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 ∆vLOS/∆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 βR∗ of the order of 10 − 20R⊙, 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 Ciii5696Å for WR111. The results match well the measured observed migration of 20-30 ms, equivalent to βR∗ ∼ 20R⊙. However, our model stellar radius of 19R⊙, typical of an O-type supergiant, is a factor 2–10 larger than generally expected for WR core radii. Such small radii leave inferred acceleration scales to be more extended than expected from dynamical models of line driving, which typically match a “beta” velocity law v(r) = v∞(1−R∗/r) β , with β ≈ 1− 2; but the severity of the discrepancy is substantially reduced compared to previous analyses. We conclude with a discussion of how using lines formed deeper in the wind would provide a stronger constraint on the key wind dynamics in the peak acceleration region, while also potentially providing a diagnostic on the radial variation of wind clumping, an issue that remains crucial for reliable determination of O-star mass loss rates.