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Disks are essential to the formation of both stars and planets, but how they form in magnetized molecular cloud cores remains debated. This work focuses on how the disk formation is affected by turbulence and ambipolar diffusion (AD), both separately and in combination, with an emphasis on the protostellar mass accretion phase of star formation. We find that a relatively strong, sonic turbulence on the core scale strongly warps but does not completely disrupt the well-known magnetically-induced flattened pseudodisk that dominates the inner protostellar accretion flow in the laminar case, in agreement with previous work. The turbulence enables the formation of a relatively large disk at early times with or without ambipolar diffusion, but such a disk remains strongly magnetized and does not persist to the end of our simulation unless a relatively strong ambipolar diffusion is also present. The AD-enabled disks in laminar simulations tend to fragment gravitationally. The disk fragmentation is suppressed by initial turbulence. The ambipolar diffusion facilitates the disk formation and survival by reducing the field strength in the circumstellar region through magnetic flux redistribution and by making the field lines there less pinched azimuthally, especially at late times. We conclude that turbulence and ambipolar diffusion complement each other in promoting disk formation. The disks formed in our simulations inherit a rather strong magnetic field from its parental core, with a typical plasma-$beta$ of order a few tens or smaller, which is 2-3 orders of magnitude lower than the values commonly adopted in MHD simulations of protoplanetary disks. To resolve this potential tension, longer-term simulations of disk formation and evolution with increasingly more realistic physics are needed.
We investigate the formation and evolution of a first core, protostar, and circumstellar disc with a three-dimensional non-ideal (including both Ohmic and ambipolar diffusion) radiation magnetohydrodynamics simulation. We found that the magnetic flux
We discuss the effects of the magnetic field observed in molecular clouds on the process of star formation, concentrating on the phase of gravitational collapse of low-mass dense cores, cradles of sunlike stars. We summarize recent analytic work and
We investigate the formation and early evolution and fragmentation of an accretion disk around a forming massive protostar. We use a grid-based self-gravity-radiation-hydrodynamics code including a sub-grid module for stellar and dust evolution. On p
The first long-baseline ALMA campaign resolved the disk around the young star HL Tau into a number of axisymmetric bright and dark rings. Despite the very young age of HL Tau these structures have been interpreted as signatures for the presence of (p
(Abridged) Context. Massive stars form in magnetized and turbulent environments, and are often located in stellar clusters. Their accretion mechanism, as well as the origin of their systems stellar multiplicity are poorly understood. Aims. We study t