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Self-Similar Solutions for ADAF with Toroidal Magnetic Fields

We examined the effect of toroidal magnetic fields on a viscous gaseous disk around a central object under an advection dominated stage. We found self-similar solutions for radial infall velocity, rotation velocity, sound speed, with additional parameter $β$ [$=c_{\rm A}^2/(2c_{\rm s}^2)$], where $c_{\rm A}$ is the Alfvén speed and $c_{\rm s}$ is the isothermal sound speed. Compared with the non-magnetic case, in general the disk becomes thick due to the magnetic pressure, and the radial infall velocity and rotation velocity become fast. In a particular case, where the magnetic field is dominant, on the other hand, the disk becomes to be magnetically supported, and the nature of the disk is significantly different from that of the weakly magnetized case.