Mass loss and the Eddington parameter: a new mass-loss recipe for hot and massive stars

Abstract

Mass loss through stellar winds plays a dominant role in the evolution of massive stars. In particular the mass-loss rates of very massive stars (VMSs, $>100M_{\odot }$) are highly uncertain. Such stars display Wolf-Rayet spectral morphologies (WNh) whilst on the main-sequence. Metal-poor VMSs are progenitors of gamma-ray bursts and pair instability supernovae. In this study we extended the widely used stellar wind theory by Castor, Abbott & Klein from the optically thin (O star) to the optically thick main-sequence (WNh) wind regime. In particular we modify the mass-loss rate formula in a way that we are able to explain the empirical mass-loss dependence on the Eddington parameter (${\Gamma }_{\mathrm{e}}$). The new mass-loss recipe is suitable for incorporation into current stellar evolution models for massive and very massive stars. It makes verifiable predictions, namely how the mass-loss rate scales with metallicity and at which Eddington parameter the transition from optically thin O star to optically thick WNh star winds occurs. In the case of the star cluster R136 in the Large Magellanic Cloud we find in the optically thin wind regime $\dot{M}\propto {\Gamma }_{\mathrm{e}}^3$ while in the optically thick wind regime $\dot{M}\propto 1/(1-{\Gamma }_{\mathrm{e}}{)}^{3.5}$. The transition from optically thin to optically thick winds occurs at ${\Gamma }_{\mathrm{e},\mathrm{trans}}\approx 0.47$. The transition mass-loss rate is $\log \dot{M}(M_{\odot }{\mathrm{yr}}^{-1})\approx -4.76\pm 0.18$, which is in line with the prediction by Vink & Gräfener assuming a volume filling factor of $f_{\mathrm{V}}=0.23_{-0.15}^{+0.40}$.

Accepted for publication in MNRAS, 9 pages, 5 figures

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