We propose a new method for generating equilibrium models of spherical systems of collisionless particles that are finite in extent, but whose central regions resemble dark matter halos from cosmological simulations. This method involves iteratively removing unbound particles from a Navarro-Frenk-White profile truncated sharply at some radius. The resulting models are extremely stable, and thus provide a good starting point for N -body simulations of isolated halos. We provide a code to generate such models for NFW and a variety of other common density profiles. We then develop an analytic approximation to this truncated distribution function. Our method proceeds by analogy with the King model, truncating and shifting the original distribution function of an infinitely extended Navarro-Frenk-White profile in energy space. We show that the density profiles of our models closely resemble the tidally truncated density profiles seen previously in studies of satellite evolution. Pursuing this analogy further with a series of simulations of tidal mass loss, we find that our models provide a good approximation to the full distribution function of tidally stripped systems, thus allowing theoretically motivated phase-space calculations for such systems.

We present the first public data release of the GOGREEN and GCLASS surveys of galaxies in dense environments, spanning a redshift range 0.8 < z < 1.5. The surveys consist of deep, multiwavelength photometry and extensive Gemini GMOS spectroscopy of galaxies in 26 overdense systems ranging in halo mass from small groups to the most massive clusters. The objective of both projects was primarily to understand how the evolution of galaxies is affected by their environment, and to determine the physical processes that lead to the quenching of star formation. There was an emphasis on obtaining unbiased spectroscopy over a wide stellar mass range (M ≳ 2 × 1010 M⊙), throughout and beyond the cluster virialized regions. The final spectroscopic sample includes 2771 unique objects, of which 2257 have reliable spectroscopic redshifts. Of these, 1704 have redshifts in the range 0.8 < z < 1.5, and nearly 800 are confirmed cluster members. Imaging spans the full optical and near-infrared wavelength range, at depths comparable to the UltraVISTA survey, and includes HST/WFC3 F160W (GOGREEN) and F140W (GCLASS). This data release includes fully reduced images and spectra, with catalogues of advanced data products including redshifts, line strengths, star formation rates, stellar masses and rest-frame colours. Here we present an overview of the data, including an analysis of the spectroscopic completeness and redshift quality.

The ability to accurately predict the evolution of tidally stripped haloes is important for understanding galaxy formation and testing the properties of dark matter. Most studies of substructure evolution make predictions based on empirical models of tidal mass loss that are calibrated using numerical simulations. This approach can be accurate in the cases considered, but lacks generality and does not provide a physical understanding of the processes involved. Recently, we demonstrated that truncating NFW distribution functions sharply in energy results in density profiles that resemble those of tidally stripped systems, offering a path to constructing physically motivated models of tidal mass loss. In this work, we review calculations of mass loss based on energy truncation alone, and then consider what secondary effects may modulate mass loss beyond this. We find that a combination of dependence on additional orbital parameters and variations in individual particle energies over an orbit results in a less abrupt truncation in energy space as a subhalo loses mass. Combining the energy truncation approach with a simple prediction for the mass-loss rate, we construct a full model of mass loss that can accurately predict the evolution of a subhalo in terms of a single parameter η eff . This parameter can be fully determined from the initial orbital and halo properties, and does not require calibration with numerical simulations.