We explore a function with two shape parameters for the dark-matter halo density profile subject to baryonic effects, which is a special case of the general Zhao family of models applied to simulated dark matter haloes by Dekel et al. This profile has variable inner slope and concentration parameter, and analytic expressions for the gravitational potential, velocity dispersion, and lensing properties. Using the NIHAO cosmological simulations, we find that it provides better fits than the Einasto profile and the generalized NFW profile with variable inner slope, in particular towards the halo centers. We show that the profile parameters are correlated with the stellar-to-halo mass ratio Mstar/Mvir. This defines a mass-dependent density profile describing the average dark matter profiles in all galaxies, which can be directly applied to observed rotation curves of galaxies, gravitational lenses, and semi-analytic models of galaxy formation or satellite-galaxy evolution. The effect of baryons manifests itself by a significant flattening of the inner density slope and a 20% decrease of the concentration parameter for Mstar/Mvir = 10−3.5 to 10−2, corresponding to Mstar ∼ 107 − 10 M⊙. The accuracy by which this profile fits simulated galaxies is similar to certain multi-parameter, mass-dependent profiles, but its fewer parameters and analytic nature make it most desirable for many purposes.

Simulations of cosmological filamentary accretion reveal flows ("streams") of warm gas, T∼10 4 K, which are efficient in bringing gas into galaxies. We present a phenomenological scenario where gas in such flows -if it is shocked as it enters the halo as we assume -become biphasic and, as a result, turbulent. We consider a collimated stream of warm gas that flows into a halo from an over dense filament of the cosmic web. The post-shock streaming gas expands because it has a higher pressure than the ambient halo gas, and fragments as it cools. The fragmented stream forms a two phase medium: a warm cloudy phase embedded in hot post-shock gas. We argue that the hot phase sustains the accretion shock. During fragmentation, a fraction of the initial kinetic energy of the infalling gas is converted into turbulence among and within the warm clouds. The thermodynamic evolution of the post-shock gas is largely determined by the relative timescales of several processes. These competing timescales characterize the cooling, the expansion of the post-shock gas, the amount of turbulence in the clouds, and the dynamical time of the halo. We expect the gas to become multiphase when the gas cooling and dynamical times are of the same order-of-magnitude. In this framework, we show that this occurs in the important mass range of M halo ∼10 11 to 10 13 M , where the bulk of stars have formed in galaxies. Due to expansion and turbulence, gas accreting along cosmic web filaments may eventually loose coherence and mix with the ambient halo gas. Through both the phase separation and "disruption" of the stream, the accretion efficiency onto a galaxy in a halo dynamical time is lowered. De-collimating flows make the direct interaction between galaxy feedback and accretion streams more likely, thereby further reducing the overall accretion efficiency. As we discuss, moderating the gas accretion efficiency through these mechanisms may help to alleviate a number of significant challenges in theoretical galaxy formation.

We present a simple model for the response of a dissipationless spherical system to an instantaneous mass change at its center, describing the formation of flat cores in dark matter haloes and ultra-diffuse galaxies (UDGs) from feedback-driven outflow episodes in a specific mass range. This model generalizes an earlier simplified analysis of an isolated shell into a system with continuous density, velocity and potential profiles. The response is divided into an instantaneous change of potential at constant velocities due to a given mass loss or gain, followed by energy-conserving relaxation to a new Jeans equilibrium. The halo profile is modeled by a two-parameter function with a variable inner slope and an analytic potential profile , which enables to determine the associated kinetic energy at equilibrium. The model is tested against NIHAO cosmological zoom-in simulations, where it successfully predicts the evolution of the inner dark-matter profile between successive snapshots in about 75% of the cases, failing mainly in merger situations. This model provides a simple understanding of the formation of dark-matter halo cores and UDGs by supernova-driven outflows, and a useful analytic tool for studying such processes.