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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.
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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. This thesis describes a semianalytic self-similar model of the collapse of rotating isothermal molecular cloud cores with both Hall and ambipolar diffusion, presenting similarity solutions that demonstrate that the Hall effect has a profound influence on the dynamics of collapse. ... Hall diffusion also determines the strength of the magnetic diffusion and centrifugal 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 would be worth exploring in future numerical simulations of star formation.
We present here a minor modification of our numerical implementation of the Hall effect for the 2D Riemann solver used in Constrained Transport schemes, as described in Marchand et al. (2018). In the previous work, the tests showed that the angular momentum was not conserved during protostellar collapse simulations, with significant impact. By removing the whistler waves speed from the characteristic speeds of non-magnetic variables in the 1D Riemann solver, we are able to improve the angular momentum conservation in our test-case by one order of magnitude, while keeping the second-order numerical convergence of the scheme. We also reproduce the simulations of Tsukamoto et al. (2015) with consistent resistivities, the three non-ideal MHD effects and initial rotation, and agree with their results. In this case, the violation of angular momentum conservation is negligible in regard to the total angular momentum and the angular momentum of the disk.
Magnetic diffusion in accretion flows changes the structure and angular momentum of the accreting material. We present two power law similarity solutions for flattened accretion flows in the presence of magnetic diffusion: a secularly-evolving Keplerian disc and a magnetically-diluted free fall onto the central object. The influence of Hall diffusion on the solutions is evident even when this is small compared to ambipolar and Ohmic diffusion, as the surface density, accretion rate and angular momentum in the flow all depend upon the product eta_H(B.Omega), and the inclusion of Hall diffusion may be the solution to the magnetic braking catastrophe of star formation simulations.
We demonstrate the formation of gravitationally unstable discs in magnetized molecular cloud cores with initial mass-to-flux ratios of 5 times the critical value, effectively solving the magnetic braking catastrophe. We model the gravitational collapse through to the formation of the stellar core, using Ohmic resistivity, ambipolar diffusion and the Hall effect and using the canonical cosmic ray ionization rate of $zeta_text{cr} = 10^{-17}$ s$^{-1}$. When the magnetic field and rotation axis are initially aligned, a $lesssim1$~au disc forms after the first core phase, whereas when they are anti-aligned, a gravitationally-unstable 25~au disc forms during the first core phase. The aligned model launches a 3~km~s$^{-1}$ first core outflow, while the anti-aligned model launches only a weak $lesssim 0.3$~km~s$^{-1}$ first core outflow. Qualitatively, we find that models with $zeta_text{cr} = 10^{-17}$ s$^{-1}$ are similar to purely hydrodynamical models if the rotation axis and magnetic field are initially anti-aligned, whereas they are qualitatively similar to ideal magnetohydrodynamical models if initially aligned.
The formation of massive stars is a long standing problem. Although a number of theories of massive star formation exist, ideas appear to converge to a disk-mediated accretion scenario. Here we present radiative hydrodynamic simulations of a star accreting mass via a disk embedded in a torus. We use a Monte Carlo based radiation hydrodynamics code to investigate the impact that ionizing radiation has on the torus. Ionized regions in the torus midplane are found to be either gravitationally trapped or in pressure driven expansion depending on whether or not the size of the ionized region exceeds a critical radius. Trapped Hii regions in the torus plane allow accretion to progress, while expanding Hii regions disrupt the accretion torus preventing the central star from aggregating more mass, thereby setting the stars final mass. We obtain constraints for the luminosities and torus densities that lead to both scenarios.
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