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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

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

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 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

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 present a study of the substructure finder dependence of subhalo clustering in the Aquarius Simulation. We run 11 different subhalo finders on the haloes of the Aquarius Simulation and study their differences in the density profile, mass fraction and two-point correlation function of subhaloes in haloes. We also study the mass and vmax dependence of subhalo clustering. As the Aquarius Simulation has been run at different resolutions, we study the convergence with higher resolutions. We find that the agreement between finders is at around the 10 per cent level inside R200 and at intermediate resolutions when a mass threshold is applied, and better than 5 per cent when vmax is restricted instead of mass. However, some discrepancies appear in the highest resolution, underlined by an observed resolution dependence of subhalo clustering. This dependence is stronger for the smallest subhaloes, which are more clustered in the highest resolution, due to the detection of subhaloes within subhaloes (the sub-subhalo term). This effect modifies the mass dependence of clustering in the highest resolutions. We discuss implications of our results for models of subhalo clustering and their relation with galaxy clustering.

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 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 present a study of a comparison of spin distributions of subhaloes found associated with a host halo. The subhaloes are found within two cosmological simulation families of Milky Way-like galaxies, namely the Aquarius and GHALO simulations. These two simulations use different gravity codes and cosmologies. We employ 10 different substructure finders, which span a wide range of methodologies from simple overdensity in configuration space to full 6D phase space analysis of particles. We subject the results to a common post-processing pipeline to analyse the results in a consistent manner, recovering the dimensionless spin parameter. We find that spin distribution is an excellent indicator of how well the removal of background particles (unbinding) has been carried out. We also find that the spin distribution decreases for substructures the nearer they are to the host haloes, and that the value of the spin parameter rises with enclosed mass towards the edge of the substructure. Finally, subhaloes are less rotationally supported than field haloes, with the peak of the spin distribution having a lower spin parameter.

The ever increasing size and complexity of data coming from simulations of cosmic structure formation demand equally sophisticated tools for their analysis. During the past decade, the art of object finding in these simulations has hence developed into an important discipline itself. A multitude of codes based upon a huge variety of methods and techniques have been spawned yet the question remained as to whether or not they will provide the same (physical) information about the structures of interest. Here we summarize and extent previous work of the `halo finder comparison project': we investigate in detail the (possible) origin of any deviations across finders. To this extent, we decipher and discuss differences in halo-finding methods, clearly separating them from the disparity in definitions of halo properties. We observe that different codes not only find different numbers of objects leading to a scatter of up to 20 per cent in the halo mass and Vmax function, but also that the particulars of those objects that are identified by all finders differ. The strength of the variation, however, depends on the property studied, e.g. the scatter in position, bulk velocity, mass and the peak value of the rotation curve is practically below a few per cent, whereas derived quantities such as spin and shape show larger deviations. Our study indicates that the prime contribution to differences in halo properties across codes stems from the distinct particle collection methods and - to a minor extent - the particular aspects of how the procedure for removing unbound particles is implemented. We close with a discussion of the relevance and implications of the scatter across different codes for other fields such as semi-analytical galaxy formation models, gravitational lensing and observables in general.

We present a detailed comparison of fundamental dark matter halo properties retrieved by a substantial number of different halo finders. These codes span a wide range of techniques including friends-of-friends, spherical-overdensity and phase-space-based algorithms. We further introduce a robust (and publicly available) suite of test scenarios that allow halo finder developers to compare the performance of their codes against those presented here. This set includes mock haloes containing various levels and distributions of substructure at a range of resolutions as well as a cosmological simulation of the large-scale structure of the universe. All the halo-finding codes tested could successfully recover the spatial location of our mock haloes. They further returned lists of particles (potentially) belonging to the object that led to coinciding values for the maximum of the circular velocity profile and the radius where it is reached. All the finders based in configuration space struggled to recover substructure that was located close to the centre of the host halo, and the radial dependence of the mass recovered varies from finder to finder. Those finders based in phase space could resolve central substructure although they found difficulties in accurately recovering its properties. Through a resolution study we found that most of the finders could not reliably recover substructure containing fewer than 30-40 particles. However, also here the phase-space finders excelled by resolving substructure down to 10-20 particles. By comparing the halo finders using a high-resolution cosmological volume, we found that they agree remarkably well on fundamental properties of astrophysical significance (e.g. mass, position, velocity and peak of the rotation curve). We further suggest to utilize the peak of the rotation curve, vmax, as a proxy for mass, given the arbitrariness in defining a proper halo edge. Airport code for Madrid, Spain

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

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

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

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

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 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 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

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 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 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 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 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 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 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 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 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 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)

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 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