[Paper Review] The Eddington factor as the key to understand the winds of the most massive stars. Evidence for a Gamma-dependence of Wolf-Rayet type mass loss

G. Gräfener, J. S. Vink+2 more|arXiv (Cornell University)|Jun 27, 2011

Stellar, planetary, and galactic studies1 references88 citations

TL;DR

This paper proposes that the Eddington factor Γₑ is the primary driver of Wolf-Rayet-type mass loss in the most massive stars, demonstrating a strong Γₑ-dependence in observed mass-loss rates. Using stellar structure models and mass-luminosity relations, the authors show that proximity to the Eddington limit—quantified by Γₑ—explains the onset of enhanced mass loss in young, hydrogen-rich WNh stars, with implications for stellar evolution, black hole formation, and gamma-ray burst progenitors.

ABSTRACT

The most massive stars are thought to be hydrogen-rich Wolf-Rayet stars of late spectral subtype (WNh stars). In previous theoretical studies the enhanced mass loss of these stars has been attributed to their proximity to the Eddington limit. Here we investigate observed trends in the mass-loss properties of such young, very massive stars. We derive theoretical mass-luminosity relations for very massive stars, based on a large grid of stellar structure models. Using these relations, we estimate Eddington factors for a sample of stars, under different assumptions of their evolutionary status. We evaluate the resulting mass-loss relations, and compare them with theoretical predictions. We find observational evidence that the mass loss in the WR regime is dominated by the Eddington parameter Gamma_e, which has important consequences for the way we understand Wolf-Rayet stars and their mass loss. In addition, we derive wind masses that support the picture that the WNh stars in young stellar clusters are very massive, hydrogen-burning stars. Our findings suggest that the proximity to the Eddington limit is the physical reason for the onset of Wolf-Rayet type mass loss. This means that, e.g. in stellar evolution models, the Wolf-Rayet stage should be identified by large Eddington parameters, instead of a helium-enriched surface composition. The latter is most likely only a consequence of strong mass loss, in combination with internal mixing. For very massive stars, the enhanced Gamma-dependent mass loss is responsible for the formation of late WNh subtypes with high hydrogen surface abundances, partly close to solar. Because mass loss dominates the evolution of very massive stars, we expect a strong impact of this effect on their end products, in particular on the potential formation of black holes, and Gamma-Ray Bursts, as well as the observed upper mass limit of stars.

Motivation & Objective

• To investigate whether Wolf-Rayet-type mass loss in the most massive stars is primarily governed by the Eddington factor Γₑ rather than surface composition.
• To determine the evolutionary status of young, luminous WNh stars in the Arches cluster using mass-luminosity relations derived from stellar structure models.
• To test the theoretical prediction that mass loss in very massive stars scales with Γₑ, particularly near the Eddington limit.
• To re-evaluate the definition of the Wolf-Rayet phase in stellar evolution models, suggesting it should be defined by high Γₑ rather than helium-enriched surface abundances.
• To assess the impact of Γₑ-dependent mass loss on the final fate of massive stars, including black hole formation and the upper stellar mass function.

Proposed method

• Derivation of theoretical mass–luminosity relations for chemically homogeneous, hydrogen-burning stars using a large grid of stellar structure models.
• Estimation of the Eddington factor Γₑ for Arches cluster stars using observed luminosities and surface abundances under different evolutionary assumptions.
• Application of a polytropic equation of state based on Eddington’s original model, assuming constant β (radiation pressure fraction), leading to the scaling relation G₄ ≡ Γₑ/(1−Γₑ)⁴ ∝ M².
• Development of empirical fitting relations for G₄ as a function of mass M and hydrogen mass fraction X_H, with coefficients derived from model grids.
• Use of the inverse relation (Eq. 24) to compute Γₑ from G₄, enabling conversion of observed luminosities into Eddington parameters.
• Derivation of mass estimates M_hom(G₄, X_H) and M_Heb(G₄) for hydrogen-burning and helium-burning stars using fitted coefficients from Table 4.

Experimental results

Research questions

• RQ1 Is the observed mass-loss rate in young, massive WNh stars correlated with the Eddington factor Γₑ rather than surface composition?
• RQ2 To what extent does the Eddington factor Γₑ explain the onset of Wolf-Rayet-type mass loss in very massive stars?
• RQ3 Can mass estimates for Arches cluster stars be reliably derived from luminosity and surface abundance data using theoretical mass–luminosity relations?
• RQ4 What is the quantitative scaling of mass loss with Γₑ for stars near the Eddington limit, and how does it compare to theoretical predictions?
• RQ5 How does Γₑ-dependent mass loss influence the evolutionary path and final fate of the most massive stars, including black hole formation and GRB progenitors?

Key findings

• Observational evidence supports a strong dependence of mass loss on the Eddington factor Γₑ, indicating that proximity to the Eddington limit is the physical driver of Wolf-Rayet-type mass loss.
• The Eddington factor Γₑ is found to be a more fundamental parameter than surface composition for identifying the Wolf-Rayet phase, with helium enrichment being a consequence of mass loss rather than its cause.
• Wind mass estimates for WNh stars in the Arches cluster support the interpretation that these are very massive, hydrogen-burning stars with masses up to 4000 M☉.
• The derived fitting relations for G₄ ≡ Γₑ/(1−Γₑ)⁴ achieve a maximum fitting error of only 0.03 in log(G₄), enabling precise Γₑ estimation from luminosity and composition.
• The Γₑ-dependent mass-loss mechanism explains the existence of late WNh subtypes with high hydrogen surface abundances, including values near solar, due to enhanced mass loss at high Γₑ.
• The results imply that Γₑ-dependent mass loss plays a critical role in shaping the upper mass function of stars and determining the potential formation of black holes and long-duration gamma-ray bursts.