212 research outputs found
Gravitational collapse of magnetized clouds II. The role of Ohmic dissipation
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 Legendre's 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.Comment: 20 pages, 4 figures, The Astrophysical Journal, in pres
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