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