Torus-Stable Zone Above Starspots

The torus instability (TI) of current-carrying magnetic flux tubes is thought to drive many solar coronal mass ejections (CMEs). The background magnetic field provides the stabilizing force: if it decreases with height at a rate slower than a critical value, the TI may be suppressed. Here we estimate the vertical extent of a "torus-stable zone" above starspots using a scaled model for the Sun. For a potential-field model comprising a bipole (as a pair of starspots) in alignment with a global dipole, we show that the upper bound of this zone h_c increases with the bipole size a, the dipole field with harmonic coefficient g₁₀, and the source surface radius R_s where the magnetic field becomes radial. The value of h_c, ranging from about 0.5a to a significant fraction of the stellar radius, depends on the interplay between the spot and dipole magnetic fields; its upper limit is set by R_s. Suppression of the TI may contribute to the lack of CME detection from active cool stars, as larger starspots, stronger dipole, and more closed magnetic topology significantly expand the torus-stable zone.