No abstract

Context. The Hall drift, namely, the transport of magnetic flux by the moving electrons giving rise to the electrical current, may be the dominant effect causing the evolution of the magnetic field in the solid crust of neutron stars. It is a nonlinear process that, despite a number of theoretical efforts, is still not fully understood. Aims. Through mostly analytic arguments and solutions, we intend to help understand this highly nonlinear process. Methods. We use the Hall induction equation in axial symmetry to obtain some general properties of nonevolving fields, as well as analyzing the evolution of purely toroidal fields, their poloidal perturbations, and current-free, purely poloidal fields. We also analyze energy conservation in Hall instabilities and write down a variational principle for Hall equilibria. Results. We show that the evolution of any toroidal magnetic field can be described by Burgers' equation, as previously found by Vainshtein and collaborators in a plane-parallel geometry. This evolution leads to sharp current sheets, which dissipate on the Hall time scale, yielding a stationary field configuration that depends on a single, suitably defined coordinate. This field, however, is unstable to poloidal perturbations, which grow as their field lines are stretched by the background electron flow, as in the instabilities found numerically by Rheinhardt and Geppert. On the other hand, current-free poloidal configurations are stable and could represent a long-lived crustal field supported by currents in the fluid stellar core. There may be additional, stable configurations, corresponding to restricted local minima or maxima of the magnetic energy. Conclusions. Hall equilibria can be described by a simple variational principle. Long-lived, toroidal fields are not expected in neutron star crusts or other regions where Hall drift is the dominant evolution mechanism. However, other stable configurations do exist, such as current-free poloidal fields and possibly others.

By using cosmological hydrodynamical simulations we study the effect of supernova (SN) and active galactic nuclei (AGN) feedback on the mass transport of gas on to galactic nuclei and the black hole (BH) growth down to redshift z ∼ 6. We study the BH growth in relation with the mass transport processes associated with gravity and pressure torques, and how they are modified by feedback. Cosmological gas funelled through cold flows reaches the galactic outer region close to free-fall. Then torques associated to pressure triggered by gas turbulent motions produced in the circum-galactic medium by shocks and explosions from SNe are the main source of mass transport beyond the central ∼ 100 pc. Due to high concentrations of mass in the central galactic region, gravitational torques tend to be more important at high redshift. The combined effect of almost free-falling material and both gravity and pressure torques produces a mass accretion rate of order ∼ 1 M /yr at ∼ pc scales. In the absence of SN feedback, AGN feedback alone does not affect significantly either star formation or BH growth until the BH reaches a sufficiently high mass of ∼ 10 6 M to self-regulate. SN feedback alone, instead, decreases both stellar and BH growth. Finally, SN and AGN feedback in tandem efficiently quench the BH growth, while star formation remains at the levels set by SN feedback alone due to the small final BH mass, ∼ few 10 5 M . SNe create a more rarefied and hot environment where energy injection from the central AGN can accelerate the gas further.

We have performed hydrodynamical simulations from cosmological initial conditions using the AMR code RAMSES to study atomic cooling haloes (ACHs) at z = 10 with masses in the range 5 × 10 7 M < ∼ M < ∼ 2 × 10 9 M . We assume the gas has primordial composition and H 2 -cooling and prior star-formation in the haloes have been suppressed. We present a comprehensive analysis of the gas and DM properties of 19 haloes at a spatial resolution of ∼ 10 (proper) pc, selected from simulations with a total volume of ∼ 2000 (comoving) Mpc 3 . This is the largest statistical hydro-simulation study of ACHs at z > 10 to date. We examine the morphology, angular momentum, thermodynamical state, and turbulent properties of these haloes, in order to assess the prevalence of disks and massive overdensities that may lead to the formation of supermassive black holes (SMBHs). We find no correlation between either the magnitude or the direction of the angular momentum of the gas and its parent DM halo. Only 3 of the haloes form rotationally supported cores. Two of the most massive haloes, however, form massive, compact over-dense blobs, which migrate to the outer region of the halo. These blobs have an accretion rate ∼ 0.5M yr −1 (at a distance of 100 pc from their center), and are possible sites of SMBH formation. Our results suggest that the degree of rotational support and the fate of the gas in a halo is determined by its large-scale environment and merger history. In particular, the two haloes that form over-dense blobs are located at knots of the cosmic web, cooled their gas early on (z > 17), and experienced many mergers. The gas in these haloes is thus lumpy and highly turbulent, with Mach numbers M > ∼ 5. In contrast, the haloes forming rotationally supported cores are relatively more isolated, located midway along filaments of the cosmic web, cooled their gas more recently, and underwent fewer mergers. As a result, the gas in these haloes is less lumpy and less turbulent (Mach numbers M < ∼ 4), and could retain most of its angular momentum. The remaining 14 haloes have a diverse range of intermediate properties. If verified in a larger sample of haloes and with additional physics to account for metals and star-formation, our results will have implications for observations of the highest-redshift galaxies and quasars with JWST.

In order to elucidate the origin of spin in both dark matter and baryons in galaxies, we have performed hydrodynamical simulations from cosmological initial conditions. We study atomic cooling haloes in the redshift range 100 > z > 9 with masses of order 10 9 M at redshift z = 10. We assume that the gas has primordial composition and that H 2 -cooling and prior star-formation in the haloes have been suppressed. We present a comprehensive analysis of the gas and dark matter properties of four halos with very low (λ ≈ 0.01), low (λ ≈ 0.04), high (λ ≈ 0.06) and very high (λ ≈ 0.1) spin parameter. Our main conclusion is that the spin orientation and magnitude is initially well described by tidal torque linear theory, but later on is determined by the merging and accretion history of each halo. We provide evidence that the topology of the merging region, i.e. the number of colliding filaments, gives an accurate prediction for the spin of dark matter and gas: halos at the center of knots will have low spin while those in the center of filaments will have high spin. The spin of a halo is given by λ ≈ 0.05 × 7.6 number of filaments 5.1 .