Runaway of line-driven winds toward critical and overloaded solutions

Line-driven winds from hot stars and accretion disks are thought to follow a unique, critical solution that corresponds to a maximum mass-loss rate and a particular velocity law. We show that in the presence of negative velocity gradients, radiative-acoustic (Abbott) waves can drive shallow wind solutions toward larger velocities and mass-loss rates. Perturbations that are introduced downstream from the critical point of the wind lead to a convergence toward the critical solution. By contrast, low-lying perturbations cause evolution toward a mass-overloaded solution, developing a broad deceleration region in the wind. Such a wind differs fundamentally from the critical solution. For sufficiently deep-seated perturbations, overloaded solutions become time-dependent and develop shocks and shells.