An on-the-fly line-driven-wind iterative mass-loss estimator (LIME) for hot, massive stars of arbitrary chemical compositions

TL;DR

This work presents LIME, an online, real-time estimator for line-driven winds of hot, massive stars that accommodates arbitrary chemical compositions. It computes the line-force multiplier $M(t)$ on-the-fly by solving excitation and ionization balance with a large atomic dataset, fits it to a CAK-inspired form to obtain $\bar{Q}$, $Q_0$, and $\alpha$, and derives $\dot{M}$ using a CAK-like analytic expression including finite-disk and sound-speed corrections. An iterative procedure updates the wind-critical-point density until convergence, typically within about four iterations, yielding predictions for $\dot{M}$ and the line-force parameters at the critical point; the tool also provides an approximate terminal velocity and can explore abundance variations directly. Validation against XShoot Ullyses empirical rates shows good agreement with current observational data, and comparisons with existing recipes indicate that LIME performs as well or better while offering greater flexibility and reduced grid-related uncertainties. This enables rapid applications to chemically peculiar stars and supports integration into stellar evolution and feedback studies, representing a practical advancement for modeling hot-star winds.

Abstract

Mass-loss rates from hot, massive stars are important for a range of astrophysical applications. We present \href{https://lime.ster.kuleuven.be/}{LIME}, a fast, efficient, and easy-to-use real-time mass-loss calculator for line-driven winds from hot, massive stars with given stellar parameters and arbitrary chemical compositions. The tool is publicly available online. We compute the line force on-the-fly from excitation and ionization balance calculations using a large atomic data base containing more than four million spectral lines. We then derive mass-loss rates from line-driven wind theory, including effects of a finite stellar disk and gas sound speed. For a given set of stellar parameters and chemical composition, we obtain predictions for mass-loss rates and for the three line-force parameters at the wind critical point. A comparison of our predicted mass-loss rates with a large sample of recent, state-of-the-art, homogeneously derived empirical mass-loss rates obtained from the XshootU collaboration project demonstrates that the simple calculator presented here performs on average as well as, or even better than, other available mass-loss recipes based on fits to restricted model grids computed from more sophisticated but less flexible methods. In addition to its speed and simplicity, a strength of our mass-loss calculator is that it avoids uncertainties related to applying fit formulae to underlying model grids calculated for more restricted parameter ranges. In particular, individual chemical abundances can be easily modified, and their effects on predicted mass-loss rates can be readily explored. This enables direct applications also to stars that are significantly chemically modified at the surface.

Figures (7)

• Figure 1: Line-force multiplier, $M(t)$, as a function of the Sobolev optical-depth-like parameter, $t$. The blue diamonds and orange circles show the line-force multiplier calculated for the characteristic density, temperature, and metallicity listed in the labels. Black lines indicate the best fits with the corresponding line-force parameters. Relative metal abundances are scaled to the solar metallicity of asplund_2009.
• Figure 2: Quantities $\dot{M}$ (top left), $\Bar{Q}$ (top right), $\alpha$ (middle left), and $Q_0$ (middle right) as a function of iteration number until convergence (after 3 iterations). The bottom panels show relative differences in $\dot{M}$ (left) and critical point density $\rho$ (right) between successive iterations.
• Figure 3: Line-force multiplier, $M(t)$, as a function of $t$ for stars with $T_{\rm eff}$ and critical point density (log $\rho_{\rm crit} \ [gcm^{-3}]$) of 42000 [K] and -12.79 (left) and 18000 [K] and -14.52 (right). The line-force parameters $\bar{Q}$, $Q_0$, and $\alpha$ at the critical point are 1043, 620, 0.73 (left) and 866, 834, 0.87 (right). Blue circles represent $M(t)$ calculated from the entire line list, with the black line indicating the fit. Green and pink lines show $M(t)$ calculated using only Fe lines and CNO lines, respectively. The vertical dashed orange line marks $t_{\rm cri}$ (see text).
• Figure 4: Logarithm of the ratio between mass-loss rates derived using our method and rates obtained empirically from observational data as described in the text. The colors and markers correspond to the different samples marked on the labels. The dashed line illustrates the position where rates would be equal.
• Figure 5: Top panel: Same as Fig. \ref{['Fig:cmp']}, but also comparing the observations with theoretical rates computed by different methods, as indicated in the labels. For clarity, error margins for empirical rates are omitted. Bottom panel: Sample averages and one standard deviation for the four methods. The dashed black line indicates where rates are equal.