Abstract
The high luminosity of Very Massive Stars (VMS) means that radiative forces play an important, dynamical role both in the structure and stability of their stellar envelope, and in driving strong stellar-wind mass loss. Focusing on the interplay of radiative flux and opacity, with emphasis on key distinctions between continuum vs. line opacity, this chapter reviews instabilities in the envelopes and winds of VMS. Specifically, we discuss how: (1) the iron opacity bump can induce an extensive inflation of the stellar envelope; (2) the density dependence of mean opacity leads to strange mode instabilities in the outer envelope; (3) desaturation of line-opacity by acceleration of near-surface layers initiates and sustains a line-driven stellar wind outflow; (4) an associated line-deshadowing instability leads to extensive small-scale structure in the outer regions of such line-driven winds; (5) a star with super-Eddington luminosity can develop extensive atmospheric structure from photon bubble instabilities, or from stagnation of flow that exceeds the “photon tiring” limit; (6) the associated porosity leads to a reduction in opacity that can regulate the extreme mass loss of such continuum-driven winds. Two overall themes are the potential links of such instabilities to Luminous Blue Variable (LBV) stars, and the potential role of radiation forces in establishing the upper mass limit of VMS.
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Notes
- 1.
As discussed in Sect. 5.5.1, even when the opacity is formally isotropic in the atom’s frame, a spherical wind expansion can lead to an anisotropy for line opacity in the stellar frame, through the directional dependence of the local velocity gradient.
- 2.
An exception is when the spectral density of lines become high enough to lead to an effective “line-blanketing” effect, as occurs in the iron opacity bump discussed in Sect. 5.3.3.
- 3.
Of course, this simple scaling relation has to be modified to accommodate gradients in the molecular weight as a star evolves from the zero-age main sequence, and it breaks down altogether in the coolest stars (both giants and dwarfs), for which convection dominates the envelope energy transport.
- 4.
- 5.
Here we use a slight variation of the standard CAK notation in which the artificial dependence on a fiducial ion thermal speed is avoided by simply setting v th = c. Back-conversion to CAK notation is achieved by multiplying t by v th ∕c and k by \(\left (v_{\mathit{th}}/c\right )^{\alpha }\). The line normalization \(\overline{Q}\) offers the advantages of being a dimensionless measure of line-opacity that is independent of the assumed ion thermal speed, with a nearly constant characteristic value of order \(\overline{Q} \sim 10^{3}\) for a wide range of ionization conditions (Gayley 1995).
- 6.
The choice of these functions is arbitrary, to illustrate the photon-tiring effect within a simple model. More physically motivated models based on a medium’s porosity are presented in Sect. 5.6.5
- 7.
Since the luminous stars are likely to be mostly convective (e.g. Sect. 5.6.2), the limiting time scale is that of the convective diffusion’s mixing length time in the stellar cores, which due to the high density is much longer than the dynamical time scales.
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Acknowledgements
This work was supported in part by NASA ATP grant NNX11AC40G, NASA Chandra grant TM3-14001A, and NSF grant 1312898 to the University of Delaware. I thank M. Giannotti for sharing his Mathematica notebook for the OPAL opacity tables, and N. Shaviv for many helpful discussions and for providing Fig. 5.12. I also acknowledge numerous discussions with G. Graefener, N. Smith, J. Sundqvist, J. Vink and A.J. van Marle.
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Owocki, S.P. (2015). Instabilities in the Envelopes and Winds of Very Massive Stars. In: Vink, J. (eds) Very Massive Stars in the Local Universe. Astrophysics and Space Science Library, vol 412. Springer, Cham. https://doi.org/10.1007/978-3-319-09596-7_5
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