We present a semi-analytic, physically motivated model for dark matter halo concentration as a function of halo mass and redshift. The semi-analytic model combines an analytic model for the halo mass accretion history (MAH), based on extended Press Schechter (EPS) theory, with an empirical relation between concentration and formation time obtained through fits to the results of numerical simulations. Because the semi-analytic model is based on EPS theory, it can be applied to wide ranges in mass, redshift and cosmology. The resulting concentration-mass (c − M ) relations are found to agree with the simulations, and because the model applies only to relaxed halos, they do not exhibit the upturn at high masses or high redshifts found by some recent works. We predict a change of slope in the z ∼ 0 c − M relation at a mass scale of 10 11 M ⊙ . We find that this is due to the change in the functional form of the halo MAH, which goes from being dominated by an exponential (for high-mass halos) to a power-law (for low-mass halos). During the latter phase, the core radius remains approximately constant, and the concentration grows due to the drop of the background density. We also analyse how the c − M relation predicted by this work affects the power produced by dark matter annihilation, finding that at z = 0 the power is two orders of magnitude lower than that obtained from extrapolating best-fitting c − M relations. We provide fits to the c − M relations as well as numerical routines to compute concentrations and MAHs †.

We investigate the relation between kinematic morphology, intrinsic colour and stellar mass of galaxies in the EAGLE cosmological hydrodynamical simulation. We calculate the intrinsic u − r colours and measure the fraction of kinetic energy invested in ordered corotation of 3562 galaxies at z = 0 with stellar masses larger than 10 10 M . We perform a visual inspection of gri-composite images and find that our kinematic morphology correlates strongly with visual morphology. EAGLE produces a galaxy population for which morphology is tightly correlated with the location in the colourmass diagram, with the red sequence mostly populated by elliptical galaxies and the blue cloud by disc galaxies. Satellite galaxies are more likely to be on the red sequence than centrals, and for satellites the red sequence is morphologically more diverse. These results show that the connection between mass, intrinsic colour and morphology arises from galaxy formation models that reproduce the observed galaxy mass function and sizes.

Understanding the universal accretion history of dark matter halos is the first step towards determining the origin of their structure. We use the extended Press-Schechter formalism to derive the halo mass accretion history from the growth rate of initial density perturbations. We show that the halo mass history is well described by an exponential function of redshift in the high-redshift regime. However, in the lowredshift regime the mass history follows a power law because the growth of density perturbations is halted in the dark energy dominated era due to the accelerated expansion of the Universe. We provide an analytic model that follows the expression, a depends on cosmology and f (M 0 ) depends only on the linear matter power spectrum. The analytic model does not rely on calibration against numerical simulations and is suitable for any cosmology. We compare our model with the latest empirical models for the mass accretion history in the literature and find very good agreement. We provide numerical routines for the model online †.

The observed anti-correlation between the central dark matter (DM) densities of the bright Milky Way (MW) dwarf spheroidal galaxies (dSphs) and their orbital pericenter distances poses a potential signature of self-interacting dark matter (SIDM). In this work we investigate this possibility by analysing the range of SIDM scattering cross section per unit mass, σ/mχ, able to explain such anti-correlation. We simulate the orbital evolution of dSphs subhaloes around the MW assuming an analytical form for the gravitational potential, adopting the proper motions from the Gaia mission and including a consistent characterization of gravitational tidal stripping. The evolution of subhalo density profiles is modelled using the gravothermal fluid formalism, where DM particle collisions induce thermal conduction that depends on σ/mχ. We find that models of dSphs, such as Carina and Fornax, reproduce the observed central DM densities with fixed σ/mχ ranging between 30 and 50 cm2g−1, whereas other dSphs prefer larger values ranging between 70 and 100 cm2g−1. These cross sections correlate with the average collision velocity of DM particles within each subhalo’s core, so that systems modelled with large cross sections have lower collision velocities. We fit the cross section-velocity correlation with a SIDM particle model, where a DM particle of mass mχ = 53.93 ± 9.81 GeV interacts under the exchange of a light mediator of mass mφ = 6.6 ± 0.43 MeV, with the self-interactions being described by a Yukawa potential. The outcome is a cross section-velocity relation that explains the diverse DM profiles of MW dSph satellites and is consistent with observational constraints on larger scales.

We explore the relation between the structure and mass accretion histories of dark matter halos using a suite of cosmological simulations. We confirm that the formation time, defined as the time when the virial mass of the main progenitor equals the mass enclosed within the scale radius, correlates strongly with concentration. We provide a semi-analytic model for halo mass history that combines analytic relations with fits to simulations. This model has the functional form, M (z) = M 0 (1 + z) α e βz , where the parameters α and β are directly correlated with concentration. We then combine this model for the halo mass history with the analytic relations between α, β and the linear power spectrum derived by Correa et al. to establish the physical link between halo concentration and the initial density perturbation field. Finally, we provide fitting formulae for the halo mass history as well as numerical routines †, we derive the accretion rate as a function of halo mass, and demonstrate how the halo mass history depends on cosmology and the adopted definition of halo mass.