A Porosity-Length Formalism for Photon-Tiring-limited Mass Loss from Stars above the Eddington Limit

By S. Owocki, K. Gayley, N. Shaviv. 2004

184 citations recorded by the source corpus.

We examine radiatively driven mass loss from stars near and above the Eddington limit. Building on the standard CAK theory of driving by scattering in an ensemble of lines with a power-law distribution of opacity, we first show that the formal divergence of such line-driven mass loss as a star approaches the Eddington limit is actually limited by the "photon tiring" associated with the work needed to lift material out of the star's gravitational potential. We also examine such tiring in simple continuum-driven models in which a specified outward increase in opacity causes a net outward acceleration above the radius where the generalized Eddington parameter exceeds unity. When the density at this radius implies a mass loss too close to the tiring limit, the overall result is flow stagnation at a finite radius. Since escape of a net steady wind is precluded, such circumstances are expected to lead to extensive variability and spatial structure. After briefly reviewing convective and other instabilities that also can be expected to lead to extensive structure in the envelope and atmosphere of a star near or above the Eddington limit, we investigate how the porosity of such a structured medium can reduce the effective coupling between the matter and radiation. Introducing a new "porosity-length" formalism, we derive a simple scaling for the reduced effective opacity and use this to derive an associated scaling for the porosity-moderated, continuum-driven mass-loss rate from stars that formally exceed the Eddington limit. For a simple super-Eddington model with a single porosity length that is assumed to be on the order of the gravitational scale height, the overall mass loss is similar to that derived in previous porosity models, given roughly by L*/a*c (where L* is the stellar luminosity and c and a* are the speed of light and the atmospheric sound speed). This is much higher than is typical of line-driven winds but is still only a few percent of the tiring limit. To obtain still stronger mass loss that approaches observationally inferred values near this limit, we draw on an analogy with the power-law distribution of line-opacity in the standard CAK model of line-driven winds and thereby introduce a "power-law-porosity" model in which the associated structure has a broad range of scales. We show that for power indices αp < 1, the mass-loss rate can be enhanced over the single-scale model by a factor that increases with the Eddington parameter as Γ. For lower αp (≈0.5-0.6) and/or moderately large Γ (>3-4), such models lead to mass-loss rates that approach the photon-tiring limit. Together with the ability to drive quite fast outflow speeds (of order the surface escape speed), the derived, near-tiring-limited mass loss offers a potential dynamical basis to explain the observationally inferred large mass loss and flow speeds of giant outbursts in η Carinae and other luminous blue variable stars.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/f9968b9b43cfadd9cd8bafe453d92723c8afaf38

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Citations in the corpus

Mass Loss: Its Effect on the Evolution and Fate of High-Mass Stars (2014, background): “These rates are too high to be driven by traditional stellar winds because the material is opaque (Owocki et al. 2004, Smith & Owocki 2006).”
The Structure of the Homunculus. I. Shape and Latitude Dependence from H2 and [Fe II] Velocity Maps of η Carinae (2006, background): “However, it remains to be seen if even a super-Eddington continuum-driven wind can fuel the required mass loss (Owocki et al. 2004).”
PREPARING FOR AN EXPLOSION: HYDRODYNAMIC INSTABILITIES AND TURBULENCE IN PRESUPERNOVAE (2013, background): “…LBVs have been cast as super-Eddington winds driven by an increase in the star’s bolometric luminosity (Humphreys & Davidson 1994; Shaviv 2000; Owocki et al. 2004; Smith & Owocki 2006), but there is growing evidence that some of them are explosive hydrodynamic ejections (see Smith 2008,…”
The Discordance of Mass-Loss Estimates for Galactic O-Type Stars (2005, background): “Owocki et al. (2004) provide a useful formalism to describe porosity in this context and discuss how it can affect the predicted mass-loss rates.”
On the Role of Continuum-driven Eruptions in the Evolution of Very Massive Stars and Population III Stars (2006, background): “If mass loss during these eruptions occurs via a wind, it must be a super-Eddington wind driven by continuum radiation pressure (i.e., Thomson scattering opacity and not lines; Owocki et al. 2004; Belyanin 1999; Quinn & Paczynski 1985).”
SPECTRAL EVOLUTION OF THE EXTRAORDINARY TYPE IIn SUPERNOVA 2006gy (2009, background): “…this phenomenon is likely to benefit from continued study of the physics of giant LBV eruptions and theoretical investigations of superEddington winds (e.g., Owocki et al. 2004; van Marle et al. 2009a), even though it is not yet clear if the two phenomena have the same underlying trigger.”
Luminous blue variables are antisocial: their isolation implies that they are kicked mass gainers in binary evolution (2014, background): “They are still stars with extreme mass loss and instability that have eruptive super-Eddington winds or explosive mass loss (see, e.g., Owocki et al. 2004; Smith et al. 2011a).”
Supermassive stars as a source of abundance anomalies of proton-capture elements in globular clusters (2013, background): “Closer to the atmosphere, where L approaches LEdd, various dynamical instabilities create spatial inhomogeneities (“a porous atmosphere”, Owocki et al. 2004).”
Ancient eruptions of η Carinae: a tale written in proper motions (2016, background): “Many theories treat it as part of single-star evolution, invoking super-Eddingto radiation-driven winds (Davidson 1971; Maeder 1983; de Jager 1984; Lamers & Fitzpatrick 1988; Stothers & Chin 1993; Glatzel & Kiriakidis 1993; Glatzel 1994; Humphreys & Davidson 1994; Shaviv 2000; Owocki et al. 2004).”
MODULES FOR EXPERIMENTS IN STELLAR ASTROPHYSICS (MESA): PLANETS, OSCILLATIONS, ROTATION, AND MASSIVE STARS (2013, background): “Potential agents for the excess transport include waves excited by turbulent convection (see, e.g., Maeder 1987a) and radiative diffusion enhanced by porous clumping of the envelope (e.g., Owocki et al. 2004).”
DISCOVERY OF PRECURSOR LUMINOUS BLUE VARIABLE OUTBURSTS IN TWO RECENT OPTICAL TRANSIENTS: THE FITFULLY VARIABLE MISSING LINKS UGC 2773-OT AND SN 2009ip (2009, background): “…nor giant LBV eruptions have a theoretical explanation, although they are suspected to be the result of luminous stars flirting with an opacity-modified Eddington limit and subsequent runaway mass loss (e.g., Smith & Owocki 2006; Humphreys & Davidson 1994; Smith et al. 2003; Owocki et al. 2004).”
Wind modelling of very massive stars up to 300 solar masses (2011, background): “Owocki et al. (2004) have investigated the mass loss of stars that formally exceed their Eddington limit and show that the expected mass loss falls well below the values required to account for the mass that is lost during LBV giant eruptions, such as that of η Carinae in the 1840s. Interestingly,…”
SN 2006tf: Precursor Eruptions and the Optically Thick Regime of Extremely Luminous Type IIn Supernovae (2008, background): “…extreme requirements point to episodic mass ejection reminiscent of the eruptions seen in η Carinae and other luminous blue variables (LBVs), which have mass-loss rates of 0.01–1 M⊙ yr −1, far exceeding the limiting mass loss in line-driven stellar winds (Smith & Owocki 2006; Owocki et al. 2004).”
The Unprecedented Third Outburst of SN 2009ip: A Luminous Blue Variable Becomes a Supernova (2012, background): “…components are quite significant — the FWHM of 8000 kms−1 for the broad emission lines implies that a substantial fraction of the outflowing mass has achieved these high velocities, which is beyond the capabilities of any nonterminal super-Eddington winddriven mechanism (Owocki et al. 2004).”
The evolution of runaway stellar collision products (2009, methodology): “A model that describes mass loss from stars that exceed their Eddington luminosity is the so-called porosity model (Owocki et al. 2004; Owocki & van Marle 2008).”
Are the Models for Type Ia Supernova Progenitors Consistent with the Properties of Supernova Remnants? (2007, background): “In principle, continuumdriven winds might reach such high efficiencies, as claimed by HKN96 (see also Owocki et al. 2004; Smith & Owocki 2006), but this has never been proved with detailed simulations.”
Core-collapse explosions of Wolf–Rayet stars and the connection to Type IIb/Ib/Ic supernovae (2011, background): “…at present, transient, and perhaps recurrent, phases of intense mass loss (e.g., of the eruptive kind seen inη Car) may be a viable alternative to steady-state mass loss (see, for example, Langer et al. 1994; Maeder & Meynet 2000; Shaviv 2000; Owocki et al. 2004; Guzik 2005; Dessart et al. 2010b).”