From supersonic winds to accretion: Comments on the stability of stellar winds and related flows

For nearly vanishing values of the interstellar pressure a supersonic flow connecting via a shock to the instellar medium is the only stationary state describing the extension of a hot corona into space. We show here that in terms of the relative pressure jump between the coronal base and distant medium the stationary flow solutions follow an hysteresis-type cycle with two catastrophy points: as the pressure of the interstellar medium increases, the termination shock moves closer toward the stellar surface, but when the shock position reaches the sonic point the wind collapses into supersonic accretion with a shock below the critical point. If the pressure of the interstellar medium decreases again, or the pressure at the coronal base increases, the flow can evolve continuously into breeze (everywhere subsonic) accretion, but the flow evolves back into a state characterized by a supersonic shocked wind, once the pressure difference corresponding to a static stratification is exceeded.