ISOSCELES project: A grid-based quantitative spectroscopic analysis of massive stars

TL;DR

ISOSCELES develops a grid-based framework that replaces the conventional $β$-law wind velocity with self-consistent $m$-CAK hydrodynamic solutions (fast and $δ$-slow) to enable quantitative spectroscopy of massive stars. By coupling Hydwind wind structures with Fastwind NLTE atmospheres, the grid spans $T_{ m eff}$, $\,\log g$, wind parameters, and line-force coefficients ($α$, $k$, $δ$) for OBA-type stars at solar metallicity, and employs a semi-automatic $\chi^2$-fitting procedure to derive stellar and wind properties from optical/IR lines. Applications to six stars show that the $δ$-slow wind solution can improve fits for cooler B-type supergiants, while hot O-type stars are often best described by the fast solution, illustrating physical differences from the $β$-law and potential resolutions to long-standing wind-diagnostics degeneracies. The ISOSCELES database provides a scalable, physics-based alternative to traditional wind modelling, with planned extensions to include UV lines and metallicity effects, enabling more robust wind parameter determinations for large stellar samples and multi-wavelength analyses.

Abstract

Massive stars play a fundamental role in galactic evolution through their strong stellar winds, chemical enrichment, and feedback mechanisms. Accurate modelling of their atmospheres and winds is critical for understanding their physical properties and evolutionary pathways. Traditional spectroscopic analyses often rely on the $β$-law approximation for wind-velocity profiles, which may not capture the complexity of observed phenomena. This study aims to introduce and validate the grId of Stellar atmOSphere and hydrodynamiC modELs for massivE Stars (ISOSCELES), a grid-based framework for the quantitative spectroscopic analysis of massive stars. The project leverages hydrodynamic wind solutions derived from the m-CAK theory, including both fast and $δ$-slow solutions, to improve the accuracy of derived stellar and wind parameters. We constructed a comprehensive grid of models based on hydrodynamic wind solutions from the Hydwind code and synthetic spectral line profiles generated by the Fastwind code. The grid spans a broad parameter space covering OBA-type stars with solar metallicity. A semi-automatic fitting procedure was developed to analyse key spectral lines and derive the stellar and wind parameters. Applying ISOSCELES to six stars demonstrates its ability to reproduce observed spectral profiles with high fidelity. The $δ$-slow solution proved effective for two early-type B supergiants. The grid also highlights the difference of using the $β$-law in modelling stellar winds compared with the m-CAK wind solutions. The ISOSCELES database represents a step forward in quantitatively analysing massive stars, offering an alternative to the $β$-law approximation. Future work will address the inclusion of UV lines and metallicity effects to further refine its applicability across diverse stellar populations.

Figures (15)

• Figure 1: Location of ISOSCELES models in $T_{\rm{eff}}$--$\log\,\mathrm{g}$ plane (red dots). Grey solid lines represent the evolutionary tracks from $2 M_{\sun}$ to $60 M_{\sun}$ without rotation ekstrom2012. Solid black lines correspond to both zero-age main sequence (ZAMS) and terminal-age main sequence (TAMS). Red (empty) circles indicate non-converged models in ISOSCELES.
• Figure 2: Histogram showing $r_{\rm{crit}}$ values from converged solutions. Blue bars represent fast solutions, and red bars correspond to $\delta$-slow solutions. Both axes are on a logarithmic scale.
• Figure 3: H$\alpha$ spectral-line fits for O-type star HD 14947. The black line represents the observed spectrum, while the best fit from the ISOSCELES database with a fast solution and $\delta$-slow solution are shown in blue and red, respectively. The fast regime provides a better fit to this line profile.
• Figure 4: Best spectral-line fits for HD 14947. The black line depicts the observed spectrum. The best fit with a fast solution is shown in blue, while the best fit with a $\delta$-slow solution is in red. Clearly, the fast solution better describes the wind of this early-type star.
• Figure 5: Velocity profiles as function of inverse radial coordinate $u$ for the best-fit solutions of HD 14947. The velocity profile for the fast solution is shown in blue, while the $\delta$-slow solution is depicted in red. Additionally, the green line represents the $\beta$-law velocity field, based on the parameters from Bouret2012.