TY - JOUR
T1 - Super-Eddington stellar winds
T2 - Unifying radiative-enthalpy versus flux-driven models
AU - Owocki, Stanley P.
AU - Townsend, Richard H.D.
AU - Quataert, Eliot
N1 - Funding Information:
The research here was initiated and substantially developed while the authors were participants in a massive-star research program at the Kavli Institute for Theoretical Physics, and as such was supported in part by the National Science Foundation under Grant No. NSF PHY-1125915. EQ was supported in part by a Simons Investigator award from the Simons Foundation and by the Gordon and Betty Moore Foundation through Grant GBMF5076. RHDT acknowledges support from NASA grant NNX14AB55G and NSF grant ACI-1339606. SPO was supported in part by NASA grant NNX15AM96G, and also acknowledges sabbatical leave support from the University of Delaware, without which the collaborative research hereinwould likely not have occurred.We thankY.-F. Jiang for pointing out the importance of the radiation-advection term in the momentum and diffusion equations.We also thank K. Gayley, N. Shaviv and J. Vink for helpful comments on an early draft. Finally, we thank the referee, Achim Feldmeier, for thoughtful comments and suggestions that helped improve the paper.
Publisher Copyright:
© 2018 The Author(s).
PY - 2017
Y1 - 2017
N2 - We derive semi-analytic solutions for optically thick, super-Eddington stellar winds, induced by an assumed steady energy addition ΔE˙ concentrated around a near-surface heating radius R in a massive star of central luminosity L*. We show that obtaining steady wind solutions requires both that the resulting total luminosity Lo = L* + ΔE˙ exceed the Eddington luminosity, Γo ≡ Lo/LEdd > 1, and that the induced mass-loss rate be such that the 'photon-tiring' parameter, m ≡ M˙ GM/RLo ≤ 1 - 1/Γo, ensuring the luminosity is sufficient to overcome the gravitational potential GM/R. Our analysis unifies previous super-Eddington wind models that either: (1) assumed a direct radiative flux-driving without accounting for the advection of radiative enthalpy that can become important in such an optically thick flow; or (2) assumed that such super-Eddington outflows are adiabatic, neglecting the effects of the diffusive radiative flux. We show that these distinct models become applicable in the asymptotic limits of small versus large values of mΓo, respectively. By solving the coupled differential equations for radiative diffusion and wind momentum, we obtain general solutions that effectively bridge the behaviours of these limiting models. Two key scaling results are for the terminal wind speed to escape speed, which is found to vary as v∞2 /vesc2 = Γo/(1 + mΓo) - 1, and for the final observed luminosity Lobs, which for all allowed steady-solutions with m < 1 - 1/Γo exceeds the Eddington luminosity, Lobs > LEdd. Our super-Eddington wind solutions have potential applicability for modelling phases of eruptive mass-loss from massive stars, classical novae, and the remnants of stellar mergers.
AB - We derive semi-analytic solutions for optically thick, super-Eddington stellar winds, induced by an assumed steady energy addition ΔE˙ concentrated around a near-surface heating radius R in a massive star of central luminosity L*. We show that obtaining steady wind solutions requires both that the resulting total luminosity Lo = L* + ΔE˙ exceed the Eddington luminosity, Γo ≡ Lo/LEdd > 1, and that the induced mass-loss rate be such that the 'photon-tiring' parameter, m ≡ M˙ GM/RLo ≤ 1 - 1/Γo, ensuring the luminosity is sufficient to overcome the gravitational potential GM/R. Our analysis unifies previous super-Eddington wind models that either: (1) assumed a direct radiative flux-driving without accounting for the advection of radiative enthalpy that can become important in such an optically thick flow; or (2) assumed that such super-Eddington outflows are adiabatic, neglecting the effects of the diffusive radiative flux. We show that these distinct models become applicable in the asymptotic limits of small versus large values of mΓo, respectively. By solving the coupled differential equations for radiative diffusion and wind momentum, we obtain general solutions that effectively bridge the behaviours of these limiting models. Two key scaling results are for the terminal wind speed to escape speed, which is found to vary as v∞2 /vesc2 = Γo/(1 + mΓo) - 1, and for the final observed luminosity Lobs, which for all allowed steady-solutions with m < 1 - 1/Γo exceeds the Eddington luminosity, Lobs > LEdd. Our super-Eddington wind solutions have potential applicability for modelling phases of eruptive mass-loss from massive stars, classical novae, and the remnants of stellar mergers.
KW - Outflows
KW - Stars: early-type
KW - Stars: mass loss
KW - Stars: winds
KW - Supernovae: general
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U2 - 10.1093/MNRAS/STX2251
DO - 10.1093/MNRAS/STX2251
M3 - Article
AN - SCOPUS:85051458771
SN - 0035-8711
VL - 472
SP - 3749
EP - 3760
JO - Monthly Notices of the Royal Astronomical Society
JF - Monthly Notices of the Royal Astronomical Society
IS - 3
ER -