Hydrodynamical mass-loss rates for Very Massive Stars. I. Investigating the wind kink

TL;DR

This work tests the existence and properties of the predicted wind kink in Very Massive Stars (VMSs) using hydrodynamically consistent PoWR_hd atmosphere models. By grid computing winds at fixed luminosity ($ L_/L__sun=10^6$), solar metallicity, and varying $M_$ and $T_$, the authors show that the kink occurs when the wind becomes optically thick as the Eddington parameter $ $ approaches a critical value, with the optical depth crossing unity at the sonic point. The models reproduce the model-independent Arches transition mass-loss rate, locate the kink near $M_ \approx 60 M_sun$ corresponding to $_e \approx 0.43$, and reveal Fe-driven bistability jumps near $T_ \approx 25$ and $15$ kK that sculpt the mass-loss scaling. They provide fitting prescriptions to capture the kink and bistability features, enabling improved VMS evolution modeling and implications for chemical yields and the black hole mass spectrum.

Abstract

Radiation-driven winds are ubiquitous in massive stars, but in Very Massive Stars (VMSs), mass loss dominates their evolution, chemical yields, and ultimate fate. Theoretical predictions have often relied on extrapolations of O star prescriptions, likely underestimating true VMS mass-loss rates. In the first of a series of papers on VMS wind properties, we investigate a feature predicted by Monte Carlo (MC) simulations: a mass-loss `kink' or upturn where the single-scattering limit is breached and winds transition from optically thin to optically thick. We calculate hydrodynamically consistent non-LTE atmosphere models using the PoWR$^\mathrm{HD}$ code, with a grid spanning $40-135M_\odot$ and 12-50 kK at fixed $\log(L_\star/L_\odot) = 6.0$ and solar-like metallicity with $Z=0.02$. Our models confirm the existence of the kink, where the wind optical depth crosses unity and spectral morphology shifts from O star to WNh types. The predicted location of the kink coincides with the transition stars in the Galactic Arches cluster and reproduces the model-independent transition mass-loss rate of $\log(\dot{M}_\mathrm{trans}) \approx -5.16$ from Vink & Gräfener (2012). For the first time, we locate the kink at $Γ_\mathrm{e} \approx 0.43$ ($M_\star \approx 60M_\odot$) without relying on uncertain stellar masses. Above the kink, mass-loss rates scale much more steeply with decreasing mass (slope ~ 10), in qualitative agreement with MC predictions. We additionally identify two bistability jumps in the mass loss driven by Fe ionisation shifts: the first from FeIV to FeIII near 25 kK and the second from FeIII to FeII near 15 kK. Our models thus provide the first comprehensive confirmation of the VMS mass-loss kink while establishing a mass-loss relation with complex mass and temperature dependencies with consequences for stellar evolution, chemical yields, and the black hole mass spectrum.

Figures (12)

• Figure 1: Total radiative acceleration and its contributions from continuum processes and line transitions. Decomposition of the total radiative acceleration (black solid) into continuum (green dashed) and line (red dashed) components, along with individual contributions from constituent elements in the atmosphere (coloured lines with symbols, see legend). Each of these element contributions consists of the sum of their line and continuum accelerations. All accelerations are normalised to gravity. The grey dotted and dashed vertical lines mark the sonic and critical points, $R_\mathrm{sonic}$ and $R_\mathrm{crit}$, respectively. The model stellar parameters are $\log(L_\star/L_\odot) = 6.0$, $M_\star = 105\,M_\odot$, $T_\star = 35\,\mathrm{kK}$, $X = 0.7$, and $Z = 0.02$.
• Figure 2: Contributions from electron scattering, free-free and bound-free continuum transitions, and line transitions of individual elements at the critical point, shown as a function of mass. The contributions are normalised to gravity and expressed as Eddington parameters. Top: absolute contributions from different opacity sources. Bottom: relative line contributions from different elements. The model sequence corresponds to a temperature of $T_\star = 35\,\mathrm{kK}$.
• Figure 3: Testing the $\texttt{PoWR}^\textsc{hd}$ model predictions against the transition mass-loss rate in the Arches cluster. Left: Predicted mass-loss rates versus stellar mass from $\texttt{PoWR}^\textsc{hd}$ models for the $T_\star = 35\,\mathrm{kK}$ sequence (black solid line) and from Vink2000 (blue dotted), compared to the transition mass-loss rate of $\log(\dot{M}) \approx -5.16$ in the Arches (red horizontal line) from Vink2012. The $\texttt{PoWR}^\textsc{hd}$ models are computed with fixed $\log(L_\star/L_\odot) = 6.0$, $X = 0.7$, and $Z = 0.02$, roughly matching the observed properties of the Arches transition objects Martins2008. The $T_\star = 35\,\mathrm{kK}$ sequence shown has surface temperatures close to the observed $T_\mathrm{eff}(\tau_\mathrm{R} = 2/3) \approx 33.4\,\mathrm{kK}$ of the transition objects. The stellar masses of the transition objects span $\sim 55-75\,M_\odot$ corresponding to their averaged luminosity and temperature. Middle: Predicted wind efficiency parameter versus mass compared to the transition value $\eta \approx 0.6$ (red dashed line) from Vink2012. Right: Predicted wind optical depth versus mass compared to the transition value $\tau_{F}(r_\mathrm{sonic}) \approx 1$ (red dashed line) from Vink2012.
• Figure 4: Synthetic spectra showing relevant wind lines in the optical for the $T_\star=35\,\mathrm{kK}$ model sequence presented in Fig. \ref{['fig: transition_mdot_Arches']}. The spectra are colour-coded based on the stellar mass.
• Figure 5: Synthetic spectra showing relevant wind lines in the UV for the $T_\star=35\,\mathrm{kK}$ model sequence presented in Fig. \ref{['fig: transition_mdot_Arches']}. The spectra are colour-coded based on the stellar mass.