. Our primary aim is to test the performance of these cluster mass estimation techniques on a diverse set of models that will increase in complexity. We begin by providing participating methods with data from a simple model that delivers idealised clusters, enabling us to quantify the underlying scatter intrinsic to these mass estimation techniques. The mock catalogue is based on a Halo Occupation Distribution (HOD) model that assumes spherical Navarro, Frenk and White (NFW) haloes truncated at R_200, with no substructure nor colour segregation, and with isotropic, isothermal Maxwellian velocities. We find that, above 10^14 M_solar, recovered cluster masses are correlated with the true underlying cluster mass with an intrinsic scatter of typically a factor of two. Below 10^14 M_solar, the scatter rises as the number of member galaxies drops and rapidly approaches an order of magnitude. We find that richness-based methods deliver the lowest scatter, but it is not clear whether such accuracy may simply be the result of using an over-simplistic model to populate the galaxies in their haloes. Even when given the true cluster membership, large scatter is observed for the majority non-richness-based approaches, suggesting that mass reconstruction with a low number of dynamical tracers is inherently problematic., Comment: 25 pages, 15 figures, 5 tables. Accepted for publication in MNRAS

We study the systematic bias introduced when selecting the spectroscopic redshifts of brighter cluster galaxies to estimate the velocity dispersion of galaxy clusters from both simulated and observational galaxy catalogues. We select clusters with Ngal > 50 at five low redshift snapshots from a semi-analytic model galaxy catalogue, and from a catalogue of SDSS DR8 groups and clusters across the redshift range 0.021

We use numerical simulations to investigate, for the first time, the joint effect of feedback from supernovae (SNe) and active galactic nuclei (AGN) on the evolution of galaxy cluster X-ray scaling relations. Our simulations are drawn from the Millennium Gas Project and are some of the largest hydrodynamical N-body simulations ever carried out. Feedback is implemented using a hybrid scheme, where the energy input into intracluster gas by SNe and AGN is taken from a semi-analytic model of galaxy formation. This ensures that the source of feedback is a population of galaxies that closely resembles that found in the real universe. We show that our feedback model is capable of reproducing observed local X-ray scaling laws, at least for non-cool core clusters, but that almost identical results can be obtained with a simplistic preheating model. However, we demonstrate that the two models predict opposing evolutionary behaviour. We have examined whether the evolution predicted by our feedback model is compatible with observations of high-redshift clusters. Broadly speaking, we find that the data seems to favour the feedback model for z<0.5, and the preheating model at higher redshift. However, a statistically meaningful comparison with observations is impossible, because the large samples of high-redshift clusters currently available are prone to strong selection biases. As the observational picture becomes clearer in the near future, it should be possible to place tight constraints on the evolution of the scaling laws, providing us with an invaluable probe of the physical processes operating in galaxy clusters., Comment: 23 pages, 14 figures, 3 tables. Minor revisons in line with referee's comments. Published in MNRAS

The physical processes that define the spine of the galaxy cluster X-ray luminosity -- temperature (L-T) relation are investigated using a large hydrodynamical simulation of the Universe. This simulation models the same volume and phases as the Millennium Simulation and has a linear extent of 500 h^{-1} Mpc. We demonstrate that mergers typically boost a cluster along but also slightly below the L-T relation. Due to this boost we expect that all of the very brightest clusters will be near the peak of a merger. Objects from near the top of the L-T relation tend to have assembled much of their mass earlier than an average halo of similar final mass. Conversely, objects from the bottom of the relation are often experiencing an ongoing or recent merger., Comment: 8 pages, 7 figures, submitted to MNRAS

We follow the growth of baryonic structure in the presence of a magnetic field within an approximate cosmological magneto-hydrodynamic simulation, produced by adding an (isotropic) magnetic pressure related to the local gas pressure. We perform an ensemble of these simulations to follow the amplification of the field with time. By using a variety of initial field strengths and changing the slope of the power law that governs the way the field grows with increasing density we span the range of current observations and demonstrate the size of the effect realistic magnetic fields could have on the central density of groups and clusters. A strong magnetic field significantly reduces the central gas density which, in turn, reduces observable quantities such as the X-ray luminosity., Comment: 9 pages, 9 figures. Accepted by MNRAS

The comparison between observations of galaxy clusters thermo-dynamical properties and theoretical predictions suggests that non-gravitational heating needs to be added into the models. We implement an internally self-consistent heating scheme into GADGET-2 for the third (and fourth) run of the Millennium gas project (Pearce et al. in preparation), a set of four hydrodynamical cosmological simulations with N=2(5x10^8) particles and with the same volume (L=500 h-1 Mpc) and structures as the the N-body Millennium Simulation (Springel et al. 2005). Our aim is to reproduce the observed thermo-dynamical properties of galaxy clusters., Comment: 3 pages, 2 figures, To appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany)

We present the results of a large library of cosmological N-body simulations, using power-law initial spectra. The nonlinear evolution of the matter power spectra is compared with the predictions of existing analytic scaling formulae based on the work of Hamilton et al. The scaling approach has assumed that highly nonlinear structures obey `stable clustering' and are frozen in proper coordinates. Our results show that, when transformed under the self-similarity scaling, the scale-free spectra define a nonlinear locus that is clearly shallower than would be required under stable clustering. Furthermore, the small-scale nonlinear power increases as both the power-spectrum index n and the density parameter Omega decrease, and this evolution is not well accounted for by the previous scaling formulae. This breakdown of stable clustering can be understood as resulting from the modification of dark-matter haloes by continuing mergers. These effects are naturally included in the analytic `halo model' for nonlinear structure; using this approach we are able to fit both our scale-free results and also our previous CDM data. This approach is more accurate than the commonly-used Peacock--Dodds formula and should be applicable to more general power spectra. Code to evaluate nonlinear power spectra using this method is available from http://as1.chem.nottingham.ac.uk/~res/software.html Following publication, we will make the power-law simulation data available through the Virgo website http://www.mpa-garching.mpg.de/Virgo, Comment: V2: 23 Latex Pages. Replaced with a version consistent with refereed journal article. Section 3.4 reduced, Fig added to section 6, references added

We use giga-particle N-body simulations to study galaxy cluster populations in Hubble Volumes of LCDM (Omega_m=0.3, Omega_Lambda=0.7) and tCDM (Omega_m=1) world models. Mapping past light-cones of locations in the computational space, we create mock sky surveys of dark matter structure to z~1.4 over 10,000 sq deg and to z~0.5 over two full spheres. Calibrating the Jenkins mass function at z=0 with samples of ~1.5 million clusters, we show that the fit describes the sky survey counts to <~20% acccuracy over all redshifts for systems larger than poor groups (M>5e13 Msun/h). Fitting the observed local temperature function determines the ratio beta of specific thermal energies in dark matter and intracluster gas. We derive a scaling with power spectrum normalization beta \propto sigma8^{5/3}, and measure a 4% error on sigma8 arising from cosmic variance in temperature-limited cluster samples. Considering distant clusters, the LCDM model matches EMSS and RDCS X-ray-selected survey observations under economical assumptions for intracluster gas evolution. Using transformations of mass-limited cluster samples that mimic sigma8 variation, we explore SZ search expectations for a 10 sq deg survey complete above 10^{14} Msun/h. Cluster counts are shown to be extremely sensitive to sigma8 uncertainty while redshift statistics, such as the sample median, are much more stable. For LCDM, the characteristic temperature at fixed sky surface density is a weak function of redshift, implying an abundance of hot clusters at z>1. Assuming constant beta, four kT>8 keV clusters lie at z>2 and 40 kT>5 keV clusters lie at z>3 on the whole sky. Detection of Coma-sized clusters at z>1 violate LCDM at 95% confidence if their surface density exceeds 0.003 per sq deg, or 120 on the whole sky., Comment: 44 pages, 20 figures. Revised estimate of cosmic variance error in sigma8 (3% for mass-, 4% for T-limited samples). Truncated entries (most massive ten clusters) of sky survey electronic tables added in Appendix C (See also at http://astro.physics.lsa.umich.edu/HV/tables.htm). ApJ, to appear v573 (July 1, 2002)

We have performed cosmological simulations in a $\Lambda$CDM cosmology with and without radiative cooling, in order to study the effect of cooling on the cluster scaling relations. Our simulations consist of 4.1 million particles each of gas and dark matter within a box-size of 100 $h^{-1}$ Mpc and the run with cooling is the largest of its kind to have been evolved to $z=0$. Our cluster catalogues both consist of over 400 objects and are complete in mass down to $\sim 10^{13} h^{-1} {\rm M_{\odot}}$. We contrast the emission-weighted temperature-mass ($T_{\rm ew}-M$) and bolometric luminosity-temperature ($L_{\rm bol}-T_{\rm ew}$) relations for the simulations at $z=0$. We find that radiative cooling \emph{increases} the temperature of intracluster gas and \emph{decreases} its total luminosity, in agreement with the results of Pearce et al. Furthermore, the temperature dependence of these effects flattens the slope of the $T_{\rm ew}-M$ relation and steepens the slope of the $L_{\rm bol}-T_{\rm ew}$ relation. Inclusion of radiative cooling in the simulations is sufficient to reproduce the observed X-ray scaling relations without requiring excessive non-gravitational energy injection., Comment: 4 pages, 2 figures. Matches version accepted for publication in ApJ Letters

We create mock pencil-beam redshift surveys from very large cosmological $N$-body simulations of two Cold Dark Matter cosmogonies, an Einstein-de Sitter model ($\tau$CDM) and a flat model with $\Omega_0 =0.3$ and a cosmological constant ($\Lambda$CDM). We use these to assess the significance of the apparent periodicity discovered by Broadhurst et al. (1990). Simulation particles are tagged as `galaxies' so as to reproduce observed present-day correlations. They are then identified along the past light-cones of hypothetical observers to create mock catalogues with the geometry and the distance distribution of the Broadhurst et al. data. We produce 1936 (2625) quasi-independent catalogues from our $\tau$CDM ($\Lambda$CDM) simulation. A couple of large clumps in a catalogue can produce a high peak at low wavenumbers in the corresponding one-dimensional power spectrum, without any apparent large-scale periodicity in the original redshift histogram. Although the simulated redshift histograms frequently display regularly spaced clumps, the spacing of these clumps varies between catalogues and there is no `preferred' period over our many realisations. We find only a 0.72 (0.49) per cent chance that the highest peak in the power spectrum of a $\tau$CDM ($\Lambda$CDM) catalogue has a peak-to-noise ratio higher than that in the Broadhurst et al. data. None of the simulated catalogues with such high peaks shows coherently spaced clumps with a significance as high as that of the real data. We conclude that in CDM universes, the kind of regularity observed by Broadhurst et al. has a priori probability well below $10^{-3}$., Comment: 8 pages, 9 figures, submitted to MNRAS

We present results of large N-body-hydrodynamic simulations of galaxy formation. Our simulations follow the formation of galaxies in cubic volumes of side 100Mpc, in two versions of the cold dark matter (CDM) cosmogony: the standard, Omega=1 SCDM model and the flat, Omega=0.3 LCDM model. Over 2000 galaxies form in each of these simulations. We examine the rate at which gas cools and condenses into dark matter halos. This roughly tracks the cosmic star formation rate inferred from observations at various redshifts. Galaxies in the simulations form gradually over time in the hierarchical fashion characteristic of the CDM cosmogony. In the LCDM model, substantial galaxies first appear at z=5 and the population builds up rapidly until z=1 after which the rate of galaxy formation declines as cold gas is consumed and the cooling time of hot gas increases. In both cosmologies, the present-day K-band luminosity function of the simulated galaxies resembles observations. The galaxy autocorrelation functions differ significantly from those of the dark matter. At the present epoch there is little bias in either model between galaxies and dark matter on large scales, but a significant anti-bias on scales of 1Mpc/h and a positive bias on scales of 100kpc/h. The galaxy correlation function evolves little with redshift in the range z=0-3, and depends on the luminosity of the galaxy sample. The projected pairwise velocity dispersion of the galaxies is much lower than that of the dark matter on scales less than 2Mpc/h. Applying a virial mass estimator to the largest galaxy clusters recovers the cluster virial masses in an unbiased way. (Abridged), Comment: 18 pages, submitted to MNRAS, Version with higher quality figures available from: http://star-www.dur.ac.uk/~frazerp/galform.ps.gz

We are making available on the WWW a selection of the archived data from N-body simulations carried out by the Virgo consortium and related groups. This currently includes: (i) time-slice, lightcone and cluster data from the two $10^9$-particle Hubble volume simulations described by Evrard 1998; (ii) time-slice data from simulations of 4 different cold dark matter cosmological models with $256^3$ particles analysed by Jenkins et al 1998; (iii) Dark halo catalogs, merger trees and galaxy catalogs from the GIF project described by Kauffmann et al 1999. Basic software is supplied to read the data. The data can be accessed from: http://www.mpa-garching.mpg.de/Virgo/data_download.html, Comment: 4 pages. 0 figures. The data is available at http://www.mpa-garching.mpg.de/Virgo/data_download.html

We have extracted over 400 clusters, covering more than 2 decades in mass, from three simulations of the TCDM cosmology. This represents the largest, uniform catalogue of simulated clusters ever produced. The clusters exhibit a wide variety of density-profiles. Only a minority are well-fit in their outer regions by the widely used density profile of Navarro, Frenk & White (1977). Others have steeper outer density profiles, show sharp breaks in their density profiles, or have significant substructure. If we force a fit to the NFW profile, then the best-fit concentrations decline with increasing mass, but this is driven primarily by an increase in substructure as one moves to higher masses. The measured temperature-mass relations for properties measured within a sphere enclosing a fixed overdensity all follow the self-similar form, T\propto M^{2/3}, however the normalisation is lower than in observed clusters. The temperature-mass relations for properties measured within a fixed physical radius are significantly steeper then this. Both can be accurately predicted using the NFW model., Comment: 14 a4 pages, 18 eps figures, submitted to MNRAS

We use very large cosmological N--body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM) cosmogonies, a critical density model ($\tau$CDM) and a flat low density model with a cosmological constant ($\Lambda$CDM). Our simulations each use $10^9$ particles to follow the mass distribution within cubes of side $2h^{-1}$Gpc ($\tau$CDM) and $3h^{-1}$Gpc ($\Lambda$CDM) with a force resolution better than $10^{-4}$ of the cube side. We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance. Very similar behaviour is found in the two cases. The correlation length increases from $r_0=12$ -- 13$h^{-1}$Mpc for samples with mean separation $d_{\rm c}=30h^{-1}$Mpc to $r_0=22$-- 27$h^{-1}$Mpc for samples with $d_{\rm c}=100h^{-1}$Mpc. The lower value here corresponds to $\tau$CDM and the upper to $\Lambda$CDM. The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale. Both correlation lengths and power spectrum biases can be predicted to better than 10% using the simple model of Sheth, Mo & Tormen (2000). This prediction requires only the linear mass power spectrum and has no adjustable parameters. We compare our predictions with published results for the APM cluster sample. The observed variation of correlation length with richness agrees well with the models, particularly for $\Lambda$CDM. The observed power spectrum (for a cluster sample of mean separation $d_{\rm c}=31h^{-1}$Mpc) lies significantly above the predictions of both models., Comment: 9 pages, 5 figures. Accepted for publication in MNRAS. Minor changes

We compare the structure and substructure of dark matter halos in model universes dominated by collisional, strongly self interacting dark matter (SIDM) and collisionless, weakly interacting dark matter (CDM). While SIDM virialised halos are more nearly spherical than CDM halos, they can be rotationally flattened by as much as 20% in their inner regions. Substructure halos suffer ram-pressure truncation and drag which are more rapid and severe than their gravitational counterparts tidal stripping and dynamical friction. Lensing constraints on the size of galactic halos in clusters are a factor of two smaller than predicted by gravitational stripping, and the recent detection of tidal streams of stars escaping from the satellite galaxy Carina suggests that its tidal radius is close to its optical radius of a few hundred parsecs --- an order of magnitude smaller than predicted by CDM models but consistent with SIDM. The orbits of SIDM satellites suffer significant velocity bias $\sigma_{SIDM}/\sigma_{CDM}=0.85$ and are more circular than CDM, $\beta_{SIDM}} \approx 0.5$, in agreement with the inferred orbits of the Galaxy's satellites. In the limit of a short mean free path, SIDM halos have singular isothermal density profiles, thus in its simplest incarnation SIDM is inconsistent with galactic rotation curves., Comment: 4 pages, submitted to ApJLetters. Further simulation details at http://www.nbody.net (www.nbody.net)

We compare the statistical properties of galaxies found in two different models of hierarchical galaxy formation: the semi-analytic model of Cole et al. and the smoothed particle hydrodynamics (SPH) simulations of Pearce et al. Using a `stripped-down' version of the semi-analytic model which mimics the resolution of the SPH simulations and excludes physical processes not included in them, we find that the two models produce an ensemble of galaxies with remarkably similar properties, although there are some differences in the gas cooling rates and in the number of galaxies that populate halos of different mass. The full semi-analytic model, which has effectively no resolution limit and includes a treatment of star formation and supernovae feedback, produces somewhat different (but readily understandable) results. Agreement is particularly good for the present-day global fractions of hot gas, cold dense (i.e. galactic) gas and uncollapsed gas, for which the SPH and stripped-down semi-analytic calculations differ by at most 25%. In the most massive halos, the stripped-down semi-analytic model predicts, on the whole, up to 50% less gas in galaxies than is seen in the SPH simulations. The two techniques apportion this cold gas somewhat differently amongst galaxies in a given halo. This difference can be tracked down to the greater cooling rate in massive halos in the SPH simulation compared to the semi-analytic model. (abridged), Comment: 19 pages, 13 figures, to appear in MNRAS. Significantly extended to explore galaxy progenitor distributions and behaviour of models at high redshifts

In this paper we use state-of-the-art N-body hydrodynamic simulations of a cosmological volume of side 100Mpc to produce many galaxy clusters simultaneously in both the standard cold dark matter (SCDM) cosmology and a cosmology with a positive cosmological constant (LCDM). We have performed simulations of the same volume both with and without the effects of radiative cooling, but in all cases neglect the effects of star formation and feedback. With radiative cooling clusters are on average five times less luminous in X-rays than the same cluster simulated without cooling. The importance of the mass of the central galaxy in determining the X-ray luminosity is stressed., Comment: 4 pages, Conference proceedings - LSS in the X-ray Universe - Santorini

We present a study of hydrodynamic drag forces in smoothed particle simulations. In particular, the deceleration of a resolution-limited cold clump of gas moving through a hot medium is examined. It is found that the drag for subsonic velocities exceeds that predicted by simple physical approximations. This is shown to be a result of the hydrodynamical method which encourages the accretion of particles from the hot medium onto a shell around the cold clump, effectively increasing the radius of the clump. For sonic and supersonic velocities, the drag is shown to be dependent on the effective cross section of the clump. The consequences for cosmological simulations are discussed., Comment: 35 pages including 3 tables and 9 figures. Submitted to MNRAS. Postscript file also available at ftp://www.astro.uwo.ca/pub/etittley/papers/Drag.ps.gz

Numerical simulations of galaxy formation require a number of parameters. Some of these are intrinsic to the numerical integration scheme (eg the timestep), while others describe the physical model (eg the gas metallicity). In this paper, we present results of a systematic exploration of the effects of varying a subset of these parameters on simulations of galaxy formation. We use N-body and ``Smoothed Particle Hydrodynamics'' techniques to follow the evolution of cold dark matter and gas in a small volume. We compare a fiducial model to 24 different simulations, in which one parameter at a time is varied, focussing on properties such as the relative fraction of hot and cold gas, and the abundance and masses of galaxies. We find that for reasonable choices of numerical values, many parameters have relatively little effect on the galaxies, with the notable exception of the parameters that control the resolution of the simulation and the efficiency with which gas cools., Comment: 22 pages, 15 figures, 4 tables, accepted for publication in MNRAS

In this paper, we investigate the effect of cooling on the X-ray properties of galaxy clusters. We have performed N-body, hydrodynamical simulations both with and without the effects of radiative cooling, but neglecting the effects of star formation and feedback. We show that radiative cooling produces an inflow of high-entropy gas from the outer parts of the cluster, thus \emph{raising} the cluster temperature and \emph{decreasing} the X-ray luminosity. With radiative cooling clusters are on average three to five times less luminous in X-rays than the same cluster simulated without cooling. However, we do not produce a large constant-density core in either the gas or the dark matter distributions. Our results contradict previous work in which cooling raises the X-ray luminosity and deposits an unreasonably large amount of mass in the central cluster galaxy. We achieve this by selecting our numerical resolution in such a way that a reasonable fraction of the baryonic material cools and by decoupling the hot and cold gas in our simulations, a first step towards modelling multiphase gas. We emphasise that globally cooling a sensible amount of material is vital and the presence or absence of massive central concentrations of cold baryonic material has a dramatic effect upon the resultant X-ray properties of the clusters., Comment: 14 pages, accepted to MNRAS, substantially revised from previous version

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including SPH and grid methods with fixed, deformable or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gas dynamical 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 different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of two. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to about 10%, and the ratio of specific kinetic to thermal energies of the gas agree to about 5%. Various factors contribute to the spread in calculated cluster properties, including differences in the internal timing of the simulations. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modelled., Comment: 18 pages, 11 figures, 8 additional colour figures available from http://star-www.dur.ac.uk/~csf/SantaBarbara/ Accepted in Astrophysical Journal

We discuss the first results from two successful simulations of galaxy formation within a cosmological volume. With over 2000 large objects forming in each we have sufficient numbers to reliably produce both galaxy correlation and luminosity functions. We find that the observed galaxy counts are well fitted by these models and that the galaxies display an almost un-evolving correlation function back to a redshift of 3 which closely resembles the featureless observed form and amplitude., Comment: 4 pages, Proceedings X Rencontres de Blois: The Birth of Galaxies

We have simulated the growth of structure in two 100 Mpc boxes for LCDM and SCDM universes. These N-body/SPH simulations include a gaseous component which is able to cool radiatively. A fraction of the gas cools into cold dense objects which we identify as galaxies. In this article we give a preliminary analysis of the clustering behaviour of these galaxies concentrating on the LCDM model. We find a galaxy correlation function which is very close to a power law and which evolves relatively little with redshift. The pairwise dispersions of the galaxies are significantly lower than the dark matter. The LCDM model gives a surprisingly good match to the observational determinations of the galaxy correlation function and pairwise dispersions., Comment: 4 pages, Proceedings X Rencontres de Blois: The Birth of Galaxies

We discuss early results from the first large N-body/hydrodynamical simulation to resolve the formation of galaxies in a cold dark matter universe. The simulation follows the formation of galaxies by gas cooling within dark halos of mass a few times $10^{11}\Msun$ and above, in a flat universe with a positive cosmological constant. Over 2200 galaxies form in our simulated volume of $(100 \Mpc)^3$. Assigning luminosities to the model galaxies using a spectral population synthesis model results in a K-band luminosity function in excellent agreement with observations. The two-point correlation function of galaxies in the simulation evolves very little since $z=3$ and has a shape close to a power-law over four orders of magnitude in amplitude. At the present day, the galaxy correlation function in the simulation is antibiased relative to the mass on small scales and unbiased on large scales. It provides a reasonable match to observations., Comment: 4 pages, submitted to ApJL

We analyse the performance of twelve different implementations of Smoothed Particle Hydrodynamics (SPH) using seven tests designed to isolate key hydrodynamic elements of cosmological simulations which are known to cause the SPH algorithm problems. In order, we consider a shock tube, spherical adiabatic collapse, cooling flow model, drag, a cosmological simulation, rotating cloud-collapse and disc stability. In the implementations special attention is given to the way in which force symmetry is enforced in the equations of motion. We study in detail how the hydrodynamics are affected by different implementations of the artificial viscosity including those with a shear-correction modification. We present an improved first-order smoothing-length update algorithm that is designed to remove instabilities that are present in the Hernquist and Katz (1989) algorithm. For all tests we find that the artificial viscosity is the most important factor distinguishing the results from the various implementations. The second most important factor is the way force symmetry is achieved in the equation of motion. Most results favour a kernel symmetrization approach. The exact method by which SPH pressure forces are included has comparatively little effect on the results. Combining the equation of motion presented in Thomas and Couchman (1992) with a modification of the Monaghan and Gingold (1983) artificial viscosity leads to an SPH scheme that is both fast and reliable., Comment: 30 pages, 26 figures and 9 tables included. Submitted to MNRAS. Postscript version available at ftp://phobos.astro.uwo.ca/pub/etittley/papers/sphtest.ps.gz

We report on analyses of cluster samples obtained from the Hubble Volume Simulations. These simulations, an $\Omega=1$ model named $\tau$CDM and a flat low $\Omega$ model with a cosmological constant ($\Lambda$CDM), comprise the largest computational efforts to date in numerical cosmology. We investigate the presence of massive galaxy clusters at $z\approx 0.8$. The $\tau$CDM model fails to form clusters at such a redshift. However, due to the small number of observed clusters around $z\approx 0.8$ and the uncertainties in the determinations of their masses, this conclusion still is somewhat preliminary. We produce cluster catalogs at $z=0$ for both cosmologies and investigate their two--point correlation function $\xi$. We show that the relationship between the mean density of subsamples of clusters, expressed via their mean separation $d_{\rm c}$, and the correlation length $r_0$, defined through $\xi(r_0) = 1$, is not linear but turns over gently for large $d_{\rm c}$. An analytic prediction by Mo & White (1996) overpredicts $r_0$. The results from the analysis of the APM cluster data by Croft et al. (1997) are nicely matched by the $\Lambda$CDM model., Comment: LaTex: 4 pages, 1 figure, includes conf_iap.sty style file. To appear in proceedings of The 14th IAP Colloquium: Wide Field Surveys in Cosmology, held in Paris, 1998 May 26-30, eds. S.Colombi, Y.Mellier

(Abridged) We investigate the importance of several numerical artifacts such as lack of resolution on spectral properties of the Lyman alpha forest as computed from cosmological hydrodynamic simulations in a standard cold dark matter universe. We assume an ionising background produced by quasars as computed by Haardt & Madau. We use a new simulation code based on P3M and SPH, which we compare in detail with a modified version of HYDRA (Couchman et al.) and published results of TREESPH (Hernquist et al.). The agreement is very good between all three codes. We then use our new code to investigate several numerical effects such as resolution on spectral statistics deduced from Voigt profile fitting. Our highest resolution simulation has a mass resolution of 2.1x10^5 solar masses. The column density distribution is converged but the b-parameter distribution is only marginally converged. The simulation reproduces both the HI column density and b-parameter distribution when we assume a high baryon density, Omega_B h^2 > 0.028. In addition we need to impose a higher IGM temperature than predicted within our basic set of assumptions. The simulated HI optical depth is in good agreement with observations but the HeII optical depth is lower than observed. Fitting the latter requires a larger jump between the photon flux at the H and He edge than is present in the Haardt & Madau spectrum., Comment: 28 pages, latex (mn.sty), 33 figures, submitted to MNRAS

We have developed a parallel Particle-Particle, Particle-Mesh (P3M) simulation code for the Cray T3E parallel supercomputer that is well suited to studying the time evolution of systems of particles interacting via gravity and gas forces in cosmological contexts. The parallel code is based upon the public-domain serial Adaptive P3M code of Couchman et al. The algorithm resolves gravitational forces into a long-range component computed by discretizing the mass distribution and solving Poisson's equation on a grid using an FFT convolution method, and a short-range component computed by direct force summation for sufficiently close particle pairs. The code consists primarily of a particle-particle computation parallelized by domain decomposition over blocks of neighbour-cells, a more regular mesh calculation distributed in planes along one dimension, and several transformations between the two distributions. The load balancing of the P3M code is static, since this greatly aids the ongoing implementation of parallel adaptive refinements of the particle and mesh systems. Great care was taken throughout to make optimal use of the available memory, so that a version of the current implementation has been used to simulate systems of up to 10^9 particles with a 1024^3 mesh for the long-range force computation. These are the largest Cosmological N-body simulations of which we are aware. We discuss these memory optimizations as well as those motivated by computational performance. Performance results are very encouraging, and, even without refinements, the code has been used effectively for simulations in which the particle distribution becomes highly clustered as well as for other non-uniform systems of astrophysical interest., Comment: html plus 9 figures (gif). submitted it to New Astronomy

We investigate the peculiar velocities predicted for galaxy clusters by theories in the cold dark matter family. A widely used hypothesis identifies rich clusters with high peaks of a suitably smoothed version of the linear density fluctuation field. Their peculiar velocities are then obtained by extrapolating the similarly smoothed linear peculiar velocities at the positions of these peaks. We test these ideas using large high resolution N-body simulations carried out within the Virgo supercomputing consortium. We find that at early times the barycentre of the material which ends up in a rich cluster is generally very close to a high peak of the initial density field. Furthermore the mean peculiar velocity of this material agrees well with the linear value at the peak. The late-time growth of peculiar velocities is, however, systematically underestimated by linear theory. At the time clusters are identified we find their rms peculiar velocity to be about 40% larger than predicted. Nonlinear effects are particularly important in superclusters. These systematics must be borne in mind when using cluster peculiar velocities to estimate the parameter combination $\sigma_8\Omega^{0.6}$., Comment: 8 pages, 4 figures; submitted to MNRAS

I investigate the process of converting gas into stars within the framework of a standard cosmological model. By examining the set of objects grown in a combined N-body plus smoothed particle hydrodynamics simulation with those obtained in similar models where some of the cold, dense gas was replaced by collisionless ``star'' particles I show that it is possible to make this substitution without affecting the subsequent gas cooling rate. With even the most basic star forming criteria the masses of isolated objects are nearly identical to the mass of cold, dense gas found within the same objects in a non-star forming run. No evidence is found to support the contention that converting gas into stars might affect the amount of cold gas obtained in a simulation by retarding the cooling rate within those objects where stars have already formed. In practice, because cold gas can be reheated by shocks but stars remain as such whatever happens the masses of the largest objects found in the star forming runs are generally higher than those in the standard run. Finally, I demonstrate that an excellent match to the observed star formation rate can be achieved with even a very basic star formation prescription., Comment: 8 pages, Latex, submitted to A&A

We use two high resolution CDM simulations to show that (i) when clusters of galaxies form the infall pattern of matter is not random but shows clear features which are correlated in time; (ii) in addition, the infall patterns are correlated with the cluster's surrounding Large Scale Structure; (iii) Large Scale Structure shows a mix of both filaments and sheets; (iv) the amount of mass in filaments is slightly larger for a low $\Omega$ model., Comment: 6 pages (incl. 7 figs)

We study the topology of the Virgo N-body simulations and compare it to the 1.2-Jy redshift survey of IRAS galaxies by means of the genus statistic. Four high-resolution simulations of variants of the CDM cosmology are considered: a flat standard model (SCDM), a variant of it with more large-scale power (tCDM), and two low density universes, one open (OCDM) and one flat (LCDM). The fully sampled N-body simulations are examined down to strongly nonlinear scales, both with spatially fixed smoothing, and with an adaptive smoothing technique. While the tCDM, LCDM, and OCDM simulations have very similar genus statistics in the regime accessible to fixed smoothing, they can be separated with adaptive smoothing at small mass scales. In order to compare the N-body models with the 1.2-Jy survey, we extract large ensembles of mock catalogues from the simulations. These mock surveys are used to test for systematic effects in the genus analysis and to establish the distribution of errors of the genus curve. We find that a simple multivariate analysis of the genus measurements is compromised both by non-Gaussian distributed errors and by noise that dominates the covariance matrix. We therefore introduce a principal components analysis of the genus curve. With a likelihood ratio test we find that the 1.2-Jy data favours the LCDM, tCDM and OCDM models compared to SCDM. When genus measurements for different smoothing scales are combined, the SCDM model can be excluded at a 99% confidence level, while the other three models fit the 1.2-Jy data well. (abridged), Comment: submitted to MNRAS, 23 pages, mn.sty, 24 eps-figures included

We present an analysis of the clustering evolution of dark matter in four cold dark matter (CDM) cosmologies. We use a suite of high resolution, 17-million particle, N-body simulations which sample volumes large enough to give clustering statistics with unprecedented accuracy. We investigate both a flat and an open model with Omega_0=0.3, and two models with Omega=1, one with the standard CDM power spectrum and the other with the same power spectrum as the Omega_0=0.3 models. The amplitude of primordial fluctuations is set so that the models reproduce the observed abundance of rich galaxy clusters by the present day. The mass 2-point correlation function and power spectrum of all the simulations differ significantly from those of the observed galaxy distribution, in both shape and amplitude. Thus, for any of these models to provide an acceptable representation of reality, the distribution of galaxies must be biased relative to the mass in a non-trivial, scale-dependent, fashion. In the Omega=1 models the required bias is always greater than unity, but in the Omega_0=0.3 models an "antibias" is required on scales smaller than \sim 5\hmpc. The mass correlation functions in the simulations are well fit by recently published analytic models. The velocity fields are remarkably similar in all the models, whether they be characterised as bulk flows, 1-particle or pairwise velocity dispersions. This similarity is a direct consequence of our adopted normalisation. The small-scale pairwise velocity dispersion of the dark matter is somewhat larger than recent determinations from galaxy redshift surveys, but the bulk-flows predicted by our models are broadly in agreement with most available data., Comment: 46 pages Accepted for publication in the Ap.J, May 20th, Vol. 499, Part I. Minor changes: addition of a table summarising results, section 3.1 on simulation details expanded, three new references added. TeX. Figures 4-11 included. The colour figures 1-3 are available as gif files from: http://star-www.dur.ac.uk:80/~arj/plates.html

We investigate the internal structure of clusters of galaxies in high-resolution N-body simulations of 4 different cosmologies. There is a higher proportion of disordered clusters in critical-density than in low-density universes, although the structure of relaxed clusters is very similar in each. Crude measures of substructure, such as the shift in the position of the centre-of-mass as the density threshold is varied, can distinguish the two in a sample of just 20 or so clusters; it is harder to differentiate between clusters in open and flat models with the same density parameter. Most clusters are in a quasi-steady state within the virial radius and are well-described by the density profile of Navarro, Frenk & White (1995)., Comment: 12 page file, MNRAS format including 15 eps figures. Also available from ftp://star.maps.susx.ac.uk/pub/papers/pat/clusters.ps.Z . Submitted to MNRAS

We describe the first parallel implementation of an adaptive particle-particle, particle-mesh code with smoothed particle hydrodynamics. Parallelisation of the serial code, ``Hydra'', is achieved by using CRAFT, a Cray proprietary language which allows rapid implementation of a serial code on a parallel machine by allowing global addressing of distributed memory. The collisionless variant of the code has already completed several 16.8 million particle cosmological simulations on a 128 processor Cray T3D whilst the full hydrodynamic code has completed several 4.2 million particle combined gas and dark matter runs. The efficiency of the code now allows parameter-space explorations to be performed routinely using $64^3$ particles of each species. A complete run including gas cooling, from high redshift to the present epoch requires approximately 10 hours on 64 processors. In this paper we present implementation details and results of the performance and scalability of the CRAFT version of Hydra under varying degrees of particle clustering., Comment: 23 pages, LaTex plus encapsulated figures

We report on work done by the Virgo consortium, an international collaboration set up in order to study the formation and evolution of Large Scale Structure using N-body simulations on the latest generation of parallel supercomputers. We show results of 256^3 particle simulations of the formation of clusters in four Dark Matter models with different cosmological parameters. Normalizing the models such that one obtains the correct abundance of rich clusters yields an interesting result: The peculiar velocities of the clusters are almost independent of \Omega, and depend only weakly on \Gamma, the shape parameter of the power spectrum. Thus, it is nearly impossible to distinguish between high and low \Omega models on the basis of the peculiar velocities., Comment: 6 pages (incl. one figure), LATEX (crckapb.sty), To appear in the Proceedings of the Ringberg Workshop on 'Large Scale Structure' (Sept. 1996), ed. D.Hamilton. A high quality (colour) version of figure 1 can be found at http://www.mpa-garching.mpg.de/~jgc/clusters.html or can be obtained from jgc@mpa-garching.mpg.de

We report on work in progress by the Virgo consortium, a collaboration set up to carry out large simulations of the formation of galaxies and large-scale structure exploiting the latest generation of parallel supercomputers. We show results of $256^3$ particle N-body simulations of the clustering evolution of dark matter in four cold dark matter models with different cosmological parameters. The high resolution and large volume of these simulations allows us to determine reliably the mass autocorrelation function for pair separations in the range $40\hkpc$ to $20\hmpc$. Comparison of these with the observed galaxy correlation function shows that for any of these models to be viable, the distribution of galaxies must be biased relative to the distribution of mass in a non-trivial, scale-dependent fashion. In particular, low $\Omega_0$ models require the galaxies to be more ``weakly'' clustered than the mass at small and intermediate pair separations. Simulations which include the evolution of gas show that cold gas knots form with approximately the abundance expected on theoretical grounds, although a few excessively massive objects grow near the centres of rich clusters. The locations where these cold gas knots form are, in general, biased relative to the distribution of mass in a scale-dependent way. Some of these biases have the required sign but they are, for the most part, weaker than is necessary for agreement with observations. The antibias present in our low $\Omega_0$ N-body/SPH simulation appears to be related to the merging and disruption of galaxies in rich clusters., Comment: 9 pages, 4 postscript figures included. To appear in "Dark and Visible Matter in Galaxies and Cosmological Implications", eds M. Persic and P. Salucci, PASP conference Series. Postscript version also available at ftp://star-ftp.dur.ac.uk/pub/preprints/arj_sesto.ps.gz

We intend to make sets of cosmological simulations available, with a large number of different output times that may be placed side-by-side to produce a complete history of the universe stretching back to high redshift. Currently there is only one series of runs under preparation as a trial. Gauging by the response, we will consider further releases. The first series consists of N-body simulations with CDM-like spectra (Gamma=0.25) in a 100/h Mpc box, in three different cosmologies: Einstein-de Sitter, low-density flat and low-density open. The parameters of each run are: 1) Run 501: Omega=1.0, lambda=0.0, sigma_8=0.64. N=128**3. 38 time-slices back to z=5.8 (a further 11 back to z=23.4 on request). 2) Run 502: Omega=0.3, lambda=0.7, sigma_8=1.22. N=86**3. 49 time-slices back to z=3.6. 3) Run 503: Omega=0.3, lambda=0.0, sigma_8=1.06. N=86**3. 49 time-slices back to z=6.2 Check out our Web pages for more details: http://coho.astro.uwo.ca/pub/consort.html, Comment: http://coho.astro.uwo.ca/pub/data.html

A revised version of Hydra, an adaptive particle-particle, particle-mesh plus smoothed particle hydrodynamics code developed by; Hugh Couchman, University of Western Ontario, Frazer Pearce, University of Durham, Peter Thomas, University of Sussex, is now available as a tar file from; http://coho.astro.uwo.ca/pub/hydra/hydra.html or http://star-www.maps.susx.ac.uk/~pat/hydra/hydra.html ., Comment: A new version of the AP3M-SPH code, Hydra, is now available as a tar file from the following sites; http://coho.astro.uwo.ca/pub/hydra/hydra.html , http://star-www.maps.susx.ac.uk/~pat/hydra/hydra.html . The release now also contains a cosmological initial conditions generator, documentation, an installation guide and installation tests. A LaTex version of the documentation is included here

We present an implementation of Smoothed Particle Hydrodynamics (SPH) in an adaptive-mesh PPPM algorithm. The code evolves a mixture of purely gravitational particles and gas particles. The code retains the desirable properties of previous PPPM--SPH implementations; speed under light clustering, naturally periodic boundary conditions and accurate pairwise forces. Under heavy clustering the cycle time of the new code is only 2--3 times slower than for a uniform particle distribution, overcoming the principal disadvantage of previous implementations\dash a dramatic loss of efficiency as clustering develops. A 1000 step simulation with 65,536 particles (half dark, half gas) runs in one day on a Sun Sparc10 workstation. The choice of time integration scheme is investigated in detail. A simple single-step Predictor--Corrector type integrator is most efficient. A method for generating an initial distribution of particles by allowing a a uniform temperature gas of SPH particles to relax within a periodic box is presented. The average SPH density that results varies by $\sim\pm1.3$\%. We present a modified form of the Layzer--Irvine equation which includes the thermal contribution of the gas together with radiative cooling. Tests of sound waves, shocks, spherical infall and collapse are presented. Appropriate timestep constraints sufficient to ensure both energy and entropy conservation are discussed. A cluster simulation, repeating Thomas and, Comment: 29 pp, uuencoded Postscript

We present a practical guide to Smoothed Particle Hydrodynamics (\SPH) and its application to astrophysical problems. Although remarkably robust, \SPH\ must be used with care if the results are to be meaningful since the accuracy of \SPH\ is sensitive to the arrangement of the particles and the form of the smoothing kernel. In particular, the initial conditions for any \SPH\ simulation must consist of particles in dynamic equilibrium. We describe some of the numerical difficulties that may be encountered when using \SPH, and how these may be overcome. Through our experience in using \SPH\ code to model convective stars, galaxy clusters and large scale structure problems we have developed many diagnostic tests. We give these here as an aid to rapid identification of errors, together with a list of basic prerequisites for the most efficient implementation of \SPH., Comment: 15 pages, 5 figures upon request, Plain Latex, SUSSEX-AST-MPT-1