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Register a new userCollapse and Fragmentation of Rotating Magnetized Clouds. II. Binary Formation and Fragmentation of First Cores
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Subsequent to Paper I, the evolution and fragmentation of a rotating magnetized cloud are studied with use of three-dimensional MHD nested-grid simulations. After the isothermal runaway collapse, an adiabatic gas forms a protostellar first core at the center of the cloud. When the isothermal gas is stable for fragmentation in a contracting disk, the adiabatic core often breaks into several fragments. Conditions for fragmentation and binary formation are studied. All the cores which show fragmentations are geometrically thin, as the diameter-to-thickness ratio is larger than 3. Two patterns of fragmentation are found. (1) When a thin disk is supported by centrifugal force, the disk fragments through a ring configuration (ring fragmentation). This is realized in a fast rotating adiabatic core as Omega >0.2 tau_ff^-1, where Omega and tau_ff represent the angular rotation speed and the free-fall time of the core, respectively. (2) On the other hand, the disk is deformed to an elongated bar in the isothermal stage for a strongly magnetized or rapidly rotating cloud. The bar breaks into 2 - 4 fragments (bar fragmentation). Even if a disk is thin, the disk dominated by the magnetic force or thermal pressure is stable and forms a single compact body. In either ring or bar fragmentation mode, the fragments contract and a pair of outflows are ejected from the vicinities of the compact cores. The orbital angular momentum is larger than the spin angular momentum in the ring fragmentation. On the other hand, fragments often quickly merge in the bar fragmentation, since the orbital angular momentum is smaller than the spin angular momentum in this case. Comparison with observations is also shown.
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We simulate the early stages of the evolution of turbulent, virialized, high-mass protostellar cores, with primary attention to how cores fragment, and whether they form a small or large number of protostars. Our simulations use the Orion adaptive mesh refinement code to follow the collapse from ~0.1 pc scales to ~10 AU scales, for durations that cover the main fragmentation phase, using three-dimensional gravito-radiation hydrodynamics. We find that for a wide range of initial conditions radiation feedback from accreting protostars inhibits the formation of fragments, so that the vast majority of the collapsed mass accretes onto one or a few objects. Most of the fragmentation that does occur takes place in massive, self-shielding disks. These are driven to gravitational instability by rapid accretion, producing rapid mass and angular momentum transport that allows most of the gas to accrete onto the central star rather than forming fragments. In contrast, a control run using the same initial conditions but an isothermal equation of state produces much more fragmentation, both in and out of the disk. We conclude that massive cores with observed properties are not likely to fragment into many stars, so that, at least at high masses, the core mass function probably determines the stellar initial mass function. Our results also demonstrate that simulations of massive star forming regions that do not include radiative transfer, and instead rely on a barotropic equation of state or optically thin heating and cooling curves, are likely to produce misleading results.
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 numerical simulations showing that a substantial level of magnetic field diffusion at high densities has to occur in order to form rotationally supported disks. Furthermore, newly formed accretion disks are threaded by the magnetic field dragged from the parent core during the gravitational collapse. These disks are expected to rotate with a sub-Keplerian speed because they are partially supported by magnetic tension against the gravity of the central star. We discuss how sub-Keplerian rotation makes it difficult to eject disk winds and accelerates the process of planet migration. Moreover, magnetic fields modify the Toomre criterion for gravitational instability via two opposing effects: magnetic tension and pressure increase the disk local stability, but sub-Keplerian rotation makes the disk more unstable. In general, magnetized disks are more stable than their nonmagnetic counterparts; thus, they can be more massive and less prone to the formation of giant planets by gravitational instability.
The origin of supermassive black holes (with $gtrsim!10^9,M_{odot}$) in the early universe (redshift $z sim 7$) remains poorly understood. Gravitational collapse of a massive primordial gas cloud is a promising initial process, but theoretical studies have difficulty growing the black hole fast enough. We focus on the magnetic effects on star formation that occurs in an atomic-cooling gas cloud. Using a set of three-dimensional magnetohydrodynamic (MHD) simulations, we investigate the star formation process in the magnetized atomic-cooling gas cloud with different initial magnetic field strengths. Our simulations show that the primordial magnetic seed field can be quickly amplified during the early accretion phase after the first protostar formation. The strong magnetic field efficiently extracts angular momentum from accreting gas and increases the accretion rate, which results in the high fragmentation rate in the gravitationally unstable disk region. On the other hand, the coalescence rate of fragments is also enhanced by the angular momentum transfer due to the magnetic effects. Almost all the fragments coalesce to the primary star, so the mass growth rate of the massive star increases due to the magnetic effects. We conclude that the magnetic effects support the direct collapse scenario of supermassive star formation.
We use ZEUS-MP to perform high resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent fragmentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic waves driven by turbulent flows, even when the turbulent Jeans mass exceeds the mass in the simulation volume. Comparison of results between 256^3 and 512^3 zone simulations reveals convergence in the collapse rate. Analysis of self-gravitating cores formed in the simulation shows that: (1) All cores formed are magnetically supercritical by at least an order of magnitude. (2) A power law relation between central magnetic field strength and density B_c propto rho_c^{1/2} is observed despite the cores being strongly supercritical. (3) Specific angular momentum j propto R^{3/2} for cores with radius R. (4) Most cores are prolate and triaxial in shape, in agreement with the results of Gammie et al.
We formulate the problem of magnetic field dissipation during the accretion phase of low-mass star formation, and we carry out the first step of an iterative solution procedure by assuming that the gas is in free-fall along radial field lines. This so-called ``kinematic approximation ignores the back reaction of the Lorentz force on the accretion flow. In quasi steady-state, and assuming the resistivity coefficient to be spatially uniform, the problem is analytically soluble in terms of Legendres polynomials and confluent hypergeometric functions. The dissipation of the magnetic field occurs inside a region of radius inversely proportional to the mass of the central star (the ``Ohm radius), where the magnetic field becomes asymptotically straight and uniform. In our solution, the magnetic flux problem of star formation is avoided because the magnetic flux dragged in the accreting protostar is always zero. Our results imply that the effective resistivity of the infalling gas must be higher by several orders of magnitude than the microscopic electric resistivity, to avoid conflict with measurements of paleomagnetism in meteorites and with the observed luminosity of regions of low-mass star formation.
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