The surprisingly weak effect of gravity in retarding hot-star wind acceleration

The overall scale for both the radiative force and the terminal speed in a line-driven wind in the Castor, Abbot, & Klein (CAK) theory is set by gravity. Thus, it could be said that gravity plays a fundamental role in hot-star winds. However, this paper will show that gravity only asserts an important influence close to the star where the mass-loss rate is set; its influence becomes virtually negligible a surprisingly small distance away from the surface. Thus, although it is well known that the maximum mass-loss rate is achieved when the acceleration near the surface is tightly scaled to gravity, it is demonstrated here that this is the only fundamentally important way that gravity enters the physics of hot-star wind acceleration. If the mass-loss rate were an external parameter instead, gravity could be completely neglected with only a small loss of accuracy in the details of the velocity curve. Since the presence of gravity seriously complicates the solution of the nonlinear force equation, its limited quantitative importance suggests alternate approximations that neglect gravity once the mass-loss rate is obtained. Using this approach, quite simple analytic expressions can be derived that approximate the velocity driven by single-line scattering of a radiation held emitted by a finite stellar disk. In the process, the importance of an effect termed radiative leveraging, due to the dynamical feedback inherent in line driving, is explored. This is an effect whereby any external forces, such as gravity, are effectively dressed by the radiative force, such that any variations in the former are strongly multiplied by the latter in the self-consistent, time-steady solution. Interestingly, this dynamical feedback implies that increases in the efficiency of the radiative force are also leveraged, and this self-leveraging produces a steep line-force gradient that dwarfs gravity over most of the wind.