Testing the reliability of X-rays as a tool for constraining mass-loss rates of hot stars

Abstract

We fit a new line shape model to Chandra X-ray spectra of the O supergiant ζ Puppis to investigate the spatial distribution of embedded shocks in the wind. Our goal is to track the hot gas by replacing the common assumption that it is proportional to the cool gas emission measure. Instead of assuming a turn-on radius for the hot gas (as appropriate for the line-deshadowing instability internal to the wind), we parametrize the hot gas in terms of a mean-free path for accelerated low-density gas to encounter slower high-density material. We find that this alternative model is equally successful as previous approaches at fitting X-ray spectral lines in the 5 – 17 Å wavelength range. The wind properties described by our model are consistent with the literature, while providing new insights into the spatial heating distribution of the shocked gas. We find that the characteristic radii where the hottest gas appears is inversely proportional to line formation temperature, suggesting that stronger shocks appear generally closer to the surface. This picture is more consistent with pockets of low-density, rapid acceleration at the lower boundary than with an internally generated wind instability. We also find that the overall wind mass-loss rates, which we infer from the profile shapes using our heating model, are broadly consistent with prior results, showing that X-ray spectra provide a means of inferring wind mass-loss rates that is robust with respect to changes in the specific heating picture used.

Deriving X-Ray Line Profiles for Massive-star Winds from Momentum-conserving Dynamical Working Surface Solutions

“…A profile can be generated by integrating the X-ray generation rate L ws (r) over radius and tracking how the emitted energy is concentrated into each dξ frequency bin. The methodology used in the defining of the VBC profile model in Gunderson et al (2022) will be employed here. In this approach, the WS is assumed to be emitting isotropically in all directions cos m q = , and the emitting plasmas are assumed to be distributed spherically symmetrically around the wind.…”

“…X-ray-generating dynamics in hypersonic massive-star winds have been studied using simple heuristic models, connecting the salient features of the dynamics to their consequences on observable line-profile shapes and flux ratios (Ignace 2001;Owocki & Cohen 2001;Gunderson et al 2022). The features of these past heuristic models connect with specific questions that those approaches are effective at answering.…”

“…The features of these past heuristic models connect with specific questions that those approaches are effective at answering. Sometimes these features included a local filling factor of hot gas (Owocki & Cohen 2001), while others focused on the spatial probability distribution of where the fast gas gets shocked (Gunderson et al 2022). What has not been explored yet is whether a model can be derived such that the line shapes can be analyzed in a way that is dynamically consistent with the momentumconserving elements of the shocked gas sandwiched between forward and reverse shocks.…”

“…Part of the complexity is the acceleration of the gas due to line driving (Puls et al 1996;Owocki 2004;Puls et al 2008) that introduces instabilities such as the line-deshadowing instability (LDI; Owocki & Rybicki 1984). In addition, parameterizing the wind shocks requires deciding if the shocks originate very near the surface due to some variable boundary condition (VBC; Gunderson et al 2022Gunderson et al , 2024, or if they require a stand-off distance, as might be seen from the LDI (Owocki & Cohen 2001).…”

“…We will concern ourselves with nonconstant velocities of the form v(r, τ) = v 0 (τ)f (r), where v 0 (τ) is variable in some chosen manner and f (r) is a unitless function describing the acceleration. By considering a separable velocity in space and time, we aim to capture the dynamics of the VBC theory from Gunderson et al (2022). Specifically, wind shocks are seeded by variations at the wind base, and anything that happens spatially with radius traces back to the time-dependent variation that is seeded at the base.…”