Toward an accurate mass function for precision cosmology

Cosmological surveys aim to use the evolution of the abundance of galaxy clusters to accurately constrain the cosmological model. In the context of LCDM, we show that it is possible to achieve the required percent level accuracy in the halo mass function with gravity-only cosmological simulations, and we provide simulation start and run parameter guidelines for doing so. Some previous works have had sufficient statistical precision, but lacked robust verification of absolute accuracy. Convergence tests of the mass function with, for example, simulation start redshift can exhibit false convergence of the mass function due to counteracting errors, potentially misleading one to infer overly optimistic estimations of simulation accuracy. Percent level accuracy is possible if initial condition particle mapping uses second order Lagrangian Perturbation Theory, and if the start epoch is between 10 and 50 expansion factors before the epoch of halo formation of interest. The mass function for halos with fewer than ~1000 particles is highly sensitive to simulation parameters and start redshift, implying a practical minimum mass resolution limit due to mass discreteness. The narrow range in converged start redshift suggests that it is not presently possible for a single simulation to capture accurately the cluster mass function while also starting early enough to model accurately the numbers of reionisation era galaxies, whose baryon feedback processes may affect later cluster properties. Ultimately, to fully exploit current and future cosmological surveys will require accurate modeling of baryon physics and observable properties, a formidable challenge for which accurate gravity-only simulations are just an initial step.Comment: revised in response to referee suggestions, MNRAS accepte

Resolving the Structure of Cold Dark Matter Halos

We examine the effects of mass resolution and force softening on the density profiles of cold dark matter halos that form within cosmological N-body simulations. As we increase the mass and force resolution, we resolve progenitor halos that collapse at higher redshifts and have very high densities. At our highest resolution we have nearly 3 million particles within the virial radius, several orders of magnitude more than previously used and we can resolve more than one thousand surviving dark matter halos within this single virialised system. The halo profiles become steeper in the central regions and we may not have achieved convergence to a unique slope within the inner 10% of the virialised region. Results from two very high resolution halo simulations yield steep inner density profiles, $\rho(r)\sim r^{-1.4}$. The abundance and properties of arcs formed within this potential will be different from calculations based on lower resolution simulations. The kinematics of disks within such a steep potential may prove problematic for the CDM model when compared with the observed properties of halos on galactic scales.Comment: Final version, to be published in the ApJLetter

Density Profiles of Cold Dark Matter Substructure: Implications for the Missing Satellites Problem

The structural evolution of substructure in cold dark matter (CDM) models is investigated combining ``low-resolution'' satellites from cosmological N-body simulations of parent halos with N=10^7 particles with high-resolution individual subhalos orbiting within a static host potential. We show that, as a result of mass loss, convergence in the central density profiles requires the initial satellites to be resolved with N=10^7 particles and parsec-scale force resolution. We find that the density profiles of substructure halos can be well fitted with a power-law central slope that is unmodified by tidal forces even after the tidal stripping of over 99% of the initial mass and an exponential cutoff in the outer parts. The solution to the missing-satellites problem advocated by Stoehr et al. in 2002 relied on the flattening of the dark matter (DM) halo central density cusps by gravitational tides, enabling the observed satellites to be embedded within DM halos with maximum circular velocities as large as 60 km/s. In contrast, our results suggest that tidal interactions do not provide the mechanism for associating the dwarf spheroidal satellites (dSphs) of the Milky Way with the most massive substructure halos expected in a CDM universe. We compare the predicted velocity dispersion profiles of Fornax and Draco to observations, assuming that they are embedded in CDM halos. Models with isotropic and tangentially anisotropic velocity distributions for the stellar component fit the data only if the surrounding DM halos have maximum circular velocities in the range 20-35 km/s. If the dSphs are embedded within halos this large then the overabundance of satellites within the concordance LCDM cosmological model is significantly alleviated, but this still does not provide the entire solution.Comment: Accepted for publication in ApJ, 17 pages, 9 figures, LaTeX (uses emulateapj5.sty

The fate of planetesimal discs in young open clusters: implications for 1I/’Oumuamua, the Kuiper belt, the Oort cloud, and more

We perform N-body simulations of the early phases of open cluster evolution including a large population of planetesimals, initially arranged in Kuiper-belt like discs around each star. Using a new, fourth-order, and time-reversible N-body code on Graphics Processing Units (GPUs), we evolve the whole system under the stellar gravity, i.e. treating planetesimals as test particles, and consider two types of initial cluster models, similar to IC348 and the Hyades, respectively. In both cases, planetesimals can be dynamically excited, transferred between stars, or liberated to become free-floating (such as A/2017 U1 or ’Oumuamua) during the early cluster evolution. We find that planetesimals captured from another star are not necessarily dynamically distinct from those native to a star. After an encounter, both native and captured planetesimals can exhibit aligned periastrons, qualitatively similar to that seen in the Solar system and commonly thought to be the signature of Planet 9. We discuss the implications of our results for both our Solar system and exoplanetary systems

The velocity anisotropy - density slope relation

One can solve the Jeans equation analytically for equilibrated dark matter structures, once given two pieces of input from numerical simulations. These inputs are 1) a connection between phase-space density and radius, and 2) a connection between velocity anisotropy and density slope, the \alpha-\beta relation. The first (phase-space density v.s. radius) has already been analysed through several different simulations, however the second (\alpha-\beta relation) has not been quantified yet. We perform a large set of numerical experiments in order to quantify the slope and zero-point of the \alpha-\beta relation. We find strong indication that the relation is indeed an attractor. When combined with the assumption of phase-space being a power-law in radius, this allows us to conclude that equilibrated dark matter structures indeed have zero central velocity anisotropy \beta_0 = 0, central density slope of \alpha_0 = -0.8, and outer anisotropy of \beta_\infty = 0.5.Comment: 15 pages, 7 figure

Intracluster stellar population properties from N-body cosmological simulations -- I. Constraints at z=0z=0

We use a high resolution collisionless simulation of a Virgo--like cluster in a $\Lambda$CDM cosmology to determine the velocity and clustering properties of the diffuse stellar component in the intracluster region at the present epoch. The simulated cluster builds up hierarchically and tidal interactions between member galaxies and the cluster potential produce a diffuse stellar component free-flying in the intracluster medium. Here we adopt an empirical scheme to identify tracers of the stellar component in the simulation and hence study its properties. We find that at $z=0$ the intracluster stellar light is mostly unrelaxed in velocity space and clustered in structures whose typical clustering radii are about 50 kpc at R=400--500 kpc from the cluster center, and predict the radial velocity distribution expected in spectroscopic follow-up surveys. Finally, we compare the spatial clustering in the simulation with the properties of the Virgo intracluster stellar population, as traced by ongoing intracluster planetary nebulae surveys in Virgo. The preliminary results indicate a substantial agreement with the observed clustering properties of the diffuse stellar population in Virgo.Comment: 39 pages, 10 figures, 8 tables, in press on ApJ. Bad image quality for some figures because resizing is neede

The descendents of Lyman Break Galaxies in galaxy clusters: spatial distribution and orbital properties

We combine semi-analytical methods with a ultra-high resolution simulation of a galaxy cluster (of mass 2.3 10^14h-1Msolar, and 4 10^6 particles within its virial radius) formed in a standard CDM universe to study the spatial distribution and orbital properties of the present-day descendents of Lyman Break Galaxies (LBGs). At the present time only five (out of 12) of halos containing LBGs survive as separate entities inside the cluster virial radius. Their circular velocities are in the range 200 - 550 km/sec. Seven halos merged together to form the central object at the very center of the cluster. Using semi-analytical modeling of galaxy evolution we show that descendents of halos containing LBGs now host giant elliptical galaxies. Galaxy orbits are radial, with a pericenter to apocenter ratio of about 1:5. The orbital eccentricities of LBGs descendents are statistically indistinguishable from those of the average galaxy population inside the cluster, suggesting that the orbits of these galaxies are not significantly affected by dynamical friction decay after the formation of the cluster's main body. In this cluster, possibly due to its early formation time, the descendents of LBGs are contained within the central 60% of the cluster virial radius and have an orbital velocity dispersion lower than the global galaxy population, originating a mild luminosity segregation for the brightest cluster members. Mass estimates based only on LBGs descendents (especially including the central cD) reflect this bias in space and velocity and underestimate the total mass of this well virialized cluster by up to a factor of two compared to estimates using at least 20 cluster members.Comment: 6 Pages, 2 Postscript figures. Submitted to Ap

Dynamical Dark Energy simulations: high accuracy Power Spectra at high redshift

Accurate predictions on non--linear power spectra, at various redshift z, will be a basic tool to interpret cosmological data from next generation mass probes, so obtaining key information on Dark Energy nature. This calls for high precision simulations, covering the whole functional space of w(z) state equations and taking also into account the admitted ranges of other cosmological parameters; surely a difficult task. A procedure was however suggested, able to match the spectra at z=0, up to k~3, hMpc^{-1}, in cosmologies with an (almost) arbitrary w(z), by making recourse to the results of N-body simulations with w = const. In this paper we extend such procedure to high redshift and test our approach through a series of N-body gravitational simulations of various models, including a model closely fitting WMAP5 and complementary data. Our approach detects w= const. models, whose spectra meet the requirement within 1% at z=0 and perform even better at higher redshift, where they are close to a permil precision. Available Halofit expressions, extended to (constant) w \neq -1 are unfortunately unsuitable to fit the spectra of the physical models considered here. Their extension to cover the desired range should be however feasible, and this will enable us to match spectra from any DE state equation.Comment: method definitely improved in semplicity and efficacy,accepted for publication on JCA