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CUSP is a powerful formalism that recovers, from first principles and with no free parameter, all the macroscopic properties of dark matter haloes found in cosmological N -body simulations and unveils the origin of their characteristic features. Since it is not restricted by the limitations of simulations, it covers the whole mass and redshift ranges. In the present Paper we use CUSP to calculate the mass–scale relations holding for halo density profiles fitted to the usual NFW and Einasto functions in the most relevant cosmologies and for the most usual mass definitions. We clarify the origin of these relations and provide accurate analytic expressions holding for all masses and redshifts. The performance of those expressions is compared to that of previous models and to the mass–concentration relation spanning more than 20 orders of magnitude in mass at z  = 0 obtained in recent simulations of a 100 GeV WIMP universe. [ABSTRACT FROM AUTHOR]

It is one of the biggest issues in black hole (BH) astrophysics how to evaluate BH feedback to its environments precisely. Aiming at studying the unique gas dynamics of super-Eddington flow around supermassive black hole (SMBH) seeds at high redshift, we carried out axisymmetric two-dimensional radiation hydrodynamic simulations using a nested simulation-box method. Here we divide the simulation box into an inner zone at (2–3 × 103) r Sch (with r Sch being the Schwarzschild radius) and an outer zone at (2 × 103–3 × 106) r Sch, with smooth connection of the physical quantities, such as gas density, velocity, and radiation energy. We start the calculation by injecting mass through the outer boundary of the inner zone at a constant rate of |$\dot{M}_{\rm {inj}}=10^3L_{\rm {Edd}}/c^2$|⁠ , where L Edd is the Eddington luminosity and c is the speed of light. A powerful outflow is generated in the innermost region and it propagates from the inner zone to the outer zone. The outflows are characterized by a velocity of 0.02 c (0.7 c) and density of 10−17 (10−19) g cm−3 for near the edge-on (face-on) direction. The outflow is gradually accelerated as it travels by accepting radiation-pressure force. The final mass outflow rate at the outermost boundary is |$\dot{M}_{\rm {out}}\sim 0.3 \times \dot{M}_{\rm {inj}}$|⁠. By extrapolating the outflow structure to a further larger scale, we find that the momentum and energy fluxes at r ∼ 0.1 pc are ∼10–100  L Edd/ c and ∼0.1–10  L Edd, respectively. Moreover, we find that the impacts are highly anisotropic, in the sense that larger impacts occur towards the face-on direction than in the edge-on direction. These results indicate that the BH feedback will work more efficiently on the interstellar medium than assumed in the cosmological simulations. [ABSTRACT FROM AUTHOR]

With this paper, we complete a comprehensive study of substructure in dark matter haloes. In Paper I, we derived the radial distribution and mass function (MF) of accreted subhaloes (scaled to the radius and mass of the host halo) and showed that they are essentially universal. This is not the case, however, for those of stripped subhaloes, which depend on halo mass and assembly history. In Paper II, we derived these latter properties in the simplest case of purely accreting haloes. Here, we extend the study to ordinary haloes having suffered major mergers. After showing that all the properties of substructure are encoded in the mean truncated-to-original subhalo mass ratio profile, we demonstrate that the dependence of the subhalo MF on halo mass arises from their mass-dependent concentration, while the shape of the subhalo radial distribution depends on the time of the last major merger of the host halo. In this sense, the latter property is a better probe of halo formation time than the former. Unfortunately, this is not the case for the radial distribution of satellites as this profile is essentially disconnected from subhalo stripping and the properties of accreted subhaloes are independent of the halo formation time. [ABSTRACT FROM AUTHOR]