Analysis of Toroidal Magnetic Fields in Accretion Disks Using the Cross-Helicity Effect and Estimate of the Jet Velocity

The magnetic fields in an accretion disk are examined using a magnetohydrodynamic (MHD) turbulent dynamo model consisting of transport equations for the mean fields, turbulent energy, dissipation rate, and cross helicity. The velocity of accreting gases is assumed to obey the Keplerian and rigid rotations in the outer and inner regions of a disk, respectively, except for the central part. Under the condition of axisymmetry around the rotation axis and uniformity in the direction perpendicular to the disk, the turbulent model is examined both numerically and analytically. As a result, it is pointed out that the cross-helicity effect generates a toroidal magnetic field, resulting in the occurrence of a current in a direction perpendicular to the disk in the central part. This toroidal magnetic field enables gas to escape from a central high-mass body as bipolar jets, because the magnetic energy may become comparable to the gravitational one. The velocity of the jets in a protoplanetary system was estimated by a numerical simulation of the preset model.