The abundance and demographics of dark matter substructure is important for many areas in astrophysics and cosmological N-body simulations have been the primary tool used to investigate them. However, it has recently become clear that the simulations are subject to numerical artefacts, which hampers a proper treatment of the tidal evolution of subhaloes. Unfortunately, no analytical models that accurately describe subhalo evolution exist either. We therefore present a library of idealized, high resolution N-body simulations of the tidal evolution of individual subhaloes that can be used to calibrate semi-analytical models and to complement cosmological simulations. The simulations focus on minor mergers, i.e., the mass of the subhalo is much smaller than that of the host halo, such that the impact of dynamical friction is negligible. This setup allows the adoption of a fixed analytical potential for modelling the host halo. The dynamical evolution of subhaloes is followed with N-body computations. In the library, four parameters, two of which characterize the subhalo orbit with respect to the host halo, and the two concentrations of the host-and subhalo, are varied over the ranges encountered in cosmological simulations. We show several representative examples from the library that illustrate the evolution of the subhalo mass and velocity dispersion profiles. Additionally, we make publicly available a pre-trained nonparametric model of the subhalo mass evolution based on random forest regression. This model is able to interpolate the simulation data at the 0.1 dex level and provides efficient access to the data for further use in modelling †. (GO) † DASH simulation data and machine learning model are available at https://cosmo.oca.eu/dash.

Several recent studies have indicated that artificial subhalo disruption (the spontaneous, non-physical disintegration of a subhalo) remains prevalent in state-of-the-art dark matter-only cosmological simulations. In order to quantify the impact of disruption on the inferred subhalo demographics, we augment the semi-analytical SatGen dynamical subhalo evolution model with an improved treatment of tidal stripping that is calibrated using the DASH database of idealized high-resolution simulations of subhalo evolution, which are free from artificial disruption. We also develop a model of artificial disruption that reproduces the statistical properties of disruption in the Bolshoi simulation. Using this framework, we predict subhalo mass functions (SHMFs), number density profiles, and substructure mass fractions and study how these quantities are impacted by artificial disruption and mass resolution limits. We find that artificial disruption affects these quantities at the $10-20\%$ level, ameliorating previous concerns that it may suppress the SHMF by as much as a factor of two. We demonstrate that semi-analytical substructure modeling must include orbit integration in order to properly account for splashback haloes, which make up roughly half of the subhalo population. We show that the resolution limit of N-body simulations, rather than artificial disruption, is the primary cause of the radial bias in subhalo number density found in dark matter-only simulations. Hence, we conclude that the mass resolution remains the primary limitation of using such simulations to study subhaloes. Our model provides a fast, flexible, and accurate alternative to studying substructure statistics in the absence of both numerical resolution limits and artificial disruption.

We present a semi-analytical model of satellite galaxies, SatGen, which can generate large statistical samples of satellite populations for a host halo of desired mass, redshift, and assembly history. The model combines dark matter (DM) halo merger trees, empirical relations for the galaxy–halo connection, and analytical prescriptions for tidal effects, dynamical friction, and ram-pressure stripping. SatGen emulates cosmological zoom-in hydrosimulations in certain aspects. Satellites can reside in cored or cuspy DM subhaloes, depending on the halo response to baryonic physics that can be formulated from hydrosimulations and physical modelling. The subhalo profile and the stellar mass and size of a satellite evolve depending on its tidal mass-loss and initial structure. The host galaxy can include a baryonic disc and a stellar bulge, each described by a density profile that allows analytic satellite orbit integration. SatGen complements simulations by propagating the effect of halo response found in simulated field galaxies to satellites (not properly resolved in simulations) and outperforms simulations by sampling the halo-to-halo variance of satellite statistics and overcoming artificial disruption due to insufficient resolution. As a first application, we use the model to study satellites of Milky Way (MW)- and M31-sized hosts, making it emulate simulations of bursty star formation and of smooth star formation, respectively, and to experiment with a disc potential in the host halo. We find that our model reproduces the observed satellite statistics reasonably well. Different physical recipes make a difference in satellite abundance and spatial distribution at the 25 per cent level, not large enough to be distinguished by current observations given the halo-to-halo variance. The MW/M31 disc depletes satellites by ${\sim } 20{{\ \rm per\ cent}}$ and has a subtle effect of diversifying the internal structure of satellites, which is important for alleviating certain small-scale problems. We discuss the conditions for a massive satellite to survive in MW/M31.

We present a method called Significant Cosmic Holes in Universe (SCHU) for identifying cosmic voids and loops of filaments in cosmological datasets and assigning their statistical significance using techniques from topological data analysis. In particular, persistent homology is used to find different dimensional holes. For dark matter halo catalogs and galaxy surveys, the 0-, 1-, and 2dimensional holes can be identified with connected components (i.e. clusters), loops of filaments, and voids. The procedure overlays dark matter halos/galaxies on a three-dimensional grid, and a distance-to-measure (DTM) function is calculated at each point of the grid. A nested set of simplicial complexes (a filtration) is generated over the lower-level sets of the DTM across increasing threshold values. The filtered simplicial complex can then be used to summarize the birth and death times of the different dimension homology group generators (i.e., the holes). Persistent homology summary diagrams, called persistence diagrams, are produced from the dimension, birth times, and death times of each homology group generator. Using the persistence diagrams and bootstrap sampling, we explain how p-values can be assigned to each homology group generator. The homology group generators on a persistence diagram are not, in general, uniquely located back in the original dataset volume so we propose a method for finding a representation of the homology group generators. This method provides a novel, statistically rigorous approach for locating informative generators in cosmological datasets, which may be useful for providing complementary cosmological constraints on the effects of, for example, the sum of the neutrino masses. The method is tested on a Voronoi foam simulation, and then subsequently applied to a subset of the SDSS galaxy survey and a cosmological simulation. Lastly, we calculate Betti functions for two of the MassiveNuS simulations and discuss implications for using the persistent homology of the density field to help break degeneracy in the cosmological parameters.

Accurately predicting the abundance and structural evolution of dark matter subhaloes is crucial for understanding galaxy formation, modelling galaxy clustering, and constraining the nature of dark matter. Due to the non-linear nature of subhalo evolution, cosmological N-body simulations remain its primary method of investigation. However, it has recently been demonstrated that such simulations are still heavily impacted by artificial disruption, diminishing the information content on small scales, and reducing the reliability of all simulation-calibrated semi-analytical models. In this paper, we utilize the recently released DASH library of high-resolution, idealized simulations of the tidal evolution of subhaloes, which are unhindered by numerical overmerging due to discreteness noise or force softening, to calibrate an improved, more accurate model of the evolution of the density profiles of subhaloes that undergo tidal heating and stripping within their host halo. By testing previous findings that the structural evolution of a tidally truncated subhalo depends solely on the fraction of mass stripped, independent of the details of the stripping, we identify an additional dependence on the initial subhalo concentration. We provide significantly improved fitting functions for the subhalo density profiles and structural parameters (Vmax and rmax) that are unimpeded by numerical systematics and applicable to a wide range of parameter space. This model will be an integral component of a future semi-analytical treatment of substructure evolution, which can be used to predict key quantities, such as the evolved subhalo mass function and annihilation boost factors, and validate such calculations performed with cosmological simulations.