Variability in X-ray line ratios in helium-like ions of massive stars: the wind-driven case

Abstract

Context. High spectral resolution and long exposure times are providing unprecedented levels of data quality of massive stars at X-ray wavelengths. Aims. A key diagnostic of the X-ray emitting plasma are the fir lines for He-like triplets. In particular, owing to radiative pumping effects, the forbidden-to-intercombination line luminosity ratio, R = f∕i, can be used to determine the proximity of the hot plasma to the UV-bright photospheres of massive stars. Moreover, the era of large observing programs additionally allows for investigation of line variability. Methods. This contribution is the second to explore how variability in the line ratio can provide new diagnostic information about distributed X-rays in a massive star wind. We focus on wind integration for total line luminosities, taking account of radiative pumping and stellar occultation. While the case of a variable stellar radiation field was explored in the first paper, the effects of wind variability are emphasized in this work. Results. We formulate an expression for the ratio of line luminosities f∕i that closely resembles the classic expression for the on-the-spot result. While there are many ways to drive variability in the line ratio, we use variable mass loss as an illustrative example for wind integration, particularly since this produces no variability for the on-the-spot case. The f∕i ratio can be significantly modulated owing to evolving wind properties. The extent of the variation depends on how the timescale for the wind flow compares to the timescale over which the line emissivities change. Conclusions. While a variety of factors can ellicit variable line ratios, a time-varying mass-loss rate serves to demonstrate the range of amplitude and phased-dependent behavior in f∕i line ratios. Importantly, we evaluate how variable mass loss might bias measures of f∕i. For observational exposures that are less than the timescale of variable mass loss, biased measures (relative to the time-averaged wind) can result; if exposures are long, the f∕i ratio is reflective of the time-averaged spherical wind.