We explore the simple inter-relationships between mass, star formation rate, and environment in the SDSS, zCOSMOS, and other deep surveys. We take a purely empirical approach in identifying those features of galaxy evolution that are demanded by the data and then explore the analytic consequences of these. We show that the differential effects of mass and environment are completely separable to z ~ 1, leading to the idea of two distinct processes of "mass quenching" and "environment quenching." The effect of environment quenching, at fixed over-density, evidently does not change with epoch to z ~ 1 in zCOSMOS, suggesting that the environment quenching occurs as large-scale structure develops in the universe, probably through the cessation of star formation in 30%-70% of satellite galaxies. In contrast, mass quenching appears to be a more dynamic process, governed by a quenching rate. We show that the observed constancy of the Schechter M* and α s for star-forming galaxies demands that the quenching of galaxies around and above M* must follow a rate that is statistically proportional to their star formation rates (or closely mimic such a dependence). We then postulate that this simple mass-quenching law in fact holds over a much broader range of stellar mass (2 dex) and cosmic time. We show that the combination of these two quenching processes, plus some additional quenching due to merging naturally produces (1) a quasi-static single Schechter mass function for star-forming galaxies with an exponential cutoff at a value M* that is set uniquely by the constant of proportionality between the star formation and mass quenching rates and (2) a double Schechter function for passive galaxies with two components. The dominant component (at high masses) is produced by mass quenching and has exactly the same M* as the star-forming galaxies but a faint end slope that differs by Δα s ~ 1. The other component is produced by environment effects and has the same M* and α s as the star-forming galaxies but an amplitude that is strongly dependent on environment. Subsequent merging of quenched galaxies will modify these predictions somewhat in the denser environments, mildly increasing M* and making α s slightly more negative. All of these detailed quantitative inter-relationships between the Schechter parameters of the star-forming and passive galaxies, across a broad range of environments, are indeed seen to high accuracy in the SDSS, lending strong support to our simple empirically based model. We find that the amount of post-quenching "dry merging" that could have occurred is quite constrained. Our model gives a prediction for the mass function of the population of transitory objects that are in the process of being quenched. Our simple empirical laws for the cessation of star formation in galaxies also naturally produce the "anti-hierarchical" run of mean age with mass for passive galaxies, as well as the qualitative variation of formation timescale indicated by the relative α-element abundances.

We study the angular-momentum profiles of a statistical sample of halos drawn from a high-resolution N -body simulation of the ΛCDM cosmology. We find that the cumulative mass distribution of specific angular momentum j in a halo of mass M v is well fit by a universal function, M (< j) = M v µj/(j 0 + j). This profile is defined by one shape parameter (µ or j 0 ) in addition to the global spin parameter λ. It follows a power-law M (< j) ∝ j over most of the mass, and flattens at large j, with the flattening more pronounced for small values of µ (or large j 0 at a fixed λ). Compared to a uniform sphere in solid-body rotation, most halos have a higher fraction of their mass in the low-and high-j tails of the distribution. High-λ halos tend to have high µ values, corresponding to a narrower, more uniform j distribution. The spatial distribution of angular momentum in halos tends to be cylindrical and is well-aligned within each halo for ∼ 80% of the halos. The more misaligned halos tend to have low-µ values. When averaged over spherical shells encompassing mass M , the halo j profiles are fit by j(M ) ∝ M s with s = 1.3 ± 0.3. We investigate two ideas for the origin of this profile. The first is based on a revised version of linear tidal-torque theory combined with extended Press-Schechter mass accretion, and the second focuses on j transport in minor mergers.Finally, we briefly explore implications of the M (< j) profile on the formation of galactic disks assuming that j is conserved during an adiabatic baryonic infall. The implied gas density profile deviates from an exponential disk, with a higher density at small radii and a tail extending to large radii. The steep central density profiles may imply disk scale lengths that are smaller than observed. This is reminiscent of the "angular-momentum problem" seen in hydrodynamic simulations, even though we have assumed perfect j conservation. A possible solution is to associate the central excesses with bulge components and the outer regions with extended gaseous disks.

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Euclid is a European Space Agency medium-class mission selected for launch in 2019 within the Cosmic Vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky.Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis.This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

Using a series of high‐resolution N‐body simulations of the concordance cosmology we investigate how the formation histories, shapes and angular momenta of dark matter haloes depend on environment. We first present a classification scheme that allows us to distinguish between haloes in clusters, filaments, sheets and voids in the large‐scale distribution of matter. This method (which goes beyond a simple measure of the local density) is based on a local‐stability criterion for the orbits of test particles and closely relates to the Zel'dovich approximation. Applying this scheme to our simulations we then find that: (i) mass assembly histories and formation redshifts strongly depend on environment for haloes of mass M < M* (haloes of a given mass tend to be older in clusters and younger in voids) and are independent of it for larger masses (M* here indicates the typical mass scale which is entering the non‐linear regime of perturbation growth); (ii) low‐mass haloes in clusters are generally less spherical and more prolate than in other regions; (iii) low‐mass haloes in clusters have a higher median spin than in filaments and present a more prominent fraction of rapidly spinning objects. We identify recent major mergers as a likely source of this effect. For all these relations, we provide accurate functional fits as a function of halo mass and environment. We also look for correlations between halo‐spin directions and the large‐scale structures: the strongest effect is seen in sheets where halo spins tend to lie within the plane of symmetry of the mass distribution. Finally, we measure the spatial autocorrelation of spin directions and the cross‐correlation between the directions of intrinsic and orbital angular momenta of neighbouring haloes. While the first quantity is always very small, we find that spin–orbit correlations are rather strong especially for low‐mass haloes in clusters and high‐mass haloes in filaments.