Screw Instability of the Magnetic Field Connecting a Rotating Black Hole with Its Surrounding Disk

We discuss the screw instability of the magnetic field connecting a rotating black hole (BH) with its surrounding disk based on the model of the coexistence of the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process (CEBZMC). We derive criteria for the screw instability with the state of CEBZMC based on the calculations of the poloidal and toroidal components of the magnetic field on the disk. By these criteria the screw instability will occur if the BH spin and the power-law index for the variation of the magnetic field on the disk are greater than some critical values. It turns out that the instability occurs outside some critical radii on the disk. We argue that the state of CEBZMC always accompanies the screw instability. In addition, we show that the screw instability contributes only a small fraction of magnetic extraction of energy from a rotating BH.