Massimo Meneghetti

Numerical study of halo concentrations in dark-energy cosmologies

We study the concentration parameters, their mass dependence and redshift evolution, of dark-matter halos in different dark-energy cosmologies with constant and time-variable equation of state, and compare them with standard ACDM and OCDM models. We find that previously proposed algorithms for predicting halo concentrations can be well adapted to dark-energy models. When centred on the analytically expected values, halo concentrations show a log-normal distribution with a uniform standard deviation of ∼0.2. The dependence of averaged halo concentrations on mass and redshift permits a simple fit of the form (1 + z) c = c 0 (M/M 0 ) α , with α -0.1 throughout. We find that the cluster concentration depends on the dark energy equation of state at the cluster formation redshift z coll through the linear growth factor D + (z coll ). As a simple correction accounting for dark-energy cosmologies, we propose scaling c 0 from ACDM with the ratio of linear growth factors, c 0 → c 0 D + (Z coll )/D +.ACDM (z coll ).

The impact of cluster mergers on arc statistics

We study the impact of merger events on the strong lensing properties of galaxy clusters. Previous lensing simulations were not able to resolve dynamical time scales of cluster lenses, which arise on time scales which are of order a Gyr. In this case study, we first describe qualitatively with an analytic model how some of the lensing properties of clusters are expected to change during merging events. We then analyse a numerically simulated lens model for the variation in its efficiency for producing both tangentia l and radial arcs while a massive substructure falls onto the main cluster body. We find that: ( 1) during the merger, the shape of the critical lines and caustics changes substantially; (2) the lensing cross sections for long and thin arcs can grow by one order of magnitude and reach their maxima when the extent of the critical curves is largest; (3) the cross section for radial arcs also grows, but the cluster can efficiently produce this kind of arcs only while the merging substructure crosses the main cluster centre; (4) while the arc cross sections pass through their m axima as the merger proceeds, the cluster’s X-ray emission increases by a factor of ∼ 5. Thus, we conclude that accounting for these dynamical processes is very important for arc statist ics studies. In particular, they may provide a possible explanation for the arc statistics probl em.

Effects of cluster galaxies on arc statistics

We present the results of a set of numerical simulations evaluating the effect of cluster galaxies on arc statistics. We perform a first set of gravitational lensing simulations using three independent projections for each of nine different galaxy clusters obtained from N-body simulations. The simulated clusters consist of dark matter only. We add a population of galaxies to each cluster, mimicking the observed luminosity function and the spatial galaxy distribution, and repeat the lensing simulations including the effects of cluster galaxies, which themselves act as individual lenses. Each galaxy is represented by a spherical Navarro, Frenk & White (1997) density profile. We consider the statistical distributions of the properties of the gravitational arcs produced by our clusters with and without galaxies. We find that the cluster galaxies do not introduce perturbations strong enough to significantly change the number of arcs and the distributions of lengths, widths, curvature radii and length-to-width ratios of long arcs. We find some changes to the distribution of short-arc properties in presence of cluster galaxies. The differences appear in the distribution of curvature radii for arc lengths smaller than 12 ′′ , while the distributions of lengths, widths and length-to-width ratios are significantly changed only for arcs shorter than 4 ′′ .

cD galaxy contribution to the strong lensing cross‐sections of galaxy clusters

We perform ray-tracing simulations evaluating the effect of a cD galaxy on the strong lensing properties of five galaxy cluster haloes obtained from N-body simulations. The cD galaxy is modelled using both axially symmetric and elliptical models and assuming several masses for its dark matter halo. The effect of the cD orientation with respect to the mass distribution of the host galaxy cluster is also investigated. The simulations are carried out in an open and a flat model universe with cosmological constant. We find that the enhancement of the cluster lensing cross-sections for long and thin arcs owing to the presence of a massive cD at the cluster centre is typically less than 100 per cent, depending on the model used for the cD galaxy and its orientation. The impact of the cD on the cluster efficiency for producing radially magnified images is larger only for those clusters with a lensing cross-section for radial arcs that is very small in absence of the central galaxy. We conclude that the presence of a cD galaxy at the cluster centre can only moderately influence the cluster efficiency for strong lensing and, in particular, fails to explain the discrepancy between the observed number of giant arcs in galaxy clusters and their abundance predicted from lensing simulations in the currently most favoured ACDM model.

Giant cluster arcs as a constraint on the scattering cross- section of dark matter

We carry out ray tracing through five high resolution simulat ions of a galaxy cluster to study how its ability to produce giant gravitationally lens ed arcs is influenced by the collision cross-section of its dark matter. In three cases typical dar k matter particles in the cluster core undergo between 1 and 100 collisions per Hubble time; two more explore the long (“collisionless”) and short (“fluid”) mean free path limits. We stud y the size and shape distributions of arcs and compute the cross-section for producing “extreme” arcs of various sizes. Even a few collisions per particle modify the core structure enou gh to destroy the cluster’s ability to produce long, thin arcs. For larger collision frequencie s the cluster must be scaled up to unrealistically large masses before it regains the ability to produce giant arcs. None of our models with self-interacting dark matter (except the “fluid ” limit) is able to produce radial arcs; even the case with the smallest scattering cross-sect ion must be scaled to the upper limit of observed cluster masses before it produces radial a rcs. Apparently the elastic collision cross-section of dark matter in clusters must be very small, below 0.1 cm 2 g −1 , to be compatible with the observed ability of clusters to produce both radial arcs and giant arcs.

Arc statistics in cosmological models with dark energy

We investigate how the probability of the formation of giant arcs in galaxy clusters is expected to change in cos- mological models dominated by dark energy with an equation of state p = wρc 2 compared to cosmological-constant or open models. To do so, we use a simple analytic model for arc cross sections based on the Navarro-Frenk-White density profile which we demonstrate reproduces essential features of numerically determined arc cross sections. Since analytic lens models are known to be inadequate for accurate absolute quantifications of arc probabilities, we use them only for studying changes rel- ative to cosmological-constant models. Our main results are (1) the order of magnitude difference between the arc probabilities in low density, spatially flat and open CDM models found numerically is reproduced by our analytic model, and (2) dark-energy cosmologies with w> −1 increase the arc optical depth by at most a factor of two and are thus unlikely to reconcile arc statistics with spatially flat cosmological models with low matter density.

Do arcs require flat halo cusps

It was recently claimed that several galaxy clusters containing radial and tangential gravitational arcs and having a measured velocity-dispersion profile for the brightest cluster galaxy had to have central density profiles considerably flatter than those found in CDM cluster simulations. Using a simple analytic mass model, we confirm this result for axially symmetric mass distributions. However, we demonstrate that steep density profiles are well in agreement with the cluster requiring the flattest axially symmetric profile once even small deviations from axial symmetry are introduced.