We study the characteristics of the galaxy cluster samples expected from the European Space Agency's Euclid satellite and forecast constraints on parameters describing a variety of cosmological models. The method used in this paper, based on the Fisher Matrix approach, is the same one used to provide the constraints presented in the Euclid Red Book (Laureijs et al. 2011). We describe the analytical approach to compute the selection function of the photometric and spectroscopic cluster surveys. Based on the photometric selection function, we forecast the constraints on a number of cosmological parameter sets corresponding to different extensions of the standard ΛCDM model, including a redshift-dependent Equation of State for Dark Energy, primordial non-Gaussianity, modified gravity and non-vanishing neutrino masses. Our results show that Euclid clusters will be extremely powerful in constraining the amplitude of the matter power spectrum σ 8 and the mass density parameter Ω m . The dynamical evolution of dark energy will be constrained to ∆w 0 = 0.03 and ∆w a = 0.2 with free curvature Ω k , resulting in a (w 0 , w a ) Figure of Merit (FoM) of 291. Including the Planck CMB covariance matrix, thereby information on the geometry of the universe, improves the constraints to ∆w 0 = 0.02, ∆w a = 0.07 and a FoM= 802. The amplitude of primordial nonGaussianity, parametrised by f NL , will be constrained to ∆ f NL ≃ 6.6 for the local shape scenario, from Euclid clusters alone. Using only Euclid clusters, the growth factor parameter γ, which signals deviations from General Relativity, will be constrained to ∆γ = 0.02, and the neutrino density parameter to ∆Ω ν = 0.0013 (or ∆ m ν = 0.01). We emphasise that knowledge of the observable-mass scaling relation will be crucial to constrain cosmological parameters from a cluster catalogue. The Euclid mission will have a clear advantage in this respect, thanks to its imaging and spectroscopic capabilities that will enable internal mass calibration from weak lensing and the dynamics of cluster galaxies. This information will be further complemented by wide-area multi-wavelength external cluster surveys that will already be available when Euclid flies. c 0000 RAS 2 B. Sartoris et al.

We investigate the variation of galaxy clustering with luminosity using the recently completed SSRS2 sample. Clustering measurements based on the two-point correlation function and the variance of counts in cells reveal the existence of a strong dependence of the clustering amplitude on luminosity for galaxies brighter than L*, while no significant variation is detected for fainter galaxies. We derive a relative bias versus magnitude relation which can be compared with theoretical predictions. Existing models of galaxy formation cannot adequately reproduce the simultaneous steep rise of biasing at high luminosities and the plateau at the low-luminosity end. Improved modeling of the halo-galaxy relation and larger samples including low luminosity galaxies are required to draw more definitive conclusions.Comment: 29 pages including 5 figures (tarred, gzipped & uuencoded LaTeX & postscript files; postscript version including figures also available at http://www.bo.astro.it/bap/BAPhome.html); ApJ, accepted for publicatio

Abstract. We present the analysis and results of a new VRI photometric and spectroscopic survey of the central ∼1.8×1.2 Mpc 2 region of the galaxy cluster A3921 (z = 0.094). We detect the presence of two dominant clumps of galaxies with a mass ratio of ∼5: a main cluster centred on the Brightest Cluster Galaxy (BCG) (A3921-A), and an NW sub-cluster (A3921-B) hosting the second brightest cluster galaxy. The distorted morphology of the two sub-clusters suggests that they are interacting, while the velocity distribution of 104 confirmed cluster members does not reveal strong signatures of merging. By applying a two-body dynamical formalism to the two sub-clusters of A3921, and by comparing our optical results to the X-ray analysis of A3921 based on XMM observations (Belsole et al. 2005), we conclude that A3921-B is probably tangentially traversing the main cluster along the SW/NE direction. The two sub-clusters are observed in the central phase of their merging process (±0.3 Gyr), with a collision axis nearly perpendicular to the line of sight. Based on the spectral features of the galaxies belonging to A3921 we estimate the star formation properties of the confirmed cluster members. Substantial fractions of both emission-line (∼13%) and post-star-forming objects (so called k+a's, ∼16%) are detected, comparable to those measured at intermediate redshifts. Our analysis reveals a lack of bright post-star-forming objects in A3921 with respect to higher redshift clusters, while the fraction of k+a's increases towards fainter magnitudes (M R AB > −20). Similar results were obtained in the Coma cluster by Poggianti et al. (2004), but at still fainter magnitudes, suggesting that the maximum mass of actively star-forming galaxies increases with redshift ("downsizing effect"). The spatial and velocity distributions of k+a galaxies do not show significant differences to those of the passive population, and to the whole cluster. Most of these objects show relatively red colours and moderate Balmer absorption lines, which suggest that star formation has ceased ∼1−1.5 Gyr ago. Their presence is therefore difficult to relate to the on-going merging event. We find that star-forming galaxies share neither the kinematics nor the projected distribution of the passive cluster members. Moreover, most emission-line galaxies are concentrated in A3921-B and in the region between the two sub-clusters. We therefore suggest that the ongoing merger may have triggered a star-formation episode in at least a fraction of the observed emission-line galaxies.