Measuring the shock-heating rate in the winds of O stars using X-ray line spectra

Abstract: We present a new method for using measured X-ray emission line fluxes from O stars to determine the shock-heating rate due to instabilities in their radiation-driven winds. The high densities of these winds means that their embedded shocks quickly cool by local radiative emission, while cooling by expansion should be negligible. Ignoring for simplicity any non-radiative mixing or conductive cooling, the method presented here exploits the idea that the cooling post-shock plasma systematically passes through the temperature characteristic of distinct emission lines in the X-ray spectrum. In this way, the observed flux distribution among these X-ray lines can be used to construct the cumulative probability distribution of shock strengths that a typical wind parcel encounters as it advects through the wind. We apply this new method (Gayley 2014) to Chandra grating spectra from five O stars with X-ray emission indicative of embedded wind shocks in effectively single massive stars. Correcting for wind absorption of the X-ray line emission is a crucial component of our analysis, and we use wind optical depth values derived from X-ray line-profile fitting (Cohen et al. 2014) in order to make that correction. The shock-heating rate results we derive for all the stars are quite similar: the average wind mass element passes through roughly one shock that heats it to at least $10^6$ K as it advects through the wind, and the cumulative distribution of shock strengths is a strongly decreasing function of temperature, consistent with a negative power-law of index $n \approx 3$, implying a marginal distribution of shock strengths that scales as $T^{-4}$, and with hints of an even steeper decline or cut-off above $10^7$ K.