Inferring hot-star-wind acceleration from Line Profile Variability

The migration of profile sub-peaks identified in time-monitored optical emission lines of Wolf-Rayet (WR) star spectra provides a direct diagnostic of the dynamics of their stellar winds via a measured $\Delta v_{{\rm LOS}}/\Delta t$, a line-of-sight velocity change per unit time. Inferring the associated wind acceleration scale from such an apparent acceleration then relies on the adopted intrinsic velocity of the wind material at the origin of this variable pattern. Such a characterization of the Line Emission Region (LER) is in principle subject to inaccuracies arising from line optical depth effects and turbulence broadening. In this paper, we develop tools to quantify such effects and then apply these to reanalyze the LER properties of time-monitored WR stars. We find that most program lines can be fitted well with a pure optically thin formation mechanism, that the observed line-broadening is dominated by the finite velocity extent of the LER, and that the level of turbulence inferred through Line Profile Variability (${lpv}$) has only a minor broadening effect in the overall profile. Our new estimates of LER velocity centroids are systematically shifted outwards closer to terminal velocity compared to previous determinations, now suggesting WR-wind acceleration length scales $\beta R_{\ast}$ of the order of $10{-}20~R_{\odot}$, a factor of a few smaller than previously inferred. Based on radiation-hydrodynamics simulations of the line-driven-instability mechanism, we compute synthetic ${lpv}$ for Cii