Gravitational Collapse of Magnetized Clouds. II. The Role of Ohmic Dissipation

We formulate the problem of magnetic field dissipation during the accretionphase of low-mass star formation, and we carry out the first step of aniterative solution procedure by assuming that the gas is in free-fall alongradial field lines. This so-called ``kinematic approximation'' ignores the backreaction of the Lorentz force on the accretion flow. In quasi steady-state, andassuming the resistivity coefficient to be spatially uniform, the problem isanalytically soluble in terms of Legendre's polynomials and confluenthypergeometric functions. The dissipation of the magnetic field occurs inside aregion of radius inversely proportional to the mass of the central star (the``Ohm radius''), where the magnetic field becomes asymptotically straight anduniform. In our solution, the magnetic flux problem of star formation isavoided because the magnetic flux dragged in the accreting protostar is alwayszero. Our results imply that the effective resistivity of the infalling gasmust be higher by several orders of magnitude than the microscopic electricresistivity, to avoid conflict with measurements of paleomagnetism inmeteorites and with the observed luminosity of regions of low-mass starformation.Comment: 20 pages, 4 figures, The Astrophysical Journal, in pres