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 gravi ty. Thus, it could be said that gravity plays a fundamental role in hot-sta r winds. However, this paper will show that gravity only asserts an importa nt influence close to the star where the mass-loss rate is set; its influen ce becomes virtually negligible a surprisingly small distance away from the surface. Thus, although it is well known that the maximum mass-loss rate i s achieved when the acceleration near the surface is tightly scaled to grav ity, it is demonstrated here that this is the only fundamentally important way that gravity enters the physics of hot-star wind acceleration. If the m ass-loss rate were an external parameter instead, gravity could be complete ly neglected with only a small loss of accuracy in the details of the veloc ity curve. Since the presence of gravity seriously complicates the solution of the nonlinear force equation, its limited quantitative importance sugge sts alternate approximations that neglect gravity once the mass-loss rate i s obtained. Using this approach, quite simple analytic expressions can be d erived 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 i s 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 solu tion. Interestingly, this dynamical feedback implies that increases in the efficiency of the radiative force are also leveraged, and this "self-levera ging" produces a steep line-force gradient that dwarfs gravity over most of the wind.