Two-dimensional solitons with hidden and explicit vorticity in bimodal cubic-quintic media

We demonstrate that two-dimensional two-component bright solitons of an annular shape, carrying vorticities $(m,\pm m)$ in the components, may be stable in media with the cubic-quintic nonlinearity, including the \textit{hidden-vorticity} (HV) solitons of the type $(m,-m)$, whose net vorticity is zero. Stability regions for the vortices of both $(m,\pm m)$ types are identified for $m=1$, 2, and 3, by dint of the calculation of stability eigenvalues, and in direct simulations. A novel feature found in the study of the HV solitons is that their stability intervals never reach the (cutoff) point at which the bright vortex carries over into a dark one, hence dark HV solitons can never be stable, contrarily to the bright ones. In addition to the well-known symmetry-breaking (\textit{external}) instability, which splits the ring soliton into a set of fragments flying away in tangential directions, we report two new scenarios of the development of weak instabilities specific to the HV solitons. One features \textit{charge flipping}, with the two components exchanging the angular momentum and periodically reversing the sign of their spins. The composite soliton does not split in this case, therefore we identify such instability as an \textit{intrinsic} one. Eventually, the soliton splits, as weak radiation loss drives it across the border of the ordinary strong (external) instability. Another scenario proceeds through separation of the vortex cores in the two components, each individual core moving toward the outer edge of the annular soliton. After expulsion of the cores, there remains a zero-vorticity breather with persistent internal vibrations.