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Register a new userGravitational collapse of magnetized clouds. I. Ideal MHD accretion flow
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We study the self-similar collapse of an isothermal magnetized rotating cloud in the ideal magnetohydrodynamic (MHD) regime. In the limit of small distance from the accreting protostar we find an analytic solution that corresponds to free-fall onto a central mass point. The density distribution is not spherically symmetric but depends on the mass loading of magnetic field lines, which can be obtained by matching our inner solution to an outer collapse solution previously computed by Allen, Shu & Li. The concentration of magnetic field trapped by the central mass point under field-freezing, independent on the details of the starting state, creates a split monopole configuration where the magnetic field strength increases as the inverse square of the distance from the center. Under such conditions, the inflow eventually becomes subalfvenic and the outward transfer of angular momentum by magnetic braking very efficient, thus preventing the formation of a centrifugally supported disk. Instead, the azimuthal velocity of the infalling gas decreases to zero at the center, and the gas spirals into the star. Therefore, the dissipation of dynamically important levels of magnetic field is a fundamental requisite for the formation of protoplanetary disks around young stars.
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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.
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.
In this paper, we revisit the governing equations for linear magnetohydrodynamic (MHD) waves and instabilities existing within a magnetized, plane-parallel, self-gravitating slab. Our approach allows for fully non-uniformly magnetized slabs, which deviate from isothermal conditions, such that the well-known Alfven and slow continuous spectra enter the description. We generalize modern MHD textbook treatments, by showing how self-gravity enters the MHD wave equation, beyond the frequently adopted Cowling approximation. This clarifies how Jeans instability generalizes from hydro to magnetohydrodynamic conditions without assuming the usual Jeans swindle approach. Our main contribution lies in reformulating the completely general governing wave equations in a number of mathematically equivalent forms, ranging from a coupled Sturm-Liouville formulation, to a Hamiltonian formulation linked to coupled harmonic oscillators, up to a convenient matrix differential form. The latter allows us to derive analytically the eigenfunctions of a magnetized, self-gravitating thin slab. In addition, as an example we give the exact closed form dispersion relations for the hydrodynamical p- and Jeans-unstable modes, with the latter demonstrating how the Cowling approximation modifies due to a proper treatment of self-gravity. The various reformulations of the MHD wave equation open up new avenues for future MHD spectral studies of instabilities as relevant for cosmic filament formation, which can e.g. use modern formal solution strategies tailored to solve coupled Sturm-Liouville or harmonic oscillator problems.
We examine the dynamics of a self--gravitating magnetized electron gas at finite temperature near the collapsing singularity of a Bianchi-I spacetime. Considering a general and appropriate and physically motivated initial conditions, we transform Einstein--Maxwell field equations into a complete and self--consistent dynamical system amenable for numerical work. The resulting numerical solutions reveal the gas collapsing into both, isotropic (point-like) and anisotropic (cigar-like) singularities, depending on the initial intensity of the magnetic field. We provide a thorough study of the near collapse behavior and interplay of all relevant state and kinematic variables: temperature, expansion scalar, shear scalar, magnetic field, magnetization and energy density. A significant qualitative difference in the behavior of the gas emerges in the temperature range $hbox{T} sim10^{4}hbox{K}$ and $hbox{T}sim 10^{7}hbox{K}$.
We study the global structure of optically thin, advection dominated, magnetized accretion flow around black holes. We consider the magnetic field to be turbulent in nature and dominated by the toroidal component. With this, we obtain the complete set of accretion solutions for dissipative flows where bremsstrahlung process is regarded as the dominant cooling mechanism. We show that rotating magnetized accretion flow experiences virtual barrier around black hole due to centrifugal repulsion that can trigger the discontinuous transition of the flow variables in the form of shock waves. We examine the properties of the shock waves and find that the dynamics of the post-shock corona (PSC) is controlled by the flow parameters, namely viscosity, cooling rate and strength of the magnetic field, respectively. We separate the effective region of the parameter space for standing shock and observe that shock can form for wide range of flow parameters. We obtain the critical viscosity parameter that allows global accretion solutions including shocks. We estimate the energy dissipation at the PSC from where a part of the accreting matter can deflect as outflows and jets. We compare the maximum energy that could be extracted from the PSC and the observed radio luminosity values for several super-massive black hole sources and the observational implications of our present analysis are discussed.
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