Super-Eddington stellar winds: unifying radiative-enthalpy vs. flux-driven models

TL;DR

This paper develops semi-analytic models for super-Eddington stellar winds, unifying previous models by incorporating radiative enthalpy and diffusive flux effects, and provides key scaling relations for wind speed and luminosity.

Contribution

It introduces a unified framework that bridges radiative-enthalpy and flux-driven super-Eddington wind models, accounting for optically thick flows and photon-tiring constraints.

Findings

Wind terminal speed scales with Eddington ratio and photon-tiring parameter.

Final observed luminosity exceeds the Eddington luminosity for all steady solutions.

Unified model applies to eruptive stellar mass loss, novae, and stellar mergers.

Abstract

We derive semi-analytic solutions for optically thick, super-Eddington stellar winds, induced by an assumed steady energy addition $\Delta {\dot E}$ concentrated around a near-surface heating radius $R$ in a massive star of central luminosity $L_\ast$. We show that obtaining steady wind solutions requires both that the resulting total luminosity $L_o = L_\ast + \Delta {\dot E}$ exceed the Eddington luminosity, $\Gamma_o \equiv L_o/L_{Edd} > 1$, and that the induced mass loss rate be such that the "photon-tiring" parameter $m \equiv {\dot M} GM/R L_o \le 1-1/\Gamma_o$, 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 vs. large values of $m \Gamma_o $, 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 $v_\infty^2/v_{esc}^2 = \Gamma_o/(1+m \Gamma_o) -1$, and for the final observed luminosity $L_{ obs}$, which for all allowed steady-solutions with $m < 1 - 1/\Gamma_o$, exceeds the Eddington luminosity, $L_{obs} > L_{Edd}$. Our super-Eddington wind solutions have potential applicability for modeling phases of eruptive mass loss from massive stars, classical novae, and the remnants of stellar mergers.