Quantum similarity of isosteres coordinate versus momentum space and influence of alignment

A

The baryonic self similarity of dark matter

The cosmological simulations indicates that the dark matter haloes have specific self similar properties. However the halo similarity is affected by the baryonic feedback, the momentum injected by the supernovae re-shape the dark matter core and transform it to a flat density core, with a scale length imposed by the baryonic feedback. Additionally the baryon feedback impose also an equilibrium condition, which when coupled with the imposed baryonic scale length induce a new type of similarity. The new self similar solution implies that the acceleration generated by dark matter is scale free, which in turns implies that the baryonic acceleration at a reference radius is also scale free. Constant dark matter and baryonic accelerations at a reference radius have effectively been observed for a large class of different galaxies, which is in support of this approach. The new self similar properties implies that the total acceleration at larger distances is scale free, the transition between the dark matter and baryons dominated regime occurs at a constant acceleration, and the maximum of the velocity curve which defines the amplitude of the velocity curve at larger distances is proportional to $M^{\frac{1}{4}}$. These results demonstrates that in this self similar model, cold dark matter is consistent with the basics of MOND phenomenology for the galaxies. In agreement with the observation the coincidence between the self similar model and MOND is expected to break at the scale of clusters of galaxies. Some numerical experiments shows that the behavior of the density near the origin is closely approximated by a Einasto profile.Comment: Last versio

Microscopic origin of self-similarity in granular blast waves

The self-similar expansion of a blast wave, well-studied in air, has peculiar counterparts in dense and dissipative media such as granular gases. Recent results have shown that, while the traditional Taylor-von Neumann-Sedov (TvNS) derivation is not applicable to such granular blasts, they can nevertheless be well understood via a combination of microscopic and hydrodynamic insights. In this article, we provide a detailed analysis of these methods associating Molecular Dynamics simulations and continuum equations, which successfully predict hydrodynamic profiles, scaling properties and the instability of the self-similar solution. We also present new results for the energy conserving case, including the particle-level analysis of the classic TvNS solution and its breakdown at higher densities.Comment: 47 pages, 9 figures Supplementary Materials: 2 appendices, 3 figure

The Hall effect in star formation

Magnetic fields play an important role in star formation by regulating the removal of angular momentum from collapsing molecular cloud cores. Hall diffusion is known to be important to the magnetic field behaviour at many of the intermediate densities and field strengths encountered during the gravitational collapse of molecular cloud cores into protostars, and yet its role in the star formation process is not well-studied. We present a semianalytic self-similar model of the collapse of rotating isothermal molecular cloud cores with both Hall and ambipolar diffusion, and similarity solutions that demonstrate the profound influence of the Hall effect on the dynamics of collapse. The solutions show that the size and sign of the Hall parameter can change the size of the protostellar disc by up to an order of magnitude and the protostellar accretion rate by fifty per cent when the ratio of the Hall to ambipolar diffusivities is varied between -0.5 <= eta_H / eta_A <= 0.2. These changes depend upon the orientation of the magnetic field with respect to the axis of rotation and create a preferred handedness to the solutions that could be observed in protostellar cores using next-generation instruments such as ALMA. Hall diffusion also determines the strength and position of the shocks that bound the pseudo and rotationally-supported discs, and can introduce subshocks that further slow accretion onto the protostar. In cores that are not initially rotating Hall diffusion can even induce rotation, which could give rise to disc formation and resolve the magnetic braking catastrophe. The Hall effect clearly influences the dynamics of gravitational collapse and its role in controlling the magnetic braking and radial diffusion of the field merits further exploration in numerical simulations of star formation.Comment: 22 pages, 10 figures, accepted by MNRA

The secondary infall model of galactic halo formation and the spectrum of cold dark matter particles on Earth

The spectrum of cold dark matter particles on Earth is expected to have peaks in velocity space associated with particles which are falling onto the Galaxy for the first time and with particles which have fallen in and out of the Galaxy only a small number of times in the past. We obtain estimates for the velocity magnitudes and the local densities of the particles in these peaks. To this end we use the secondary infall model of galactic halo formation which we have generalized to take account of the angular momentum of the dark matter particles. The new model is still spherically symmetric and it admits self-similar solutions. In the absence of angular momentum, the model produces flat rotation curves for a large range of values of a parameter $\epsilon$ which is related to the spectrum of primordial density perturbations. We find that the presence of angular momentum produces an effective core radius, i.e. it makes the contribution of the halo to the rotation curve go to zero at zero radius. The model provides a detailed description of the large scale properties of galactic halos including their density profiles, their extent and total mass. We obtain predictions for the kinetic energies of the particles in the velocity peaks and estimates for their local densities as functions of the amount of angular momentum, the age of the universe and $\epsilon$.Comment: LaTeX, 39 pages including 18 figure