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Register a new userMagnetic fields and large-scale structure in a hot universe. II. Magnetic flux tubes and filamentary structure
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In paper I, we obtained an equation for the evolution of density inhomogeneities in a radiation dominated universe when they are affected by magnetic fields. In this second paper we apply this equation to the case in which the subjacent magnetic configuration is a flux tube. For scales of the order of 1 Mpc or less the differential equation is elliptical. To solve it, we have used the numerical method based on Simultaneous Over Relaxation, SOR, with Chebyshev acceleration and we have treated the problem as a boundary value problem, which restricts the prediction ability of the integration. For large-scale flux tubes, much larger than 1 Mpc, the equation can be analytically integrated and no assumption about the final shape or magnitude of the inhomogeneity is required. In both cases we obtain an evolution which does not differ very much from linear in time. The inhomogeneity in the density becomes filamentary. Large scale structures ($ge$ 10 Mpc) are probably unaffected by damping, non-linear and amplification mechanisms after Equality, so that this model provides a tool to interpret the present observed large scale structure. Filaments are very frequently found in the large-scale structure in the Universe. It is suggested here that they could arise from primordial magnetic flux tubes, thus providing an alternative hypothesis for its interpretation; in particular we consider the case of the Coma-A1367 supercluster, where the magnetic field is known to be high.
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We consider that no mean magnetic field exists during this epoch, but that there is a mean magnetic energy associated with large-scale magnetic inhomogeneities. We study the evolution of these inhomogeneities and their influence on the large scale density structure, by introducing linear perturbations in Maxwell equations, the conservation of momentum-energy equation, and in Einstein field equations. The primordial magnetic field structure is time independent in the linear approximation, only being diluted by the general expansion, so that $vec{B}R^2$ is conserved in comoving coordinates. Magnetic fields have a strong influence on the formation of large-scale structure. Firstly, relatively low fields are able to generate density structures even if they were inexistent at earlier times. Second, magnetic fields act anisotropically more recently, modifying the evolution of individual density clouds. Magnetic flux tubes have a tendency to concentrate photons in filamentary patterns.
The nature and origin of turbulence and magnetic fields in the intergalactic space are important problems that are yet to be understood. We propose a scenario in which turbulent flow motions are induced via the cascade of the vorticity generated at cosmological shocks during the formation of the large scale structure. The turbulence in turn amplifies weak seed magnetic fields of any origin. Supercomputer simulations show that the turbulence is subsonic inside clusters/groups of galaxies, whereas it is transonic or mildly supersonic in filaments. Based on a turbulence dynamo model, we then estimate that the average magnetic field strength would be a few microgauss inside clusters/groups, approximately 0.1 microgauss around clusters/groups, and approximately 10 nanogauss in filaments. Our model presents a physical mechanism that transfers the gravitation energy to the turbulence and magnetic field energies in the large scale structure of the universe.
The origin of the micro-Gauss magnetic fields in galaxy clusters is one of the outstanding problem of modern cosmology. We have performed three-dimensional particle-in-cell simulations of the nonrelativistic Weibel instability in an electron-proton plasma, in conditions typical of cosmological shocks. These simulations indicate that cluster fields could have been produced by shocks propagating through the intergalactic medium during the formation of large-scale structure or by shocks within the cluster. The strengths of the shock-generated fields range from tens of nano-Gauss in the intercluster medium to a few micro-Gauss inside galaxy clusters.
In the first part of these lecture notes, new high-resolution observations of small-scale magnetic flux concentrations are presented and compared to results from new three-dimensional magnetohydrodynamic simulations. Special attention is paid to the physics of faculae and to new three-dimensional radiation magnetohydrodynamic simulations of the integral layers from the top of the convection zone to the mid-chromosphere. The second part is devoted to a few basic properties of magnetic flux tubes, which can be considered to be an abstraction of the more complicated flux concentrations known from observations and numerical simulations. We treat electrical current sheets, the mechanical equilibrium condition at magnetic interfaces, the equations for constructing a magnetohydrostatic flux tube embedded in a gravitationally stratified atmosphere, the condition of radiative equilibrium, and the condition for interchange stability.
We perform ideal MHD high resolution AMR simulations with driven turbulence and self-gravity and find that long filamentary molecular clouds are formed at the converging locations of large-scale turbulence flows and the filaments are bounded by gravity. The magnetic field helps shape and reinforce the long filamentary structures. The main filamentary cloud has a length of ~4.4 pc. Instead of a monolithic cylindrical structure, the main cloud is shown to be a collection of fiber/web-like sub-structures similar to filamentary clouds such as L1495. Unless the line-of-sight is close to the mean field direction, the large-scale magnetic field and striations in the simulation are found roughly perpendicular to the long axis of the main cloud, similar to 1495. This provides strong support for a large-scale moderately strong magnetic field surrounding L1495. We find that the projection effect from observations can lead to incorrect interpretations of the true three-dimensional physical shape, size, and velocity structure of the clouds. Helical magnetic field structures found around filamentary clouds that are interpreted from Zeeman observations can be explained by a simple bending of the magnetic field that pierces through the cloud. We demonstrate that two dark clouds form a T-shape configuration which are strikingly similar to the Infrared dark cloud SDC13 leading to the interpretation that SDC13 results from a collision of two long filamentary clouds. We show that a moderately strong magnetic field (M_A ~ 1) is crucial for maintaining a long and slender filamentary cloud for a long period of time ~0.5 million years.
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